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

Percentage Accurate: 99.2% → 99.8%

Time: 4.9s

Alternatives: 20

Speedup: 1.1×

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: 99.2% 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, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

   1. lift-+.f64 N/A

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

   2. lift--.f64 N/A

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

   3. lift-/.f64 N/A

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

   4. lift--.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. +-commutative N/A

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

   7. lift-*.f64 N/A

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

   8. lower-fma.f64 N/A

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

   9. lower-/.f64 N/A

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

   10. *-commutative N/A

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

   11. lower-*.f64 N/A

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

   12. lift--.f64 N/A

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

   13. lift--.f64 99.3

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

3. Applied rewrites 99.3%

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

   1. lift-fma.f64 N/A

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

   2. lift--.f64 N/A

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

   3. lift-/.f64 N/A

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

   4. lift--.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. +-commutative N/A

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

   8. associate-/l* N/A

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

   9. metadata-eval N/A

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

   10. associate-*r/ N/A

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

   11. lift-*.f64 N/A

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

   12. *-commutative N/A

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

   13. lower-fma.f64 N/A

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

   14. lift--.f64 N/A

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

   15. associate-*r/ N/A

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

   16. metadata-eval N/A

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

   17. lower-/.f64 N/A

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

   18. lift--.f64 N/A

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

   19. lift-*.f64 99.8

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

5. Applied rewrites 99.8%

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

Alternative 2: 99.3% accurate, 1.1× speedup

Math

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

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(Float64(x - y) * 60.0) / Float64(z - t)))
end

Wolfram

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

Derivation

1. Initial program 99.2%

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

   1. lift-+.f64 N/A

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

   2. lift--.f64 N/A

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

   3. lift-/.f64 N/A

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

   4. lift--.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. +-commutative N/A

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

   7. lift-*.f64 N/A

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

   8. lower-fma.f64 N/A

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

   9. lower-/.f64 N/A

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

   10. *-commutative N/A

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

   11. lower-*.f64 N/A

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

   12. lift--.f64 N/A

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

   13. lift--.f64 99.3

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

3. Applied rewrites 99.3%

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

Alternative 3: 89.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+43}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{-60 \cdot y}{z - t}\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+19}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x}{z - t} \cdot 60\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{z - t} \cdot y + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -5.5e+43)
   (fma a 120.0 (/ (* -60.0 y) (- z t)))
   (if (<= y 4.2e+19)
     (fma a 120.0 (* (/ x (- z t)) 60.0))
     (+ (* (/ -60.0 (- z t)) y) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5.5e+43) {
		tmp = fma(a, 120.0, ((-60.0 * y) / (z - t)));
	} else if (y <= 4.2e+19) {
		tmp = fma(a, 120.0, ((x / (z - t)) * 60.0));
	} else {
		tmp = ((-60.0 / (z - t)) * y) + (a * 120.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -5.5e+43)
		tmp = fma(a, 120.0, Float64(Float64(-60.0 * y) / Float64(z - t)));
	elseif (y <= 4.2e+19)
		tmp = fma(a, 120.0, Float64(Float64(x / Float64(z - t)) * 60.0));
	else
		tmp = Float64(Float64(Float64(-60.0 / Float64(z - t)) * y) + Float64(a * 120.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -5.5e+43], N[(a * 120.0 + N[(N[(-60.0 * y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+19], N[(a * 120.0 + N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.49999999999999989e43

   1. Initial program 98.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 84.7

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

   4. Applied rewrites 84.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 84.8

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

   6. Applied rewrites 84.8%

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

   if -5.49999999999999989e43 < y < 4.2e19

   1. Initial program 99.5%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 99.6

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

   3. Applied rewrites 99.6%

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

   4. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 93.5

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

   6. Applied rewrites 93.5%

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

   if 4.2e19 < y

   1. Initial program 99.1%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(60 \cdot \frac{x}{y \cdot \left(z - t\right)} - 60 \cdot \frac{1}{z - t}\right)} + a \cdot 120 \]
   3. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. distribute-lft-out-- N/A

         \[\leadsto \left(60 \cdot \left(\frac{x}{y \cdot \left(z - t\right)} - \frac{1}{z - t}\right)\right) \cdot y + a \cdot 120 \]

      4. lower-*.f64 N/A

         \[\leadsto \left(60 \cdot \left(\frac{x}{y \cdot \left(z - t\right)} - \frac{1}{z - t}\right)\right) \cdot y + a \cdot 120 \]

      5. associate-/r* N/A

         \[\leadsto \left(60 \cdot \left(\frac{\frac{x}{y}}{z - t} - \frac{1}{z - t}\right)\right) \cdot y + a \cdot 120 \]

      6. sub-div N/A

         \[\leadsto \left(60 \cdot \frac{\frac{x}{y} - 1}{z - t}\right) \cdot y + a \cdot 120 \]

      7. lower-/.f64 N/A

         \[\leadsto \left(60 \cdot \frac{\frac{x}{y} - 1}{z - t}\right) \cdot y + a \cdot 120 \]

      8. lower--.f64 N/A

         \[\leadsto \left(60 \cdot \frac{\frac{x}{y} - 1}{z - t}\right) \cdot y + a \cdot 120 \]

      9. lower-/.f64 N/A

         \[\leadsto \left(60 \cdot \frac{\frac{x}{y} - 1}{z - t}\right) \cdot y + a \cdot 120 \]

      10. lift--.f64 99.7

          \[\leadsto \left(60 \cdot \frac{\frac{x}{y} - 1}{z - t}\right) \cdot y + a \cdot 120 \]

