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

Percentage Accurate: 99.4% → 99.8%

Time: 8.8s

Alternatives: 17

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: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((60.0d0 * (x - y)) / (z - t)) + (a * 120.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.3%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
2. Add Preprocessing
3. 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

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

   3. fp-cancel-sign-sub-inv N/A

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

   4. fp-cancel-sub-sign-inv N/A

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

   5. +-commutative N/A

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

   6. remove-double-neg N/A

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

   7. lower-fma.f64 99.4

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

   8. lift-/.f64 N/A

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

   9. lift-*.f64 N/A

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

   10. *-commutative N/A

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

   11. associate-/l* N/A

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

   12. *-commutative N/A

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

   13. lower-*.f64 N/A

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

   14. lower-/.f64 99.8

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

4. Applied rewrites 99.8%

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

Alternative 2: 60.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+163}:\\ \;\;\;\;\frac{x}{z - t} \cdot 60\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+110}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -5e+163)
     (* (/ x (- z t)) 60.0)
     (if (<= t_1 2e+110) (* 120.0 a) (* (- x y) (/ -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 <= -5e+163) {
		tmp = (x / (z - t)) * 60.0;
	} else if (t_1 <= 2e+110) {
		tmp = 120.0 * a;
	} else {
		tmp = (x - y) * (-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 <= (-5d+163)) then
        tmp = (x / (z - t)) * 60.0d0
    else if (t_1 <= 2d+110) then
        tmp = 120.0d0 * a
    else
        tmp = (x - y) * ((-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 <= -5e+163) {
		tmp = (x / (z - t)) * 60.0;
	} else if (t_1 <= 2e+110) {
		tmp = 120.0 * a;
	} else {
		tmp = (x - y) * (-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 <= -5e+163:
		tmp = (x / (z - t)) * 60.0
	elif t_1 <= 2e+110:
		tmp = 120.0 * a
	else:
		tmp = (x - y) * (-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 <= -5e+163)
		tmp = Float64(Float64(x / Float64(z - t)) * 60.0);
	elseif (t_1 <= 2e+110)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(x - y) * Float64(-60.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -5e+163)
		tmp = (x / (z - t)) * 60.0;
	elseif (t_1 <= 2e+110)
		tmp = 120.0 * a;
	else
		tmp = (x - y) * (-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, -5e+163], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $MachinePrecision], If[LessEqual[t$95$1, 2e+110], N[(120.0 * a), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5e163

   1. Initial program 95.5%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 66.4

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

   5. Applied rewrites 66.4%

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

   if -5e163 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2e110

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 68.4

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

   5. Applied rewrites 68.4%

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

   if 2e110 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.6%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 85.3

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

   5. Applied rewrites 85.3%

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

   6. Taylor expanded in z around 0

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

      1. lower-/.f64 60.5

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

   8. Applied rewrites 60.5%

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

Alternative 3: 55.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+163} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+240}\right):\\ \;\;\;\;y \cdot \frac{60}{t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (or (<= t_1 -5e+163) (not (<= t_1 5e+240)))
     (* y (/ 60.0 t))
     (* 120.0 a))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if ((t_1 <= -5e+163) || !(t_1 <= 5e+240)) {
		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) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if ((t_1 <= (-5d+163)) .or. (.not. (t_1 <= 5d+240))) 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 t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if ((t_1 <= -5e+163) || !(t_1 <= 5e+240)) {
		tmp = y * (60.0 / t);
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if (t_1 <= -5e+163) or not (t_1 <= 5e+240):
		tmp = y * (60.0 / t)
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if ((t_1 <= -5e+163) || !(t_1 <= 5e+240))
		tmp = Float64(y * Float64(60.0 / t));
	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)) / (z - t);
	tmp = 0.0;
	if ((t_1 <= -5e+163) || ~((t_1 <= 5e+240)))
		tmp = y * (60.0 / t);
	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] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+163], N[Not[LessEqual[t$95$1, 5e+240]], $MachinePrecision]], N[(y * N[(60.0 / t), $MachinePrecision]), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5e163 or 5.0000000000000003e240 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.3%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} \]
   4. 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. lower--.f64 48.7

