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

Percentage Accurate: 85.5% → 98.4%

Time: 3.7s

Alternatives: 17

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.2 \cdot 10^{+187}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - y}{z - a}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t}{a - z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 5.2e+187)
   (fma (/ (- z y) (- z a)) t x)
   (fma (- y z) (/ t (- a z)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 5.2e+187) {
		tmp = fma(((z - y) / (z - a)), t, x);
	} else {
		tmp = fma((y - z), (t / (a - z)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 5.2e+187)
		tmp = fma(Float64(Float64(z - y) / Float64(z - a)), t, x);
	else
		tmp = fma(Float64(y - z), Float64(t / Float64(a - z)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 5.2e+187], N[(N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 5.1999999999999997e187

   1. Initial program 86.1%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-div N/A

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

      13. negate-sub2 N/A

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

      14. negate-sub2 N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 N/A

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

      18. lower--.f64 98.6

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

   3. Applied rewrites 98.6%

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

   if 5.1999999999999997e187 < y

   1. Initial program 80.5%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate-/l* N/A

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

      8. lower-fma.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lift--.f64 96.2

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

   3. Applied rewrites 96.2%

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

Alternative 2: 96.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 85.5%

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

   1. lift-+.f64 N/A

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

   2. lift--.f64 N/A

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

   3. lift-/.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. lift--.f64 N/A

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

   6. +-commutative N/A

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

   7. associate-/l* N/A

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

   8. lower-fma.f64 N/A

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

   9. lift--.f64 N/A

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

   10. lower-/.f64 N/A

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

   11. lift--.f64 96.0

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

3. Applied rewrites 96.0%

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

Alternative 3: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+59}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, t, x\right)\\ \mathbf{elif}\;z \leq 700000:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - y}{z}, t, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.4e+59)
   (fma (/ z (- z a)) t x)
   (if (<= z 700000.0) (+ x (/ (* y t) (- a z))) (fma (/ (- z y) z) t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.4e+59) {
		tmp = fma((z / (z - a)), t, x);
	} else if (z <= 700000.0) {
		tmp = x + ((y * t) / (a - z));
	} else {
		tmp = fma(((z - y) / z), t, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.4e+59)
		tmp = fma(Float64(z / Float64(z - a)), t, x);
	elseif (z <= 700000.0)
		tmp = Float64(x + Float64(Float64(y * t) / Float64(a - z)));
	else
		tmp = fma(Float64(Float64(z - y) / z), t, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.4e+59], N[(N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision], If[LessEqual[z, 700000.0], N[(x + N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision] * t + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4000000000000002e59

   1. Initial program 70.8%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-div N/A

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

      13. negate-sub2 N/A

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

      14. negate-sub2 N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 N/A

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

      18. lower--.f64 99.9

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 88.5%

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

   if -5.4000000000000002e59 < z < 7e5

   1. Initial program 95.5%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 86.4%

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

   if 7e5 < z

   1. Initial program 74.6%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-div N/A

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

      13. negate-sub2 N/A

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

      14. negate-sub2 N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 N/A

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

      18. lower--.f64 99.9

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in z around inf

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

   6. Applied rewrites 85.6%

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

Alternative 4: 81.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t, \frac{y - z}{a}, x\right)\\ \mathbf{if}\;a \leq -5.5 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+37}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - y}{z}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma t (/ (- y z) a) x)))
   (if (<= a -5.5e+124) t_1 (if (<= a 1.35e+37) (fma (/ (- z y) z) t x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(t, ((y - z) / a), x);
	double tmp;
	if (a <= -5.5e+124) {
		tmp = t_1;
	} else if (a <= 1.35e+37) {
		tmp = fma(((z - y) / z), t, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(t, Float64(Float64(y - z) / a), x)
	tmp = 0.0
	if (a <= -5.5e+124)
		tmp = t_1;
	elseif (a <= 1.35e+37)
		tmp = fma(Float64(Float64(z - y) / z), t, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -5.5e+124], t$95$1, If[LessEqual[a, 1.35e+37], N[(N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision] * t + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -5.49999999999999977e124 or 1.34999999999999993e37 < a