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lift--.f64 84.5

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

   7. Applied rewrites 84.5%

      \[\leadsto \frac{-60}{z - t} \cdot y + a \cdot 120 \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 89.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, 120, \frac{-60 \cdot y}{z - t}\right)\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+19}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x}{z - t} \cdot 60\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma a 120.0 (/ (* -60.0 y) (- z t)))))
   (if (<= y -5.5e+43)
     t_1
     (if (<= y 4.2e+19) (fma a 120.0 (* (/ x (- z 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, ((-60.0 * y) / (z - t)));
	double tmp;
	if (y <= -5.5e+43) {
		tmp = t_1;
	} else if (y <= 4.2e+19) {
		tmp = fma(a, 120.0, ((x / (z - t)) * 60.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(a, 120.0, Float64(Float64(-60.0 * y) / Float64(z - t)))
	tmp = 0.0
	if (y <= -5.5e+43)
		tmp = t_1;
	elseif (y <= 4.2e+19)
		tmp = fma(a, 120.0, Float64(Float64(x / 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[(a * 120.0 + N[(N[(-60.0 * y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e+43], t$95$1, If[LessEqual[y, 4.2e+19], N[(a * 120.0 + N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.49999999999999989e43 or 4.2e19 < y

   1. Initial program 98.9%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 84.4

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

   4. Applied rewrites 84.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 84.5

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

   6. Applied rewrites 84.5%

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

   if -5.49999999999999989e43 < y < 4.2e19

   1. Initial program 99.5%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 99.6

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

   3. Applied rewrites 99.6%

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

   4. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 93.5

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

   6. Applied rewrites 93.5%

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

Alternative 5: 83.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, 120, \frac{x}{z - t} \cdot 60\right)\\ \mathbf{if}\;a \leq -7.5 \cdot 10^{-73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6.7 \cdot 10^{-62}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma a 120.0 (* (/ x (- z t)) 60.0))))
   (if (<= a -7.5e-73)
     t_1
     (if (<= a 6.7e-62) (* (- x y) (/ 60.0 (- z t))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(a, 120.0, ((x / (z - t)) * 60.0));
	double tmp;
	if (a <= -7.5e-73) {
		tmp = t_1;
	} else if (a <= 6.7e-62) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(a, 120.0, Float64(Float64(x / Float64(z - t)) * 60.0))
	tmp = 0.0
	if (a <= -7.5e-73)
		tmp = t_1;
	elseif (a <= 6.7e-62)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a * 120.0 + N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.5e-73], t$95$1, If[LessEqual[a, 6.7e-62], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -7.5e-73 or 6.69999999999999992e-62 < a

   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

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 99.4

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

   3. Applied rewrites 99.4%

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

   4. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 85.6

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

   6. Applied rewrites 85.6%

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

   if -7.5e-73 < a < 6.69999999999999992e-62

   1. Initial program 99.2%

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

   2. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 79.9

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

   4. Applied rewrites 79.9%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. lower-*.f64 N/A

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

      9. lift--.f64 N/A

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

      10. associate-*r/ N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 80.3

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

   6. Applied rewrites 80.3%

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

Alternative 6: 83.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-36}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{z}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- x y) t) -60.0 (* 120.0 a))))
   (if (<= t -3.4e+15)
     t_1
     (if (<= t 1.9e-36) (fma (/ (- x y) z) 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) / t), -60.0, (120.0 * a));
	double tmp;
	if (t <= -3.4e+15) {
		tmp = t_1;
	} else if (t <= 1.9e-36) {
		tmp = fma(((x - y) / z), 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) / t), -60.0, Float64(120.0 * a))
	tmp = 0.0
	if (t <= -3.4e+15)
		tmp = t_1;
	elseif (t <= 1.9e-36)
		tmp = fma(Float64(Float64(x - y) / z), 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] / t), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.4e+15], t$95$1, If[LessEqual[t, 1.9e-36], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.4e15 or 1.89999999999999985e-36 < t

   1. Initial program 99.1%

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

   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 85.7

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

   4. Applied rewrites 85.7%

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

   if -3.4e15 < t < 1.89999999999999985e-36

   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 81.6

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

   4. Applied rewrites 81.6%

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

Alternative 7: 72.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, 120, \frac{x}{z} \cdot 60\right)\\ \mathbf{if}\;a \leq -4.1 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-17}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-62}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma a 120.0 (* (/ x z) 60.0))))
   (if (<= a -4.1e+23)
     t_1
     (if (<= a -2e-17)
       (fma (/ (- x y) t) -60.0 (* 120.0 a))
       (if (<= a 7.5e-62) (* (- x y) (/ 60.0 (- z t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(a, 120.0, ((x / z) * 60.0));
	double tmp;
	if (a <= -4.1e+23) {
		tmp = t_1;
	} else if (a <= -2e-17) {
		tmp = fma(((x - y) / t), -60.0, (120.0 * a));
	} else if (a <= 7.5e-62) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(a, 120.0, Float64(Float64(x / z) * 60.0))
	tmp = 0.0
	if (a <= -4.1e+23)
		tmp = t_1;
	elseif (a <= -2e-17)
		tmp = fma(Float64(Float64(x - y) / t), -60.0, Float64(120.0 * a));
	elseif (a <= 7.5e-62)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a * 120.0 + N[(N[(x / z), $MachinePrecision] * 60.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.1e+23], t$95$1, If[LessEqual[a, -2e-17], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.5e-62], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.09999999999999996e23 or 7.5000000000000003e-62 < a