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

   5. Applied rewrites 48.7%

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

   6. Taylor expanded in z around 0

      \[\leadsto 60 \cdot \color{blue}{\frac{y}{t}} \]
   7. 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 39.3

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

   8. Applied rewrites 39.3%

      \[\leadsto \frac{y}{t} \cdot \color{blue}{60} \]
   9. 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. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 39.3

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

   10. Applied rewrites 39.3%

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

   if -5e163 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 5.0000000000000003e240

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 64.3

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

   5. Applied rewrites 64.3%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{+163} \lor \neg \left(\frac{60 \cdot \left(x - y\right)}{z - t} \leq 5 \cdot 10^{+240}\right):\\ \;\;\;\;y \cdot \frac{60}{t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 55.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+163}:\\ \;\;\;\;x \cdot \frac{-60}{t}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+240}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -5e+163)
     (* x (/ -60.0 t))
     (if (<= t_1 5e+240) (* 120.0 a) (* y (/ 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 <= -5e+163) {
		tmp = x * (-60.0 / t);
	} else if (t_1 <= 5e+240) {
		tmp = 120.0 * a;
	} else {
		tmp = y * (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 <= (-5d+163)) then
        tmp = x * ((-60.0d0) / t)
    else if (t_1 <= 5d+240) then
        tmp = 120.0d0 * a
    else
        tmp = y * (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 <= -5e+163) {
		tmp = x * (-60.0 / t);
	} else if (t_1 <= 5e+240) {
		tmp = 120.0 * a;
	} else {
		tmp = y * (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 <= -5e+163:
		tmp = x * (-60.0 / t)
	elif t_1 <= 5e+240:
		tmp = 120.0 * a
	else:
		tmp = y * (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 <= -5e+163)
		tmp = Float64(x * Float64(-60.0 / t));
	elseif (t_1 <= 5e+240)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(y * Float64(60.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -5e+163)
		tmp = x * (-60.0 / t);
	elseif (t_1 <= 5e+240)
		tmp = 120.0 * a;
	else
		tmp = y * (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, -5e+163], N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+240], N[(120.0 * a), $MachinePrecision], N[(y * N[(60.0 / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5e163

   1. Initial program 95.5%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 95.2

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

   5. Applied rewrites 95.2%

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

   6. Taylor expanded in z around 0

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

      1. lower-/.f64 58.1

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

   8. Applied rewrites 58.1%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 36.8%

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

   if -5e163 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 5.0000000000000003e240

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 64.3

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

   5. Applied rewrites 64.3%

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

   if 5.0000000000000003e240 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} \]
   4. 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. lower--.f64 73.0

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

   5. Applied rewrites 73.0%

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

   6. Taylor expanded in z around 0

      \[\leadsto 60 \cdot \color{blue}{\frac{y}{t}} \]
   7. 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 56.5

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

   8. Applied rewrites 56.5%

      \[\leadsto \frac{y}{t} \cdot \color{blue}{60} \]
   9. 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. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 56.5

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

   10. Applied rewrites 56.5%

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

Alternative 5: 55.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+163}:\\ \;\;\;\;\frac{y}{t} \cdot 60\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+240}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -5e+163)
     (* (/ y t) 60.0)
     (if (<= t_1 5e+240) (* 120.0 a) (* y (/ 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 <= -5e+163) {
		tmp = (y / t) * 60.0;
	} else if (t_1 <= 5e+240) {
		tmp = 120.0 * a;
	} else {
		tmp = y * (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 <= (-5d+163)) then
        tmp = (y / t) * 60.0d0
    else if (t_1 <= 5d+240) then
        tmp = 120.0d0 * a
    else
        tmp = y * (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 <= -5e+163) {
		tmp = (y / t) * 60.0;
	} else if (t_1 <= 5e+240) {
		tmp = 120.0 * a;
	} else {
		tmp = y * (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 <= -5e+163:
		tmp = (y / t) * 60.0
	elif t_1 <= 5e+240:
		tmp = 120.0 * a
	else:
		tmp = y * (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 <= -5e+163)
		tmp = Float64(Float64(y / t) * 60.0);
	elseif (t_1 <= 5e+240)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(y * Float64(60.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -5e+163)
		tmp = (y / t) * 60.0;
	elseif (t_1 <= 5e+240)
		tmp = 120.0 * a;
	else
		tmp = y * (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, -5e+163], N[(N[(y / t), $MachinePrecision] * 60.0), $MachinePrecision], If[LessEqual[t$95$1, 5e+240], N[(120.0 * a), $MachinePrecision], N[(y * N[(60.0 / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5e163

