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

Percentage Accurate: 99.4% → 99.8%

Time: 12.0s

Alternatives: 17

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.0%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
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 99.0

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

4. Applied rewrites 99.0%

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

   1. lift-fma.f64 N/A

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

   2. lift--.f64 N/A

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

   3. lift-/.f64 N/A

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

   4. lift--.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. +-commutative N/A

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

   7. associate-/l* N/A

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

   8. metadata-eval N/A

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

   9. associate-*r/ N/A

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

   10. *-commutative N/A

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

   11. lower-fma.f64 N/A

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

   12. lift--.f64 N/A

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

   13. associate-*r/ N/A

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

   14. metadata-eval N/A

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

   15. lower-/.f64 N/A

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

   16. lift--.f64 N/A

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

   17. lift-*.f64 99.8

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

6. Applied rewrites 99.8%

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

Alternative 2: 61.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z} \cdot 60\\ t_2 := \frac{x - y}{t} \cdot -60\\ t_3 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_3 \leq -2 \cdot 10^{+182}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq -2 \cdot 10^{+43}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+81}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+144}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ (- x y) z) 60.0))
        (t_2 (* (/ (- x y) t) -60.0))
        (t_3 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_3 -2e+182)
     t_1
     (if (<= t_3 -2e+43)
       t_2
       (if (<= t_3 2e+81) (* 120.0 a) (if (<= t_3 5e+144) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) / z) * 60.0;
	double t_2 = ((x - y) / t) * -60.0;
	double t_3 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_3 <= -2e+182) {
		tmp = t_1;
	} else if (t_3 <= -2e+43) {
		tmp = t_2;
	} else if (t_3 <= 2e+81) {
		tmp = 120.0 * a;
	} else if (t_3 <= 5e+144) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = ((x - y) / z) * 60.0d0
    t_2 = ((x - y) / t) * (-60.0d0)
    t_3 = (60.0d0 * (x - y)) / (z - t)
    if (t_3 <= (-2d+182)) then
        tmp = t_1
    else if (t_3 <= (-2d+43)) then
        tmp = t_2
    else if (t_3 <= 2d+81) then
        tmp = 120.0d0 * a
    else if (t_3 <= 5d+144) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) / z) * 60.0;
	double t_2 = ((x - y) / t) * -60.0;
	double t_3 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_3 <= -2e+182) {
		tmp = t_1;
	} else if (t_3 <= -2e+43) {
		tmp = t_2;
	} else if (t_3 <= 2e+81) {
		tmp = 120.0 * a;
	} else if (t_3 <= 5e+144) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((x - y) / z) * 60.0
	t_2 = ((x - y) / t) * -60.0
	t_3 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_3 <= -2e+182:
		tmp = t_1
	elif t_3 <= -2e+43:
		tmp = t_2
	elif t_3 <= 2e+81:
		tmp = 120.0 * a
	elif t_3 <= 5e+144:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x - y) / z) * 60.0)
	t_2 = Float64(Float64(Float64(x - y) / t) * -60.0)
	t_3 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_3 <= -2e+182)
		tmp = t_1;
	elseif (t_3 <= -2e+43)
		tmp = t_2;
	elseif (t_3 <= 2e+81)
		tmp = Float64(120.0 * a);
	elseif (t_3 <= 5e+144)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((x - y) / z) * 60.0;
	t_2 = ((x - y) / t) * -60.0;
	t_3 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_3 <= -2e+182)
		tmp = t_1;
	elseif (t_3 <= -2e+43)
		tmp = t_2;
	elseif (t_3 <= 2e+81)
		tmp = 120.0 * a;
	elseif (t_3 <= 5e+144)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -2e+182], t$95$1, If[LessEqual[t$95$3, -2e+43], t$95$2, If[LessEqual[t$95$3, 2e+81], N[(120.0 * a), $MachinePrecision], If[LessEqual[t$95$3, 5e+144], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.0000000000000001e182 or 1.99999999999999984e81 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.9999999999999999e144

   1. Initial program 97.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 95.6

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

   5. Applied rewrites 95.6%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 65.2

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

   8. Applied rewrites 65.2%

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

   if -2.0000000000000001e182 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.00000000000000003e43 or 4.9999999999999999e144 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 86.2

