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

Percentage Accurate: 99.3% → 99.4%

Time: 4.4s

Alternatives: 15

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: 99.3% 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: 99.4% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.3%

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

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

   3. lift-/.f64 N/A

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

   4. lift--.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. +-commutative N/A

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

   7. lift-*.f64 N/A

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

   8. lower-fma.f64 N/A

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

   9. lower-/.f64 N/A

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

   10. *-commutative N/A

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

   11. lower-*.f64 N/A

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

   12. lift--.f64 N/A

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

   13. lift--.f64 99.4

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

4. Applied rewrites 99.4%

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

Alternative 2: 74.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - y\right) \cdot \frac{60}{z - t}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{-39}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- x y) (/ 60.0 (- z t)))) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -1e+51) t_1 (if (<= t_2 1e-39) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - y) * (60.0 / (z - t));
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -1e+51) {
		tmp = t_1;
	} else if (t_2 <= 1e-39) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) * (60.0d0 / (z - t))
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-1d+51)) then
        tmp = t_1
    else if (t_2 <= 1d-39) then
        tmp = 120.0d0 * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - y) * (60.0 / (z - t));
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -1e+51) {
		tmp = t_1;
	} else if (t_2 <= 1e-39) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - y) * (60.0 / (z - t))
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -1e+51:
		tmp = t_1
	elif t_2 <= 1e-39:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)))
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -1e+51)
		tmp = t_1;
	elseif (t_2 <= 1e-39)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - y) * (60.0 / (z - t));
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -1e+51)
		tmp = t_1;
	elseif (t_2 <= 1e-39)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+51], t$95$1, If[LessEqual[t$95$2, 1e-39], N[(120.0 * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1e51 or 9.99999999999999929e-40 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 98.8%

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

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 98.8

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

   4. Applied rewrites 98.8%

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

   5. Taylor expanded in a around 0

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r/ N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. metadata-eval N/A

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

      9. associate-*r/ N/A

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

      10. lower-*.f64 N/A

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

      11. lift--.f64 N/A

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

      12. associate-*r/ N/A

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

      13. metadata-eval N/A

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

      14. lower-/.f64 N/A

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

      15. lift--.f64 74.7

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

   7. Applied rewrites 74.7%

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

   if -1e51 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.99999999999999929e-40

   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 73.9

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

   5. Applied rewrites 73.9%

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

Alternative 3: 59.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+21}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) z)) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -2e+137) t_1 (if (<= t_2 1e+21) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / z;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -2e+137) {
		tmp = t_1;
	} else if (t_2 <= 1e+21) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x - y) * 60.0d0) / z
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-2d+137)) then
        tmp = t_1
    else if (t_2 <= 1d+21) then
        tmp = 120.0d0 * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / z;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -2e+137) {
		tmp = t_1;
	} else if (t_2 <= 1e+21) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((x - y) * 60.0) / z
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -2e+137:
		tmp = t_1
	elif t_2 <= 1e+21:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x - y) * 60.0) / z)
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -2e+137)
		tmp = t_1;
	elseif (t_2 <= 1e+21)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((x - y) * 60.0) / z;
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -2e+137)
		tmp = t_1;
	elseif (t_2 <= 1e+21)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+137], t$95$1, If[LessEqual[t$95$2, 1e+21], N[(120.0 * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.0000000000000001e137 or 1e21 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 98.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 79.8

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

   5. Applied rewrites 79.8%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 45.5%

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

   if -2.0000000000000001e137 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1e21

