Data.Colour.RGB:hslsv from colour-2.3.3, B

Percentage Accurate: 99.4% → 99.8%

Time: 10.9s

Alternatives: 15

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

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 = ((60.0d0 * (x - y)) / (z - t)) + (a * 120.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

Python

def code(x, y, z, t, a):
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t)) + Float64(a * 120.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

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 = ((60.0d0 * (x - y)) / (z - t)) + (a * 120.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

Python

def code(x, y, z, t, a):
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t)) + Float64(a * 120.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{60}{z - t}\right) \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (fma a 120.0 (* (- x y) (/ 60.0 (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	return fma(a, 120.0, ((x - y) * (60.0 / (z - t))));
}

Julia

function code(x, y, z, t, a)
	return fma(a, 120.0, Float64(Float64(x - y) * Float64(60.0 / Float64(z - t))))
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(a * 120.0 + N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.4%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
2. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \frac{60 \cdot \left(x - y\right)}{z - t} + \color{blue}{a \cdot 120} \]

   2. lift-+.f64 N/A

      \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120} \]

   3. lift--.f64 N/A

      \[\leadsto \frac{60 \cdot \left(x - y\right)}{\color{blue}{z - t}} + a \cdot 120 \]

   4. lift-/.f64 N/A

      \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} + a \cdot 120 \]

   5. lift-*.f64 N/A

      \[\leadsto \frac{\color{blue}{60 \cdot \left(x - y\right)}}{z - t} + a \cdot 120 \]

   6. lift--.f64 N/A

      \[\leadsto \frac{60 \cdot \color{blue}{\left(x - y\right)}}{z - t} + a \cdot 120 \]

   7. *-commutative N/A

      \[\leadsto \frac{60 \cdot \left(x - y\right)}{z - t} + \color{blue}{120 \cdot a} \]

   8. +-commutative N/A

      \[\leadsto \color{blue}{120 \cdot a + \frac{60 \cdot \left(x - y\right)}{z - t}} \]

   9. *-commutative N/A

      \[\leadsto \color{blue}{a \cdot 120} + \frac{60 \cdot \left(x - y\right)}{z - t} \]

   10. lower-fma.f64 N/A

       \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60 \cdot \left(x - y\right)}{z - t}\right)} \]

   11. *-commutative N/A

       \[\leadsto \mathsf{fma}\left(a, 120, \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t}\right) \]

   12. associate-/l* N/A

       \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}}\right) \]

   13. metadata-eval N/A

       \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{\color{blue}{60 \cdot 1}}{z - t}\right) \]

   14. associate-*r/ N/A

       \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \color{blue}{\left(60 \cdot \frac{1}{z - t}\right)}\right) \]

   15. lower-*.f64 N/A

       \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)}\right) \]

   16. lift--.f64 N/A

       \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right)\right) \]

   17. associate-*r/ N/A

       \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \color{blue}{\frac{60 \cdot 1}{z - t}}\right) \]

   18. metadata-eval N/A

       \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{\color{blue}{60}}{z - t}\right) \]

   19. lower-/.f64 N/A

       \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \color{blue}{\frac{60}{z - t}}\right) \]

   20. lift--.f64 99.8

       \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{60}{\color{blue}{z - t}}\right) \]

3. Applied rewrites 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{60}{z - t}\right)} \]
4. Add Preprocessing

Alternative 2: 85.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-14}:\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+104}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y}{z - t} \cdot -60\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{1}{z - t} \cdot 60\right) \cdot \left(x - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -3e-14)
   (+ (/ (* 60.0 x) (- z t)) (* a 120.0))
   (if (<= x 5.6e+104)
     (fma a 120.0 (* (/ y (- z t)) -60.0))
     (* (* (/ 1.0 (- z t)) 60.0) (- x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -3e-14) {
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	} else if (x <= 5.6e+104) {
		tmp = fma(a, 120.0, ((y / (z - t)) * -60.0));
	} else {
		tmp = ((1.0 / (z - t)) * 60.0) * (x - y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -3e-14)
		tmp = Float64(Float64(Float64(60.0 * x) / Float64(z - t)) + Float64(a * 120.0));
	elseif (x <= 5.6e+104)
		tmp = fma(a, 120.0, Float64(Float64(y / Float64(z - t)) * -60.0));
	else
		tmp = Float64(Float64(Float64(1.0 / Float64(z - t)) * 60.0) * Float64(x - y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -3e-14], N[(N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.6e+104], N[(a * 120.0 + N[(N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision] * -60.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.9999999999999998e-14

   1. Initial program 99.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in x around inf

      \[\leadsto \frac{60 \cdot \color{blue}{x}}{z - t} + a \cdot 120 \]
   3. Step-by-step derivation

   4. Applied rewrites 83.7%

      \[\leadsto \frac{60 \cdot \color{blue}{x}}{z - t} + a \cdot 120 \]

   if -2.9999999999999998e-14 < x < 5.6e104

   1. Initial program 99.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{z - t} + \color{blue}{a \cdot 120} \]

      2. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120} \]

      3. lift--.f64 N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{\color{blue}{z - t}} + a \cdot 120 \]

      4. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} + a \cdot 120 \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{60 \cdot \left(x - y\right)}}{z - t} + a \cdot 120 \]

      6. lift--.f64 N/A

         \[\leadsto \frac{60 \cdot \color{blue}{\left(x - y\right)}}{z - t} + a \cdot 120 \]

      7. *-commutative N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{z - t} + \color{blue}{120 \cdot a} \]

      8. +-commutative N/A

         \[\leadsto \color{blue}{120 \cdot a + \frac{60 \cdot \left(x - y\right)}{z - t}} \]

      9. *-commutative N/A

         \[\leadsto \color{blue}{a \cdot 120} + \frac{60 \cdot \left(x - y\right)}{z - t} \]

      10. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60 \cdot \left(x - y\right)}{z - t}\right)} \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t}\right) \]

      12. associate-/l* N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}}\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{\color{blue}{60 \cdot 1}}{z - t}\right) \]

      14. associate-*r/ N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \color{blue}{\left(60 \cdot \frac{1}{z - t}\right)}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)}\right) \]

      16. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right)\right) \]

      17. associate-*r/ N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \color{blue}{\frac{60 \cdot 1}{z - t}}\right) \]

      18. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{\color{blue}{60}}{z - t}\right) \]

      19. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \color{blue}{\frac{60}{z - t}}\right) \]

      20. lift--.f64 99.8

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{60}{\color{blue}{z - t}}\right) \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{60}{z - t}\right)} \]

   4. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{-60 \cdot \frac{y}{z - t}}\right) \]
   5. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{-60} \cdot \frac{y}{z - t}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(a, 120, -60 \cdot \frac{y}{z - t}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{y}{z - t} \cdot \color{blue}{-60}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{y}{z - t} \cdot \color{blue}{-60}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{y}{z - t} \cdot -60\right) \]

      6. lift--.f64 91.6

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{y}{z - t} \cdot -60\right) \]

   6. Applied rewrites 91.6%

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{y}{z - t} \cdot -60}\right) \]

   if 5.6e104 < x

   1. Initial program 99.0%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{z - t} + \color{blue}{a \cdot 120} \]

      2. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120} \]

      3. lift--.f64 N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{\color{blue}{z - t}} + a \cdot 120 \]

      4. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} + a \cdot 120 \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{60 \cdot \left(x - y\right)}}{z - t} + a \cdot 120 \]

      6. lift--.f64 N/A

         \[\leadsto \frac{60 \cdot \color{blue}{\left(x - y\right)}}{z - t} + a \cdot 120 \]

      7. *-commutative N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{z - t} + \color{blue}{120 \cdot a} \]

      8. +-commutative N/A

         \[\leadsto \color{blue}{120 \cdot a + \frac{60 \cdot \left(x - y\right)}{z - t}} \]

      9. *-commutative N/A

         \[\leadsto \color{blue}{a \cdot 120} + \frac{60 \cdot \left(x - y\right)}{z - t} \]

      10. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60 \cdot \left(x - y\right)}{z - t}\right)} \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t}\right) \]

      12. associate-/l* N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}}\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{\color{blue}{60 \cdot 1}}{z - t}\right) \]

      14. associate-*r/ N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \color{blue}{\left(60 \cdot \frac{1}{z - t}\right)}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)}\right) \]

