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

Percentage Accurate: 85.9% → 98.3%

Time: 4.2s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 85.9%

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

   1. lift-+.f64 N/A

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

   2. lift--.f64 N/A

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

   3. lift-/.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. lift--.f64 N/A

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

   6. +-commutative N/A

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

   7. associate-/l* N/A

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

   8. sub-div N/A

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

   9. *-commutative N/A

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

   10. lower-fma.f64 N/A

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

   11. sub-div N/A

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

   12. negate-sub2 N/A

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

   13. negate-sub2 N/A

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

   14. frac-2neg-rev N/A

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

   15. lower-/.f64 N/A

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

   16. lower--.f64 N/A

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

   17. lower--.f64 98.3

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

3. Applied rewrites 98.3%

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

Alternative 2: 87.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{t}{t - a}, y, x\right)\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+71}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ t (- t a)) y x)))
   (if (<= t -2.9e+112)
     t_1
     (if (<= t 1.6e+71) (+ x (* y (/ z (- a t)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((t / (t - a)), y, x);
	double tmp;
	if (t <= -2.9e+112) {
		tmp = t_1;
	} else if (t <= 1.6e+71) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(t / Float64(t - a)), y, x)
	tmp = 0.0
	if (t <= -2.9e+112)
		tmp = t_1;
	elseif (t <= 1.6e+71)
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[t, -2.9e+112], t$95$1, If[LessEqual[t, 1.6e+71], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.9000000000000002e112 or 1.60000000000000012e71 < t

   1. Initial program 70.6%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate-/l* N/A

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

      8. sub-div N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. sub-div N/A

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

      12. negate-sub2 N/A

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

      13. negate-sub2 N/A

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

      14. frac-2neg-rev N/A

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

      15. lower-/.f64 N/A

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

      16. lower--.f64 N/A

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

      17. lower--.f64 99.9

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 90.9%

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

   if -2.9000000000000002e112 < t < 1.60000000000000012e71

   1. Initial program 94.2%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 85.3

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

   4. Applied rewrites 85.3%

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

Alternative 3: 82.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+48}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{t - a}, y, x\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-152}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - z}{t}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.8e+48)
   (fma (/ t (- t a)) y x)
   (if (<= t 9.5e-152) (fma y (/ (- z t) a) x) (fma (/ (- t z) t) y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e+48) {
		tmp = fma((t / (t - a)), y, x);
	} else if (t <= 9.5e-152) {
		tmp = fma(y, ((z - t) / a), x);
	} else {
		tmp = fma(((t - z) / t), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.8e+48)
		tmp = fma(Float64(t / Float64(t - a)), y, x);
	elseif (t <= 9.5e-152)
		tmp = fma(y, Float64(Float64(z - t) / a), x);
	else
		tmp = fma(Float64(Float64(t - z) / t), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.8e+48], N[(N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[t, 9.5e-152], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision] * y + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.80000000000000012e48

   1. Initial program 74.1%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate-/l* N/A

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

      8. sub-div N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. sub-div N/A

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

      12. negate-sub2 N/A

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

      13. negate-sub2 N/A

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

      14. frac-2neg-rev N/A

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

      15. lower-/.f64 N/A

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

      16. lower--.f64 N/A

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

      17. lower--.f64 99.9

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 87.7%

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

   if -2.80000000000000012e48 < t < 9.49999999999999925e-152

   1. Initial program 95.0%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 80.7

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

   4. Applied rewrites 80.7%

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

   if 9.49999999999999925e-152 < t

   1. Initial program 82.7%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate-/l* N/A

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

      8. sub-div N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. sub-div N/A

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

      12. negate-sub2 N/A

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

      13. negate-sub2 N/A

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

      14. frac-2neg-rev N/A

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

      15. lower-/.f64 N/A

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

      16. lower--.f64 N/A

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

      17. lower--.f64 99.2

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

   3. Applied rewrites 99.2%

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

   4. Taylor expanded in t around inf

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

   6. Applied rewrites 77.2%

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

Alternative 4: 80.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{t}{t - a}, y, x\right)\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-46}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ t (- t a)) y x)))
   (if (<= t -2.8e+48) t_1 (if (<= t 6.4e-46) (fma y (/ (- z t) a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((t / (t - a)), y, x);
	double tmp;
	if (t <= -2.8e+48) {
		tmp = t_1;
	} else if (t <= 6.4e-46) {
		tmp = fma(y, ((z - t) / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(t / Float64(t - a)), y, x)
	tmp = 0.0
	if (t <= -2.8e+48)
		tmp = t_1;
	elseif (t <= 6.4e-46)
		tmp = fma(y, Float64(Float64(z - t) / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[t, -2.8e+48], t$95$1, If[LessEqual[t, 6.4e-46], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.80000000000000012e48 or 6.3999999999999998e-46 < t

   1. Initial program 76.6%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate-/l* N/A

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

      8. sub-div N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. sub-div N/A

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

      12. negate-sub2 N/A

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

      13. negate-sub2 N/A

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

      14. frac-2neg-rev N/A

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

      15. lower-/.f64 N/A

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

      16. lower--.f64 N/A

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

      17. lower--.f64 99.9

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 86.0%

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

   if -2.80000000000000012e48 < t < 6.3999999999999998e-46

   1. Initial program 95.2%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 79.6

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

   4. Applied rewrites 79.6%

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

Alternative 5: 77.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+111}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+54}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.65e+111)
   (+ x y)
   (if (<= t 1.45e+54) (fma y (/ (- z t) a) x) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.65e+111) {
		tmp = x + y;
	} else if (t <= 1.45e+54) {
		tmp = fma(y, ((z - t) / a), x);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.65e+111)
		tmp = Float64(x + y);
	elseif (t <= 1.45e+54)
		tmp = fma(y, Float64(Float64(z - t) / a), x);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.65e+111], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.45e+54], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.6500000000000001e111 or 1.4499999999999999e54 < t

