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

Percentage Accurate: 99.4% → 99.4%

Time: 5.5s

Alternatives: 20

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% 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: 99.4% 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 99.8%

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

   1. lift-+.f64 N/A

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

   2. lift--.f64 N/A

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

   3. lift-/.f64 N/A

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

   4. lift--.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. +-commutative N/A

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

   7. lift-*.f64 N/A

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

   8. lower-fma.f64 N/A

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

   9. lower-/.f64 N/A

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

   10. *-commutative N/A

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

   11. lower-*.f64 N/A

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

   12. lift--.f64 N/A

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

   13. lift--.f64 99.8

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

4. Applied rewrites 99.8%

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

Alternative 2: 55.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot 60\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+284}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+227}:\\ \;\;\;\;\frac{y}{t} \cdot 60\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+149}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ x z) 60.0)) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -1e+284)
     t_1
     (if (<= t_2 -5e+227)
       (* (/ y t) 60.0)
       (if (<= t_2 2e+149) (* 120.0 a) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x / z) * 60.0;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -1e+284) {
		tmp = t_1;
	} else if (t_2 <= -5e+227) {
		tmp = (y / t) * 60.0;
	} else if (t_2 <= 2e+149) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / z) * 60.0d0
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-1d+284)) then
        tmp = t_1
    else if (t_2 <= (-5d+227)) then
        tmp = (y / t) * 60.0d0
    else if (t_2 <= 2d+149) then
        tmp = 120.0d0 * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x / z) * 60.0;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -1e+284) {
		tmp = t_1;
	} else if (t_2 <= -5e+227) {
		tmp = (y / t) * 60.0;
	} else if (t_2 <= 2e+149) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x / z) * 60.0
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -1e+284:
		tmp = t_1
	elif t_2 <= -5e+227:
		tmp = (y / t) * 60.0
	elif t_2 <= 2e+149:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x / z) * 60.0)
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -1e+284)
		tmp = t_1;
	elseif (t_2 <= -5e+227)
		tmp = Float64(Float64(y / t) * 60.0);
	elseif (t_2 <= 2e+149)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x / z) * 60.0;
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -1e+284)
		tmp = t_1;
	elseif (t_2 <= -5e+227)
		tmp = (y / t) * 60.0;
	elseif (t_2 <= 2e+149)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] * 60.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+284], t$95$1, If[LessEqual[t$95$2, -5e+227], N[(N[(y / t), $MachinePrecision] * 60.0), $MachinePrecision], If[LessEqual[t$95$2, 2e+149], N[(120.0 * a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.00000000000000008e284 or 2.0000000000000001e149 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 58.8

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

   5. Applied rewrites 58.8%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 42.5%

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

   if -1.00000000000000008e284 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -4.9999999999999996e227

   1. Initial program 99.5%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 80.0

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

   5. Applied rewrites 80.0%

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

   6. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 60.4

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

   8. Applied rewrites 60.4%

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

   if -4.9999999999999996e227 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2.0000000000000001e149

   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 61.9

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

   5. Applied rewrites 61.9%

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

Alternative 3: 61.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+134}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+110}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -1e+134)
     (* (- x y) (/ -60.0 t))
     (if (<= t_1 2e+110) (* 120.0 a) (* (- x y) (/ 60.0 z))))))

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+134) {
		tmp = (x - y) * (-60.0 / t);
	} else if (t_1 <= 2e+110) {
		tmp = 120.0 * a;
	} else {
		tmp = (x - y) * (60.0 / z);
	}
	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+134)) then
        tmp = (x - y) * ((-60.0d0) / t)
    else if (t_1 <= 2d+110) then
        tmp = 120.0d0 * a
    else
        tmp = (x - y) * (60.0d0 / z)
    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+134) {
		tmp = (x - y) * (-60.0 / t);
	} else if (t_1 <= 2e+110) {
		tmp = 120.0 * a;
	} else {
		tmp = (x - y) * (60.0 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -1e+134:
		tmp = (x - y) * (-60.0 / t)
	elif t_1 <= 2e+110:
		tmp = 120.0 * a
	else:
		tmp = (x - y) * (60.0 / z)
	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+134)
		tmp = Float64(Float64(x - y) * Float64(-60.0 / t));
	elseif (t_1 <= 2e+110)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(x - y) * Float64(60.0 / z));
	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+134)
		tmp = (x - y) * (-60.0 / t);
	elseif (t_1 <= 2e+110)
		tmp = 120.0 * a;
	else
		tmp = (x - y) * (60.0 / z);
	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+134], N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+110], N[(120.0 * a), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(60.0 / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -9.99999999999999921e133