      16. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right)\right) \]

      17. associate-*r/ N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \color{blue}{\frac{60 \cdot 1}{z - t}}\right) \]

      18. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{\color{blue}{60}}{z - t}\right) \]

      19. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \color{blue}{\frac{60}{z - t}}\right) \]

      20. lift--.f64 99.8

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{60}{\color{blue}{z - t}}\right) \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{60}{z - t}\right)} \]

   4. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   5. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto 60 \cdot \frac{x - y}{z - t} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{60} \cdot \frac{x - y}{z - t} \]

      3. associate-*r/ N/A

         \[\leadsto 60 \cdot \frac{x - y}{z - t} \]

      4. *-commutative N/A

         \[\leadsto 60 \cdot \frac{x - y}{z - t} \]

      5. *-commutative N/A

         \[\leadsto 60 \cdot \frac{x - y}{z - t} \]

      6. associate-/l* N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{\color{blue}{z - t}} \]

      7. *-commutative N/A

         \[\leadsto \frac{\left(x - y\right) \cdot 60}{\color{blue}{z} - t} \]

      8. associate-*r/ N/A

         \[\leadsto \left(x - y\right) \cdot \color{blue}{\frac{60}{z - t}} \]

      9. *-commutative N/A

         \[\leadsto \frac{60}{z - t} \cdot \color{blue}{\left(x - y\right)} \]

      10. lower-*.f64 N/A

          \[\leadsto \frac{60}{z - t} \cdot \color{blue}{\left(x - y\right)} \]

      11. lift-/.f64 N/A

          \[\leadsto \frac{60}{z - t} \cdot \left(\color{blue}{x} - y\right) \]

      12. lift--.f64 N/A

          \[\leadsto \frac{60}{z - t} \cdot \left(x - y\right) \]

      13. lift--.f64 67.9

          \[\leadsto \frac{60}{z - t} \cdot \left(x - \color{blue}{y}\right) \]

   6. Applied rewrites 67.9%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} \]
   7. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \frac{60}{z - t} \cdot \left(x - y\right) \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{60}{z - t} \cdot \left(\color{blue}{x} - y\right) \]

      3. metadata-eval N/A

         \[\leadsto \frac{60 \cdot 1}{z - t} \cdot \left(x - y\right) \]

      4. associate-*r/ N/A

         \[\leadsto \left(60 \cdot \frac{1}{z - t}\right) \cdot \left(\color{blue}{x} - y\right) \]

      5. *-commutative N/A

         \[\leadsto \left(\frac{1}{z - t} \cdot 60\right) \cdot \left(\color{blue}{x} - y\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{z - t} \cdot 60\right) \cdot \left(\color{blue}{x} - y\right) \]

      7. lower-/.f64 N/A

         \[\leadsto \left(\frac{1}{z - t} \cdot 60\right) \cdot \left(x - y\right) \]

      8. lift--.f64 67.8

         \[\leadsto \left(\frac{1}{z - t} \cdot 60\right) \cdot \left(x - y\right) \]

   8. Applied rewrites 67.8%

      \[\leadsto \left(\frac{1}{z - t} \cdot 60\right) \cdot \left(\color{blue}{x} - y\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 83.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+101}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+104}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y}{z - t} \cdot -60\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{1}{z - t} \cdot 60\right) \cdot \left(x - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.45e+101)
   (* (- x y) (/ 60.0 (- z t)))
   (if (<= x 5.6e+104)
     (fma a 120.0 (* (/ y (- z t)) -60.0))
     (* (* (/ 1.0 (- z t)) 60.0) (- x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.45e+101) {
		tmp = (x - y) * (60.0 / (z - t));
	} else if (x <= 5.6e+104) {
		tmp = fma(a, 120.0, ((y / (z - t)) * -60.0));
	} else {
		tmp = ((1.0 / (z - t)) * 60.0) * (x - y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.45e+101)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	elseif (x <= 5.6e+104)
		tmp = fma(a, 120.0, Float64(Float64(y / Float64(z - t)) * -60.0));
	else
		tmp = Float64(Float64(Float64(1.0 / Float64(z - t)) * 60.0) * Float64(x - y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.45e+101], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.6e+104], N[(a * 120.0 + N[(N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision] * -60.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.44999999999999994e101

   1. Initial program 99.0%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x - y}{z - t} \cdot \color{blue}{60} \]

      2. associate-*l/ N/A

         \[\leadsto \frac{\left(x - y\right) \cdot 60}{\color{blue}{z - t}} \]

      3. associate-/l* N/A

         \[\leadsto \left(x - y\right) \cdot \color{blue}{\frac{60}{z - t}} \]

      4. metadata-eval N/A

         \[\leadsto \left(x - y\right) \cdot \frac{60 \cdot 1}{\color{blue}{z} - t} \]

      5. associate-*r/ N/A

         \[\leadsto \left(x - y\right) \cdot \left(60 \cdot \color{blue}{\frac{1}{z - t}}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \left(x - y\right) \cdot \color{blue}{\left(60 \cdot \frac{1}{z - t}\right)} \]

      7. lift--.f64 N/A

         \[\leadsto \left(x - y\right) \cdot \left(\color{blue}{60} \cdot \frac{1}{z - t}\right) \]

      8. associate-*r/ N/A

         \[\leadsto \left(x - y\right) \cdot \frac{60 \cdot 1}{\color{blue}{z - t}} \]

      9. metadata-eval N/A

         \[\leadsto \left(x - y\right) \cdot \frac{60}{\color{blue}{z} - t} \]

      10. lower-/.f64 N/A

          \[\leadsto \left(x - y\right) \cdot \frac{60}{\color{blue}{z - t}} \]

      11. lift--.f64 64.8

          \[\leadsto \left(x - y\right) \cdot \frac{60}{z - \color{blue}{t}} \]

   4. Applied rewrites 64.8%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} \]

   if -1.44999999999999994e101 < x < 5.6e104

   1. Initial program 99.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{z - t} + \color{blue}{a \cdot 120} \]

      2. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120} \]

      3. lift--.f64 N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{\color{blue}{z - t}} + a \cdot 120 \]

      4. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} + a \cdot 120 \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{60 \cdot \left(x - y\right)}}{z - t} + a \cdot 120 \]

      6. lift--.f64 N/A

         \[\leadsto \frac{60 \cdot \color{blue}{\left(x - y\right)}}{z - t} + a \cdot 120 \]

      7. *-commutative N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{z - t} + \color{blue}{120 \cdot a} \]

      8. +-commutative N/A

         \[\leadsto \color{blue}{120 \cdot a + \frac{60 \cdot \left(x - y\right)}{z - t}} \]

      9. *-commutative N/A

         \[\leadsto \color{blue}{a \cdot 120} + \frac{60 \cdot \left(x - y\right)}{z - t} \]

      10. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60 \cdot \left(x - y\right)}{z - t}\right)} \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t}\right) \]

      12. associate-/l* N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}}\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{\color{blue}{60 \cdot 1}}{z - t}\right) \]

      14. associate-*r/ N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \color{blue}{\left(60 \cdot \frac{1}{z - t}\right)}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)}\right) \]

      16. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right)\right) \]

      17. associate-*r/ N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \color{blue}{\frac{60 \cdot 1}{z - t}}\right) \]

      18. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{\color{blue}{60}}{z - t}\right) \]

      19. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \color{blue}{\frac{60}{z - t}}\right) \]

      20. lift--.f64 99.8

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{60}{\color{blue}{z - t}}\right) \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{60}{z - t}\right)} \]

   4. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{-60 \cdot \frac{y}{z - t}}\right) \]
   5. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{-60} \cdot \frac{y}{z - t}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(a, 120, -60 \cdot \frac{y}{z - t}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{y}{z - t} \cdot \color{blue}{-60}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{y}{z - t} \cdot \color{blue}{-60}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{y}{z - t} \cdot -60\right) \]

      6. lift--.f64 89.4

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{y}{z - t} \cdot -60\right) \]

   6. Applied rewrites 89.4%

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{y}{z - t} \cdot -60}\right) \]

   if 5.6e104 < x

   1. Initial program 99.0%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{z - t} + \color{blue}{a \cdot 120} \]

      2. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120} \]

      3. lift--.f64 N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{\color{blue}{z - t}} + a \cdot 120 \]