   1. Initial program 95.5%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} \]
   4. 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. lower--.f64 29.7

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

   5. Applied rewrites 29.7%

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

   6. Taylor expanded in z around 0

      \[\leadsto 60 \cdot \color{blue}{\frac{y}{t}} \]
   7. 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 25.9

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

   8. Applied rewrites 25.9%

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

   if -5e163 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 5.0000000000000003e240

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 64.3

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

   5. Applied rewrites 64.3%

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

   if 5.0000000000000003e240 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} \]
   4. 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. lower--.f64 73.0

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

   5. Applied rewrites 73.0%

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

   6. Taylor expanded in z around 0

      \[\leadsto 60 \cdot \color{blue}{\frac{y}{t}} \]
   7. 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 56.5

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

   8. Applied rewrites 56.5%

      \[\leadsto \frac{y}{t} \cdot \color{blue}{60} \]
   9. 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. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 56.5

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

   10. Applied rewrites 56.5%

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

Alternative 6: 74.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.4 \cdot 10^{+72}:\\ \;\;\;\;\frac{x}{z} \cdot 60 + a \cdot 120\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-32}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y}{t} \cdot 60\right)\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-20}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.4e+72)
   (+ (* (/ x z) 60.0) (* a 120.0))
   (if (<= a -4e-32)
     (fma a 120.0 (* (/ y t) 60.0))
     (if (<= a 2.25e-20) (* (- x y) (/ 60.0 (- z t))) (* 120.0 a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.4e+72) {
		tmp = ((x / z) * 60.0) + (a * 120.0);
	} else if (a <= -4e-32) {
		tmp = fma(a, 120.0, ((y / t) * 60.0));
	} else if (a <= 2.25e-20) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.4e+72)
		tmp = Float64(Float64(Float64(x / z) * 60.0) + Float64(a * 120.0));
	elseif (a <= -4e-32)
		tmp = fma(a, 120.0, Float64(Float64(y / t) * 60.0));
	elseif (a <= 2.25e-20)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.4e+72], N[(N[(N[(x / z), $MachinePrecision] * 60.0), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4e-32], N[(a * 120.0 + N[(N[(y / t), $MachinePrecision] * 60.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.25e-20], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.4000000000000003e72

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 84.3

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

   5. Applied rewrites 84.3%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 88.8%

      \[\leadsto \frac{x}{z} \cdot 60 + a \cdot 120 \]

   if -6.4000000000000003e72 < a < -4.00000000000000022e-32

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing
   3. 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