   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

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 99.4

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

   3. Applied rewrites 99.4%

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

   4. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 86.9

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

   6. Applied rewrites 86.9%

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

   7. Taylor expanded in z around inf

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

      1. lower-/.f64 69.0

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

   9. Applied rewrites 69.0%

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

   if -4.09999999999999996e23 < a < -2.00000000000000014e-17

   1. Initial program 99.4%

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

   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 63.1

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

   4. Applied rewrites 63.1%

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

   if -2.00000000000000014e-17 < a < 7.5000000000000003e-62

   1. Initial program 99.2%

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

   2. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 77.2

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

   4. Applied rewrites 77.2%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. lower-*.f64 N/A

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

      9. lift--.f64 N/A

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

      10. associate-*r/ N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 77.7

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

   6. Applied rewrites 77.7%

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

Alternative 8: 72.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, 120, \frac{x}{z} \cdot 60\right)\\ \mathbf{if}\;a \leq -1.05 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-62}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma a 120.0 (* (/ x z) 60.0))))
   (if (<= a -1.05e-9)
     t_1
     (if (<= a 7.5e-62) (* (- x y) (/ 60.0 (- z t))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(a, 120.0, ((x / z) * 60.0));
	double tmp;
	if (a <= -1.05e-9) {
		tmp = t_1;
	} else if (a <= 7.5e-62) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(a, 120.0, Float64(Float64(x / z) * 60.0))
	tmp = 0.0
	if (a <= -1.05e-9)
		tmp = t_1;
	elseif (a <= 7.5e-62)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a * 120.0 + N[(N[(x / z), $MachinePrecision] * 60.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.05e-9], t$95$1, If[LessEqual[a, 7.5e-62], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.0500000000000001e-9 or 7.5000000000000003e-62 < a

   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

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 99.4

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

   3. Applied rewrites 99.4%

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

   4. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 86.5

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

   6. Applied rewrites 86.5%

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

   7. Taylor expanded in z around inf

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

      1. lower-/.f64 68.3

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

   9. Applied rewrites 68.3%

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

   if -1.0500000000000001e-9 < a < 7.5000000000000003e-62

   1. Initial program 99.2%

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

   2. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 76.8

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

   4. Applied rewrites 76.8%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. lower-*.f64 N/A

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

      9. lift--.f64 N/A

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

      10. associate-*r/ N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 77.3

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

   6. Applied rewrites 77.3%

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

Alternative 9: 59.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{-73}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x}{t} \cdot -60\right)\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-257}:\\ \;\;\;\;\frac{y}{z - t} \cdot -60\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-183}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-62}:\\ \;\;\;\;\frac{-60 \cdot \left(x - y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7.5e-73)
   (fma a 120.0 (* (/ x t) -60.0))
   (if (<= a -1.95e-257)
     (* (/ y (- z t)) -60.0)
     (if (<= a 5.2e-183)
       (* (/ (- x y) z) 60.0)
       (if (<= a 6.5e-62) (/ (* -60.0 (- x y)) t) (* 120.0 a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.5e-73) {
		tmp = fma(a, 120.0, ((x / t) * -60.0));
	} else if (a <= -1.95e-257) {
		tmp = (y / (z - t)) * -60.0;
	} else if (a <= 5.2e-183) {
		tmp = ((x - y) / z) * 60.0;
	} else if (a <= 6.5e-62) {
		tmp = (-60.0 * (x - y)) / t;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7.5e-73)
		tmp = fma(a, 120.0, Float64(Float64(x / t) * -60.0));
	elseif (a <= -1.95e-257)
		tmp = Float64(Float64(y / Float64(z - t)) * -60.0);
	elseif (a <= 5.2e-183)
		tmp = Float64(Float64(Float64(x - y) / z) * 60.0);
	elseif (a <= 6.5e-62)
		tmp = Float64(Float64(-60.0 * Float64(x - y)) / t);
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7.5e-73], N[(a * 120.0 + N[(N[(x / t), $MachinePrecision] * -60.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.95e-257], N[(N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision] * -60.0), $MachinePrecision], If[LessEqual[a, 5.2e-183], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0), $MachinePrecision], If[LessEqual[a, 6.5e-62], N[(N[(-60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -7.5e-73

   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

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 99.4

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

   3. Applied rewrites 99.4%

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

   4. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 85.6

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

   6. Applied rewrites 85.6%

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

   7. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 67.5

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

   9. Applied rewrites 67.5%

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

   if -7.5e-73 < a < -1.9500000000000001e-257

   1. Initial program 99.3%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 42.2

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

   4. Applied rewrites 42.2%

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

   if -1.9500000000000001e-257 < a < 5.1999999999999998e-183

   1. Initial program 99.2%

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

   2. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 87.1

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

   4. Applied rewrites 87.1%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 46.7

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

   7. Applied rewrites 46.7%

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

   if 5.1999999999999998e-183 < a < 6.50000000000000026e-62

   1. Initial program 98.9%

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

   2. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 72.3

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

   4. Applied rewrites 72.3%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 37.2

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

   7. Applied rewrites 37.2%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*r/ N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 37.0