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

   5. Applied rewrites 86.2%

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

   6. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift--.f64 61.5

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

   8. Applied rewrites 61.5%

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

   if -2.00000000000000003e43 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.99999999999999984e81

   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 67.9

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

   5. Applied rewrites 67.9%

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

Alternative 3: 60.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+182}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{+43}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{-t}\\ \mathbf{elif}\;t\_1 \leq 10^{+36}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{-60 \cdot y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -2e+182)
     (* (/ (- x y) z) 60.0)
     (if (<= t_1 -2e+43)
       (/ (* (- x y) 60.0) (- t))
       (if (<= t_1 1e+36) (* 120.0 a) (/ (* -60.0 y) (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -2e+182) {
		tmp = ((x - y) / z) * 60.0;
	} else if (t_1 <= -2e+43) {
		tmp = ((x - y) * 60.0) / -t;
	} else if (t_1 <= 1e+36) {
		tmp = 120.0 * a;
	} else {
		tmp = (-60.0 * y) / (z - t);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-2d+182)) then
        tmp = ((x - y) / z) * 60.0d0
    else if (t_1 <= (-2d+43)) then
        tmp = ((x - y) * 60.0d0) / -t
    else if (t_1 <= 1d+36) then
        tmp = 120.0d0 * a
    else
        tmp = ((-60.0d0) * y) / (z - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -2e+182) {
		tmp = ((x - y) / z) * 60.0;
	} else if (t_1 <= -2e+43) {
		tmp = ((x - y) * 60.0) / -t;
	} else if (t_1 <= 1e+36) {
		tmp = 120.0 * a;
	} else {
		tmp = (-60.0 * y) / (z - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -2e+182:
		tmp = ((x - y) / z) * 60.0
	elif t_1 <= -2e+43:
		tmp = ((x - y) * 60.0) / -t
	elif t_1 <= 1e+36:
		tmp = 120.0 * a
	else:
		tmp = (-60.0 * y) / (z - t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -2e+182)
		tmp = Float64(Float64(Float64(x - y) / z) * 60.0);
	elseif (t_1 <= -2e+43)
		tmp = Float64(Float64(Float64(x - y) * 60.0) / Float64(-t));
	elseif (t_1 <= 1e+36)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(-60.0 * y) / Float64(z - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -2e+182)
		tmp = ((x - y) / z) * 60.0;
	elseif (t_1 <= -2e+43)
		tmp = ((x - y) * 60.0) / -t;
	elseif (t_1 <= 1e+36)
		tmp = 120.0 * a;
	else
		tmp = (-60.0 * y) / (z - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+182], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0), $MachinePrecision], If[LessEqual[t$95$1, -2e+43], N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / (-t)), $MachinePrecision], If[LessEqual[t$95$1, 1e+36], N[(120.0 * a), $MachinePrecision], N[(N[(-60.0 * y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.0000000000000001e182

   1. Initial program 97.1%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 94.2

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

   5. Applied rewrites 94.2%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 63.6

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

   8. Applied rewrites 63.6%

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

   if -2.0000000000000001e182 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.00000000000000003e43

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. 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 85.7

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

   5. Applied rewrites 85.7%

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

   6. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 59.3

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

   8. Applied rewrites 59.3%

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

   if -2.00000000000000003e43 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.00000000000000004e36

   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 70.1

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

   5. Applied rewrites 70.1%

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

   if 1.00000000000000004e36 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 85.0