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. +-commutative N/A

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

      6. remove-double-neg N/A

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

      7. lower-fma.f64 99.8

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 81.2

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

   7. Applied rewrites 81.2%

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

   8. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 74.2

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

   10. Applied rewrites 74.2%

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

   if -4.00000000000000022e-32 < a < 2.2500000000000001e-20

   1. Initial program 98.8%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 78.0

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

   5. Applied rewrites 78.0%

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

   if 2.2500000000000001e-20 < a

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 88.2

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

   5. Applied rewrites 88.2%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.4 \cdot 10^{+72}:\\ \;\;\;\;\frac{x}{z} \cdot 60 + a \cdot 120\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-32}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y}{t} \cdot 60\right)\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-20}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 89.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+57} \lor \neg \left(y \leq 1.35 \cdot 10^{+52}\right):\\ \;\;\;\;\frac{-60 \cdot y}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -8.2e+57) (not (<= y 1.35e+52)))
   (+ (/ (* -60.0 y) (- z t)) (* a 120.0))
   (+ (/ (* 60.0 x) (- z t)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -8.2e+57) || !(y <= 1.35e+52)) {
		tmp = ((-60.0 * y) / (z - t)) + (a * 120.0);
	} else {
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-8.2d+57)) .or. (.not. (y <= 1.35d+52))) then
        tmp = (((-60.0d0) * y) / (z - t)) + (a * 120.0d0)
    else
        tmp = ((60.0d0 * x) / (z - t)) + (a * 120.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -8.2e+57) || !(y <= 1.35e+52)) {
		tmp = ((-60.0 * y) / (z - t)) + (a * 120.0);
	} else {
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -8.2e+57) or not (y <= 1.35e+52):
		tmp = ((-60.0 * y) / (z - t)) + (a * 120.0)
	else:
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -8.2e+57) || !(y <= 1.35e+52))
		tmp = Float64(Float64(Float64(-60.0 * y) / Float64(z - t)) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(Float64(60.0 * x) / Float64(z - t)) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -8.2e+57) || ~((y <= 1.35e+52)))
		tmp = ((-60.0 * y) / (z - t)) + (a * 120.0);
	else
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -8.2e+57], N[Not[LessEqual[y, 1.35e+52]], $MachinePrecision]], N[(N[(N[(-60.0 * y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.2e57 or 1.35e52 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 90.8

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

   5. Applied rewrites 90.8%

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

   if -8.2e57 < y < 1.35e52

   1. Initial program 99.1%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 93.9%

      \[\leadsto \frac{60 \cdot \color{blue}{x}}{z - t} + a \cdot 120 \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+57} \lor \neg \left(y \leq 1.35 \cdot 10^{+52}\right):\\ \;\;\;\;\frac{-60 \cdot y}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-13} \lor \neg \left(z \leq 3.5 \cdot 10^{+20}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{z}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x - y}{t} \cdot -60\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.45e-13) (not (<= z 3.5e+20)))
   (fma (/ (- x y) z) 60.0 (* 120.0 a))
   (fma a 120.0 (* (/ (- x y) t) -60.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.45e-13) || !(z <= 3.5e+20)) {
		tmp = fma(((x - y) / z), 60.0, (120.0 * a));
	} else {
		tmp = fma(a, 120.0, (((x - y) / t) * -60.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.45e-13) || !(z <= 3.5e+20))
		tmp = fma(Float64(Float64(x - y) / z), 60.0, Float64(120.0 * a));
	else
		tmp = fma(a, 120.0, Float64(Float64(Float64(x - y) / t) * -60.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.45e-13], N[Not[LessEqual[z, 3.5e+20]], $MachinePrecision]], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], N[(a * 120.0 + N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4499999999999999e-13 or 3.5e20 < z

   1. Initial program 99.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. fp-cancel-sign-sub-inv N/A

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

      3. fp-cancel-sub-sign-inv N/A

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

      4. *-commutative N/A

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

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

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

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

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

      7. *-commutative N/A

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

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

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

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

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

      10. metadata-eval N/A

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

      11. metadata-eval N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lower--.f64 N/A

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

      15. lower-*.f64 92.1

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

   5. Applied rewrites 92.1%

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

   if -1.4499999999999999e-13 < z < 3.5e20

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing
   3. 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

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. +-commutative N/A

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

      6. remove-double-neg N/A

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

      7. lower-fma.f64 99.7

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 87.4

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

   7. Applied rewrites 87.4%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-13} \lor \neg \left(z \leq 3.5 \cdot 10^{+20}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{z}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x - y}{t} \cdot -60\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-13} \lor \neg \left(z \leq 3.5 \cdot 10^{+20}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{z}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.45e-13) (not (<= z 3.5e+20)))
   (fma (/ (- x y) z) 60.0 (* 120.0 a))
   (fma (/ (- x y) t) -60.0 (* 120.0 a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.45e-13) || !(z <= 3.5e+20)) {
		tmp = fma(((x - y) / z), 60.0, (120.0 * a));
	} else {
		tmp = fma(((x - y) / t), -60.0, (120.0 * a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.45e-13) || !(z <= 3.5e+20))
		tmp = fma(Float64(Float64(x - y) / z), 60.0, Float64(120.0 * a));
	else
		tmp = fma(Float64(Float64(x - y) / t), -60.0, Float64(120.0 * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.45e-13], N[Not[LessEqual[z, 3.5e+20]], $MachinePrecision]], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4499999999999999e-13 or 3.5e20 < z