   1. Initial program 82.9%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 87.9

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

   4. Applied rewrites 87.9%

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

   if -5.49999999999999977e124 < a < 1.34999999999999993e37

   1. Initial program 87.1%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-div N/A

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

      13. negate-sub2 N/A

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

      14. negate-sub2 N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 N/A

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

      18. lower--.f64 97.5

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

   3. Applied rewrites 97.5%

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

   4. Taylor expanded in z around inf

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

   6. Applied rewrites 77.0%

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

Alternative 5: 78.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z}{z - a}, t, x\right)\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-168}:\\ \;\;\;\;x + \frac{y \cdot t}{-z}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-76}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y - z}{a}, x\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+99}:\\ \;\;\;\;x + y \cdot \frac{t}{-z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ z (- z a)) t x)))
   (if (<= z -1.95e-20)
     t_1
     (if (<= z -1.4e-168)
       (+ x (/ (* y t) (- z)))
       (if (<= z 3.1e-76)
         (fma t (/ (- y z) a) x)
         (if (<= z 1.4e+99) (+ x (* y (/ t (- z)))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((z / (z - a)), t, x);
	double tmp;
	if (z <= -1.95e-20) {
		tmp = t_1;
	} else if (z <= -1.4e-168) {
		tmp = x + ((y * t) / -z);
	} else if (z <= 3.1e-76) {
		tmp = fma(t, ((y - z) / a), x);
	} else if (z <= 1.4e+99) {
		tmp = x + (y * (t / -z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(z / Float64(z - a)), t, x)
	tmp = 0.0
	if (z <= -1.95e-20)
		tmp = t_1;
	elseif (z <= -1.4e-168)
		tmp = Float64(x + Float64(Float64(y * t) / Float64(-z)));
	elseif (z <= 3.1e-76)
		tmp = fma(t, Float64(Float64(y - z) / a), x);
	elseif (z <= 1.4e+99)
		tmp = Float64(x + Float64(y * Float64(t / Float64(-z))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision]}, If[LessEqual[z, -1.95e-20], t$95$1, If[LessEqual[z, -1.4e-168], N[(x + N[(N[(y * t), $MachinePrecision] / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e-76], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 1.4e+99], N[(x + N[(y * N[(t / (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.95000000000000004e-20 or 1.4e99 < z

   1. Initial program 73.0%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-div N/A

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

      13. negate-sub2 N/A

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

      14. negate-sub2 N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 N/A

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

      18. lower--.f64 99.9

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 86.7%

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

   if -1.95000000000000004e-20 < z < -1.4000000000000001e-168

   1. Initial program 96.4%

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

   2. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 58.4

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

   4. Applied rewrites 58.4%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 56.9%

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

   if -1.4000000000000001e-168 < z < 3.0999999999999997e-76

   1. Initial program 95.3%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 85.3

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

   4. Applied rewrites 85.3%

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

   if 3.0999999999999997e-76 < z < 1.4e99

   1. Initial program 92.2%

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

   2. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 68.0

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

   4. Applied rewrites 68.0%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 58.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 59.2

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

   9. Applied rewrites 59.2%

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

Alternative 6: 76.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+118}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-168}:\\ \;\;\;\;x + \frac{y \cdot t}{-z}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-76}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y - z}{a}, x\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+102}:\\ \;\;\;\;x + y \cdot \frac{t}{-z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.2e+118)
   (+ x t)
   (if (<= z -1.4e-168)
     (+ x (/ (* y t) (- z)))
     (if (<= z 3.1e-76)
       (fma t (/ (- y z) a) x)
       (if (<= z 1.25e+102) (+ x (* y (/ t (- z)))) (+ x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.2e+118) {
		tmp = x + t;
	} else if (z <= -1.4e-168) {
		tmp = x + ((y * t) / -z);
	} else if (z <= 3.1e-76) {
		tmp = fma(t, ((y - z) / a), x);
	} else if (z <= 1.25e+102) {
		tmp = x + (y * (t / -z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.2e+118)
		tmp = Float64(x + t);
	elseif (z <= -1.4e-168)
		tmp = Float64(x + Float64(Float64(y * t) / Float64(-z)));
	elseif (z <= 3.1e-76)
		tmp = fma(t, Float64(Float64(y - z) / a), x);
	elseif (z <= 1.25e+102)
		tmp = Float64(x + Float64(y * Float64(t / Float64(-z))));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.2e+118], N[(x + t), $MachinePrecision], If[LessEqual[z, -1.4e-168], N[(x + N[(N[(y * t), $MachinePrecision] / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e-76], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 1.25e+102], N[(x + N[(y * N[(t / (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.2e118 or 1.25e102 < z