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

   5. Applied rewrites 85.0%

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

   6. Taylor expanded in x around 0

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

      1. lower-*.f64 53.4

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

   8. Applied rewrites 53.4%

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

Alternative 4: 60.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+182}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{+43}:\\ \;\;\;\;\frac{x - y}{t} \cdot -60\\ \mathbf{elif}\;t\_1 \leq 10^{+36}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{-60 \cdot y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -2e+182)
     (* (/ (- x y) z) 60.0)
     (if (<= t_1 -2e+43)
       (* (/ (- x y) t) -60.0)
       (if (<= t_1 1e+36) (* 120.0 a) (/ (* -60.0 y) (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -2e+182) {
		tmp = ((x - y) / z) * 60.0;
	} else if (t_1 <= -2e+43) {
		tmp = ((x - y) / t) * -60.0;
	} else if (t_1 <= 1e+36) {
		tmp = 120.0 * a;
	} else {
		tmp = (-60.0 * y) / (z - t);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-2d+182)) then
        tmp = ((x - y) / z) * 60.0d0
    else if (t_1 <= (-2d+43)) then
        tmp = ((x - y) / t) * (-60.0d0)
    else if (t_1 <= 1d+36) then
        tmp = 120.0d0 * a
    else
        tmp = ((-60.0d0) * y) / (z - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -2e+182) {
		tmp = ((x - y) / z) * 60.0;
	} else if (t_1 <= -2e+43) {
		tmp = ((x - y) / t) * -60.0;
	} else if (t_1 <= 1e+36) {
		tmp = 120.0 * a;
	} else {
		tmp = (-60.0 * y) / (z - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -2e+182:
		tmp = ((x - y) / z) * 60.0
	elif t_1 <= -2e+43:
		tmp = ((x - y) / t) * -60.0
	elif t_1 <= 1e+36:
		tmp = 120.0 * a
	else:
		tmp = (-60.0 * y) / (z - t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -2e+182)
		tmp = Float64(Float64(Float64(x - y) / z) * 60.0);
	elseif (t_1 <= -2e+43)
		tmp = Float64(Float64(Float64(x - y) / t) * -60.0);
	elseif (t_1 <= 1e+36)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(-60.0 * y) / Float64(z - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -2e+182)
		tmp = ((x - y) / z) * 60.0;
	elseif (t_1 <= -2e+43)
		tmp = ((x - y) / t) * -60.0;
	elseif (t_1 <= 1e+36)
		tmp = 120.0 * a;
	else
		tmp = (-60.0 * y) / (z - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+182], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0), $MachinePrecision], If[LessEqual[t$95$1, -2e+43], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0), $MachinePrecision], If[LessEqual[t$95$1, 1e+36], N[(120.0 * a), $MachinePrecision], N[(N[(-60.0 * y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.0000000000000001e182

   1. Initial program 97.1%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 94.2

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

   5. Applied rewrites 94.2%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 63.6

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

   8. Applied rewrites 63.6%

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

   if -2.0000000000000001e182 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.00000000000000003e43

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. 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 85.7

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

   5. Applied rewrites 85.7%

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

   6. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift--.f64 59.2

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

   8. Applied rewrites 59.2%

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

   if -2.00000000000000003e43 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.00000000000000004e36

   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 70.1

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

   5. Applied rewrites 70.1%

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

   if 1.00000000000000004e36 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 85.0

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

   5. Applied rewrites 85.0%

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

   6. Taylor expanded in x around 0

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

      1. lower-*.f64 53.4

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

   8. Applied rewrites 53.4%

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

Alternative 5: 60.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+182}:\\ \;\;\;\;\frac{x - y}{z} \cdot 60\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{+43}:\\ \;\;\;\;\frac{x - y}{t} \cdot -60\\ \mathbf{elif}\;t\_1 \leq 10^{+36}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z - t} \cdot -60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -2e+182)
     (* (/ (- x y) z) 60.0)
     (if (<= t_1 -2e+43)
       (* (/ (- x y) t) -60.0)
       (if (<= t_1 1e+36) (* 120.0 a) (* (/ y (- z t)) -60.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -2e+182) {
		tmp = ((x - y) / z) * 60.0;
	} else if (t_1 <= -2e+43) {
		tmp = ((x - y) / t) * -60.0;
	} else if (t_1 <= 1e+36) {
		tmp = 120.0 * a;
	} else {
		tmp = (y / (z - t)) * -60.0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-2d+182)) then
        tmp = ((x - y) / z) * 60.0d0
    else if (t_1 <= (-2d+43)) then
        tmp = ((x - y) / t) * (-60.0d0)
    else if (t_1 <= 1d+36) then
        tmp = 120.0d0 * a
    else
        tmp = (y / (z - t)) * (-60.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -2e+182) {
		tmp = ((x - y) / z) * 60.0;
	} else if (t_1 <= -2e+43) {
		tmp = ((x - y) / t) * -60.0;
	} else if (t_1 <= 1e+36) {
		tmp = 120.0 * a;
	} else {
		tmp = (y / (z - t)) * -60.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -2e+182:
		tmp = ((x - y) / z) * 60.0
	elif t_1 <= -2e+43:
		tmp = ((x - y) / t) * -60.0
	elif t_1 <= 1e+36:
		tmp = 120.0 * a
	else:
		tmp = (y / (z - t)) * -60.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -2e+182)
		tmp = Float64(Float64(Float64(x - y) / z) * 60.0);
	elseif (t_1 <= -2e+43)
		tmp = Float64(Float64(Float64(x - y) / t) * -60.0);
	elseif (t_1 <= 1e+36)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(y / Float64(z - t)) * -60.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -2e+182)
		tmp = ((x - y) / z) * 60.0;
	elseif (t_1 <= -2e+43)
		tmp = ((x - y) / t) * -60.0;
	elseif (t_1 <= 1e+36)
		tmp = 120.0 * a;
	else
		tmp = (y / (z - t)) * -60.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+182], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * 60.0), $MachinePrecision], If[LessEqual[t$95$1, -2e+43], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0), $MachinePrecision], If[LessEqual[t$95$1, 1e+36], N[(120.0 * a), $MachinePrecision], N[(N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision] * -60.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.0000000000000001e182