   1. Initial program 99.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. fp-cancel-sign-sub-inv N/A

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

      3. fp-cancel-sub-sign-inv N/A

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

      4. *-commutative N/A

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

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

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

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

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

      7. *-commutative N/A

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

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

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

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

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

      10. metadata-eval N/A

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

      11. metadata-eval N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lower--.f64 N/A

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

      15. lower-*.f64 92.1

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

   5. Applied rewrites 92.1%

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

   if -1.4499999999999999e-13 < z < 3.5e20

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t} + 120 \cdot a} \]
   4. 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. lower--.f64 N/A

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

      5. lower-*.f64 87.3

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

   5. Applied rewrites 87.3%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-13} \lor \neg \left(z \leq 3.5 \cdot 10^{+20}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{z}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{-52}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-214}:\\ \;\;\;\;\frac{y}{z - t} \cdot -60\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-104}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.5e-52)
   (* 120.0 a)
   (if (<= a -4.6e-214)
     (* (/ y (- z t)) -60.0)
     (if (<= a 1.08e-104) (* (- x y) (/ -60.0 t)) (* 120.0 a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e-52) {
		tmp = 120.0 * a;
	} else if (a <= -4.6e-214) {
		tmp = (y / (z - t)) * -60.0;
	} else if (a <= 1.08e-104) {
		tmp = (x - 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 <= (-9.5d-52)) then
        tmp = 120.0d0 * a
    else if (a <= (-4.6d-214)) then
        tmp = (y / (z - t)) * (-60.0d0)
    else if (a <= 1.08d-104) then
        tmp = (x - 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 <= -9.5e-52) {
		tmp = 120.0 * a;
	} else if (a <= -4.6e-214) {
		tmp = (y / (z - t)) * -60.0;
	} else if (a <= 1.08e-104) {
		tmp = (x - y) * (-60.0 / t);
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.5e-52:
		tmp = 120.0 * a
	elif a <= -4.6e-214:
		tmp = (y / (z - t)) * -60.0
	elif a <= 1.08e-104:
		tmp = (x - y) * (-60.0 / t)
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.5e-52)
		tmp = Float64(120.0 * a);
	elseif (a <= -4.6e-214)
		tmp = Float64(Float64(y / Float64(z - t)) * -60.0);
	elseif (a <= 1.08e-104)
		tmp = Float64(Float64(x - y) * Float64(-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 <= -9.5e-52)
		tmp = 120.0 * a;
	elseif (a <= -4.6e-214)
		tmp = (y / (z - t)) * -60.0;
	elseif (a <= 1.08e-104)
		tmp = (x - y) * (-60.0 / t);
	else
		tmp = 120.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.5e-52], N[(120.0 * a), $MachinePrecision], If[LessEqual[a, -4.6e-214], N[(N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision] * -60.0), $MachinePrecision], If[LessEqual[a, 1.08e-104], N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.50000000000000007e-52 or 1.07999999999999997e-104 < a

   1. Initial program 99.2%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 77.3

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

   5. Applied rewrites 77.3%

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

   if -9.50000000000000007e-52 < a < -4.60000000000000022e-214

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} \]
   4. 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. lower--.f64 59.6