   1. Initial program 67.5%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 83.3%

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

   if -7.2e118 < z < -1.4000000000000001e-168

   1. Initial program 93.4%

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

   2. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 64.1

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

   4. Applied rewrites 64.1%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 59.4%

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

   if -1.4000000000000001e-168 < z < 3.0999999999999997e-76

   1. Initial program 95.3%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 85.3

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

   4. Applied rewrites 85.3%

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

   if 3.0999999999999997e-76 < z < 1.25e102

   1. Initial program 92.1%

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

   2. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 67.9

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

   4. Applied rewrites 67.9%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 58.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 59.1

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

   9. Applied rewrites 59.1%

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

Alternative 7: 76.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+118}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-87}:\\ \;\;\;\;x + \frac{y \cdot t}{-z}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-76}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+102}:\\ \;\;\;\;x + y \cdot \frac{t}{-z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.2e+118)
   (+ x t)
   (if (<= z -2.7e-87)
     (+ x (/ (* y t) (- z)))
     (if (<= z 3.1e-76)
       (+ x (/ (* t y) a))
       (if (<= z 1.25e+102) (+ x (* y (/ t (- z)))) (+ x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.2e+118) {
		tmp = x + t;
	} else if (z <= -2.7e-87) {
		tmp = x + ((y * t) / -z);
	} else if (z <= 3.1e-76) {
		tmp = x + ((t * y) / a);
	} else if (z <= 1.25e+102) {
		tmp = x + (y * (t / -z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-7.2d+118)) then
        tmp = x + t
    else if (z <= (-2.7d-87)) then
        tmp = x + ((y * t) / -z)
    else if (z <= 3.1d-76) then
        tmp = x + ((t * y) / a)
    else if (z <= 1.25d+102) then
        tmp = x + (y * (t / -z))
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.2e+118) {
		tmp = x + t;
	} else if (z <= -2.7e-87) {
		tmp = x + ((y * t) / -z);
	} else if (z <= 3.1e-76) {
		tmp = x + ((t * y) / a);
	} else if (z <= 1.25e+102) {
		tmp = x + (y * (t / -z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.2e+118:
		tmp = x + t
	elif z <= -2.7e-87:
		tmp = x + ((y * t) / -z)
	elif z <= 3.1e-76:
		tmp = x + ((t * y) / a)
	elif z <= 1.25e+102:
		tmp = x + (y * (t / -z))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.2e+118)
		tmp = Float64(x + t);
	elseif (z <= -2.7e-87)
		tmp = Float64(x + Float64(Float64(y * t) / Float64(-z)));
	elseif (z <= 3.1e-76)
		tmp = Float64(x + Float64(Float64(t * y) / a));
	elseif (z <= 1.25e+102)
		tmp = Float64(x + Float64(y * Float64(t / Float64(-z))));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.2e+118)
		tmp = x + t;
	elseif (z <= -2.7e-87)
		tmp = x + ((y * t) / -z);
	elseif (z <= 3.1e-76)
		tmp = x + ((t * y) / a);
	elseif (z <= 1.25e+102)
		tmp = x + (y * (t / -z));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.2e+118], N[(x + t), $MachinePrecision], If[LessEqual[z, -2.7e-87], N[(x + N[(N[(y * t), $MachinePrecision] / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e-76], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+102], N[(x + N[(y * N[(t / (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.2e118 or 1.25e102 < z

   1. Initial program 67.5%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 83.3%

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

   if -7.2e118 < z < -2.69999999999999984e-87

   1. Initial program 92.5%

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

   2. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 68.1

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

   4. Applied rewrites 68.1%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 61.6%

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

   if -2.69999999999999984e-87 < z < 3.0999999999999997e-76

   1. Initial program 95.3%

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

   2. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 80.4

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

   4. Applied rewrites 80.4%

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

   if 3.0999999999999997e-76 < z < 1.25e102

   1. Initial program 92.1%

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

   2. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 67.9

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

   4. Applied rewrites 67.9%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 58.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 59.1