   1. Initial program 99.6%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift--.f64 99.6

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

   4. Applied rewrites 99.6%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative 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 83.2

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

   7. Applied rewrites 83.2%

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

   8. Taylor expanded in z around 0

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

      1. lower-/.f64 49.6

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

   10. Applied rewrites 49.6%

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

   if -9.99999999999999921e133 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2e110

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 68.5

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

   5. Applied rewrites 68.5%

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

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

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing
   3. 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 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative 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 88.1

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

   7. Applied rewrites 88.1%

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

   8. Taylor expanded in z around inf

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

      1. lower-/.f64 54.5

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

   10. Applied rewrites 54.5%

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

Alternative 4: 55.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+227} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+149}\right):\\ \;\;\;\;\frac{y}{t} \cdot 60\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (or (<= t_1 -5e+227) (not (<= t_1 2e+149)))
     (* (/ 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 <= -5e+227) || !(t_1 <= 2e+149)) {
		tmp = (y / t) * 60.0;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if ((t_1 <= (-5d+227)) .or. (.not. (t_1 <= 2d+149))) then
        tmp = (y / t) * 60.0d0
    else
        tmp = 120.0d0 * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if ((t_1 <= -5e+227) || !(t_1 <= 2e+149)) {
		tmp = (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 <= -5e+227) or not (t_1 <= 2e+149):
		tmp = (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 <= -5e+227) || !(t_1 <= 2e+149))
		tmp = Float64(Float64(y / t) * 60.0);
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if ((t_1 <= -5e+227) || ~((t_1 <= 2e+149)))
		tmp = (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, -5e+227], N[Not[LessEqual[t$95$1, 2e+149]], $MachinePrecision]], N[(N[(y / 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)) < -4.9999999999999996e227 or 2.0000000000000001e149 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   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 inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 45.5

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

   5. Applied rewrites 45.5%

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

   6. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 36.0

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

   8. Applied rewrites 36.0%

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

   if -4.9999999999999996e227 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2.0000000000000001e149

   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 61.9

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

   5. Applied rewrites 61.9%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{+227} \lor \neg \left(\frac{60 \cdot \left(x - y\right)}{z - t} \leq 2 \cdot 10^{+149}\right):\\ \;\;\;\;\frac{y}{t} \cdot 60\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+151} \lor \neg \left(y \leq 4.8 \cdot 10^{+113}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z - t}, -60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z - t}, 60, 120 \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -4.1e+151) (not (<= y 4.8e+113)))
   (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 <= -4.1e+151) || !(y <= 4.8e+113)) {
		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 <= -4.1e+151) || !(y <= 4.8e+113))
		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, -4.1e+151], N[Not[LessEqual[y, 4.8e+113]], $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 < -4.0999999999999998e151 or 4.79999999999999966e113 < y

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 91.5

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

   5. Applied rewrites 91.5%

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

   if -4.0999999999999998e151 < y < 4.79999999999999966e113

   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 91.5

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

   5. Applied rewrites 91.5%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+151} \lor \neg \left(y \leq 4.8 \cdot 10^{+113}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z - t}, -60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z - t}, 60, 120 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+20} \lor \neg \left(a \leq 1.15 \cdot 10^{-22}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z - t}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.2e+20) (not (<= a 1.15e-22)))
   (fma (/ x (- z t)) 60.0 (* 120.0 a))
   (/ (* (- x y) 60.0) (- z t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.2e+20) || !(a <= 1.15e-22)) {
		tmp = fma((x / (z - t)), 60.0, (120.0 * a));
	} else {
		tmp = ((x - y) * 60.0) / (z - t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.2e+20) || !(a <= 1.15e-22))
		tmp = fma(Float64(x / Float64(z - t)), 60.0, Float64(120.0 * a));
	else
		tmp = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.2e+20], N[Not[LessEqual[a, 1.15e-22]], $MachinePrecision]], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.2e20 or 1.1499999999999999e-22 < a