   1. Initial program 97.1%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 94.2

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

   5. Applied rewrites 94.2%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 63.6

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

   8. Applied rewrites 63.6%

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

   if -2.0000000000000001e182 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.00000000000000003e43

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. 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 85.7

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

   5. Applied rewrites 85.7%

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

   6. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift--.f64 59.2

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

   8. Applied rewrites 59.2%

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

   if -2.00000000000000003e43 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.00000000000000004e36

   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 70.1

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

   5. Applied rewrites 70.1%

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

   if 1.00000000000000004e36 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.7%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      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 97.7

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

   4. Applied rewrites 97.7%

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

      1. lift-fma.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. associate-/l* N/A

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

      8. metadata-eval N/A

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

      9. associate-*r/ N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lift--.f64 N/A

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

      13. associate-*r/ N/A

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

      14. metadata-eval N/A

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

      15. lower-/.f64 N/A

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

      16. lift--.f64 N/A

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

      17. lift-*.f64 99.8

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

   6. Applied rewrites 99.8%

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

   7. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 53.3

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

   9. Applied rewrites 53.3%

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

Alternative 6: 53.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+157}:\\ \;\;\;\;\frac{y}{z} \cdot -60\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{+43}:\\ \;\;\;\;\frac{-60 \cdot x}{t}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+83}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot 60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -1e+157)
     (* (/ y z) -60.0)
     (if (<= t_1 -2e+43)
       (/ (* -60.0 x) t)
       (if (<= t_1 2e+83) (* 120.0 a) (* (/ y t) 60.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+157) {
		tmp = (y / z) * -60.0;
	} else if (t_1 <= -2e+43) {
		tmp = (-60.0 * x) / t;
	} else if (t_1 <= 2e+83) {
		tmp = 120.0 * a;
	} else {
		tmp = (y / t) * 60.0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-1d+157)) then
        tmp = (y / z) * (-60.0d0)
    else if (t_1 <= (-2d+43)) then
        tmp = ((-60.0d0) * x) / t
    else if (t_1 <= 2d+83) then
        tmp = 120.0d0 * a
    else
        tmp = (y / t) * 60.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+157) {
		tmp = (y / z) * -60.0;
	} else if (t_1 <= -2e+43) {
		tmp = (-60.0 * x) / t;
	} else if (t_1 <= 2e+83) {
		tmp = 120.0 * a;
	} else {
		tmp = (y / t) * 60.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -1e+157:
		tmp = (y / z) * -60.0
	elif t_1 <= -2e+43:
		tmp = (-60.0 * x) / t
	elif t_1 <= 2e+83:
		tmp = 120.0 * a
	else:
		tmp = (y / t) * 60.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -1e+157)
		tmp = Float64(Float64(y / z) * -60.0);
	elseif (t_1 <= -2e+43)
		tmp = Float64(Float64(-60.0 * x) / t);
	elseif (t_1 <= 2e+83)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(y / t) * 60.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -1e+157)
		tmp = (y / z) * -60.0;
	elseif (t_1 <= -2e+43)
		tmp = (-60.0 * x) / t;
	elseif (t_1 <= 2e+83)
		tmp = 120.0 * a;
	else
		tmp = (y / t) * 60.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+157], N[(N[(y / z), $MachinePrecision] * -60.0), $MachinePrecision], If[LessEqual[t$95$1, -2e+43], N[(N[(-60.0 * x), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t$95$1, 2e+83], N[(120.0 * a), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * 60.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -9.99999999999999983e156