      4. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} + a \cdot 120 \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{60 \cdot \left(x - y\right)}}{z - t} + a \cdot 120 \]

      6. lift--.f64 N/A

         \[\leadsto \frac{60 \cdot \color{blue}{\left(x - y\right)}}{z - t} + a \cdot 120 \]

      7. *-commutative N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{z - t} + \color{blue}{120 \cdot a} \]

      8. +-commutative N/A

         \[\leadsto \color{blue}{120 \cdot a + \frac{60 \cdot \left(x - y\right)}{z - t}} \]

      9. *-commutative N/A

         \[\leadsto \color{blue}{a \cdot 120} + \frac{60 \cdot \left(x - y\right)}{z - t} \]

      10. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60 \cdot \left(x - y\right)}{z - t}\right)} \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t}\right) \]

      12. associate-/l* N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}}\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{\color{blue}{60 \cdot 1}}{z - t}\right) \]

      14. associate-*r/ N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \color{blue}{\left(60 \cdot \frac{1}{z - t}\right)}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)}\right) \]

      16. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right)\right) \]

      17. associate-*r/ N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \color{blue}{\frac{60 \cdot 1}{z - t}}\right) \]

      18. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{\color{blue}{60}}{z - t}\right) \]

      19. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \color{blue}{\frac{60}{z - t}}\right) \]

      20. lift--.f64 99.8

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{60}{\color{blue}{z - t}}\right) \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{60}{z - t}\right)} \]

   4. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   5. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto 60 \cdot \frac{x - y}{z - t} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{60} \cdot \frac{x - y}{z - t} \]

      3. associate-*r/ N/A

         \[\leadsto 60 \cdot \frac{x - y}{z - t} \]

      4. *-commutative N/A

         \[\leadsto 60 \cdot \frac{x - y}{z - t} \]

      5. *-commutative N/A

         \[\leadsto 60 \cdot \frac{x - y}{z - t} \]

      6. associate-/l* N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{\color{blue}{z - t}} \]

      7. *-commutative N/A

         \[\leadsto \frac{\left(x - y\right) \cdot 60}{\color{blue}{z} - t} \]

      8. associate-*r/ N/A

         \[\leadsto \left(x - y\right) \cdot \color{blue}{\frac{60}{z - t}} \]

      9. *-commutative N/A

         \[\leadsto \frac{60}{z - t} \cdot \color{blue}{\left(x - y\right)} \]

      10. lower-*.f64 N/A

          \[\leadsto \frac{60}{z - t} \cdot \color{blue}{\left(x - y\right)} \]

      11. lift-/.f64 N/A

          \[\leadsto \frac{60}{z - t} \cdot \left(\color{blue}{x} - y\right) \]

      12. lift--.f64 N/A

          \[\leadsto \frac{60}{z - t} \cdot \left(x - y\right) \]

      13. lift--.f64 67.9

          \[\leadsto \frac{60}{z - t} \cdot \left(x - \color{blue}{y}\right) \]

   6. Applied rewrites 67.9%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} \]
   7. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \frac{60}{z - t} \cdot \left(x - y\right) \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{60}{z - t} \cdot \left(\color{blue}{x} - y\right) \]

      3. metadata-eval N/A

         \[\leadsto \frac{60 \cdot 1}{z - t} \cdot \left(x - y\right) \]

      4. associate-*r/ N/A

         \[\leadsto \left(60 \cdot \frac{1}{z - t}\right) \cdot \left(\color{blue}{x} - y\right) \]

      5. *-commutative N/A

         \[\leadsto \left(\frac{1}{z - t} \cdot 60\right) \cdot \left(\color{blue}{x} - y\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{z - t} \cdot 60\right) \cdot \left(\color{blue}{x} - y\right) \]

      7. lower-/.f64 N/A

         \[\leadsto \left(\frac{1}{z - t} \cdot 60\right) \cdot \left(x - y\right) \]

      8. lift--.f64 67.8

         \[\leadsto \left(\frac{1}{z - t} \cdot 60\right) \cdot \left(x - y\right) \]

   8. Applied rewrites 67.8%

      \[\leadsto \left(\frac{1}{z - t} \cdot 60\right) \cdot \left(\color{blue}{x} - y\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 81.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{if}\;x \leq -1.45 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+104}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y}{z - t} \cdot -60\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- x y) (/ 60.0 (- z t)))))
   (if (<= x -1.45e+101)
     t_1
     (if (<= x 5.6e+104) (fma a 120.0 (* (/ y (- z t)) -60.0)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - y) * (60.0 / (z - t));
	double tmp;
	if (x <= -1.45e+101) {
		tmp = t_1;
	} else if (x <= 5.6e+104) {
		tmp = fma(a, 120.0, ((y / (z - t)) * -60.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)))
	tmp = 0.0
	if (x <= -1.45e+101)
		tmp = t_1;
	elseif (x <= 5.6e+104)
		tmp = fma(a, 120.0, Float64(Float64(y / Float64(z - t)) * -60.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.45e+101], t$95$1, If[LessEqual[x, 5.6e+104], N[(a * 120.0 + N[(N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision] * -60.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.44999999999999994e101 or 5.6e104 < x

   1. Initial program 99.0%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x - y}{z - t} \cdot \color{blue}{60} \]

      2. associate-*l/ N/A

         \[\leadsto \frac{\left(x - y\right) \cdot 60}{\color{blue}{z - t}} \]

      3. associate-/l* N/A

         \[\leadsto \left(x - y\right) \cdot \color{blue}{\frac{60}{z - t}} \]

      4. metadata-eval N/A

         \[\leadsto \left(x - y\right) \cdot \frac{60 \cdot 1}{\color{blue}{z} - t} \]

      5. associate-*r/ N/A

         \[\leadsto \left(x - y\right) \cdot \left(60 \cdot \color{blue}{\frac{1}{z - t}}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \left(x - y\right) \cdot \color{blue}{\left(60 \cdot \frac{1}{z - t}\right)} \]

      7. lift--.f64 N/A

         \[\leadsto \left(x - y\right) \cdot \left(\color{blue}{60} \cdot \frac{1}{z - t}\right) \]

      8. associate-*r/ N/A

         \[\leadsto \left(x - y\right) \cdot \frac{60 \cdot 1}{\color{blue}{z - t}} \]

      9. metadata-eval N/A

         \[\leadsto \left(x - y\right) \cdot \frac{60}{\color{blue}{z} - t} \]

      10. lower-/.f64 N/A

          \[\leadsto \left(x - y\right) \cdot \frac{60}{\color{blue}{z - t}} \]

      11. lift--.f64 66.4

          \[\leadsto \left(x - y\right) \cdot \frac{60}{z - \color{blue}{t}} \]

   4. Applied rewrites 66.4%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} \]

   if -1.44999999999999994e101 < x < 5.6e104

   1. Initial program 99.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{z - t} + \color{blue}{a \cdot 120} \]

      2. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120} \]

      3. lift--.f64 N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{\color{blue}{z - t}} + a \cdot 120 \]

      4. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} + a \cdot 120 \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{60 \cdot \left(x - y\right)}}{z - t} + a \cdot 120 \]

      6. lift--.f64 N/A

         \[\leadsto \frac{60 \cdot \color{blue}{\left(x - y\right)}}{z - t} + a \cdot 120 \]

      7. *-commutative N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{z - t} + \color{blue}{120 \cdot a} \]

      8. +-commutative N/A

         \[\leadsto \color{blue}{120 \cdot a + \frac{60 \cdot \left(x - y\right)}{z - t}} \]

      9. *-commutative N/A

         \[\leadsto \color{blue}{a \cdot 120} + \frac{60 \cdot \left(x - y\right)}{z - t} \]

      10. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60 \cdot \left(x - y\right)}{z - t}\right)} \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t}\right) \]

      12. associate-/l* N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}}\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{\color{blue}{60 \cdot 1}}{z - t}\right) \]

      14. associate-*r/ N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \color{blue}{\left(60 \cdot \frac{1}{z - t}\right)}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)}\right) \]

      16. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right)\right) \]

      17. associate-*r/ N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \color{blue}{\frac{60 \cdot 1}{z - t}}\right) \]

      18. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{\color{blue}{60}}{z - t}\right) \]

      19. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \color{blue}{\frac{60}{z - t}}\right) \]

      20. lift--.f64 99.8

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{60}{\color{blue}{z - t}}\right) \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{60}{z - t}\right)} \]