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

   5. Applied rewrites 59.6%

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

   if -4.60000000000000022e-214 < a < 1.07999999999999997e-104

   1. Initial program 99.5%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 83.8

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

   5. Applied rewrites 83.8%

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

   6. Taylor expanded in z around 0

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

      1. lower-/.f64 51.0

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

   8. Applied rewrites 51.0%

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

Alternative 11: 58.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{-32}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-214}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-104}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.9e-32)
   (* 120.0 a)
   (if (<= a -3.8e-214)
     (* (- x y) (/ 60.0 z))
     (if (<= a 1.08e-104) (* (- x y) (/ -60.0 t)) (* 120.0 a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.9e-32) {
		tmp = 120.0 * a;
	} else if (a <= -3.8e-214) {
		tmp = (x - y) * (60.0 / z);
	} else if (a <= 1.08e-104) {
		tmp = (x - 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 <= (-3.9d-32)) then
        tmp = 120.0d0 * a
    else if (a <= (-3.8d-214)) then
        tmp = (x - y) * (60.0d0 / z)
    else if (a <= 1.08d-104) then
        tmp = (x - 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 <= -3.9e-32) {
		tmp = 120.0 * a;
	} else if (a <= -3.8e-214) {
		tmp = (x - y) * (60.0 / z);
	} else if (a <= 1.08e-104) {
		tmp = (x - y) * (-60.0 / t);
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.9e-32:
		tmp = 120.0 * a
	elif a <= -3.8e-214:
		tmp = (x - y) * (60.0 / z)
	elif a <= 1.08e-104:
		tmp = (x - y) * (-60.0 / t)
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.9e-32)
		tmp = Float64(120.0 * a);
	elseif (a <= -3.8e-214)
		tmp = Float64(Float64(x - y) * Float64(60.0 / z));
	elseif (a <= 1.08e-104)
		tmp = Float64(Float64(x - y) * Float64(-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 <= -3.9e-32)
		tmp = 120.0 * a;
	elseif (a <= -3.8e-214)
		tmp = (x - y) * (60.0 / z);
	elseif (a <= 1.08e-104)
		tmp = (x - y) * (-60.0 / t);
	else
		tmp = 120.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.9e-32], N[(120.0 * a), $MachinePrecision], If[LessEqual[a, -3.8e-214], N[(N[(x - y), $MachinePrecision] * N[(60.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.08e-104], N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.9000000000000001e-32 or 1.07999999999999997e-104 < a

   1. Initial program 99.2%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 78.0

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

   5. Applied rewrites 78.0%

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

   if -3.9000000000000001e-32 < a < -3.8000000000000003e-214

   1. Initial program 99.6%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 84.1

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

   5. Applied rewrites 84.1%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 54.2%

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

   if -3.8000000000000003e-214 < a < 1.07999999999999997e-104

   1. Initial program 99.5%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 83.8

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

   5. Applied rewrites 83.8%

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

   6. Taylor expanded in z around 0

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

      1. lower-/.f64 51.0

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

   8. Applied rewrites 51.0%

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

Alternative 12: 83.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-13}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60 + a \cdot 120\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+20}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x - y}{t} \cdot -60\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{60}{z} \cdot \left(x - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.45e-13)
   (+ (* (/ (- x y) z) 60.0) (* a 120.0))
   (if (<= z 3.5e+20)
     (fma a 120.0 (* (/ (- x y) t) -60.0))
     (fma a 120.0 (* (/ 60.0 z) (- x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.45e-13) {
		tmp = (((x - y) / z) * 60.0) + (a * 120.0);
	} else if (z <= 3.5e+20) {
		tmp = fma(a, 120.0, (((x - y) / t) * -60.0));
	} else {
		tmp = fma(a, 120.0, ((60.0 / z) * (x - y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.45e-13)
		tmp = Float64(Float64(Float64(Float64(x - y) / z) * 60.0) + Float64(a * 120.0));
	elseif (z <= 3.5e+20)
		tmp = fma(a, 120.0, Float64(Float64(Float64(x - y) / t) * -60.0));
	else
		tmp = fma(a, 120.0, Float64(Float64(60.0 / z) * Float64(x - y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.45e-13], N[(N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+20], N[(a * 120.0 + N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0), $MachinePrecision]), $MachinePrecision], N[(a * 120.0 + N[(N[(60.0 / z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4499999999999999e-13

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 90.8

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

   5. Applied rewrites 90.8%

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

   if -1.4499999999999999e-13 < z < 3.5e20

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing
   3. 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

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. +-commutative N/A

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

      6. remove-double-neg N/A

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

      7. lower-fma.f64 99.7

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 87.4

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

   7. Applied rewrites 87.4%

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

   if 3.5e20 < z

   1. Initial program 98.5%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing
   3. 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