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

   9. Applied rewrites 59.1%

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

Alternative 8: 75.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{-z}\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+118}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-87}:\\ \;\;\;\;\mathsf{fma}\left(y, t\_1, x\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-76}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+102}:\\ \;\;\;\;x + y \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (- z))))
   (if (<= z -7.5e+118)
     (+ x t)
     (if (<= z -3.2e-87)
       (fma y t_1 x)
       (if (<= z 3.1e-76)
         (+ x (/ (* t y) a))
         (if (<= z 1.25e+102) (+ x (* y t_1)) (+ x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / -z;
	double tmp;
	if (z <= -7.5e+118) {
		tmp = x + t;
	} else if (z <= -3.2e-87) {
		tmp = fma(y, t_1, x);
	} else if (z <= 3.1e-76) {
		tmp = x + ((t * y) / a);
	} else if (z <= 1.25e+102) {
		tmp = x + (y * t_1);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(-z))
	tmp = 0.0
	if (z <= -7.5e+118)
		tmp = Float64(x + t);
	elseif (z <= -3.2e-87)
		tmp = fma(y, t_1, x);
	elseif (z <= 3.1e-76)
		tmp = Float64(x + Float64(Float64(t * y) / a));
	elseif (z <= 1.25e+102)
		tmp = Float64(x + Float64(y * t_1));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / (-z)), $MachinePrecision]}, If[LessEqual[z, -7.5e+118], N[(x + t), $MachinePrecision], If[LessEqual[z, -3.2e-87], N[(y * t$95$1 + x), $MachinePrecision], If[LessEqual[z, 3.1e-76], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+102], N[(x + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.50000000000000003e118 or 1.25e102 < z

   1. Initial program 67.4%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 83.3%

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

   if -7.50000000000000003e118 < z < -3.19999999999999979e-87

   1. Initial program 92.5%

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

   2. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 68.2

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

   4. Applied rewrites 68.2%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 61.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-/.f64 62.9

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

   9. Applied rewrites 62.9%

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

   if -3.19999999999999979e-87 < z < 3.0999999999999997e-76

   1. Initial program 95.3%

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

   2. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 80.4

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

   4. Applied rewrites 80.4%

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

   if 3.0999999999999997e-76 < z < 1.25e102

   1. Initial program 92.1%

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

   2. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 67.9

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

   4. Applied rewrites 67.9%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 58.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 59.1

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

   9. Applied rewrites 59.1%

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

Alternative 9: 75.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+118}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-87}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{-z}, x\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-76}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+102}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-y}{z}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.5e+118)
   (+ x t)
   (if (<= z -3.2e-87)
     (fma y (/ t (- z)) x)
     (if (<= z 3.1e-76)
       (+ x (/ (* t y) a))
       (if (<= z 1.25e+102) (fma (/ (- y) z) t x) (+ x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.5e+118) {
		tmp = x + t;
	} else if (z <= -3.2e-87) {
		tmp = fma(y, (t / -z), x);
	} else if (z <= 3.1e-76) {
		tmp = x + ((t * y) / a);
	} else if (z <= 1.25e+102) {
		tmp = fma((-y / z), t, x);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.5e+118)
		tmp = Float64(x + t);
	elseif (z <= -3.2e-87)
		tmp = fma(y, Float64(t / Float64(-z)), x);
	elseif (z <= 3.1e-76)
		tmp = Float64(x + Float64(Float64(t * y) / a));
	elseif (z <= 1.25e+102)
		tmp = fma(Float64(Float64(-y) / z), t, x);
	else
		tmp = Float64(x + t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.5e+118], N[(x + t), $MachinePrecision], If[LessEqual[z, -3.2e-87], N[(y * N[(t / (-z)), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 3.1e-76], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+102], N[(N[((-y) / z), $MachinePrecision] * t + x), $MachinePrecision], N[(x + t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.50000000000000003e118 or 1.25e102 < z

   1. Initial program 67.4%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 83.3%

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

   if -7.50000000000000003e118 < z < -3.19999999999999979e-87

   1. Initial program 92.5%

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

   2. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 68.2

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

   4. Applied rewrites 68.2%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 61.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-/.f64 62.9