   1. Initial program 99.9%

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

   3. Taylor expanded in 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 92.5

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

   5. Applied rewrites 92.5%

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

   if -4.2e20 < a < 1.1499999999999999e-22

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 81.1

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

   5. Applied rewrites 81.1%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+20} \lor \neg \left(a \leq 1.15 \cdot 10^{-22}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z - t}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.16 \cdot 10^{-77}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-305}:\\ \;\;\;\;\frac{x}{z - t} \cdot 60\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-22}:\\ \;\;\;\;\frac{y}{z - t} \cdot -60\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.16e-77)
   (* 120.0 a)
   (if (<= a -1.95e-305)
     (* (/ x (- z t)) 60.0)
     (if (<= a 1.15e-22) (* (/ y (- z t)) -60.0) (* 120.0 a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.16e-77) {
		tmp = 120.0 * a;
	} else if (a <= -1.95e-305) {
		tmp = (x / (z - t)) * 60.0;
	} else if (a <= 1.15e-22) {
		tmp = (y / (z - t)) * -60.0;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.16d-77)) then
        tmp = 120.0d0 * a
    else if (a <= (-1.95d-305)) then
        tmp = (x / (z - t)) * 60.0d0
    else if (a <= 1.15d-22) then
        tmp = (y / (z - t)) * (-60.0d0)
    else
        tmp = 120.0d0 * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.16e-77) {
		tmp = 120.0 * a;
	} else if (a <= -1.95e-305) {
		tmp = (x / (z - t)) * 60.0;
	} else if (a <= 1.15e-22) {
		tmp = (y / (z - t)) * -60.0;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.16e-77:
		tmp = 120.0 * a
	elif a <= -1.95e-305:
		tmp = (x / (z - t)) * 60.0
	elif a <= 1.15e-22:
		tmp = (y / (z - t)) * -60.0
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.16e-77)
		tmp = Float64(120.0 * a);
	elseif (a <= -1.95e-305)
		tmp = Float64(Float64(x / Float64(z - t)) * 60.0);
	elseif (a <= 1.15e-22)
		tmp = Float64(Float64(y / Float64(z - t)) * -60.0);
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.16e-77)
		tmp = 120.0 * a;
	elseif (a <= -1.95e-305)
		tmp = (x / (z - t)) * 60.0;
	elseif (a <= 1.15e-22)
		tmp = (y / (z - t)) * -60.0;
	else
		tmp = 120.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.16e-77], N[(120.0 * a), $MachinePrecision], If[LessEqual[a, -1.95e-305], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $MachinePrecision], If[LessEqual[a, 1.15e-22], N[(N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision] * -60.0), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.16e-77 or 1.1499999999999999e-22 < a