   1. Initial program 97.2%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 97.2

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

   4. Applied rewrites 97.2%

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

      1. lift-fma.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. associate-/l* N/A

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

      8. metadata-eval N/A

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

      9. associate-*r/ N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lift--.f64 N/A

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

      13. associate-*r/ N/A

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

      14. metadata-eval N/A

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

      15. lower-/.f64 N/A

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

      16. lift--.f64 N/A

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

      17. lift-*.f64 99.6

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

   6. Applied rewrites 99.6%

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

   7. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 55.0

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

   9. Applied rewrites 55.0%

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

   10. Taylor expanded in z around inf

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

   12. Applied rewrites 39.2%

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

   if -9.99999999999999983e156 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.00000000000000003e43

   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 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 69.7

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

   5. Applied rewrites 69.7%

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

   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 51.7

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

   8. Applied rewrites 51.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 51.9

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

   10. Applied rewrites 51.9%

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

   if -2.00000000000000003e43 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2.00000000000000006e83

   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 67.1

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

   5. Applied rewrites 67.1%

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

   if 2.00000000000000006e83 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.0%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 61.8

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

   5. Applied rewrites 61.8%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 38.8

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

   8. Applied rewrites 38.8%

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

Alternative 7: 83.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -3 \cdot 10^{+91} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+44}\right):\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z - t}, 60, 120 \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (or (<= t_1 -3e+91) (not (<= t_1 5e+44)))
     (* (- x y) (/ 60.0 (- z t)))
     (fma (/ x (- z t)) 60.0 (* 120.0 a)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if ((t_1 <= -3e+91) || !(t_1 <= 5e+44)) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = fma((x / (z - t)), 60.0, (120.0 * a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if ((t_1 <= -3e+91) || !(t_1 <= 5e+44))
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	else
		tmp = fma(Float64(x / Float64(z - t)), 60.0, Float64(120.0 * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -3e+91], N[Not[LessEqual[t$95$1, 5e+44]], $MachinePrecision]], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -3.00000000000000006e91 or 4.9999999999999996e44 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 88.0

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

   5. Applied rewrites 88.0%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. lower-*.f64 N/A

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

      9. lift--.f64 N/A

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

      10. associate-*r/ N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 88.9

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

   7. Applied rewrites 88.9%

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

   if -3.00000000000000006e91 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.9999999999999996e44

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-*.f64 84.2

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

   5. Applied rewrites 84.2%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -3 \cdot 10^{+91} \lor \neg \left(\frac{60 \cdot \left(x - y\right)}{z - t} \leq 5 \cdot 10^{+44}\right):\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z - t}, 60, 120 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-50} \lor \neg \left(t\_1 \leq 10^{+36}\right):\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (or (<= t_1 -2e-50) (not (<= t_1 1e+36)))
     (* (- x y) (/ 60.0 (- z t)))
     (* 120.0 a))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if ((t_1 <= -2e-50) || !(t_1 <= 1e+36)) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if ((t_1 <= (-2d-50)) .or. (.not. (t_1 <= 1d+36))) then
        tmp = (x - y) * (60.0d0 / (z - t))
    else
        tmp = 120.0d0 * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if ((t_1 <= -2e-50) || !(t_1 <= 1e+36)) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if (t_1 <= -2e-50) or not (t_1 <= 1e+36):
		tmp = (x - y) * (60.0 / (z - t))
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if ((t_1 <= -2e-50) || !(t_1 <= 1e+36))
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if ((t_1 <= -2e-50) || ~((t_1 <= 1e+36)))
		tmp = (x - y) * (60.0 / (z - t));
	else
		tmp = 120.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-50], N[Not[LessEqual[t$95$1, 1e+36]], $MachinePrecision]], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.00000000000000002e-50 or 1.00000000000000004e36 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 98.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. 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 82.0