   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 66.8

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

   5. Applied rewrites 66.8%

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

Alternative 4: 58.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z - t} \cdot 60\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+171}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+43}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ x (- z t)) 60.0)) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -1e+171) t_1 (if (<= t_2 4e+43) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x / (z - t)) * 60.0;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -1e+171) {
		tmp = t_1;
	} else if (t_2 <= 4e+43) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / (z - t)) * 60.0d0
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-1d+171)) then
        tmp = t_1
    else if (t_2 <= 4d+43) then
        tmp = 120.0d0 * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x / (z - t)) * 60.0;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -1e+171) {
		tmp = t_1;
	} else if (t_2 <= 4e+43) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x / (z - t)) * 60.0
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -1e+171:
		tmp = t_1
	elif t_2 <= 4e+43:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x / Float64(z - t)) * 60.0)
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -1e+171)
		tmp = t_1;
	elseif (t_2 <= 4e+43)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x / (z - t)) * 60.0;
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -1e+171)
		tmp = t_1;
	elseif (t_2 <= 4e+43)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+171], t$95$1, If[LessEqual[t$95$2, 4e+43], N[(120.0 * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -9.99999999999999954e170 or 4.00000000000000006e43 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 98.2%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. lift--.f64 43.1

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

   5. Applied rewrites 43.1%

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

   if -9.99999999999999954e170 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.00000000000000006e43

   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 65.1

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

   5. Applied rewrites 65.1%

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

Alternative 5: 60.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{t} \cdot -60\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+36}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ (- x y) t) -60.0)) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -5e+119) t_1 (if (<= t_2 5e+36) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) / t) * -60.0;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e+119) {
		tmp = t_1;
	} else if (t_2 <= 5e+36) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x - y) / t) * (-60.0d0)
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-5d+119)) then
        tmp = t_1
    else if (t_2 <= 5d+36) then
        tmp = 120.0d0 * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) / t) * -60.0;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e+119) {
		tmp = t_1;
	} else if (t_2 <= 5e+36) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((x - y) / t) * -60.0
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -5e+119:
		tmp = t_1
	elif t_2 <= 5e+36:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x - y) / t) * -60.0)
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -5e+119)
		tmp = t_1;
	elseif (t_2 <= 5e+36)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((x - y) / t) * -60.0;
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -5e+119)
		tmp = t_1;
	elseif (t_2 <= 5e+36)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+119], t$95$1, If[LessEqual[t$95$2, 5e+36], N[(120.0 * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -4.9999999999999999e119 or 4.99999999999999977e36 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 98.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. lift--.f64 N/A

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

      5. lower-*.f64 58.7

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

   5. Applied rewrites 58.7%

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

   6. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 47.6

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

   8. Applied rewrites 47.6%

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

   if -4.9999999999999999e119 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.99999999999999977e36

   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 67.0

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

   5. Applied rewrites 67.0%

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

Alternative 6: 54.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot 60\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+171}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+113}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ x z) 60.0)) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -1e+171) t_1 (if (<= t_2 5e+113) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x / z) * 60.0;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -1e+171) {
		tmp = t_1;
	} else if (t_2 <= 5e+113) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / z) * 60.0d0
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-1d+171)) then
        tmp = t_1
    else if (t_2 <= 5d+113) then
        tmp = 120.0d0 * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x / z) * 60.0;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -1e+171) {
		tmp = t_1;
	} else if (t_2 <= 5e+113) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x / z) * 60.0
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -1e+171:
		tmp = t_1
	elif t_2 <= 5e+113:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x / z) * 60.0)
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -1e+171)
		tmp = t_1;
	elseif (t_2 <= 5e+113)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x / z) * 60.0;
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -1e+171)
		tmp = t_1;
	elseif (t_2 <= 5e+113)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] * 60.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+171], t$95$1, If[LessEqual[t$95$2, 5e+113], N[(120.0 * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -9.99999999999999954e170 or 5e113 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. lift--.f64 45.3

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

   5. Applied rewrites 45.3%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 29.6%

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

   if -9.99999999999999954e170 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 5e113