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

   9. Applied rewrites 37.0%

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

   if 6.50000000000000026e-62 < a

   1. Initial program 99.2%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 70.4

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

   4. Applied rewrites 70.4%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 10: 59.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{-16}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-257}:\\ \;\;\;\;\frac{-60 \cdot y}{z - t}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-183}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-62}:\\ \;\;\;\;\frac{-60 \cdot \left(x - y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.2e-16)
   (* 120.0 a)
   (if (<= a -6e-257)
     (/ (* -60.0 y) (- z t))
     (if (<= a 5.2e-183)
       (* (/ (- x y) z) 60.0)
       (if (<= a 6.5e-62) (/ (* -60.0 (- x y)) t) (* 120.0 a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.2e-16) {
		tmp = 120.0 * a;
	} else if (a <= -6e-257) {
		tmp = (-60.0 * y) / (z - t);
	} else if (a <= 5.2e-183) {
		tmp = ((x - y) / z) * 60.0;
	} else if (a <= 6.5e-62) {
		tmp = (-60.0 * (x - y)) / t;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.2d-16)) then
        tmp = 120.0d0 * a
    else if (a <= (-6d-257)) then
        tmp = ((-60.0d0) * y) / (z - t)
    else if (a <= 5.2d-183) then
        tmp = ((x - y) / z) * 60.0d0
    else if (a <= 6.5d-62) then
        tmp = ((-60.0d0) * (x - y)) / t
    else
        tmp = 120.0d0 * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.2e-16) {
		tmp = 120.0 * a;
	} else if (a <= -6e-257) {
		tmp = (-60.0 * y) / (z - t);
	} else if (a <= 5.2e-183) {
		tmp = ((x - y) / z) * 60.0;
	} else if (a <= 6.5e-62) {
		tmp = (-60.0 * (x - y)) / t;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.2e-16:
		tmp = 120.0 * a
	elif a <= -6e-257:
		tmp = (-60.0 * y) / (z - t)
	elif a <= 5.2e-183:
		tmp = ((x - y) / z) * 60.0
	elif a <= 6.5e-62:
		tmp = (-60.0 * (x - y)) / t
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.2e-16)
		tmp = Float64(120.0 * a);
	elseif (a <= -6e-257)
		tmp = Float64(Float64(-60.0 * y) / Float64(z - t));
	elseif (a <= 5.2e-183)
		tmp = Float64(Float64(Float64(x - y) / z) * 60.0);
	elseif (a <= 6.5e-62)
		tmp = Float64(Float64(-60.0 * Float64(x - y)) / t);
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.2e-16)
		tmp = 120.0 * a;
	elseif (a <= -6e-257)
		tmp = (-60.0 * y) / (z - t);
	elseif (a <= 5.2e-183)
		tmp = ((x - y) / z) * 60.0;
	elseif (a <= 6.5e-62)
		tmp = (-60.0 * (x - y)) / t;
	else
		tmp = 120.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.2e-16], N[(120.0 * a), $MachinePrecision], If[LessEqual[a, -6e-257], N[(N[(-60.0 * y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.2e-183], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0), $MachinePrecision], If[LessEqual[a, 6.5e-62], N[(N[(-60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.20000000000000023e-16 or 6.50000000000000026e-62 < a

   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 72.5

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

   4. Applied rewrites 72.5%

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

   if -3.20000000000000023e-16 < a < -5.9999999999999999e-257

   1. Initial program 99.3%

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

   2. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 72.1

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

   4. Applied rewrites 72.1%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 37.1%

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

   8. Taylor expanded in x around 0

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

      1. lower-*.f64 37.9

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

   10. Applied rewrites 37.9%

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

   if -5.9999999999999999e-257 < a < 5.1999999999999998e-183

   1. Initial program 99.2%

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

   2. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 87.1

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

   4. Applied rewrites 87.1%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 46.7

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

   7. Applied rewrites 46.7%

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

   if 5.1999999999999998e-183 < a < 6.50000000000000026e-62

   1. Initial program 98.9%

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

   2. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 72.3

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

   4. Applied rewrites 72.3%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 37.2

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

   7. Applied rewrites 37.2%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*r/ N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 37.0

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

   9. Applied rewrites 37.0%

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

Alternative 11: 58.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{-16}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-257}:\\ \;\;\;\;\frac{y}{z - t} \cdot -60\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-183}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-62}:\\ \;\;\;\;\frac{-60 \cdot \left(x - y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.2e-16)
   (* 120.0 a)
   (if (<= a -1.95e-257)
     (* (/ y (- z t)) -60.0)
     (if (<= a 5.2e-183)
       (* (/ (- x y) z) 60.0)
       (if (<= a 6.5e-62) (/ (* -60.0 (- x y)) t) (* 120.0 a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.2e-16) {
		tmp = 120.0 * a;
	} else if (a <= -1.95e-257) {
		tmp = (y / (z - t)) * -60.0;
	} else if (a <= 5.2e-183) {
		tmp = ((x - y) / z) * 60.0;
	} else if (a <= 6.5e-62) {
		tmp = (-60.0 * (x - y)) / t;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.2d-16)) then
        tmp = 120.0d0 * a
    else if (a <= (-1.95d-257)) then
        tmp = (y / (z - t)) * (-60.0d0)
    else if (a <= 5.2d-183) then
        tmp = ((x - y) / z) * 60.0d0
    else if (a <= 6.5d-62) then
        tmp = ((-60.0d0) * (x - y)) / t
    else
        tmp = 120.0d0 * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.2e-16) {
		tmp = 120.0 * a;
	} else if (a <= -1.95e-257) {
		tmp = (y / (z - t)) * -60.0;
	} else if (a <= 5.2e-183) {
		tmp = ((x - y) / z) * 60.0;
	} else if (a <= 6.5e-62) {
		tmp = (-60.0 * (x - y)) / t;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.2e-16:
		tmp = 120.0 * a
	elif a <= -1.95e-257:
		tmp = (y / (z - t)) * -60.0
	elif a <= 5.2e-183:
		tmp = ((x - y) / z) * 60.0
	elif a <= 6.5e-62:
		tmp = (-60.0 * (x - y)) / t
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.2e-16)
		tmp = Float64(120.0 * a);
	elseif (a <= -1.95e-257)
		tmp = Float64(Float64(y / Float64(z - t)) * -60.0);
	elseif (a <= 5.2e-183)
		tmp = Float64(Float64(Float64(x - y) / z) * 60.0);
	elseif (a <= 6.5e-62)
		tmp = Float64(Float64(-60.0 * Float64(x - y)) / t);
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.2e-16)
		tmp = 120.0 * a;
	elseif (a <= -1.95e-257)
		tmp = (y / (z - t)) * -60.0;
	elseif (a <= 5.2e-183)
		tmp = ((x - y) / z) * 60.0;
	elseif (a <= 6.5e-62)
		tmp = (-60.0 * (x - y)) / t;
	else
		tmp = 120.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.2e-16], N[(120.0 * a), $MachinePrecision], If[LessEqual[a, -1.95e-257], N[(N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision] * -60.0), $MachinePrecision], If[LessEqual[a, 5.2e-183], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0), $MachinePrecision], If[LessEqual[a, 6.5e-62], N[(N[(-60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.20000000000000023e-16 or 6.50000000000000026e-62 < a