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

   5. Applied rewrites 82.0%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. lower-*.f64 N/A

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

      9. lift--.f64 N/A

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

      10. associate-*r/ N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 82.6

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

   7. Applied rewrites 82.6%

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

   if -2.00000000000000002e-50 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.00000000000000004e36

   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 79.4

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

   5. Applied rewrites 79.4%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -2 \cdot 10^{-50} \lor \neg \left(\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+36}\right):\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+43} \lor \neg \left(t\_1 \leq 10^{+36}\right):\\ \;\;\;\;\frac{x - y}{t} \cdot -60\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (or (<= t_1 -2e+43) (not (<= t_1 1e+36)))
     (* (/ (- x y) t) -60.0)
     (* 120.0 a))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if ((t_1 <= -2e+43) || !(t_1 <= 1e+36)) {
		tmp = ((x - y) / t) * -60.0;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if ((t_1 <= (-2d+43)) .or. (.not. (t_1 <= 1d+36))) then
        tmp = ((x - y) / t) * (-60.0d0)
    else
        tmp = 120.0d0 * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if ((t_1 <= -2e+43) || !(t_1 <= 1e+36)) {
		tmp = ((x - y) / t) * -60.0;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if (t_1 <= -2e+43) or not (t_1 <= 1e+36):
		tmp = ((x - y) / t) * -60.0
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if ((t_1 <= -2e+43) || !(t_1 <= 1e+36))
		tmp = Float64(Float64(Float64(x - y) / t) * -60.0);
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if ((t_1 <= -2e+43) || ~((t_1 <= 1e+36)))
		tmp = ((x - y) / t) * -60.0;
	else
		tmp = 120.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+43], N[Not[LessEqual[t$95$1, 1e+36]], $MachinePrecision]], N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * -60.0), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.00000000000000003e43 or 1.00000000000000004e36 < (/.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 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 88.2

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

   5. Applied rewrites 88.2%

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

   6. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift--.f64 50.8

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

   8. Applied rewrites 50.8%

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

   if -2.00000000000000003e43 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.00000000000000004e36

   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 70.1

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

   5. Applied rewrites 70.1%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -2 \cdot 10^{+43} \lor \neg \left(\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+36}\right):\\ \;\;\;\;\frac{x - y}{t} \cdot -60\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+43}:\\ \;\;\;\;\frac{-60 \cdot x}{t}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+83}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot 60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -2e+43)
     (/ (* -60.0 x) t)
     (if (<= t_1 2e+83) (* 120.0 a) (* (/ y t) 60.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -2e+43) {
		tmp = (-60.0 * x) / t;
	} else if (t_1 <= 2e+83) {
		tmp = 120.0 * a;
	} else {
		tmp = (y / t) * 60.0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-2d+43)) then
        tmp = ((-60.0d0) * x) / t
    else if (t_1 <= 2d+83) then
        tmp = 120.0d0 * a
    else
        tmp = (y / t) * 60.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -2e+43) {
		tmp = (-60.0 * x) / t;
	} else if (t_1 <= 2e+83) {
		tmp = 120.0 * a;
	} else {
		tmp = (y / t) * 60.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -2e+43:
		tmp = (-60.0 * x) / t
	elif t_1 <= 2e+83:
		tmp = 120.0 * a
	else:
		tmp = (y / t) * 60.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -2e+43)
		tmp = Float64(Float64(-60.0 * x) / t);
	elseif (t_1 <= 2e+83)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(y / t) * 60.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -2e+43)
		tmp = (-60.0 * x) / t;
	elseif (t_1 <= 2e+83)
		tmp = 120.0 * a;
	else
		tmp = (y / t) * 60.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+43], N[(N[(-60.0 * x), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t$95$1, 2e+83], N[(120.0 * a), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * 60.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.00000000000000003e43

   1. Initial program 98.1%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 58.2

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

   5. Applied rewrites 58.2%

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

   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 34.3

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

   8. Applied rewrites 34.3%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 34.3

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

   10. Applied rewrites 34.3%

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

   if -2.00000000000000003e43 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2.00000000000000006e83

   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 67.1

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

   5. Applied rewrites 67.1%

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

   if 2.00000000000000006e83 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.0%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 61.8