   4. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{-60 \cdot \frac{y}{z - t}}\right) \]
   5. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{-60} \cdot \frac{y}{z - t}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(a, 120, -60 \cdot \frac{y}{z - t}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{y}{z - t} \cdot \color{blue}{-60}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{y}{z - t} \cdot \color{blue}{-60}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{y}{z - t} \cdot -60\right) \]

      6. lift--.f64 89.4

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{y}{z - t} \cdot -60\right) \]

   6. Applied rewrites 89.4%

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{y}{z - t} \cdot -60}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 81.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x - y}{z}, 60, 120 \cdot a\right)\\ \mathbf{if}\;z \leq -2.55 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+16}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- x y) z) 60.0 (* 120.0 a))))
   (if (<= z -2.55e-52)
     t_1
     (if (<= z 4.1e+16) (fma (/ (- x y) t) -60.0 (* 120.0 a)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((x - y) / z), 60.0, (120.0 * a));
	double tmp;
	if (z <= -2.55e-52) {
		tmp = t_1;
	} else if (z <= 4.1e+16) {
		tmp = fma(((x - y) / t), -60.0, (120.0 * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(x - y) / z), 60.0, Float64(120.0 * a))
	tmp = 0.0
	if (z <= -2.55e-52)
		tmp = t_1;
	elseif (z <= 4.1e+16)
		tmp = fma(Float64(Float64(x - y) / t), -60.0, Float64(120.0 * a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.55e-52], t$95$1, If[LessEqual[z, 4.1e+16], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.54999999999999995e-52 or 4.1e16 < z

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x - y}{z} \cdot 60 + \color{blue}{120} \cdot a \]

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{z}, \color{blue}{60}, 120 \cdot a\right) \]

      3. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{z}, 60, 120 \cdot a\right) \]

      4. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{z}, 60, 120 \cdot a\right) \]

      5. lower-*.f64 84.8

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{z}, 60, 120 \cdot a\right) \]

   4. Applied rewrites 84.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x - y}{z}, 60, 120 \cdot a\right)} \]

   if -2.54999999999999995e-52 < z < 4.1e16

   1. Initial program 99.5%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x - y}{t} \cdot -60 + \color{blue}{120} \cdot a \]

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, \color{blue}{-60}, 120 \cdot a\right) \]

      3. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

      4. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

      5. lower-*.f64 81.7

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

   4. Applied rewrites 81.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 74.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{-18}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-5}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, x \cdot \frac{60}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.5e-18)
   (* 120.0 a)
   (if (<= a 2.7e-5)
     (* (- x y) (/ 60.0 (- z t)))
     (fma a 120.0 (* x (/ 60.0 z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.5e-18) {
		tmp = 120.0 * a;
	} else if (a <= 2.7e-5) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = fma(a, 120.0, (x * (60.0 / z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.5e-18)
		tmp = Float64(120.0 * a);
	elseif (a <= 2.7e-5)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	else
		tmp = fma(a, 120.0, Float64(x * Float64(60.0 / z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.5e-18], N[(120.0 * a), $MachinePrecision], If[LessEqual[a, 2.7e-5], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0 + N[(x * N[(60.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.4999999999999999e-18

   1. Initial program 99.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-*.f64 74.8

         \[\leadsto 120 \cdot \color{blue}{a} \]

   4. Applied rewrites 74.8%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -3.4999999999999999e-18 < a < 2.6999999999999999e-5

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x - y}{z - t} \cdot \color{blue}{60} \]

      2. associate-*l/ N/A

         \[\leadsto \frac{\left(x - y\right) \cdot 60}{\color{blue}{z - t}} \]

      3. associate-/l* N/A

         \[\leadsto \left(x - y\right) \cdot \color{blue}{\frac{60}{z - t}} \]

      4. metadata-eval N/A

         \[\leadsto \left(x - y\right) \cdot \frac{60 \cdot 1}{\color{blue}{z} - t} \]

      5. associate-*r/ N/A

         \[\leadsto \left(x - y\right) \cdot \left(60 \cdot \color{blue}{\frac{1}{z - t}}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \left(x - y\right) \cdot \color{blue}{\left(60 \cdot \frac{1}{z - t}\right)} \]

      7. lift--.f64 N/A

         \[\leadsto \left(x - y\right) \cdot \left(\color{blue}{60} \cdot \frac{1}{z - t}\right) \]

      8. associate-*r/ N/A

         \[\leadsto \left(x - y\right) \cdot \frac{60 \cdot 1}{\color{blue}{z - t}} \]

      9. metadata-eval N/A

         \[\leadsto \left(x - y\right) \cdot \frac{60}{\color{blue}{z} - t} \]

      10. lower-/.f64 N/A

          \[\leadsto \left(x - y\right) \cdot \frac{60}{\color{blue}{z - t}} \]

      11. lift--.f64 76.3

          \[\leadsto \left(x - y\right) \cdot \frac{60}{z - \color{blue}{t}} \]

   4. Applied rewrites 76.3%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} \]

   if 2.6999999999999999e-5 < a

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{z - t} + \color{blue}{a \cdot 120} \]

      2. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120} \]

      3. lift--.f64 N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{\color{blue}{z - t}} + a \cdot 120 \]

      4. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} + a \cdot 120 \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{60 \cdot \left(x - y\right)}}{z - t} + a \cdot 120 \]

      6. lift--.f64 N/A

         \[\leadsto \frac{60 \cdot \color{blue}{\left(x - y\right)}}{z - t} + a \cdot 120 \]

      7. *-commutative N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{z - t} + \color{blue}{120 \cdot a} \]

      8. +-commutative N/A

         \[\leadsto \color{blue}{120 \cdot a + \frac{60 \cdot \left(x - y\right)}{z - t}} \]

      9. *-commutative N/A

         \[\leadsto \color{blue}{a \cdot 120} + \frac{60 \cdot \left(x - y\right)}{z - t} \]

      10. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60 \cdot \left(x - y\right)}{z - t}\right)} \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t}\right) \]

      12. associate-/l* N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}}\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{\color{blue}{60 \cdot 1}}{z - t}\right) \]

      14. associate-*r/ N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \color{blue}{\left(60 \cdot \frac{1}{z - t}\right)}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)}\right) \]

      16. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right)\right) \]

      17. associate-*r/ N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \color{blue}{\frac{60 \cdot 1}{z - t}}\right) \]

      18. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{\color{blue}{60}}{z - t}\right) \]

      19. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \color{blue}{\frac{60}{z - t}}\right) \]

      20. lift--.f64 99.9

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{60}{\color{blue}{z - t}}\right) \]

   3. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{60}{z - t}\right)} \]

   4. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{60}{\color{blue}{z}}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 72.8%

      \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{60}{\color{blue}{z}}\right) \]

   7. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{x} \cdot \frac{60}{z}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 70.9%

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{x} \cdot \frac{60}{z}\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 65.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, 120, x \cdot \frac{60}{z}\right)\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-164}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y}{t} \cdot 60\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma a 120.0 (* x (/ 60.0 z)))))
   (if (<= z -6.5e-19)
     t_1
     (if (<= z 2.4e-164) (fma a 120.0 (* (/ y t) 60.0)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(a, 120.0, (x * (60.0 / z)));
	double tmp;
	if (z <= -6.5e-19) {
		tmp = t_1;
	} else if (z <= 2.4e-164) {
		tmp = fma(a, 120.0, ((y / t) * 60.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(a, 120.0, Float64(x * Float64(60.0 / z)))
	tmp = 0.0
	if (z <= -6.5e-19)
		tmp = t_1;
	elseif (z <= 2.4e-164)
		tmp = fma(a, 120.0, Float64(Float64(y / t) * 60.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a * 120.0 + N[(x * N[(60.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e-19], t$95$1, If[LessEqual[z, 2.4e-164], N[(a * 120.0 + N[(N[(y / t), $MachinePrecision] * 60.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5000000000000001e-19 or 2.39999999999999983e-164 < z

   1. Initial program 99.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{z - t} + \color{blue}{a \cdot 120} \]

      2. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120} \]

      3. lift--.f64 N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{\color{blue}{z - t}} + a \cdot 120 \]

      4. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} + a \cdot 120 \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{60 \cdot \left(x - y\right)}}{z - t} + a \cdot 120 \]