   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 72.5

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

   4. Applied rewrites 72.5%

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

   if -3.20000000000000023e-16 < a < -1.9500000000000001e-257

   1. Initial program 99.3%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 38.2

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

   4. Applied rewrites 38.2%

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

   if -1.9500000000000001e-257 < a < 5.1999999999999998e-183

   1. Initial program 99.2%

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

   2. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 87.1

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

   4. Applied rewrites 87.1%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 46.7

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

   7. Applied rewrites 46.7%

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

   if 5.1999999999999998e-183 < a < 6.50000000000000026e-62

   1. Initial program 98.9%

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

   2. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 72.3

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

   4. Applied rewrites 72.3%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 37.2

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

   7. Applied rewrites 37.2%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*r/ N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 37.0

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

   9. Applied rewrites 37.0%

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

Alternative 12: 58.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-60 \cdot \left(x - y\right)}{t}\\ \mathbf{if}\;a \leq -2.7 \cdot 10^{-10}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-212}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-183}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-62}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* -60.0 (- x y)) t)))
   (if (<= a -2.7e-10)
     (* 120.0 a)
     (if (<= a -3.4e-212)
       t_1
       (if (<= a 5.2e-183)
         (* (/ (- x y) z) 60.0)
         (if (<= a 6.5e-62) t_1 (* 120.0 a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (-60.0 * (x - y)) / t;
	double tmp;
	if (a <= -2.7e-10) {
		tmp = 120.0 * a;
	} else if (a <= -3.4e-212) {
		tmp = t_1;
	} else if (a <= 5.2e-183) {
		tmp = ((x - y) / z) * 60.0;
	} else if (a <= 6.5e-62) {
		tmp = t_1;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((-60.0d0) * (x - y)) / t
    if (a <= (-2.7d-10)) then
        tmp = 120.0d0 * a
    else if (a <= (-3.4d-212)) then
        tmp = t_1
    else if (a <= 5.2d-183) then
        tmp = ((x - y) / z) * 60.0d0
    else if (a <= 6.5d-62) then
        tmp = t_1
    else
        tmp = 120.0d0 * a
    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)) / t;
	double tmp;
	if (a <= -2.7e-10) {
		tmp = 120.0 * a;
	} else if (a <= -3.4e-212) {
		tmp = t_1;
	} else if (a <= 5.2e-183) {
		tmp = ((x - y) / z) * 60.0;
	} else if (a <= 6.5e-62) {
		tmp = t_1;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (-60.0 * (x - y)) / t
	tmp = 0
	if a <= -2.7e-10:
		tmp = 120.0 * a
	elif a <= -3.4e-212:
		tmp = t_1
	elif a <= 5.2e-183:
		tmp = ((x - y) / z) * 60.0
	elif a <= 6.5e-62:
		tmp = t_1
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-60.0 * Float64(x - y)) / t)
	tmp = 0.0
	if (a <= -2.7e-10)
		tmp = Float64(120.0 * a);
	elseif (a <= -3.4e-212)
		tmp = t_1;
	elseif (a <= 5.2e-183)
		tmp = Float64(Float64(Float64(x - y) / z) * 60.0);
	elseif (a <= 6.5e-62)
		tmp = t_1;
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (-60.0 * (x - y)) / t;
	tmp = 0.0;
	if (a <= -2.7e-10)
		tmp = 120.0 * a;
	elseif (a <= -3.4e-212)
		tmp = t_1;
	elseif (a <= 5.2e-183)
		tmp = ((x - y) / z) * 60.0;
	elseif (a <= 6.5e-62)
		tmp = t_1;
	else
		tmp = 120.0 * a;
	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] / t), $MachinePrecision]}, If[LessEqual[a, -2.7e-10], N[(120.0 * a), $MachinePrecision], If[LessEqual[a, -3.4e-212], t$95$1, If[LessEqual[a, 5.2e-183], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0), $MachinePrecision], If[LessEqual[a, 6.5e-62], t$95$1, N[(120.0 * a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.7e-10 or 6.50000000000000026e-62 < a