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

   5. Applied rewrites 61.8%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 38.8

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

   8. Applied rewrites 38.8%

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

Alternative 11: 53.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+43}:\\ \;\;\;\;\frac{x}{t} \cdot -60\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+83}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot 60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -2e+43)
     (* (/ x t) -60.0)
     (if (<= t_1 2e+83) (* 120.0 a) (* (/ y t) 60.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -2e+43) {
		tmp = (x / t) * -60.0;
	} else if (t_1 <= 2e+83) {
		tmp = 120.0 * a;
	} else {
		tmp = (y / t) * 60.0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-2d+43)) then
        tmp = (x / t) * (-60.0d0)
    else if (t_1 <= 2d+83) then
        tmp = 120.0d0 * a
    else
        tmp = (y / t) * 60.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -2e+43) {
		tmp = (x / t) * -60.0;
	} else if (t_1 <= 2e+83) {
		tmp = 120.0 * a;
	} else {
		tmp = (y / t) * 60.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -2e+43:
		tmp = (x / t) * -60.0
	elif t_1 <= 2e+83:
		tmp = 120.0 * a
	else:
		tmp = (y / t) * 60.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -2e+43)
		tmp = Float64(Float64(x / t) * -60.0);
	elseif (t_1 <= 2e+83)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(y / t) * 60.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -2e+43)
		tmp = (x / t) * -60.0;
	elseif (t_1 <= 2e+83)
		tmp = 120.0 * a;
	else
		tmp = (y / t) * 60.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+43], N[(N[(x / t), $MachinePrecision] * -60.0), $MachinePrecision], If[LessEqual[t$95$1, 2e+83], N[(120.0 * a), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * 60.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.00000000000000003e43

   1. Initial program 98.1%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 58.2

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

   5. Applied rewrites 58.2%

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

   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 34.3

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

   8. Applied rewrites 34.3%

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

   if -2.00000000000000003e43 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2.00000000000000006e83

   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 67.1

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

   5. Applied rewrites 67.1%

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

   if 2.00000000000000006e83 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.0%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 61.8

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

   5. Applied rewrites 61.8%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 38.8

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

   8. Applied rewrites 38.8%

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

Alternative 12: 52.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -2 \cdot 10^{+43}:\\ \;\;\;\;\frac{x}{t} \cdot -60\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (/ (* 60.0 (- x y)) (- z t)) -2e+43) (* (/ x t) -60.0) (* 120.0 a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((60.0 * (x - y)) / (z - t)) <= -2e+43) {
		tmp = (x / t) * -60.0;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((60.0d0 * (x - y)) / (z - t)) <= (-2d+43)) then
        tmp = (x / t) * (-60.0d0)
    else
        tmp = 120.0d0 * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((60.0 * (x - y)) / (z - t)) <= -2e+43) {
		tmp = (x / t) * -60.0;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((60.0 * (x - y)) / (z - t)) <= -2e+43:
		tmp = (x / t) * -60.0
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t)) <= -2e+43)
		tmp = Float64(Float64(x / t) * -60.0);
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((60.0 * (x - y)) / (z - t)) <= -2e+43)
		tmp = (x / t) * -60.0;
	else
		tmp = 120.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.00000000000000003e43

   1. Initial program 98.1%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 58.2

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

   5. Applied rewrites 58.2%

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

   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 34.3

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

   8. Applied rewrites 34.3%

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

   if -2.00000000000000003e43 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   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 57.0

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

   5. Applied rewrites 57.0%

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

Alternative 13: 88.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+79} \lor \neg \left(y \leq 3.7 \cdot 10^{-60}\right):\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{-60 \cdot y}{z - t}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z - t}, 60, 120 \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.6e+79) (not (<= y 3.7e-60)))
   (fma a 120.0 (/ (* -60.0 y) (- z t)))
   (fma (/ x (- z t)) 60.0 (* 120.0 a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.6e+79) || !(y <= 3.7e-60)) {
		tmp = fma(a, 120.0, ((-60.0 * y) / (z - t)));
	} else {
		tmp = fma((x / (z - t)), 60.0, (120.0 * a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.6e+79) || !(y <= 3.7e-60))
		tmp = fma(a, 120.0, Float64(Float64(-60.0 * y) / Float64(z - t)));
	else
		tmp = fma(Float64(x / Float64(z - t)), 60.0, Float64(120.0 * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.6e+79], N[Not[LessEqual[y, 3.7e-60]], $MachinePrecision]], N[(a * 120.0 + N[(N[(-60.0 * y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.60000000000000015e79 or 3.70000000000000025e-60 < y