      6. lift--.f64 N/A

         \[\leadsto \frac{60 \cdot \color{blue}{\left(x - y\right)}}{z - t} + a \cdot 120 \]

      7. *-commutative N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{z - t} + \color{blue}{120 \cdot a} \]

      8. +-commutative N/A

         \[\leadsto \color{blue}{120 \cdot a + \frac{60 \cdot \left(x - y\right)}{z - t}} \]

      9. *-commutative N/A

         \[\leadsto \color{blue}{a \cdot 120} + \frac{60 \cdot \left(x - y\right)}{z - t} \]

      10. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60 \cdot \left(x - y\right)}{z - t}\right)} \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t}\right) \]

      12. associate-/l* N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}}\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{\color{blue}{60 \cdot 1}}{z - t}\right) \]

      14. associate-*r/ N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \color{blue}{\left(60 \cdot \frac{1}{z - t}\right)}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)}\right) \]

      16. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right)\right) \]

      17. associate-*r/ N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \color{blue}{\frac{60 \cdot 1}{z - t}}\right) \]

      18. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{\color{blue}{60}}{z - t}\right) \]

      19. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \color{blue}{\frac{60}{z - t}}\right) \]

      20. lift--.f64 99.8

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{60}{\color{blue}{z - t}}\right) \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{60}{z - t}\right)} \]

   4. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{60}{\color{blue}{z}}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 79.1%

      \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{60}{\color{blue}{z}}\right) \]

   7. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{x} \cdot \frac{60}{z}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 67.1%

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{x} \cdot \frac{60}{z}\right) \]

   if -6.5000000000000001e-19 < z < 2.39999999999999983e-164

   1. Initial program 99.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x - y}{t} \cdot -60 + \color{blue}{120} \cdot a \]

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, \color{blue}{-60}, 120 \cdot a\right) \]

      3. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

      4. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

      5. lower-*.f64 85.4

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

   4. Applied rewrites 85.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto 60 \cdot \frac{y}{t} + \color{blue}{120 \cdot a} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{y}{t} \cdot 60 + 120 \cdot a \]

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{y}{t}, 60, 120 \cdot a\right) \]

      3. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{y}{t}, 60, 120 \cdot a\right) \]

      4. lift-*.f64 63.5

         \[\leadsto \mathsf{fma}\left(\frac{y}{t}, 60, 120 \cdot a\right) \]

   7. Applied rewrites 63.5%

      \[\leadsto \mathsf{fma}\left(\frac{y}{t}, \color{blue}{60}, 120 \cdot a\right) \]
   8. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{y}{t}, 60, 120 \cdot a\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{y}{t}, 60, 120 \cdot a\right) \]

      3. lift-fma.f64 N/A

         \[\leadsto \frac{y}{t} \cdot 60 + 120 \cdot \color{blue}{a} \]

      4. *-commutative N/A

         \[\leadsto 60 \cdot \frac{y}{t} + 120 \cdot a \]

      5. +-commutative N/A

         \[\leadsto 120 \cdot a + 60 \cdot \color{blue}{\frac{y}{t}} \]

      6. *-commutative N/A

         \[\leadsto a \cdot 120 + 60 \cdot \frac{\color{blue}{y}}{t} \]

      7. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(a, 120, 60 \cdot \frac{y}{t}\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{y}{t} \cdot 60\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{y}{t} \cdot 60\right) \]

      10. lift-/.f64 63.5

          \[\leadsto \mathsf{fma}\left(a, 120, \frac{y}{t} \cdot 60\right) \]

   9. Applied rewrites 63.5%

      \[\leadsto \mathsf{fma}\left(a, 120, \frac{y}{t} \cdot 60\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 60.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ t_2 := \frac{60}{z} \cdot \left(x - y\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+253}:\\ \;\;\;\;\frac{x - y}{t} \cdot -60\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{+45}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+89}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+267}:\\ \;\;\;\;\frac{-60 \cdot \left(x - y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))) (t_2 (* (/ 60.0 z) (- x y))))
   (if (<= t_1 -1e+253)
     (* (/ (- x y) t) -60.0)
     (if (<= t_1 -2e+45)
       t_2
       (if (<= t_1 1e+89)
         (* 120.0 a)
         (if (<= t_1 5e+267) (/ (* -60.0 (- x y)) t) t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double t_2 = (60.0 / z) * (x - y);
	double tmp;
	if (t_1 <= -1e+253) {
		tmp = ((x - y) / t) * -60.0;
	} else if (t_1 <= -2e+45) {
		tmp = t_2;
	} else if (t_1 <= 1e+89) {
		tmp = 120.0 * a;
	} else if (t_1 <= 5e+267) {
		tmp = (-60.0 * (x - y)) / t;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    t_2 = (60.0d0 / z) * (x - y)
    if (t_1 <= (-1d+253)) then
        tmp = ((x - y) / t) * (-60.0d0)
    else if (t_1 <= (-2d+45)) then
        tmp = t_2
    else if (t_1 <= 1d+89) then
        tmp = 120.0d0 * a
    else if (t_1 <= 5d+267) then
        tmp = ((-60.0d0) * (x - y)) / t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double t_2 = (60.0 / z) * (x - y);
	double tmp;
	if (t_1 <= -1e+253) {
		tmp = ((x - y) / t) * -60.0;
	} else if (t_1 <= -2e+45) {
		tmp = t_2;
	} else if (t_1 <= 1e+89) {
		tmp = 120.0 * a;
	} else if (t_1 <= 5e+267) {
		tmp = (-60.0 * (x - y)) / t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	t_2 = (60.0 / z) * (x - y)
	tmp = 0
	if t_1 <= -1e+253:
		tmp = ((x - y) / t) * -60.0
	elif t_1 <= -2e+45:
		tmp = t_2
	elif t_1 <= 1e+89:
		tmp = 120.0 * a
	elif t_1 <= 5e+267:
		tmp = (-60.0 * (x - y)) / t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	t_2 = Float64(Float64(60.0 / z) * Float64(x - y))
	tmp = 0.0
	if (t_1 <= -1e+253)
		tmp = Float64(Float64(Float64(x - y) / t) * -60.0);
	elseif (t_1 <= -2e+45)
		tmp = t_2;
	elseif (t_1 <= 1e+89)
		tmp = Float64(120.0 * a);
	elseif (t_1 <= 5e+267)
		tmp = Float64(Float64(-60.0 * Float64(x - y)) / t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	t_2 = (60.0 / z) * (x - y);
	tmp = 0.0;
	if (t_1 <= -1e+253)
		tmp = ((x - y) / t) * -60.0;
	elseif (t_1 <= -2e+45)
		tmp = t_2;
	elseif (t_1 <= 1e+89)
		tmp = 120.0 * a;
	elseif (t_1 <= 5e+267)
		tmp = (-60.0 * (x - y)) / t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 / z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+253], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0), $MachinePrecision], If[LessEqual[t$95$1, -2e+45], t$95$2, If[LessEqual[t$95$1, 1e+89], N[(120.0 * a), $MachinePrecision], If[LessEqual[t$95$1, 5e+267], N[(N[(-60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -9.9999999999999994e252

   1. Initial program 95.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x - y}{t} \cdot -60 + \color{blue}{120} \cdot a \]

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, \color{blue}{-60}, 120 \cdot a\right) \]

      3. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

      4. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

      5. lower-*.f64 66.2

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

   4. Applied rewrites 66.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)} \]

   5. Taylor expanded in t around 0

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x - y}{t} \cdot -60 \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{x - y}{t} \cdot -60 \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{x - y}{t} \cdot -60 \]

      4. lift--.f64 64.9

         \[\leadsto \frac{x - y}{t} \cdot -60 \]

   7. Applied rewrites 64.9%

      \[\leadsto \frac{x - y}{t} \cdot \color{blue}{-60} \]

   if -9.9999999999999994e252 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.9999999999999999e45 or 4.9999999999999999e267 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 98.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{z - t} + \color{blue}{a \cdot 120} \]

      2. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120} \]

      3. lift--.f64 N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{\color{blue}{z - t}} + a \cdot 120 \]

      4. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} + a \cdot 120 \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{60 \cdot \left(x - y\right)}}{z - t} + a \cdot 120 \]

      6. lift--.f64 N/A

         \[\leadsto \frac{60 \cdot \color{blue}{\left(x - y\right)}}{z - t} + a \cdot 120 \]