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 75.3

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

   5. Applied rewrites 75.3%

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

   if -1.16e-77 < a < -1.95000000000000013e-305

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 58.5

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

   5. Applied rewrites 58.5%

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

   if -1.95000000000000013e-305 < a < 1.1499999999999999e-22

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 55.8

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

   5. Applied rewrites 55.8%

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

Alternative 8: 58.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.16 \cdot 10^{-77}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{-266}:\\ \;\;\;\;\frac{x}{z - t} \cdot 60\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{-98}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.16e-77)
   (* 120.0 a)
   (if (<= a 1.42e-266)
     (* (/ x (- z t)) 60.0)
     (if (<= a 2.55e-98) (* (- x y) (/ 60.0 z)) (* 120.0 a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.16e-77) {
		tmp = 120.0 * a;
	} else if (a <= 1.42e-266) {
		tmp = (x / (z - t)) * 60.0;
	} else if (a <= 2.55e-98) {
		tmp = (x - y) * (60.0 / z);
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.16d-77)) then
        tmp = 120.0d0 * a
    else if (a <= 1.42d-266) then
        tmp = (x / (z - t)) * 60.0d0
    else if (a <= 2.55d-98) then
        tmp = (x - y) * (60.0d0 / z)
    else
        tmp = 120.0d0 * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.16e-77) {
		tmp = 120.0 * a;
	} else if (a <= 1.42e-266) {
		tmp = (x / (z - t)) * 60.0;
	} else if (a <= 2.55e-98) {
		tmp = (x - y) * (60.0 / z);
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.16e-77:
		tmp = 120.0 * a
	elif a <= 1.42e-266:
		tmp = (x / (z - t)) * 60.0
	elif a <= 2.55e-98:
		tmp = (x - y) * (60.0 / z)
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.16e-77)
		tmp = Float64(120.0 * a);
	elseif (a <= 1.42e-266)
		tmp = Float64(Float64(x / Float64(z - t)) * 60.0);
	elseif (a <= 2.55e-98)
		tmp = Float64(Float64(x - y) * Float64(60.0 / z));
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.16e-77)
		tmp = 120.0 * a;
	elseif (a <= 1.42e-266)
		tmp = (x / (z - t)) * 60.0;
	elseif (a <= 2.55e-98)
		tmp = (x - y) * (60.0 / z);
	else
		tmp = 120.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.16e-77], N[(120.0 * a), $MachinePrecision], If[LessEqual[a, 1.42e-266], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $MachinePrecision], If[LessEqual[a, 2.55e-98], N[(N[(x - y), $MachinePrecision] * N[(60.0 / z), $MachinePrecision]), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.16e-77 or 2.55000000000000011e-98 < a

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 71.0

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

   5. Applied rewrites 71.0%

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

   if -1.16e-77 < a < 1.42000000000000001e-266

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 53.4

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

   5. Applied rewrites 53.4%

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

   if 1.42000000000000001e-266 < a < 2.55000000000000011e-98

   1. Initial program 99.7%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      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 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative 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 84.9

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

   7. Applied rewrites 84.9%

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

   8. Taylor expanded in z around inf

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

      1. lower-/.f64 57.4

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

   10. Applied rewrites 57.4%

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

Alternative 9: 88.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z - t}\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{+151}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, t\_1 \cdot -60\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+113}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x \cdot 60}{z - t}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, -60, 120 \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (- z t))))
   (if (<= y -4.1e+151)
     (fma a 120.0 (* t_1 -60.0))
     (if (<= y 4.8e+113)
       (fma a 120.0 (/ (* x 60.0) (- z t)))
       (fma t_1 -60.0 (* 120.0 a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (z - t);
	double tmp;
	if (y <= -4.1e+151) {
		tmp = fma(a, 120.0, (t_1 * -60.0));
	} else if (y <= 4.8e+113) {
		tmp = fma(a, 120.0, ((x * 60.0) / (z - t)));
	} else {
		tmp = fma(t_1, -60.0, (120.0 * a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(z - t))
	tmp = 0.0
	if (y <= -4.1e+151)
		tmp = fma(a, 120.0, Float64(t_1 * -60.0));
	elseif (y <= 4.8e+113)
		tmp = fma(a, 120.0, Float64(Float64(x * 60.0) / Float64(z - t)));
	else
		tmp = fma(t_1, -60.0, Float64(120.0 * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.1e+151], N[(a * 120.0 + N[(t$95$1 * -60.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e+113], N[(a * 120.0 + N[(N[(x * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.0999999999999998e151

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      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 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 89.0

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

   7. Applied rewrites 89.0%

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

   if -4.0999999999999998e151 < y < 4.79999999999999966e113

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 91.5%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 91.5