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. +-commutative N/A

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

      6. remove-double-neg N/A

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

      7. lower-fma.f64 98.6

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 93.4%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-13}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60 + a \cdot 120\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+20}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x - y}{t} \cdot -60\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{60}{z} \cdot \left(x - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 83.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-13}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{z}, 60, 120 \cdot a\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+20}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x - y}{t} \cdot -60\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{60}{z} \cdot \left(x - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.45e-13)
   (fma (/ (- x y) z) 60.0 (* 120.0 a))
   (if (<= z 3.5e+20)
     (fma a 120.0 (* (/ (- x y) t) -60.0))
     (fma a 120.0 (* (/ 60.0 z) (- x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.45e-13) {
		tmp = fma(((x - y) / z), 60.0, (120.0 * a));
	} else if (z <= 3.5e+20) {
		tmp = fma(a, 120.0, (((x - y) / t) * -60.0));
	} else {
		tmp = fma(a, 120.0, ((60.0 / z) * (x - y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.45e-13)
		tmp = fma(Float64(Float64(x - y) / z), 60.0, Float64(120.0 * a));
	elseif (z <= 3.5e+20)
		tmp = fma(a, 120.0, Float64(Float64(Float64(x - y) / t) * -60.0));
	else
		tmp = fma(a, 120.0, Float64(Float64(60.0 / z) * Float64(x - y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.45e-13], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+20], N[(a * 120.0 + N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0), $MachinePrecision]), $MachinePrecision], N[(a * 120.0 + N[(N[(60.0 / z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4499999999999999e-13

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. fp-cancel-sign-sub-inv N/A

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

      3. fp-cancel-sub-sign-inv N/A

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

      4. *-commutative N/A

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

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

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

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

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

      7. *-commutative N/A

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

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

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

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

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

      10. metadata-eval N/A

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

      11. metadata-eval N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lower--.f64 N/A

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

      15. lower-*.f64 90.7

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

   5. Applied rewrites 90.7%

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

   if -1.4499999999999999e-13 < z < 3.5e20

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing
   3. 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

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. +-commutative N/A

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

      6. remove-double-neg N/A

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

      7. lower-fma.f64 99.7

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 87.4

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

   7. Applied rewrites 87.4%

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

   if 3.5e20 < z

   1. Initial program 98.5%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing
   3. 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

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. +-commutative N/A

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

      6. remove-double-neg N/A

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

      7. lower-fma.f64 98.6

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 93.4%

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

Alternative 14: 77.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-12}:\\ \;\;\;\;\frac{y}{z} \cdot -60 + a \cdot 120\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+20}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot 60 + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.2e-12)
   (+ (* (/ y z) -60.0) (* a 120.0))
   (if (<= z 5.1e+20)
     (fma (/ (- x y) t) -60.0 (* 120.0 a))
     (+ (* (/ x z) 60.0) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.2e-12) {
		tmp = ((y / z) * -60.0) + (a * 120.0);
	} else if (z <= 5.1e+20) {
		tmp = fma(((x - y) / t), -60.0, (120.0 * a));
	} else {
		tmp = ((x / z) * 60.0) + (a * 120.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.2e-12)
		tmp = Float64(Float64(Float64(y / z) * -60.0) + Float64(a * 120.0));
	elseif (z <= 5.1e+20)
		tmp = fma(Float64(Float64(x - y) / t), -60.0, Float64(120.0 * a));
	else
		tmp = Float64(Float64(Float64(x / z) * 60.0) + Float64(a * 120.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.2e-12], N[(N[(N[(y / z), $MachinePrecision] * -60.0), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.1e+20], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / z), $MachinePrecision] * 60.0), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.19999999999999957e-12

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 90.8

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

   5. Applied rewrites 90.8%

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

   6. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 80.1

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

   8. Applied rewrites 80.1%

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

   if -9.19999999999999957e-12 < z < 5.1e20

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t} + 120 \cdot a} \]
   4. 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. lower--.f64 N/A

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

      5. lower-*.f64 87.3

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

   5. Applied rewrites 87.3%

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

   if 5.1e20 < z

   1. Initial program 98.5%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 93.2

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

   5. Applied rewrites 93.2%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 84.3%

      \[\leadsto \frac{x}{z} \cdot 60 + a \cdot 120 \]
3. Recombined 3 regimes into one program.