      7. *-commutative N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{z - t} + \color{blue}{120 \cdot a} \]

      8. +-commutative N/A

         \[\leadsto \color{blue}{120 \cdot a + \frac{60 \cdot \left(x - y\right)}{z - t}} \]

      9. *-commutative N/A

         \[\leadsto \color{blue}{a \cdot 120} + \frac{60 \cdot \left(x - y\right)}{z - t} \]

      10. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60 \cdot \left(x - y\right)}{z - t}\right)} \]

      11. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t}\right) \]

      12. associate-/l* N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}}\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{\color{blue}{60 \cdot 1}}{z - t}\right) \]

      14. associate-*r/ N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \color{blue}{\left(60 \cdot \frac{1}{z - t}\right)}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)}\right) \]

      16. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right)\right) \]

      17. associate-*r/ N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \color{blue}{\frac{60 \cdot 1}{z - t}}\right) \]

      18. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{\color{blue}{60}}{z - t}\right) \]

      19. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \color{blue}{\frac{60}{z - t}}\right) \]

      20. lift--.f64 99.7

          \[\leadsto \mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{60}{\color{blue}{z - t}}\right) \]

   3. Applied rewrites 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{60}{z - t}\right)} \]

   4. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   5. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto 60 \cdot \frac{x - y}{z - t} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{60} \cdot \frac{x - y}{z - t} \]

      3. associate-*r/ N/A

         \[\leadsto 60 \cdot \frac{x - y}{z - t} \]

      4. *-commutative N/A

         \[\leadsto 60 \cdot \frac{x - y}{z - t} \]

      5. *-commutative N/A

         \[\leadsto 60 \cdot \frac{x - y}{z - t} \]

      6. associate-/l* N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{\color{blue}{z - t}} \]

      7. *-commutative N/A

         \[\leadsto \frac{\left(x - y\right) \cdot 60}{\color{blue}{z} - t} \]

      8. associate-*r/ N/A

         \[\leadsto \left(x - y\right) \cdot \color{blue}{\frac{60}{z - t}} \]

      9. *-commutative N/A

         \[\leadsto \frac{60}{z - t} \cdot \color{blue}{\left(x - y\right)} \]

      10. lower-*.f64 N/A

          \[\leadsto \frac{60}{z - t} \cdot \color{blue}{\left(x - y\right)} \]

      11. lift-/.f64 N/A

          \[\leadsto \frac{60}{z - t} \cdot \left(\color{blue}{x} - y\right) \]

      12. lift--.f64 N/A

          \[\leadsto \frac{60}{z - t} \cdot \left(x - y\right) \]

      13. lift--.f64 78.5

          \[\leadsto \frac{60}{z - t} \cdot \left(x - \color{blue}{y}\right) \]

   6. Applied rewrites 78.5%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} \]

   7. Taylor expanded in z around inf

      \[\leadsto \frac{60}{z} \cdot \left(x - y\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 44.7%

      \[\leadsto \frac{60}{z} \cdot \left(x - y\right) \]

   if -1.9999999999999999e45 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.99999999999999995e88

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-*.f64 68.6

         \[\leadsto 120 \cdot \color{blue}{a} \]

   4. Applied rewrites 68.6%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if 9.99999999999999995e88 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.9999999999999999e267

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x - y}{t} \cdot -60 + \color{blue}{120} \cdot a \]

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, \color{blue}{-60}, 120 \cdot a\right) \]

      3. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

      4. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

      5. lower-*.f64 53.4

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

   4. Applied rewrites 53.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)} \]

   5. Taylor expanded in t around 0

      \[\leadsto \frac{-60 \cdot \left(x - y\right) + 120 \cdot \left(a \cdot t\right)}{\color{blue}{t}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{-60 \cdot \left(x - y\right) + 120 \cdot \left(a \cdot t\right)}{t} \]

      2. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(-60, x - y, 120 \cdot \left(a \cdot t\right)\right)}{t} \]

      3. lift--.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(-60, x - y, 120 \cdot \left(a \cdot t\right)\right)}{t} \]

      4. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(-60, x - y, \left(a \cdot t\right) \cdot 120\right)}{t} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(-60, x - y, \left(a \cdot t\right) \cdot 120\right)}{t} \]

      6. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(-60, x - y, \left(t \cdot a\right) \cdot 120\right)}{t} \]

      7. lower-*.f64 49.8

         \[\leadsto \frac{\mathsf{fma}\left(-60, x - y, \left(t \cdot a\right) \cdot 120\right)}{t} \]

   7. Applied rewrites 49.8%

      \[\leadsto \frac{\mathsf{fma}\left(-60, x - y, \left(t \cdot a\right) \cdot 120\right)}{\color{blue}{t}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \frac{-60 \cdot \left(x - y\right)}{t} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{-60 \cdot \left(x - y\right)}{t} \]

      2. lift--.f64 38.3

         \[\leadsto \frac{-60 \cdot \left(x - y\right)}{t} \]

   10. Applied rewrites 38.3%

       \[\leadsto \frac{-60 \cdot \left(x - y\right)}{t} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 9: 60.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z - t} \cdot 60\\ \mathbf{if}\;x \leq -1.36 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+104}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y}{t} \cdot 60\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ x (- z t)) 60.0)))
   (if (<= x -1.36e+101)
     t_1
     (if (<= x 5.8e+104) (fma a 120.0 (* (/ y t) 60.0)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x / (z - t)) * 60.0;
	double tmp;
	if (x <= -1.36e+101) {
		tmp = t_1;
	} else if (x <= 5.8e+104) {
		tmp = fma(a, 120.0, ((y / t) * 60.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x / Float64(z - t)) * 60.0)
	tmp = 0.0
	if (x <= -1.36e+101)
		tmp = t_1;
	elseif (x <= 5.8e+104)
		tmp = fma(a, 120.0, Float64(Float64(y / t) * 60.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $MachinePrecision]}, If[LessEqual[x, -1.36e+101], t$95$1, If[LessEqual[x, 5.8e+104], N[(a * 120.0 + N[(N[(y / t), $MachinePrecision] * 60.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.35999999999999998e101 or 5.7999999999999997e104 < x

   1. Initial program 99.0%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x}{z - t} \cdot \color{blue}{60} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{x}{z - t} \cdot \color{blue}{60} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{x}{z - t} \cdot 60 \]

      4. lift--.f64 55.3

         \[\leadsto \frac{x}{z - t} \cdot 60 \]

   4. Applied rewrites 55.3%

      \[\leadsto \color{blue}{\frac{x}{z - t} \cdot 60} \]

   if -1.35999999999999998e101 < x < 5.7999999999999997e104

   1. Initial program 99.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x - y}{t} \cdot -60 + \color{blue}{120} \cdot a \]

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, \color{blue}{-60}, 120 \cdot a\right) \]

      3. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

      4. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

      5. lower-*.f64 66.1

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

   4. Applied rewrites 66.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto 60 \cdot \frac{y}{t} + \color{blue}{120 \cdot a} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{y}{t} \cdot 60 + 120 \cdot a \]

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{y}{t}, 60, 120 \cdot a\right) \]

      3. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{y}{t}, 60, 120 \cdot a\right) \]

      4. lift-*.f64 63.5

         \[\leadsto \mathsf{fma}\left(\frac{y}{t}, 60, 120 \cdot a\right) \]

   7. Applied rewrites 63.5%

      \[\leadsto \mathsf{fma}\left(\frac{y}{t}, \color{blue}{60}, 120 \cdot a\right) \]
   8. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{y}{t}, 60, 120 \cdot a\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{y}{t}, 60, 120 \cdot a\right) \]

      3. lift-fma.f64 N/A

         \[\leadsto \frac{y}{t} \cdot 60 + 120 \cdot \color{blue}{a} \]

      4. *-commutative N/A

         \[\leadsto 60 \cdot \frac{y}{t} + 120 \cdot a \]

      5. +-commutative N/A

         \[\leadsto 120 \cdot a + 60 \cdot \color{blue}{\frac{y}{t}} \]

      6. *-commutative N/A

         \[\leadsto a \cdot 120 + 60 \cdot \frac{\color{blue}{y}}{t} \]

      7. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(a, 120, 60 \cdot \frac{y}{t}\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{y}{t} \cdot 60\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{y}{t} \cdot 60\right) \]