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 91.5

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

   7. Applied rewrites 91.5%

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

   if 4.79999999999999966e113 < y

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 93.5

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

   5. Applied rewrites 93.5%

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

Alternative 10: 88.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z - t}\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{+151}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, t\_1 \cdot -60\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+113}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z - t}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, -60, 120 \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (- z t))))
   (if (<= y -4.1e+151)
     (fma a 120.0 (* t_1 -60.0))
     (if (<= y 4.8e+113)
       (fma (/ x (- z t)) 60.0 (* 120.0 a))
       (fma t_1 -60.0 (* 120.0 a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (z - t);
	double tmp;
	if (y <= -4.1e+151) {
		tmp = fma(a, 120.0, (t_1 * -60.0));
	} else if (y <= 4.8e+113) {
		tmp = fma((x / (z - t)), 60.0, (120.0 * a));
	} else {
		tmp = fma(t_1, -60.0, (120.0 * a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(z - t))
	tmp = 0.0
	if (y <= -4.1e+151)
		tmp = fma(a, 120.0, Float64(t_1 * -60.0));
	elseif (y <= 4.8e+113)
		tmp = fma(Float64(x / Float64(z - t)), 60.0, Float64(120.0 * a));
	else
		tmp = fma(t_1, -60.0, Float64(120.0 * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.1e+151], N[(a * 120.0 + N[(t$95$1 * -60.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e+113], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.0999999999999998e151

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      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 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 89.0

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

   7. Applied rewrites 89.0%

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

   if -4.0999999999999998e151 < y < 4.79999999999999966e113

   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 91.5

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

   5. Applied rewrites 91.5%

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

   if 4.79999999999999966e113 < y

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 93.5

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

   5. Applied rewrites 93.5%

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

Alternative 11: 74.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.95 \cdot 10^{+29} \lor \neg \left(a \leq 2.5 \cdot 10^{-20}\right):\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.95e+29) (not (<= a 2.5e-20)))
   (* 120.0 a)
   (/ (* (- x y) 60.0) (- z t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.95e+29) || !(a <= 2.5e-20)) {
		tmp = 120.0 * a;
	} else {
		tmp = ((x - y) * 60.0) / (z - t);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.95d+29)) .or. (.not. (a <= 2.5d-20))) then
        tmp = 120.0d0 * a
    else
        tmp = ((x - y) * 60.0d0) / (z - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.95e+29) || !(a <= 2.5e-20)) {
		tmp = 120.0 * a;
	} else {
		tmp = ((x - y) * 60.0) / (z - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.95e+29) or not (a <= 2.5e-20):
		tmp = 120.0 * a
	else:
		tmp = ((x - y) * 60.0) / (z - t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.95e+29) || !(a <= 2.5e-20))
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.95e+29) || ~((a <= 2.5e-20)))
		tmp = 120.0 * a;
	else
		tmp = ((x - y) * 60.0) / (z - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.95e+29], N[Not[LessEqual[a, 2.5e-20]], $MachinePrecision]], N[(120.0 * a), $MachinePrecision], N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.9499999999999999e29 or 2.4999999999999999e-20 < a

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 79.9

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

   5. Applied rewrites 79.9%

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

   if -2.9499999999999999e29 < a < 2.4999999999999999e-20

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 80.6

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

   5. Applied rewrites 80.6%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.95 \cdot 10^{+29} \lor \neg \left(a \leq 2.5 \cdot 10^{-20}\right):\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 74.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+32} \lor \neg \left(a \leq 2.5 \cdot 10^{-20}\right):\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.8e+32) (not (<= a 2.5e-20)))
   (* 120.0 a)
   (* (- x y) (/ 60.0 (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.8e+32) || !(a <= 2.5e-20)) {
		tmp = 120.0 * a;
	} else {
		tmp = (x - y) * (60.0 / (z - t));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.8d+32)) .or. (.not. (a <= 2.5d-20))) then
        tmp = 120.0d0 * a
    else
        tmp = (x - y) * (60.0d0 / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.8e+32) || !(a <= 2.5e-20)) {
		tmp = 120.0 * a;
	} else {
		tmp = (x - y) * (60.0 / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.8e+32) or not (a <= 2.5e-20):
		tmp = 120.0 * a
	else:
		tmp = (x - y) * (60.0 / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.8e+32) || !(a <= 2.5e-20))
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.8e+32) || ~((a <= 2.5e-20)))
		tmp = 120.0 * a;
	else
		tmp = (x - y) * (60.0 / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.8e+32], N[Not[LessEqual[a, 2.5e-20]], $MachinePrecision]], N[(120.0 * a), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.8e32 or 2.4999999999999999e-20 < a