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

   9. Applied rewrites 62.9%

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

   if -3.19999999999999979e-87 < z < 3.0999999999999997e-76

   1. Initial program 95.3%

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

   2. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 80.4

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

   4. Applied rewrites 80.4%

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

   if 3.0999999999999997e-76 < z < 1.25e102

   1. Initial program 92.1%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-div N/A

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

      13. negate-sub2 N/A

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

      14. negate-sub2 N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 N/A

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

      18. lower--.f64 99.1

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

   3. Applied rewrites 99.1%

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

   4. Taylor expanded in z around inf

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

   6. Applied rewrites 70.2%

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

   7. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 58.7

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

   9. Applied rewrites 58.7%

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

Alternative 10: 75.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \frac{t}{-z}, x\right)\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+118}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-76}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (/ t (- z)) x)))
   (if (<= z -7.5e+118)
     (+ x t)
     (if (<= z -3.2e-87)
       t_1
       (if (<= z 3.1e-76)
         (+ x (/ (* t y) a))
         (if (<= z 1.25e+102) t_1 (+ x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, (t / -z), x);
	double tmp;
	if (z <= -7.5e+118) {
		tmp = x + t;
	} else if (z <= -3.2e-87) {
		tmp = t_1;
	} else if (z <= 3.1e-76) {
		tmp = x + ((t * y) / a);
	} else if (z <= 1.25e+102) {
		tmp = t_1;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(t / Float64(-z)), x)
	tmp = 0.0
	if (z <= -7.5e+118)
		tmp = Float64(x + t);
	elseif (z <= -3.2e-87)
		tmp = t_1;
	elseif (z <= 3.1e-76)
		tmp = Float64(x + Float64(Float64(t * y) / a));
	elseif (z <= 1.25e+102)
		tmp = t_1;
	else
		tmp = Float64(x + t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(t / (-z)), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -7.5e+118], N[(x + t), $MachinePrecision], If[LessEqual[z, -3.2e-87], t$95$1, If[LessEqual[z, 3.1e-76], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+102], t$95$1, N[(x + t), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.50000000000000003e118 or 1.25e102 < z

   1. Initial program 67.4%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 83.3%

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

   if -7.50000000000000003e118 < z < -3.19999999999999979e-87 or 3.0999999999999997e-76 < z < 1.25e102

   1. Initial program 92.3%

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

   2. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 68.1

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

   4. Applied rewrites 68.1%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 59.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-/.f64 61.1

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

   9. Applied rewrites 61.1%

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

   if -3.19999999999999979e-87 < z < 3.0999999999999997e-76

   1. Initial program 95.3%

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

   2. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 80.4

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

   4. Applied rewrites 80.4%

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

Alternative 11: 75.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+22}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.9e+22) (+ x t) (if (<= z 1.8e-13) (+ x (/ (* t y) a)) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.9e+22) {
		tmp = x + t;
	} else if (z <= 1.8e-13) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.9d+22)) then
        tmp = x + t
    else if (z <= 1.8d-13) then
        tmp = x + ((t * y) / a)
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.9e+22) {
		tmp = x + t;
	} else if (z <= 1.8e-13) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.9e+22:
		tmp = x + t
	elif z <= 1.8e-13:
		tmp = x + ((t * y) / a)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.9e+22)
		tmp = Float64(x + t);
	elseif (z <= 1.8e-13)
		tmp = Float64(x + Float64(Float64(t * y) / a));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.9e+22)
		tmp = x + t;
	elseif (z <= 1.8e-13)
		tmp = x + ((t * y) / a);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.9e+22], N[(x + t), $MachinePrecision], If[LessEqual[z, 1.8e-13], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.89999999999999979e22 or 1.7999999999999999e-13 < z

   1. Initial program 74.7%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 76.1%

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

   if -4.89999999999999979e22 < z < 1.7999999999999999e-13

   1. Initial program 95.7%

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

   2. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 75.9

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

   4. Applied rewrites 75.9%

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

Alternative 12: 75.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+22}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-13}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.4e+22) (+ x t) (if (<= z 1.8e-13) (fma t (/ y a) x) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.4e+22) {
		tmp = x + t;
	} else if (z <= 1.8e-13) {
		tmp = fma(t, (y / a), x);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.4e+22)
		tmp = Float64(x + t);
	elseif (z <= 1.8e-13)
		tmp = fma(t, Float64(y / a), x);
	else
		tmp = Float64(x + t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.4e+22], N[(x + t), $MachinePrecision], If[LessEqual[z, 1.8e-13], N[(t * N[(y / a), $MachinePrecision] + x), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4000000000000004e22 or 1.7999999999999999e-13 < z