   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 72.7

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

   4. Applied rewrites 72.7%

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

   if -2.7e-10 < a < -3.39999999999999998e-212 or 5.1999999999999998e-183 < a < 6.50000000000000026e-62

   1. Initial program 99.1%

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

   2. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 69.6

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

   4. Applied rewrites 69.6%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 37.2

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

   7. Applied rewrites 37.2%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*r/ N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 36.9

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

   9. Applied rewrites 36.9%

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

   if -3.39999999999999998e-212 < a < 5.1999999999999998e-183

   1. Initial program 99.3%

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

   2. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 87.2

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

   4. Applied rewrites 87.2%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 46.8

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

   7. Applied rewrites 46.8%

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

Alternative 13: 58.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{t} \cdot -60\\ \mathbf{if}\;a \leq -2.7 \cdot 10^{-10}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-212}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-183}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-62}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ (- x y) t) -60.0)))
   (if (<= a -2.7e-10)
     (* 120.0 a)
     (if (<= a -3.4e-212)
       t_1
       (if (<= a 5.2e-183)
         (* (/ (- x y) z) 60.0)
         (if (<= a 6.5e-62) t_1 (* 120.0 a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) / t) * -60.0;
	double tmp;
	if (a <= -2.7e-10) {
		tmp = 120.0 * a;
	} else if (a <= -3.4e-212) {
		tmp = t_1;
	} else if (a <= 5.2e-183) {
		tmp = ((x - y) / z) * 60.0;
	} else if (a <= 6.5e-62) {
		tmp = t_1;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x - y) / t) * (-60.0d0)
    if (a <= (-2.7d-10)) then
        tmp = 120.0d0 * a
    else if (a <= (-3.4d-212)) then
        tmp = t_1
    else if (a <= 5.2d-183) then
        tmp = ((x - y) / z) * 60.0d0
    else if (a <= 6.5d-62) then
        tmp = t_1
    else
        tmp = 120.0d0 * a
    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 tmp;
	if (a <= -2.7e-10) {
		tmp = 120.0 * a;
	} else if (a <= -3.4e-212) {
		tmp = t_1;
	} else if (a <= 5.2e-183) {
		tmp = ((x - y) / z) * 60.0;
	} else if (a <= 6.5e-62) {
		tmp = t_1;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((x - y) / t) * -60.0
	tmp = 0
	if a <= -2.7e-10:
		tmp = 120.0 * a
	elif a <= -3.4e-212:
		tmp = t_1
	elif a <= 5.2e-183:
		tmp = ((x - y) / z) * 60.0
	elif a <= 6.5e-62:
		tmp = t_1
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x - y) / t) * -60.0)
	tmp = 0.0
	if (a <= -2.7e-10)
		tmp = Float64(120.0 * a);
	elseif (a <= -3.4e-212)
		tmp = t_1;
	elseif (a <= 5.2e-183)
		tmp = Float64(Float64(Float64(x - y) / z) * 60.0);
	elseif (a <= 6.5e-62)
		tmp = t_1;
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((x - y) / t) * -60.0;
	tmp = 0.0;
	if (a <= -2.7e-10)
		tmp = 120.0 * a;
	elseif (a <= -3.4e-212)
		tmp = t_1;
	elseif (a <= 5.2e-183)
		tmp = ((x - y) / z) * 60.0;
	elseif (a <= 6.5e-62)
		tmp = t_1;
	else
		tmp = 120.0 * a;
	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]}, If[LessEqual[a, -2.7e-10], N[(120.0 * a), $MachinePrecision], If[LessEqual[a, -3.4e-212], t$95$1, If[LessEqual[a, 5.2e-183], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0), $MachinePrecision], If[LessEqual[a, 6.5e-62], t$95$1, N[(120.0 * a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.7e-10 or 6.50000000000000026e-62 < a

   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 72.7

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

   4. Applied rewrites 72.7%

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

   if -2.7e-10 < a < -3.39999999999999998e-212 or 5.1999999999999998e-183 < a < 6.50000000000000026e-62

   1. Initial program 99.1%

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

   2. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 69.6

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

   4. Applied rewrites 69.6%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 37.2

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

   7. Applied rewrites 37.2%

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

   if -3.39999999999999998e-212 < a < 5.1999999999999998e-183

   1. Initial program 99.3%

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

   2. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 87.2

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

   4. Applied rewrites 87.2%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 46.8

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

   7. Applied rewrites 46.8%

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

Alternative 14: 58.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 9.5 \cdot 10^{+20}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x}{z} \cdot 60\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z - t} \cdot -60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 9.5e+20) (fma a 120.0 (* (/ x z) 60.0)) (* (/ y (- z t)) -60.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 9.5e+20) {
		tmp = fma(a, 120.0, ((x / z) * 60.0));
	} else {
		tmp = (y / (z - t)) * -60.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 9.5e+20)
		tmp = fma(a, 120.0, Float64(Float64(x / z) * 60.0));
	else
		tmp = Float64(Float64(y / Float64(z - t)) * -60.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 9.5e+20], N[(a * 120.0 + N[(N[(x / z), $MachinePrecision] * 60.0), $MachinePrecision]), $MachinePrecision], N[(N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision] * -60.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 9.5e20