   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 62.8

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

   5. Applied rewrites 62.8%

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

Alternative 7: 54.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t} \cdot -60\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+171}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+213}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ x t) -60.0)) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -1e+171) t_1 (if (<= t_2 1e+213) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x / t) * -60.0;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -1e+171) {
		tmp = t_1;
	} else if (t_2 <= 1e+213) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / t) * (-60.0d0)
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-1d+171)) then
        tmp = t_1
    else if (t_2 <= 1d+213) then
        tmp = 120.0d0 * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x / t) * -60.0;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -1e+171) {
		tmp = t_1;
	} else if (t_2 <= 1e+213) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x / t) * -60.0
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -1e+171:
		tmp = t_1
	elif t_2 <= 1e+213:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x / t) * -60.0)
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -1e+171)
		tmp = t_1;
	elseif (t_2 <= 1e+213)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x / t) * -60.0;
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -1e+171)
		tmp = t_1;
	elseif (t_2 <= 1e+213)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x / t), $MachinePrecision] * -60.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+171], t$95$1, If[LessEqual[t$95$2, 1e+213], N[(120.0 * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -9.99999999999999954e170 or 9.99999999999999984e212 < (/.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 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. lift--.f64 N/A

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

      5. lower-*.f64 60.1

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

   5. Applied rewrites 60.1%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 29.5

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

   8. Applied rewrites 29.5%

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

   if -9.99999999999999954e170 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.99999999999999984e212

   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 59.9

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

   5. Applied rewrites 59.9%

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

Alternative 8: 75.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)\\ \mathbf{if}\;t \leq -1.4:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-104}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-181}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x}{z} \cdot 60\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-48}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- x y) t) -60.0 (* 120.0 a))))
   (if (<= t -1.4)
     t_1
     (if (<= t -4.4e-104)
       (* (- x y) (/ 60.0 (- z t)))
       (if (<= t 8e-181)
         (fma a 120.0 (* (/ x z) 60.0))
         (if (<= t 4.8e-48) (/ (* (- x y) 60.0) (- z t)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((x - y) / t), -60.0, (120.0 * a));
	double tmp;
	if (t <= -1.4) {
		tmp = t_1;
	} else if (t <= -4.4e-104) {
		tmp = (x - y) * (60.0 / (z - t));
	} else if (t <= 8e-181) {
		tmp = fma(a, 120.0, ((x / z) * 60.0));
	} else if (t <= 4.8e-48) {
		tmp = ((x - y) * 60.0) / (z - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(x - y) / t), -60.0, Float64(120.0 * a))
	tmp = 0.0
	if (t <= -1.4)
		tmp = t_1;
	elseif (t <= -4.4e-104)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	elseif (t <= 8e-181)
		tmp = fma(a, 120.0, Float64(Float64(x / z) * 60.0));
	elseif (t <= 4.8e-48)
		tmp = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.4], t$95$1, If[LessEqual[t, -4.4e-104], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e-181], N[(a * 120.0 + N[(N[(x / z), $MachinePrecision] * 60.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e-48], N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.3999999999999999 or 4.8e-48 < t

   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 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. lift--.f64 N/A

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

      5. lower-*.f64 85.0

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

   5. Applied rewrites 85.0%

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

   if -1.3999999999999999 < t < -4.40000000000000023e-104

   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

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 99.5

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

   4. Applied rewrites 99.5%

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

   5. Taylor expanded in a around 0

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r/ N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. metadata-eval N/A

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

      9. associate-*r/ N/A

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

      10. lower-*.f64 N/A

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

      11. lift--.f64 N/A

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

      12. associate-*r/ N/A

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

      13. metadata-eval N/A

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

      14. lower-/.f64 N/A

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

      15. lift--.f64 60.6

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

   7. Applied rewrites 60.6%

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

   if -4.40000000000000023e-104 < t < 8.00000000000000038e-181

   1. Initial program 99.4%

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

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 99.5

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

   4. Applied rewrites 99.5%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 90.7

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

   7. Applied rewrites 90.7%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 65.5%

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

   if 8.00000000000000038e-181 < t < 4.8e-48

   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. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 60.4