   1. Initial program 74.7%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 76.1%

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

   if -5.4000000000000004e22 < z < 1.7999999999999999e-13

   1. Initial program 95.7%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 77.3

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

   4. Applied rewrites 77.3%

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

Alternative 13: 62.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+142}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+111}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.5e+142) x (if (<= a 8.5e+111) (+ x t) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.5e+142) {
		tmp = x;
	} else if (a <= 8.5e+111) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5.5d+142)) then
        tmp = x
    else if (a <= 8.5d+111) then
        tmp = x + t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.5e+142) {
		tmp = x;
	} else if (a <= 8.5e+111) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.5e+142:
		tmp = x
	elif a <= 8.5e+111:
		tmp = x + t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.5e+142)
		tmp = x;
	elseif (a <= 8.5e+111)
		tmp = Float64(x + t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.5e+142)
		tmp = x;
	elseif (a <= 8.5e+111)
		tmp = x + t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.5e+142], x, If[LessEqual[a, 8.5e+111], N[(x + t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -5.50000000000000035e142 or 8.49999999999999983e111 < a

   1. Initial program 82.2%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 66.7%

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

   if -5.50000000000000035e142 < a < 8.49999999999999983e111

   1. Initial program 86.9%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 61.0%

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

Alternative 14: 60.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+242}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3.3e+242) (* t (/ y a)) (+ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.3e+242) {
		tmp = t * (y / a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-3.3d+242)) then
        tmp = t * (y / a)
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.3e+242) {
		tmp = t * (y / a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -3.3e+242:
		tmp = t * (y / a)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3.3e+242)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -3.3e+242)
		tmp = t * (y / a);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3.3e+242], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.30000000000000023e242

   1. Initial program 77.9%

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

   2. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 66.8

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

   4. Applied rewrites 66.8%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 40.4%

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

   if -3.30000000000000023e242 < y

   1. Initial program 85.9%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 61.2%

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

Alternative 15: 60.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+242}:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3.3e+242) (/ (* t y) a) (+ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.3e+242) {
		tmp = (t * y) / a;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-3.3d+242)) then
        tmp = (t * y) / a
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.3e+242) {
		tmp = (t * y) / a;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -3.3e+242:
		tmp = (t * y) / a
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3.3e+242)
		tmp = Float64(Float64(t * y) / a);
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -3.3e+242)
		tmp = (t * y) / a;
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3.3e+242], N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision], N[(x + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.30000000000000023e242

   1. Initial program 77.9%

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

   2. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 72.1

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

   4. Applied rewrites 72.1%

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

   5. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 36.7

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

   7. Applied rewrites 36.7%

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

   if -3.30000000000000023e242 < y

   1. Initial program 85.9%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 61.2%

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

Alternative 16: 54.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+72}:\\ \;\;\;\;t\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+168}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y z) t) (- a z))))
   (if (<= t_1 -1e+72) t (if (<= t_1 4e+168) x t))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_1 <= -1e+72) {
		tmp = t;
	} else if (t_1 <= 4e+168) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y - z) * t) / (a - z)
    if (t_1 <= (-1d+72)) then
        tmp = t
    else if (t_1 <= 4d+168) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_1 <= -1e+72) {
		tmp = t;
	} else if (t_1 <= 4e+168) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y - z) * t) / (a - z)
	tmp = 0
	if t_1 <= -1e+72:
		tmp = t
	elif t_1 <= 4e+168:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if (t_1 <= -1e+72)
		tmp = t;
	elseif (t_1 <= 4e+168)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y - z) * t) / (a - z);
	tmp = 0.0;
	if (t_1 <= -1e+72)
		tmp = t;
	elseif (t_1 <= 4e+168)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+72], t, If[LessEqual[t$95$1, 4e+168], x, t]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -9.99999999999999944e71 or 3.9999999999999997e168 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 60.7%

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

   2. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 80.6

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

   4. Applied rewrites 80.6%

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

   5. Taylor expanded in z around inf

      \[\leadsto t \]
   6. Step-by-step derivation

      1. associate-*r/ 26.5

         \[\leadsto t \]

   7. Applied rewrites 26.5%

      \[\leadsto t \]

   if -9.99999999999999944e71 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 3.9999999999999997e168

   1. Initial program 99.5%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 69.6%

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

Alternative 17: 50.7% accurate, 15.3× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.5%

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

2. Taylor expanded in x around inf

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

4. Applied rewrites 50.7%

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

Reproduce

herbie shell --seed 2025110 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64
  (+ x (/ (* (- y z) t) (- a z))))