   1. Initial program 71.5%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 82.3%

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

   if -1.6500000000000001e111 < t < 1.4499999999999999e54

   1. Initial program 94.3%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 75.1

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

   4. Applied rewrites 75.1%

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

Alternative 6: 75.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+110}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+51}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.2e+110) (+ x y) (if (<= t 6.8e+51) (fma y (/ z a) x) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.2e+110) {
		tmp = x + y;
	} else if (t <= 6.8e+51) {
		tmp = fma(y, (z / a), x);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.2e+110)
		tmp = Float64(x + y);
	elseif (t <= 6.8e+51)
		tmp = fma(y, Float64(z / a), x);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.2e+110], N[(x + y), $MachinePrecision], If[LessEqual[t, 6.8e+51], N[(y * N[(z / a), $MachinePrecision] + x), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.1999999999999994e110 or 6.79999999999999969e51 < t

   1. Initial program 71.7%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 82.2%

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

   if -7.1999999999999994e110 < t < 6.79999999999999969e51

   1. Initial program 94.2%

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

   2. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 72.3

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

   4. Applied rewrites 72.3%

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

Alternative 7: 63.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+209}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+176}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.2e+209)
   (/ (* y z) a)
   (if (<= z 2.3e+176) (+ x y) (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.2e+209) {
		tmp = (y * z) / a;
	} else if (z <= 2.3e+176) {
		tmp = x + y;
	} else {
		tmp = y * (z / a);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-9.2d+209)) then
        tmp = (y * z) / a
    else if (z <= 2.3d+176) then
        tmp = x + y
    else
        tmp = y * (z / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.2e+209) {
		tmp = (y * z) / a;
	} else if (z <= 2.3e+176) {
		tmp = x + y;
	} else {
		tmp = y * (z / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.2e+209:
		tmp = (y * z) / a
	elif z <= 2.3e+176:
		tmp = x + y
	else:
		tmp = y * (z / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.2e+209)
		tmp = Float64(Float64(y * z) / a);
	elseif (z <= 2.3e+176)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(z / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.2e+209)
		tmp = (y * z) / a;
	elseif (z <= 2.3e+176)
		tmp = x + y;
	else
		tmp = y * (z / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.2e+209], N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 2.3e+176], N[(x + y), $MachinePrecision], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.20000000000000038e209

   1. Initial program 81.4%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 59.5

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

   4. Applied rewrites 59.5%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 34.2

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

   7. Applied rewrites 34.2%

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

   if -9.20000000000000038e209 < z < 2.29999999999999996e176

   1. Initial program 86.9%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 65.2%

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

   if 2.29999999999999996e176 < z

   1. Initial program 81.5%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 56.5

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

   4. Applied rewrites 56.5%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 38.2%

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

Alternative 8: 59.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot z}{a}\\ \mathbf{if}\;z \leq -9.2 \cdot 10^{+209}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+177}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y z) a)))
   (if (<= z -9.2e+209) t_1 (if (<= z 3.05e+177) (+ x y) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * z) / a;
	double tmp;
	if (z <= -9.2e+209) {
		tmp = t_1;
	} else if (z <= 3.05e+177) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * z) / a
    if (z <= (-9.2d+209)) then
        tmp = t_1
    else if (z <= 3.05d+177) then
        tmp = x + y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * z) / a;
	double tmp;
	if (z <= -9.2e+209) {
		tmp = t_1;
	} else if (z <= 3.05e+177) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * z) / a
	tmp = 0
	if z <= -9.2e+209:
		tmp = t_1
	elif z <= 3.05e+177:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * z) / a)
	tmp = 0.0
	if (z <= -9.2e+209)
		tmp = t_1;
	elseif (z <= 3.05e+177)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * z) / a;
	tmp = 0.0;
	if (z <= -9.2e+209)
		tmp = t_1;
	elseif (z <= 3.05e+177)
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -9.2e+209], t$95$1, If[LessEqual[z, 3.05e+177], N[(x + y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.20000000000000038e209 or 3.0499999999999999e177 < z

   1. Initial program 81.4%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 60.1

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

   4. Applied rewrites 60.1%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 33.8

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

   7. Applied rewrites 33.8%

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

   if -9.20000000000000038e209 < z < 3.0499999999999999e177

   1. Initial program 86.9%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 65.2%

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

Alternative 9: 59.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+121}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+52}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7.5e+121) x (if (<= a 9.5e+52) (+ x y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.5e+121) {
		tmp = x;
	} else if (a <= 9.5e+52) {
		tmp = x + y;
	} 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 <= (-7.5d+121)) then
        tmp = x
    else if (a <= 9.5d+52) then
        tmp = x + y
    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 <= -7.5e+121) {
		tmp = x;
	} else if (a <= 9.5e+52) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7.5e+121:
		tmp = x
	elif a <= 9.5e+52:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7.5e+121)
		tmp = x;
	elseif (a <= 9.5e+52)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7.5e+121)
		tmp = x;
	elseif (a <= 9.5e+52)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7.5e+121], x, If[LessEqual[a, 9.5e+52], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -7.49999999999999965e121 or 9.49999999999999994e52 < a

   1. Initial program 81.8%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 63.4%

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

   if -7.49999999999999965e121 < a < 9.49999999999999994e52

   1. Initial program 88.2%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 63.3%

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

Alternative 10: 50.9% 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 85.9%

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

2. Taylor expanded in x around inf

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

4. Applied rewrites 50.9%

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

Reproduce

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