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

   5. Applied rewrites 60.4%

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

Alternative 9: 52.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z - t} \cdot -60\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-213}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;y \leq 0.00175:\\ \;\;\;\;\frac{x}{z - t} \cdot 60\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+76}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y (- z t)) -60.0)))
   (if (<= y -6.2e+57)
     t_1
     (if (<= y 4.3e-213)
       (* 120.0 a)
       (if (<= y 0.00175)
         (* (/ x (- z t)) 60.0)
         (if (<= y 2.7e+76) (* 120.0 a) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / (z - t)) * -60.0;
	double tmp;
	if (y <= -6.2e+57) {
		tmp = t_1;
	} else if (y <= 4.3e-213) {
		tmp = 120.0 * a;
	} else if (y <= 0.00175) {
		tmp = (x / (z - t)) * 60.0;
	} else if (y <= 2.7e+76) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y / (z - t)) * (-60.0d0)
    if (y <= (-6.2d+57)) then
        tmp = t_1
    else if (y <= 4.3d-213) then
        tmp = 120.0d0 * a
    else if (y <= 0.00175d0) then
        tmp = (x / (z - t)) * 60.0d0
    else if (y <= 2.7d+76) then
        tmp = 120.0d0 * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / (z - t)) * -60.0;
	double tmp;
	if (y <= -6.2e+57) {
		tmp = t_1;
	} else if (y <= 4.3e-213) {
		tmp = 120.0 * a;
	} else if (y <= 0.00175) {
		tmp = (x / (z - t)) * 60.0;
	} else if (y <= 2.7e+76) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / (z - t)) * -60.0
	tmp = 0
	if y <= -6.2e+57:
		tmp = t_1
	elif y <= 4.3e-213:
		tmp = 120.0 * a
	elif y <= 0.00175:
		tmp = (x / (z - t)) * 60.0
	elif y <= 2.7e+76:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / Float64(z - t)) * -60.0)
	tmp = 0.0
	if (y <= -6.2e+57)
		tmp = t_1;
	elseif (y <= 4.3e-213)
		tmp = Float64(120.0 * a);
	elseif (y <= 0.00175)
		tmp = Float64(Float64(x / Float64(z - t)) * 60.0);
	elseif (y <= 2.7e+76)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / (z - t)) * -60.0;
	tmp = 0.0;
	if (y <= -6.2e+57)
		tmp = t_1;
	elseif (y <= 4.3e-213)
		tmp = 120.0 * a;
	elseif (y <= 0.00175)
		tmp = (x / (z - t)) * 60.0;
	elseif (y <= 2.7e+76)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision] * -60.0), $MachinePrecision]}, If[LessEqual[y, -6.2e+57], t$95$1, If[LessEqual[y, 4.3e-213], N[(120.0 * a), $MachinePrecision], If[LessEqual[y, 0.00175], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $MachinePrecision], If[LessEqual[y, 2.7e+76], N[(120.0 * a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.20000000000000026e57 or 2.6999999999999999e76 < y

   1. Initial program 98.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. lift--.f64 52.1

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

   5. Applied rewrites 52.1%

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

   if -6.20000000000000026e57 < y < 4.3000000000000003e-213 or 0.00175000000000000004 < y < 2.6999999999999999e76

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 59.5

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

   5. Applied rewrites 59.5%

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

   if 4.3000000000000003e-213 < y < 0.00175000000000000004

   1. Initial program 99.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. lift--.f64 32.8

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

   5. Applied rewrites 32.8%

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

Alternative 10: 74.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+152}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y}{z} \cdot -60\right)\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-25}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x}{z} \cdot 60\right)\\ \mathbf{elif}\;a \leq 100:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.6e+152)
   (fma a 120.0 (* (/ y z) -60.0))
   (if (<= a -2.6e-25)
     (fma a 120.0 (* (/ x z) 60.0))
     (if (<= a 100.0) (* (- 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 <= -3.6e+152) {
		tmp = fma(a, 120.0, ((y / z) * -60.0));
	} else if (a <= -2.6e-25) {
		tmp = fma(a, 120.0, ((x / z) * 60.0));
	} else if (a <= 100.0) {
		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 <= -3.6e+152)
		tmp = fma(a, 120.0, Float64(Float64(y / z) * -60.0));
	elseif (a <= -2.6e-25)
		tmp = fma(a, 120.0, Float64(Float64(x / z) * 60.0));
	elseif (a <= 100.0)
		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, -3.6e+152], N[(a * 120.0 + N[(N[(y / z), $MachinePrecision] * -60.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.6e-25], N[(a * 120.0 + N[(N[(x / z), $MachinePrecision] * 60.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 100.0], 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 < -3.5999999999999999e152