   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

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 99.4

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

   3. Applied rewrites 99.4%

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

   4. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 81.5

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

   6. Applied rewrites 81.5%

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

   7. Taylor expanded in z around inf

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

      1. lower-/.f64 58.9

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

   9. Applied rewrites 58.9%

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

   if 9.5e20 < y

   1. Initial program 99.1%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 44.1

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

   4. Applied rewrites 44.1%

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

Alternative 15: 55.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{-10}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-62}:\\ \;\;\;\;\frac{x - y}{t} \cdot -60\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.7e-10)
   (* 120.0 a)
   (if (<= a 6.5e-62) (* (/ (- x y) t) -60.0) (* 120.0 a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.7e-10) {
		tmp = 120.0 * a;
	} else if (a <= 6.5e-62) {
		tmp = ((x - y) / t) * -60.0;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.7d-10)) then
        tmp = 120.0d0 * a
    else if (a <= 6.5d-62) then
        tmp = ((x - y) / t) * (-60.0d0)
    else
        tmp = 120.0d0 * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.7e-10) {
		tmp = 120.0 * a;
	} else if (a <= 6.5e-62) {
		tmp = ((x - y) / t) * -60.0;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.7e-10:
		tmp = 120.0 * a
	elif a <= 6.5e-62:
		tmp = ((x - y) / t) * -60.0
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.7e-10)
		tmp = Float64(120.0 * a);
	elseif (a <= 6.5e-62)
		tmp = Float64(Float64(Float64(x - y) / t) * -60.0);
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.7e-10)
		tmp = 120.0 * a;
	elseif (a <= 6.5e-62)
		tmp = ((x - y) / t) * -60.0;
	else
		tmp = 120.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.7e-10], N[(120.0 * a), $MachinePrecision], If[LessEqual[a, 6.5e-62], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.7e-10 or 6.50000000000000026e-62 < a

   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 72.7

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

   4. Applied rewrites 72.7%

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

   if -2.7e-10 < a < 6.50000000000000026e-62

   1. Initial program 99.2%

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

   2. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 76.8

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

   4. Applied rewrites 76.8%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 41.0

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

   7. Applied rewrites 41.0%

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

Alternative 16: 55.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+246}:\\ \;\;\;\;\frac{x}{z} \cdot 60\\ \mathbf{elif}\;t\_1 \leq 10^{+184}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 60}{-t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -2e+246)
     (* (/ x z) 60.0)
     (if (<= t_1 1e+184) (* 120.0 a) (/ (* x 60.0) (- 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 <= -2e+246) {
		tmp = (x / z) * 60.0;
	} else if (t_1 <= 1e+184) {
		tmp = 120.0 * a;
	} else {
		tmp = (x * 60.0) / -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 <= (-2d+246)) then
        tmp = (x / z) * 60.0d0
    else if (t_1 <= 1d+184) then
        tmp = 120.0d0 * a
    else
        tmp = (x * 60.0d0) / -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 <= -2e+246) {
		tmp = (x / z) * 60.0;
	} else if (t_1 <= 1e+184) {
		tmp = 120.0 * a;
	} else {
		tmp = (x * 60.0) / -t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -2e+246:
		tmp = (x / z) * 60.0
	elif t_1 <= 1e+184:
		tmp = 120.0 * a
	else:
		tmp = (x * 60.0) / -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 <= -2e+246)
		tmp = Float64(Float64(x / z) * 60.0);
	elseif (t_1 <= 1e+184)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(x * 60.0) / Float64(-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 <= -2e+246)
		tmp = (x / z) * 60.0;
	elseif (t_1 <= 1e+184)
		tmp = 120.0 * a;
	else
		tmp = (x * 60.0) / -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, -2e+246], N[(N[(x / z), $MachinePrecision] * 60.0), $MachinePrecision], If[LessEqual[t$95$1, 1e+184], N[(120.0 * a), $MachinePrecision], N[(N[(x * 60.0), $MachinePrecision] / (-t)), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.00000000000000014e246

   1. Initial program 94.8%

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

   2. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 93.1

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

   4. Applied rewrites 93.1%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 59.6

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

   7. Applied rewrites 59.6%

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

   8. Taylor expanded in x around inf

      \[\leadsto \frac{x}{z} \cdot 60 \]
   9. Step-by-step derivation

      1. lower-/.f64 33.5

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

   10. Applied rewrites 33.5%

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

   if -2.00000000000000014e246 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.00000000000000002e184

   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 59.9

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

   4. Applied rewrites 59.9%

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

   if 1.00000000000000002e184 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.4%

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

   2. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 90.9

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

   4. Applied rewrites 90.9%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 50.2%

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

   8. Taylor expanded in z around 0

      \[\leadsto \frac{x \cdot 60}{-1 \cdot \color{blue}{t}} \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \frac{x \cdot 60}{\mathsf{neg}\left(t\right)} \]

      2. lower-neg.f64 31.0

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

   10. Applied rewrites 31.0%

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

Alternative 17: 55.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+246}:\\ \;\;\;\;\frac{x}{z} \cdot 60\\ \mathbf{elif}\;t\_1 \leq 10^{+184}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot -60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -2e+246)
     (* (/ x z) 60.0)
     (if (<= t_1 1e+184) (* 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 <= -2e+246) {
		tmp = (x / z) * 60.0;
	} else if (t_1 <= 1e+184) {
		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 <= (-2d+246)) then
        tmp = (x / z) * 60.0d0
    else if (t_1 <= 1d+184) 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 <= -2e+246) {
		tmp = (x / z) * 60.0;
	} else if (t_1 <= 1e+184) {
		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 <= -2e+246:
		tmp = (x / z) * 60.0
	elif t_1 <= 1e+184:
		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 <= -2e+246)
		tmp = Float64(Float64(x / z) * 60.0);
	elseif (t_1 <= 1e+184)
		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 <= -2e+246)
		tmp = (x / z) * 60.0;
	elseif (t_1 <= 1e+184)
		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, -2e+246], N[(N[(x / z), $MachinePrecision] * 60.0), $MachinePrecision], If[LessEqual[t$95$1, 1e+184], 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)) < -2.00000000000000014e246