      10. lift-/.f64 63.5

          \[\leadsto \mathsf{fma}\left(a, 120, \frac{y}{t} \cdot 60\right) \]

   9. Applied rewrites 63.5%

      \[\leadsto \mathsf{fma}\left(a, 120, \frac{y}{t} \cdot 60\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 59.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+32}:\\ \;\;\;\;\frac{x - y}{t} \cdot -60\\ \mathbf{elif}\;t\_1 \leq 10^{+89}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{-60 \cdot \left(x - y\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -5e+32)
     (* (/ (- x y) t) -60.0)
     (if (<= t_1 1e+89) (* 120.0 a) (/ (* -60.0 (- x y)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -5e+32) {
		tmp = ((x - y) / t) * -60.0;
	} else if (t_1 <= 1e+89) {
		tmp = 120.0 * a;
	} else {
		tmp = (-60.0 * (x - y)) / 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 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-5d+32)) then
        tmp = ((x - y) / t) * (-60.0d0)
    else if (t_1 <= 1d+89) then
        tmp = 120.0d0 * a
    else
        tmp = ((-60.0d0) * (x - y)) / 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 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -5e+32) {
		tmp = ((x - y) / t) * -60.0;
	} else if (t_1 <= 1e+89) {
		tmp = 120.0 * a;
	} else {
		tmp = (-60.0 * (x - y)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -5e+32:
		tmp = ((x - y) / t) * -60.0
	elif t_1 <= 1e+89:
		tmp = 120.0 * a
	else:
		tmp = (-60.0 * (x - y)) / t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -5e+32)
		tmp = Float64(Float64(Float64(x - y) / t) * -60.0);
	elseif (t_1 <= 1e+89)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(-60.0 * Float64(x - y)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -5e+32)
		tmp = ((x - y) / t) * -60.0;
	elseif (t_1 <= 1e+89)
		tmp = 120.0 * a;
	else
		tmp = (-60.0 * (x - y)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+32], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0), $MachinePrecision], If[LessEqual[t$95$1, 1e+89], N[(120.0 * a), $MachinePrecision], N[(N[(-60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -4.9999999999999997e32

   1. Initial program 98.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x - y}{t} \cdot -60 + \color{blue}{120} \cdot a \]

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, \color{blue}{-60}, 120 \cdot a\right) \]

      3. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

      4. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

      5. lower-*.f64 58.4

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

   4. Applied rewrites 58.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)} \]

   5. Taylor expanded in t around 0

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x - y}{t} \cdot -60 \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{x - y}{t} \cdot -60 \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{x - y}{t} \cdot -60 \]

      4. lift--.f64 44.2

         \[\leadsto \frac{x - y}{t} \cdot -60 \]

   7. Applied rewrites 44.2%

      \[\leadsto \frac{x - y}{t} \cdot \color{blue}{-60} \]

   if -4.9999999999999997e32 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.99999999999999995e88

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-*.f64 68.9

         \[\leadsto 120 \cdot \color{blue}{a} \]

   4. Applied rewrites 68.9%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if 9.99999999999999995e88 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 98.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x - y}{t} \cdot -60 + \color{blue}{120} \cdot a \]

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, \color{blue}{-60}, 120 \cdot a\right) \]

      3. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

      4. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

      5. lower-*.f64 56.3

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

   4. Applied rewrites 56.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)} \]

   5. Taylor expanded in t around 0

      \[\leadsto \frac{-60 \cdot \left(x - y\right) + 120 \cdot \left(a \cdot t\right)}{\color{blue}{t}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{-60 \cdot \left(x - y\right) + 120 \cdot \left(a \cdot t\right)}{t} \]

      2. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(-60, x - y, 120 \cdot \left(a \cdot t\right)\right)}{t} \]

      3. lift--.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(-60, x - y, 120 \cdot \left(a \cdot t\right)\right)}{t} \]

      4. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(-60, x - y, \left(a \cdot t\right) \cdot 120\right)}{t} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(-60, x - y, \left(a \cdot t\right) \cdot 120\right)}{t} \]

      6. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(-60, x - y, \left(t \cdot a\right) \cdot 120\right)}{t} \]

      7. lower-*.f64 53.2

         \[\leadsto \frac{\mathsf{fma}\left(-60, x - y, \left(t \cdot a\right) \cdot 120\right)}{t} \]

   7. Applied rewrites 53.2%

      \[\leadsto \frac{\mathsf{fma}\left(-60, x - y, \left(t \cdot a\right) \cdot 120\right)}{\color{blue}{t}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \frac{-60 \cdot \left(x - y\right)}{t} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{-60 \cdot \left(x - y\right)}{t} \]

      2. lift--.f64 45.2

         \[\leadsto \frac{-60 \cdot \left(x - y\right)}{t} \]

   10. Applied rewrites 45.2%

       \[\leadsto \frac{-60 \cdot \left(x - y\right)}{t} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 59.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{t} \cdot -60\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+89}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ (- x y) t) -60.0)) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -5e+32) t_1 (if (<= t_2 1e+89) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) / t) * -60.0;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e+32) {
		tmp = t_1;
	} else if (t_2 <= 1e+89) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x - y) / t) * (-60.0d0)
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-5d+32)) then
        tmp = t_1
    else if (t_2 <= 1d+89) then
        tmp = 120.0d0 * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) / t) * -60.0;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e+32) {
		tmp = t_1;
	} else if (t_2 <= 1e+89) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((x - y) / t) * -60.0
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -5e+32:
		tmp = t_1
	elif t_2 <= 1e+89:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x - y) / t) * -60.0)
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -5e+32)
		tmp = t_1;
	elseif (t_2 <= 1e+89)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((x - y) / t) * -60.0;
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -5e+32)
		tmp = t_1;
	elseif (t_2 <= 1e+89)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+32], t$95$1, If[LessEqual[t$95$2, 1e+89], N[(120.0 * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -4.9999999999999997e32 or 9.99999999999999995e88 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 98.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x - y}{t} \cdot -60 + \color{blue}{120} \cdot a \]

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, \color{blue}{-60}, 120 \cdot a\right) \]

      3. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

      4. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

      5. lower-*.f64 57.5

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

   4. Applied rewrites 57.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)} \]

   5. Taylor expanded in t around 0

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x - y}{t} \cdot -60 \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{x - y}{t} \cdot -60 \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{x - y}{t} \cdot -60 \]

      4. lift--.f64 44.7

         \[\leadsto \frac{x - y}{t} \cdot -60 \]

   7. Applied rewrites 44.7%

      \[\leadsto \frac{x - y}{t} \cdot \color{blue}{-60} \]

   if -4.9999999999999997e32 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.99999999999999995e88

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-*.f64 68.9

         \[\leadsto 120 \cdot \color{blue}{a} \]

   4. Applied rewrites 68.9%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 54.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+227}:\\ \;\;\;\;\frac{y}{t} \cdot 60\\ \mathbf{elif}\;t\_1 \leq 10^{+162}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{-60 \cdot x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -1e+227)
     (* (/ y t) 60.0)
     (if (<= t_1 1e+162) (* 120.0 a) (/ (* -60.0 x) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+227) {
		tmp = (y / t) * 60.0;
	} else if (t_1 <= 1e+162) {
		tmp = 120.0 * a;
	} else {
		tmp = (-60.0 * 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) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-1d+227)) then
        tmp = (y / t) * 60.0d0
    else if (t_1 <= 1d+162) then
        tmp = 120.0d0 * a
    else
        tmp = ((-60.0d0) * x) / 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 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+227) {
		tmp = (y / t) * 60.0;
	} else if (t_1 <= 1e+162) {
		tmp = 120.0 * a;
	} else {
		tmp = (-60.0 * x) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -1e+227:
		tmp = (y / t) * 60.0
	elif t_1 <= 1e+162:
		tmp = 120.0 * a
	else:
		tmp = (-60.0 * x) / t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -1e+227)
		tmp = Float64(Float64(y / t) * 60.0);
	elseif (t_1 <= 1e+162)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(-60.0 * x) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -1e+227)
		tmp = (y / t) * 60.0;
	elseif (t_1 <= 1e+162)
		tmp = 120.0 * a;
	else
		tmp = (-60.0 * x) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+227], N[(N[(y / t), $MachinePrecision] * 60.0), $MachinePrecision], If[LessEqual[t$95$1, 1e+162], N[(120.0 * a), $MachinePrecision], N[(N[(-60.0 * x), $MachinePrecision] / t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.0000000000000001e227