   1. Initial program 99.5%

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

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 99.6

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

   4. Applied rewrites 99.6%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 78.1

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

   7. Applied rewrites 78.1%

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

   8. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 78.8

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

   10. Applied rewrites 78.8%

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

   if -3.5999999999999999e152 < a < -2.6e-25

   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

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 99.3

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

   4. Applied rewrites 99.3%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 65.3

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

   7. Applied rewrites 65.3%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 61.6%

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

   if -2.6e-25 < a < 100

   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

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 99.3

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

   4. Applied rewrites 99.3%

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

   5. Taylor expanded in a around 0

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r/ N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. metadata-eval N/A

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

      9. associate-*r/ N/A

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

      10. lower-*.f64 N/A

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

      11. lift--.f64 N/A

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

      12. associate-*r/ N/A

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

      13. metadata-eval N/A

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

      14. lower-/.f64 N/A

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

      15. lift--.f64 76.4

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

   7. Applied rewrites 76.4%

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

   if 100 < a

   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 76.0

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

   5. Applied rewrites 76.0%

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

Alternative 11: 81.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+168}:\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- x y) (/ 60.0 (- z t)))))
   (if (<= y -6.2e+57)
     t_1
     (if (<= y 5.4e+168) (+ (/ (* 60.0 x) (- z t)) (* a 120.0)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - y) * (60.0 / (z - t));
	double tmp;
	if (y <= -6.2e+57) {
		tmp = t_1;
	} else if (y <= 5.4e+168) {
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - y) * (60.0d0 / (z - t))
    if (y <= (-6.2d+57)) then
        tmp = t_1
    else if (y <= 5.4d+168) then
        tmp = ((60.0d0 * x) / (z - t)) + (a * 120.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - y) * (60.0 / (z - t));
	double tmp;
	if (y <= -6.2e+57) {
		tmp = t_1;
	} else if (y <= 5.4e+168) {
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - y) * (60.0 / (z - t))
	tmp = 0
	if y <= -6.2e+57:
		tmp = t_1
	elif y <= 5.4e+168:
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)))
	tmp = 0.0
	if (y <= -6.2e+57)
		tmp = t_1;
	elseif (y <= 5.4e+168)
		tmp = Float64(Float64(Float64(60.0 * x) / Float64(z - t)) + Float64(a * 120.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - y) * (60.0 / (z - t));
	tmp = 0.0;
	if (y <= -6.2e+57)
		tmp = t_1;
	elseif (y <= 5.4e+168)
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.2e+57], t$95$1, If[LessEqual[y, 5.4e+168], N[(N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.20000000000000026e57 or 5.40000000000000031e168 < y

   1. Initial program 98.8%

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

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 98.8

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

   4. Applied rewrites 98.8%

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

   5. Taylor expanded in a around 0

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r/ N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. metadata-eval N/A