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 79.9

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

   5. Applied rewrites 79.9%

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

   if -2.8e32 < a < 2.4999999999999999e-20

   1. Initial program 99.7%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      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 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. lower-*.f64 N/A

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

      9. lift--.f64 N/A

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

      10. associate-*r/ N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 80.5

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

   7. Applied rewrites 80.5%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+32} \lor \neg \left(a \leq 2.5 \cdot 10^{-20}\right):\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 73.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{+30}:\\ \;\;\;\;\frac{60 \cdot x}{z} + a \cdot 120\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-20}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.25e+30)
   (+ (/ (* 60.0 x) z) (* a 120.0))
   (if (<= a 2.5e-20) (/ (* (- x y) 60.0) (- z t)) (* 120.0 a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.25e+30) {
		tmp = ((60.0 * x) / z) + (a * 120.0);
	} else if (a <= 2.5e-20) {
		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) :: tmp
    if (a <= (-1.25d+30)) then
        tmp = ((60.0d0 * x) / z) + (a * 120.0d0)
    else if (a <= 2.5d-20) 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 tmp;
	if (a <= -1.25e+30) {
		tmp = ((60.0 * x) / z) + (a * 120.0);
	} else if (a <= 2.5e-20) {
		tmp = ((x - y) * 60.0) / (z - t);
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.25e+30:
		tmp = ((60.0 * x) / z) + (a * 120.0)
	elif a <= 2.5e-20:
		tmp = ((x - y) * 60.0) / (z - t)
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.25e+30)
		tmp = Float64(Float64(Float64(60.0 * x) / z) + Float64(a * 120.0));
	elseif (a <= 2.5e-20)
		tmp = Float64(Float64(Float64(x - y) * 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)
	tmp = 0.0;
	if (a <= -1.25e+30)
		tmp = ((60.0 * x) / z) + (a * 120.0);
	elseif (a <= 2.5e-20)
		tmp = ((x - y) * 60.0) / (z - t);
	else
		tmp = 120.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.25e+30], N[(N[(N[(60.0 * x), $MachinePrecision] / z), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.5e-20], N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.25e30

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 94.3%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 84.6%

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

   if -1.25e30 < a < 2.4999999999999999e-20

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 80.6

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

   5. Applied rewrites 80.6%

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

   if 2.4999999999999999e-20 < a

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 79.5

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

   5. Applied rewrites 79.5%

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

Alternative 14: 73.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{+30}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, 60, 120 \cdot a\right)\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-20}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.25e+30)
   (fma (/ x z) 60.0 (* 120.0 a))
   (if (<= a 2.5e-20) (/ (* (- x y) 60.0) (- z t)) (* 120.0 a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.25e+30) {
		tmp = fma((x / z), 60.0, (120.0 * a));
	} else if (a <= 2.5e-20) {
		tmp = ((x - y) * 60.0) / (z - t);
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.25e+30)
		tmp = fma(Float64(x / z), 60.0, Float64(120.0 * a));
	elseif (a <= 2.5e-20)
		tmp = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t));
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.25e+30], N[(N[(x / z), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.5e-20], N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.25e30

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 94.3

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

   5. Applied rewrites 94.3%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 84.6%

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

   if -1.25e30 < a < 2.4999999999999999e-20

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 80.6

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

   5. Applied rewrites 80.6%

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

   if 2.4999999999999999e-20 < a

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 79.5

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

   5. Applied rewrites 79.5%

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

Alternative 15: 61.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+186}:\\ \;\;\;\;\frac{-60 \cdot y}{z - t}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+214}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, -60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z - t} \cdot -60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3.1e+186)
   (/ (* -60.0 y) (- z t))
   (if (<= y 1.9e+214)
     (fma (/ x t) -60.0 (* 120.0 a))
     (* (/ y (- z t)) -60.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.1e+186) {
		tmp = (-60.0 * y) / (z - t);
	} else if (y <= 1.9e+214) {
		tmp = fma((x / t), -60.0, (120.0 * a));
	} else {
		tmp = (y / (z - t)) * -60.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3.1e+186)
		tmp = Float64(Float64(-60.0 * y) / Float64(z - t));
	elseif (y <= 1.9e+214)
		tmp = fma(Float64(x / t), -60.0, Float64(120.0 * a));
	else
		tmp = Float64(Float64(y / Float64(z - t)) * -60.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3.1e+186], N[(N[(-60.0 * y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e+214], N[(N[(x / t), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], N[(N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision] * -60.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.1000000000000001e186