   1. Initial program 99.1%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 99.1

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

   4. Applied rewrites 99.1%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 85.3

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

   7. Applied rewrites 85.3%

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

   if -2.60000000000000015e79 < y < 3.70000000000000025e-60

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-*.f64 96.8

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

   5. Applied rewrites 96.8%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+79} \lor \neg \left(y \leq 3.7 \cdot 10^{-60}\right):\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{-60 \cdot y}{z - t}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z - t}, 60, 120 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 88.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+79} \lor \neg \left(y \leq 3.7 \cdot 10^{-60}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z - t}, -60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z - t}, 60, 120 \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.6e+79) (not (<= y 3.7e-60)))
   (fma (/ y (- z t)) -60.0 (* 120.0 a))
   (fma (/ x (- z t)) 60.0 (* 120.0 a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.6e+79) || !(y <= 3.7e-60)) {
		tmp = fma((y / (z - t)), -60.0, (120.0 * a));
	} else {
		tmp = fma((x / (z - t)), 60.0, (120.0 * a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.6e+79) || !(y <= 3.7e-60))
		tmp = fma(Float64(y / Float64(z - t)), -60.0, Float64(120.0 * a));
	else
		tmp = fma(Float64(x / Float64(z - t)), 60.0, Float64(120.0 * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.6e+79], N[Not[LessEqual[y, 3.7e-60]], $MachinePrecision]], N[(N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.60000000000000015e79 or 3.70000000000000025e-60 < y

   1. Initial program 99.1%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-*.f64 85.3

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

   5. Applied rewrites 85.3%

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

   if -2.60000000000000015e79 < y < 3.70000000000000025e-60

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-*.f64 96.8

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

   5. Applied rewrites 96.8%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+79} \lor \neg \left(y \leq 3.7 \cdot 10^{-60}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z - t}, -60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z - t}, 60, 120 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 60.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+105} \lor \neg \left(x \leq 3.45 \cdot 10^{+81}\right):\\ \;\;\;\;\frac{x}{z - t} \cdot 60\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y}{t} \cdot 60\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.85e+105) (not (<= x 3.45e+81)))
   (* (/ x (- z t)) 60.0)
   (fma a 120.0 (* (/ y t) 60.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.85e+105) || !(x <= 3.45e+81)) {
		tmp = (x / (z - t)) * 60.0;
	} else {
		tmp = fma(a, 120.0, ((y / t) * 60.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.85e+105) || !(x <= 3.45e+81))
		tmp = Float64(Float64(x / Float64(z - t)) * 60.0);
	else
		tmp = fma(a, 120.0, Float64(Float64(y / t) * 60.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.85e+105], N[Not[LessEqual[x, 3.45e+81]], $MachinePrecision]], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $MachinePrecision], N[(a * 120.0 + N[(N[(y / t), $MachinePrecision] * 60.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.84999999999999992e105 or 3.4499999999999998e81 < x

   1. Initial program 97.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 58.2

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

   5. Applied rewrites 58.2%

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

   if -1.84999999999999992e105 < x < 3.4499999999999998e81

   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 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 66.2

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

   5. Applied rewrites 66.2%

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

   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 67.8

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

   8. Applied rewrites 67.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lift-/.f64 67.8

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

   10. Applied rewrites 67.8%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+105} \lor \neg \left(x \leq 3.45 \cdot 10^{+81}\right):\\ \;\;\;\;\frac{x}{z - t} \cdot 60\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y}{t} \cdot 60\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 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 99.0%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
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 99.0

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

4. Applied rewrites 99.0%

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

Alternative 17: 51.5% 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 99.0%

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

3. Taylor expanded in z around inf

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

   1. lower-*.f64 46.7

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

5. Applied rewrites 46.7%

   \[\leadsto \color{blue}{120 \cdot a} \]
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 2025043 
(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)))