   1. Initial program 94.8%

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

   2. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 93.1

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

   4. Applied rewrites 93.1%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 59.6

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

   7. Applied rewrites 59.6%

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

   8. Taylor expanded in x around inf

      \[\leadsto \frac{x}{z} \cdot 60 \]
   9. Step-by-step derivation

      1. lower-/.f64 33.5

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

   10. Applied rewrites 33.5%

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

   if -2.00000000000000014e246 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.00000000000000002e184

   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 59.9

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

   4. Applied rewrites 59.9%

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

   if 1.00000000000000002e184 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.4%

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

   2. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 90.9

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

   4. Applied rewrites 90.9%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 55.3

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

   7. Applied rewrites 55.3%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 31.4%

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

Alternative 18: 53.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{-163}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-62}:\\ \;\;\;\;\frac{y \cdot 60}{t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.5e-163)
   (* 120.0 a)
   (if (<= a 6.5e-62) (/ (* y 60.0) t) (* 120.0 a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.5e-163) {
		tmp = 120.0 * a;
	} else if (a <= 6.5e-62) {
		tmp = (y * 60.0) / t;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5.5d-163)) then
        tmp = 120.0d0 * a
    else if (a <= 6.5d-62) then
        tmp = (y * 60.0d0) / t
    else
        tmp = 120.0d0 * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.5e-163) {
		tmp = 120.0 * a;
	} else if (a <= 6.5e-62) {
		tmp = (y * 60.0) / t;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.5e-163:
		tmp = 120.0 * a
	elif a <= 6.5e-62:
		tmp = (y * 60.0) / t
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.5e-163)
		tmp = Float64(120.0 * a);
	elseif (a <= 6.5e-62)
		tmp = Float64(Float64(y * 60.0) / t);
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.5e-163)
		tmp = 120.0 * a;
	elseif (a <= 6.5e-62)
		tmp = (y * 60.0) / t;
	else
		tmp = 120.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.5e-163], N[(120.0 * a), $MachinePrecision], If[LessEqual[a, 6.5e-62], N[(N[(y * 60.0), $MachinePrecision] / t), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -5.4999999999999998e-163 or 6.50000000000000026e-62 < a

   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 66.3

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

   4. Applied rewrites 66.3%

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

   if -5.4999999999999998e-163 < a < 6.50000000000000026e-62

   1. Initial program 99.1%

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

   2. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 81.8

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

   4. Applied rewrites 81.8%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 43.6

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

   7. Applied rewrites 43.6%

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

   8. Taylor expanded in x around 0

      \[\leadsto 60 \cdot \frac{y}{\color{blue}{t}} \]
   9. 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 24.6

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

   10. Applied rewrites 24.6%

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

       1. lift-*.f64 N/A

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

       2. lift-/.f64 N/A

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

       3. associate-*l/ N/A

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

       4. lower-/.f64 N/A

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

       5. lower-*.f64 24.5

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

   12. Applied rewrites 24.5%

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

Alternative 19: 53.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{-163}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-62}:\\ \;\;\;\;\frac{y}{t} \cdot 60\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.5e-163)
   (* 120.0 a)
   (if (<= a 6.5e-62) (* (/ y t) 60.0) (* 120.0 a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.5e-163) {
		tmp = 120.0 * a;
	} else if (a <= 6.5e-62) {
		tmp = (y / t) * 60.0;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5.5d-163)) then
        tmp = 120.0d0 * a
    else if (a <= 6.5d-62) then
        tmp = (y / t) * 60.0d0
    else
        tmp = 120.0d0 * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.5e-163) {
		tmp = 120.0 * a;
	} else if (a <= 6.5e-62) {
		tmp = (y / t) * 60.0;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.5e-163:
		tmp = 120.0 * a
	elif a <= 6.5e-62:
		tmp = (y / t) * 60.0
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.5e-163)
		tmp = Float64(120.0 * a);
	elseif (a <= 6.5e-62)
		tmp = Float64(Float64(y / t) * 60.0);
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.5e-163)
		tmp = 120.0 * a;
	elseif (a <= 6.5e-62)
		tmp = (y / t) * 60.0;
	else
		tmp = 120.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.5e-163], N[(120.0 * a), $MachinePrecision], If[LessEqual[a, 6.5e-62], N[(N[(y / t), $MachinePrecision] * 60.0), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -5.4999999999999998e-163 or 6.50000000000000026e-62 < a

   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 66.3

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

   4. Applied rewrites 66.3%

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

   if -5.4999999999999998e-163 < a < 6.50000000000000026e-62

   1. Initial program 99.1%

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

   2. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 81.8

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

   4. Applied rewrites 81.8%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 43.6

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

   7. Applied rewrites 43.6%

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

   8. Taylor expanded in x around 0

      \[\leadsto 60 \cdot \frac{y}{\color{blue}{t}} \]
   9. 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 24.6

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

   10. Applied rewrites 24.6%

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

Alternative 20: 51.7% accurate, 4.3× 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 99.2%

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

2. Taylor expanded in z around inf

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

   1. lower-*.f64 51.7

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

4. Applied rewrites 51.7%

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

Reproduce

herbie shell --seed 2025101 
(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)))