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-12}:\\ \;\;\;\;\frac{y}{z} \cdot -60 + a \cdot 120\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+20}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot 60 + a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 74.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{-32} \lor \neg \left(a \leq 2.25 \cdot 10^{-20}\right):\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.9e-32) (not (<= a 2.25e-20)))
   (* 120.0 a)
   (* (- x y) (/ 60.0 (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.9e-32) || !(a <= 2.25e-20)) {
		tmp = 120.0 * a;
	} else {
		tmp = (x - y) * (60.0 / (z - t));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-3.9d-32)) .or. (.not. (a <= 2.25d-20))) then
        tmp = 120.0d0 * a
    else
        tmp = (x - y) * (60.0d0 / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.9e-32) || !(a <= 2.25e-20)) {
		tmp = 120.0 * a;
	} else {
		tmp = (x - y) * (60.0 / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.9e-32) or not (a <= 2.25e-20):
		tmp = 120.0 * a
	else:
		tmp = (x - y) * (60.0 / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.9e-32) || !(a <= 2.25e-20))
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.9e-32) || ~((a <= 2.25e-20)))
		tmp = 120.0 * a;
	else
		tmp = (x - y) * (60.0 / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.9e-32], N[Not[LessEqual[a, 2.25e-20]], $MachinePrecision]], N[(120.0 * a), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.9000000000000001e-32 or 2.2500000000000001e-20 < a

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 82.2

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

   5. Applied rewrites 82.2%

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

   if -3.9000000000000001e-32 < a < 2.2500000000000001e-20

   1. Initial program 98.8%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 78.0

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

   5. Applied rewrites 78.0%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{-32} \lor \neg \left(a \leq 2.25 \cdot 10^{-20}\right):\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 59.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.32 \cdot 10^{-66} \lor \neg \left(a \leq 1.08 \cdot 10^{-104}\right):\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.32e-66) (not (<= a 1.08e-104)))
   (* 120.0 a)
   (* (- x y) (/ -60.0 t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.32e-66) || !(a <= 1.08e-104)) {
		tmp = 120.0 * a;
	} else {
		tmp = (x - y) * (-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) :: tmp
    if ((a <= (-1.32d-66)) .or. (.not. (a <= 1.08d-104))) then
        tmp = 120.0d0 * a
    else
        tmp = (x - y) * ((-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 tmp;
	if ((a <= -1.32e-66) || !(a <= 1.08e-104)) {
		tmp = 120.0 * a;
	} else {
		tmp = (x - y) * (-60.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.32e-66) or not (a <= 1.08e-104):
		tmp = 120.0 * a
	else:
		tmp = (x - y) * (-60.0 / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.32e-66) || !(a <= 1.08e-104))
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(x - y) * Float64(-60.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.32e-66) || ~((a <= 1.08e-104)))
		tmp = 120.0 * a;
	else
		tmp = (x - y) * (-60.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.32e-66], N[Not[LessEqual[a, 1.08e-104]], $MachinePrecision]], N[(120.0 * a), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.3200000000000001e-66 or 1.07999999999999997e-104 < a

   1. Initial program 99.2%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 76.4

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

   5. Applied rewrites 76.4%

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

   if -1.3200000000000001e-66 < a < 1.07999999999999997e-104

   1. Initial program 99.5%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 84.9

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

   5. Applied rewrites 84.9%

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

   6. Taylor expanded in z around 0

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

      1. lower-/.f64 48.4

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

   8. Applied rewrites 48.4%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.32 \cdot 10^{-66} \lor \neg \left(a \leq 1.08 \cdot 10^{-104}\right):\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 51.1% accurate, 5.2× 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 99.3%

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

3. Taylor expanded in z around inf

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

   1. lower-*.f64 54.6

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

5. Applied rewrites 54.6%

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

Developer Target 1: 99.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return (60.0 / ((z - t) / (x - y))) + (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 / ((z - t) / (x - y))) + (a * 120.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2025026 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (/ 60 (/ (- z t) (- x y))) (* a 120)))

  (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))