   1. Initial program 96.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x - y}{t} \cdot -60 + \color{blue}{120} \cdot a \]

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, \color{blue}{-60}, 120 \cdot a\right) \]

      3. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

      4. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

      5. lower-*.f64 64.0

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

   4. Applied rewrites 64.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)} \]

   5. Taylor expanded in y around inf

      \[\leadsto 60 \cdot \color{blue}{\frac{y}{t}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{y}{t} \cdot 60 \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{y}{t} \cdot 60 \]

      3. lower-/.f64 36.2

         \[\leadsto \frac{y}{t} \cdot 60 \]

   7. Applied rewrites 36.2%

      \[\leadsto \frac{y}{t} \cdot \color{blue}{60} \]

   if -1.0000000000000001e227 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.9999999999999994e161

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-*.f64 60.0

         \[\leadsto 120 \cdot \color{blue}{a} \]

   4. Applied rewrites 60.0%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if 9.9999999999999994e161 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 98.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x - y}{t} \cdot -60 + \color{blue}{120} \cdot a \]

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, \color{blue}{-60}, 120 \cdot a\right) \]

      3. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

      4. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

      5. lower-*.f64 58.0

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

   4. Applied rewrites 58.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto -60 \cdot \color{blue}{\frac{x}{t}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x}{t} \cdot -60 \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{x}{t} \cdot -60 \]

      3. lower-/.f64 26.9

         \[\leadsto \frac{x}{t} \cdot -60 \]

   7. Applied rewrites 26.9%

      \[\leadsto \frac{x}{t} \cdot \color{blue}{-60} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{x}{t} \cdot -60 \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{x}{t} \cdot -60 \]

      3. *-commutative N/A

         \[\leadsto -60 \cdot \frac{x}{\color{blue}{t}} \]

      4. associate-*r/ N/A

         \[\leadsto \frac{-60 \cdot x}{t} \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{-60 \cdot x}{t} \]

      6. lower-*.f64 26.6

         \[\leadsto \frac{-60 \cdot x}{t} \]

   9. Applied rewrites 26.6%

      \[\leadsto \frac{-60 \cdot x}{t} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 13: 54.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+227}:\\ \;\;\;\;\frac{y}{t} \cdot 60\\ \mathbf{elif}\;t\_1 \leq 10^{+162}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot -60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -1e+227)
     (* (/ y t) 60.0)
     (if (<= t_1 1e+162) (* 120.0 a) (* (/ x t) -60.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+227) {
		tmp = (y / t) * 60.0;
	} else if (t_1 <= 1e+162) {
		tmp = 120.0 * a;
	} else {
		tmp = (x / t) * -60.0;
	}
	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 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-1d+227)) then
        tmp = (y / t) * 60.0d0
    else if (t_1 <= 1d+162) then
        tmp = 120.0d0 * a
    else
        tmp = (x / t) * (-60.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+227) {
		tmp = (y / t) * 60.0;
	} else if (t_1 <= 1e+162) {
		tmp = 120.0 * a;
	} else {
		tmp = (x / t) * -60.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -1e+227:
		tmp = (y / t) * 60.0
	elif t_1 <= 1e+162:
		tmp = 120.0 * a
	else:
		tmp = (x / t) * -60.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -1e+227)
		tmp = Float64(Float64(y / t) * 60.0);
	elseif (t_1 <= 1e+162)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(x / t) * -60.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -1e+227)
		tmp = (y / t) * 60.0;
	elseif (t_1 <= 1e+162)
		tmp = 120.0 * a;
	else
		tmp = (x / t) * -60.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+227], N[(N[(y / t), $MachinePrecision] * 60.0), $MachinePrecision], If[LessEqual[t$95$1, 1e+162], N[(120.0 * a), $MachinePrecision], N[(N[(x / t), $MachinePrecision] * -60.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.0000000000000001e227

   1. Initial program 96.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x - y}{t} \cdot -60 + \color{blue}{120} \cdot a \]

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, \color{blue}{-60}, 120 \cdot a\right) \]

      3. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

      4. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

      5. lower-*.f64 64.0

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

   4. Applied rewrites 64.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)} \]

   5. Taylor expanded in y around inf

      \[\leadsto 60 \cdot \color{blue}{\frac{y}{t}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{y}{t} \cdot 60 \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{y}{t} \cdot 60 \]

      3. lower-/.f64 36.2

         \[\leadsto \frac{y}{t} \cdot 60 \]

   7. Applied rewrites 36.2%

      \[\leadsto \frac{y}{t} \cdot \color{blue}{60} \]

   if -1.0000000000000001e227 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.9999999999999994e161

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-*.f64 60.0

         \[\leadsto 120 \cdot \color{blue}{a} \]

   4. Applied rewrites 60.0%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if 9.9999999999999994e161 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 98.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x - y}{t} \cdot -60 + \color{blue}{120} \cdot a \]

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, \color{blue}{-60}, 120 \cdot a\right) \]

      3. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

      4. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

      5. lower-*.f64 58.0

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

   4. Applied rewrites 58.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto -60 \cdot \color{blue}{\frac{x}{t}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x}{t} \cdot -60 \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{x}{t} \cdot -60 \]

      3. lower-/.f64 26.9

         \[\leadsto \frac{x}{t} \cdot -60 \]

   7. Applied rewrites 26.9%

      \[\leadsto \frac{x}{t} \cdot \color{blue}{-60} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 52.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+162}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot -60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (/ (* 60.0 (- x y)) (- z t)) 1e+162) (* 120.0 a) (* (/ x t) -60.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((60.0 * (x - y)) / (z - t)) <= 1e+162) {
		tmp = 120.0 * a;
	} else {
		tmp = (x / t) * -60.0;
	}
	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 (((60.0d0 * (x - y)) / (z - t)) <= 1d+162) then
        tmp = 120.0d0 * a
    else
        tmp = (x / t) * (-60.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((60.0 * (x - y)) / (z - t)) <= 1e+162) {
		tmp = 120.0 * a;
	} else {
		tmp = (x / t) * -60.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((60.0 * (x - y)) / (z - t)) <= 1e+162:
		tmp = 120.0 * a
	else:
		tmp = (x / t) * -60.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t)) <= 1e+162)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(x / t) * -60.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((60.0 * (x - y)) / (z - t)) <= 1e+162)
		tmp = 120.0 * a;
	else
		tmp = (x / t) * -60.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], 1e+162], N[(120.0 * a), $MachinePrecision], N[(N[(x / t), $MachinePrecision] * -60.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.9999999999999994e161

   1. Initial program 99.5%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-*.f64 55.6

         \[\leadsto 120 \cdot \color{blue}{a} \]

   4. Applied rewrites 55.6%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if 9.9999999999999994e161 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 98.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x - y}{t} \cdot -60 + \color{blue}{120} \cdot a \]

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, \color{blue}{-60}, 120 \cdot a\right) \]

      3. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

      4. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

      5. lower-*.f64 58.0

         \[\leadsto \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right) \]

   4. Applied rewrites 58.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto -60 \cdot \color{blue}{\frac{x}{t}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{x}{t} \cdot -60 \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{x}{t} \cdot -60 \]

      3. lower-/.f64 26.9

         \[\leadsto \frac{x}{t} \cdot -60 \]

   7. Applied rewrites 26.9%

      \[\leadsto \frac{x}{t} \cdot \color{blue}{-60} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 50.9% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ 120 \cdot a \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (* 120.0 a))

C

double code(double x, double y, double z, double t, double a) {
	return 120.0 * a;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = 120.0d0 * a
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 120.0 * a;
}

Python

def code(x, y, z, t, a):
	return 120.0 * a

Julia

function code(x, y, z, t, a)
	return Float64(120.0 * a)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 120.0 * a;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(120.0 * a), $MachinePrecision]

Derivation

1. Initial program 99.4%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

2. Taylor expanded in z around inf

   \[\leadsto \color{blue}{120 \cdot a} \]
3. Step-by-step derivation

   1. lower-*.f64 50.9

      \[\leadsto 120 \cdot \color{blue}{a} \]

4. Applied rewrites 50.9%

   \[\leadsto \color{blue}{120 \cdot a} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025130 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64
  (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))