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 72.7

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

   5. Applied rewrites 72.7%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*r/ N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 72.8

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

   7. Applied rewrites 72.8%

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

   if -3.1000000000000001e186 < y < 1.89999999999999999e214

   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 87.3

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

   5. Applied rewrites 87.3%

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

   6. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift-*.f64 64.4

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

   8. Applied rewrites 64.4%

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

   if 1.89999999999999999e214 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 78.8

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

   5. Applied rewrites 78.8%

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

Alternative 16: 58.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.0001 \lor \neg \left(a \leq 1.45 \cdot 10^{-20}\right):\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -0.0001) (not (<= a 1.45e-20)))
   (* 120.0 a)
   (* (- x y) (/ -60.0 t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -0.0001) || !(a <= 1.45e-20)) {
		tmp = 120.0 * a;
	} else {
		tmp = (x - y) * (-60.0 / t);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-0.0001d0)) .or. (.not. (a <= 1.45d-20))) then
        tmp = 120.0d0 * a
    else
        tmp = (x - y) * ((-60.0d0) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -0.0001) || !(a <= 1.45e-20)) {
		tmp = 120.0 * a;
	} else {
		tmp = (x - y) * (-60.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -0.0001) or not (a <= 1.45e-20):
		tmp = 120.0 * a
	else:
		tmp = (x - y) * (-60.0 / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -0.0001) || !(a <= 1.45e-20))
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(x - y) * Float64(-60.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -0.0001) || ~((a <= 1.45e-20)))
		tmp = 120.0 * a;
	else
		tmp = (x - y) * (-60.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -0.0001], N[Not[LessEqual[a, 1.45e-20]], $MachinePrecision]], N[(120.0 * a), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.00000000000000005e-4 or 1.45e-20 < a

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 78.5

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

   5. Applied rewrites 78.5%

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

   if -1.00000000000000005e-4 < a < 1.45e-20

   1. Initial program 99.7%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      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 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative 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 81.3

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

   7. Applied rewrites 81.3%

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

   8. Taylor expanded in z around 0

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

      1. lower-/.f64 44.8

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

   10. Applied rewrites 44.8%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.0001 \lor \neg \left(a \leq 1.45 \cdot 10^{-20}\right):\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 52.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-85} \lor \neg \left(a \leq 2.55 \cdot 10^{-98}\right):\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.5e-85) (not (<= a 2.55e-98))) (* 120.0 a) (* -60.0 (/ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.5e-85) || !(a <= 2.55e-98)) {
		tmp = 120.0 * a;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-4.5d-85)) .or. (.not. (a <= 2.55d-98))) then
        tmp = 120.0d0 * a
    else
        tmp = (-60.0d0) * (x / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.5e-85) || !(a <= 2.55e-98)) {
		tmp = 120.0 * a;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.5e-85) or not (a <= 2.55e-98):
		tmp = 120.0 * a
	else:
		tmp = -60.0 * (x / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.5e-85) || !(a <= 2.55e-98))
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(-60.0 * Float64(x / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.5e-85) || ~((a <= 2.55e-98)))
		tmp = 120.0 * a;
	else
		tmp = -60.0 * (x / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.5e-85], N[Not[LessEqual[a, 2.55e-98]], $MachinePrecision]], N[(120.0 * a), $MachinePrecision], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.50000000000000004e-85 or 2.55000000000000011e-98 < a

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 71.0

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

   5. Applied rewrites 71.0%

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

   if -4.50000000000000004e-85 < a < 2.55000000000000011e-98

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 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 57.3