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

      9. associate-*r/ N/A

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

      10. lower-*.f64 N/A

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

      11. lift--.f64 N/A

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

      12. associate-*r/ N/A

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

      13. metadata-eval N/A

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

      14. lower-/.f64 N/A

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

      15. lift--.f64 66.5

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

   7. Applied rewrites 66.5%

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

   if -6.20000000000000026e57 < y < 5.40000000000000031e168

   1. Initial program 99.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 87.9%

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

Alternative 12: 82.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, 120, \frac{x - y}{t} \cdot -60\right)\\ \mathbf{if}\;t \leq -5.6 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-48}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{z}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma a 120.0 (* (/ (- x y) t) -60.0))))
   (if (<= t -5.6e+96)
     t_1
     (if (<= t 5.2e-48) (fma (/ (- x y) z) 60.0 (* 120.0 a)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(a, 120.0, (((x - y) / t) * -60.0));
	double tmp;
	if (t <= -5.6e+96) {
		tmp = t_1;
	} else if (t <= 5.2e-48) {
		tmp = fma(((x - y) / z), 60.0, (120.0 * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(a, 120.0, Float64(Float64(Float64(x - y) / t) * -60.0))
	tmp = 0.0
	if (t <= -5.6e+96)
		tmp = t_1;
	elseif (t <= 5.2e-48)
		tmp = fma(Float64(Float64(x - y) / z), 60.0, Float64(120.0 * a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a * 120.0 + N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.6e+96], t$95$1, If[LessEqual[t, 5.2e-48], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.59999999999999999e96 or 5.19999999999999975e-48 < t

   1. Initial program 99.2%

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

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 99.3

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

   4. Applied rewrites 99.3%

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

   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

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift--.f64 86.8

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

   7. Applied rewrites 86.8%

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

   if -5.59999999999999999e96 < t < 5.19999999999999975e-48

   1. Initial program 99.4%

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

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-*.f64 78.6

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

   5. Applied rewrites 78.6%

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

Alternative 13: 82.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x - y}{t}, -60, 120 \cdot a\right)\\ \mathbf{if}\;t \leq -5.6 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-48}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - y}{z}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- x y) t) -60.0 (* 120.0 a))))
   (if (<= t -5.6e+96)
     t_1
     (if (<= t 5.2e-48) (fma (/ (- x y) z) 60.0 (* 120.0 a)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((x - y) / t), -60.0, (120.0 * a));
	double tmp;
	if (t <= -5.6e+96) {
		tmp = t_1;
	} else if (t <= 5.2e-48) {
		tmp = fma(((x - y) / z), 60.0, (120.0 * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(x - y) / t), -60.0, Float64(120.0 * a))
	tmp = 0.0
	if (t <= -5.6e+96)
		tmp = t_1;
	elseif (t <= 5.2e-48)
		tmp = fma(Float64(Float64(x - y) / z), 60.0, Float64(120.0 * a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.6e+96], t$95$1, If[LessEqual[t, 5.2e-48], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.59999999999999999e96 or 5.19999999999999975e-48 < t

   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 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. lift--.f64 N/A

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

      5. lower-*.f64 86.8

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

   5. Applied rewrites 86.8%

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

   if -5.59999999999999999e96 < t < 5.19999999999999975e-48

   1. Initial program 99.4%

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

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-*.f64 78.6

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

   5. Applied rewrites 78.6%

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

Alternative 14: 60.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y}{t}, 60, 120 \cdot a\right)\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-50}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ y t) 60.0 (* 120.0 a))))
   (if (<= t -5.5e-11) t_1 (if (<= t 1.4e-50) (/ (* (- x y) 60.0) z) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y / t), 60.0, (120.0 * a));
	double tmp;
	if (t <= -5.5e-11) {
		tmp = t_1;
	} else if (t <= 1.4e-50) {
		tmp = ((x - y) * 60.0) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y / t), 60.0, Float64(120.0 * a))
	tmp = 0.0
	if (t <= -5.5e-11)
		tmp = t_1;
	elseif (t <= 1.4e-50)
		tmp = Float64(Float64(Float64(x - y) * 60.0) / z);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / t), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.5e-11], t$95$1, If[LessEqual[t, 1.4e-50], N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.49999999999999975e-11 or 1.3999999999999999e-50 < t

   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 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. lift--.f64 N/A

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

      5. lower-*.f64 84.7

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

   5. Applied rewrites 84.7%

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

   6. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift-*.f64 72.0

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

   8. Applied rewrites 72.0%

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

   if -5.49999999999999975e-11 < t < 1.3999999999999999e-50

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift--.f64 61.8

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

   5. Applied rewrites 61.8%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 47.2%

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

Alternative 15: 50.5% 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 50.5

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

5. Applied rewrites 50.5%

   \[\leadsto \color{blue}{120 \cdot a} \]
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 2025089 
(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)))