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

   5. Applied rewrites 57.3%

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

   6. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift-*.f64 37.9

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

   8. Applied rewrites 37.9%

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

   9. Taylor expanded in x around inf

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

       1. lower-*.f64 N/A

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

       2. lift-/.f64 29.5

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

   11. Applied rewrites 29.5%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-85} \lor \neg \left(a \leq 2.55 \cdot 10^{-98}\right):\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 52.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.05 \cdot 10^{+160}:\\ \;\;\;\;\frac{-60 \cdot y}{z}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+259}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot 60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -5.05e+160)
   (/ (* -60.0 y) z)
   (if (<= y 4e+259) (* 120.0 a) (* (/ y t) 60.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5.05e+160) {
		tmp = (-60.0 * y) / z;
	} else if (y <= 4e+259) {
		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) :: tmp
    if (y <= (-5.05d+160)) then
        tmp = ((-60.0d0) * y) / z
    else if (y <= 4d+259) 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 tmp;
	if (y <= -5.05e+160) {
		tmp = (-60.0 * y) / z;
	} else if (y <= 4e+259) {
		tmp = 120.0 * a;
	} else {
		tmp = (y / t) * 60.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -5.05e+160:
		tmp = (-60.0 * y) / z
	elif y <= 4e+259:
		tmp = 120.0 * a
	else:
		tmp = (y / t) * 60.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -5.05e+160)
		tmp = Float64(Float64(-60.0 * y) / z);
	elseif (y <= 4e+259)
		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)
	tmp = 0.0;
	if (y <= -5.05e+160)
		tmp = (-60.0 * y) / z;
	elseif (y <= 4e+259)
		tmp = 120.0 * a;
	else
		tmp = (y / t) * 60.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -5.05e+160], N[(N[(-60.0 * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 4e+259], N[(120.0 * a), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * 60.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.0500000000000002e160

   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 inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 68.3

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

   5. Applied rewrites 68.3%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 51.9%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. *-commutative N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 52.0

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

   10. Applied rewrites 52.0%

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

   if -5.0500000000000002e160 < y < 4e259

   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 57.8

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

   5. Applied rewrites 57.8%

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

   if 4e259 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 92.2

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

   5. Applied rewrites 92.2%

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

   6. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 77.7

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

   8. Applied rewrites 77.7%

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

Alternative 19: 52.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.05 \cdot 10^{+160}:\\ \;\;\;\;\frac{y}{z} \cdot -60\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+259}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot 60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -5.05e+160)
   (* (/ y z) -60.0)
   (if (<= y 4e+259) (* 120.0 a) (* (/ y t) 60.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5.05e+160) {
		tmp = (y / z) * -60.0;
	} else if (y <= 4e+259) {
		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) :: tmp
    if (y <= (-5.05d+160)) then
        tmp = (y / z) * (-60.0d0)
    else if (y <= 4d+259) 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 tmp;
	if (y <= -5.05e+160) {
		tmp = (y / z) * -60.0;
	} else if (y <= 4e+259) {
		tmp = 120.0 * a;
	} else {
		tmp = (y / t) * 60.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -5.05e+160:
		tmp = (y / z) * -60.0
	elif y <= 4e+259:
		tmp = 120.0 * a
	else:
		tmp = (y / t) * 60.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -5.05e+160)
		tmp = Float64(Float64(y / z) * -60.0);
	elseif (y <= 4e+259)
		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)
	tmp = 0.0;
	if (y <= -5.05e+160)
		tmp = (y / z) * -60.0;
	elseif (y <= 4e+259)
		tmp = 120.0 * a;
	else
		tmp = (y / t) * 60.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -5.05e+160], N[(N[(y / z), $MachinePrecision] * -60.0), $MachinePrecision], If[LessEqual[y, 4e+259], N[(120.0 * a), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * 60.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.0500000000000002e160

   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 inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 68.3

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

   5. Applied rewrites 68.3%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 51.9%

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

   if -5.0500000000000002e160 < y < 4e259

   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 57.8

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

   5. Applied rewrites 57.8%

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

   if 4e259 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 92.2

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

   5. Applied rewrites 92.2%

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

   6. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 77.7

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

   8. Applied rewrites 77.7%

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

Alternative 20: 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 99.8%

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

3. Taylor expanded in z around inf

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

   1. lower-*.f64 51.3

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

5. Applied rewrites 51.3%

   \[\leadsto \color{blue}{120 \cdot a} \]
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 2025057 
(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)))