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

Percentage Accurate: 99.3% → 99.8%

Time: 13.8s

Alternatives: 19

Speedup: 1.0×

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× 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

real(8) function code(x, y, z, t, a)
    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]

Derivation

1. Initial program 99.0%

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

   1. associate-/l* 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 89.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot -60}{z - t} + a \cdot 120\\ t_2 := \frac{60}{z - t}\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+73}:\\ \;\;\;\;x \cdot t_2 + a \cdot 120\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+179} \lor \neg \left(y \leq 8.5 \cdot 10^{+220}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (/ (* y -60.0) (- z t)) (* a 120.0))) (t_2 (/ 60.0 (- z t))))
   (if (<= y -1.3e+57)
     t_1
     (if (<= y 5.2e+73)
       (+ (* x t_2) (* a 120.0))
       (if (or (<= y 7e+179) (not (<= y 8.5e+220))) t_1 (* (- x y) t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y * -60.0) / (z - t)) + (a * 120.0);
	double t_2 = 60.0 / (z - t);
	double tmp;
	if (y <= -1.3e+57) {
		tmp = t_1;
	} else if (y <= 5.2e+73) {
		tmp = (x * t_2) + (a * 120.0);
	} else if ((y <= 7e+179) || !(y <= 8.5e+220)) {
		tmp = t_1;
	} else {
		tmp = (x - y) * t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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 = ((y * (-60.0d0)) / (z - t)) + (a * 120.0d0)
    t_2 = 60.0d0 / (z - t)
    if (y <= (-1.3d+57)) then
        tmp = t_1
    else if (y <= 5.2d+73) then
        tmp = (x * t_2) + (a * 120.0d0)
    else if ((y <= 7d+179) .or. (.not. (y <= 8.5d+220))) then
        tmp = t_1
    else
        tmp = (x - y) * t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y * -60.0) / (z - t)) + (a * 120.0);
	double t_2 = 60.0 / (z - t);
	double tmp;
	if (y <= -1.3e+57) {
		tmp = t_1;
	} else if (y <= 5.2e+73) {
		tmp = (x * t_2) + (a * 120.0);
	} else if ((y <= 7e+179) || !(y <= 8.5e+220)) {
		tmp = t_1;
	} else {
		tmp = (x - y) * t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y * -60.0) / (z - t)) + (a * 120.0)
	t_2 = 60.0 / (z - t)
	tmp = 0
	if y <= -1.3e+57:
		tmp = t_1
	elif y <= 5.2e+73:
		tmp = (x * t_2) + (a * 120.0)
	elif (y <= 7e+179) or not (y <= 8.5e+220):
		tmp = t_1
	else:
		tmp = (x - y) * t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y * -60.0) / Float64(z - t)) + Float64(a * 120.0))
	t_2 = Float64(60.0 / Float64(z - t))
	tmp = 0.0
	if (y <= -1.3e+57)
		tmp = t_1;
	elseif (y <= 5.2e+73)
		tmp = Float64(Float64(x * t_2) + Float64(a * 120.0));
	elseif ((y <= 7e+179) || !(y <= 8.5e+220))
		tmp = t_1;
	else
		tmp = Float64(Float64(x - y) * t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y * -60.0) / (z - t)) + (a * 120.0);
	t_2 = 60.0 / (z - t);
	tmp = 0.0;
	if (y <= -1.3e+57)
		tmp = t_1;
	elseif (y <= 5.2e+73)
		tmp = (x * t_2) + (a * 120.0);
	elseif ((y <= 7e+179) || ~((y <= 8.5e+220)))
		tmp = t_1;
	else
		tmp = (x - y) * t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3e+57], t$95$1, If[LessEqual[y, 5.2e+73], N[(N[(x * t$95$2), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 7e+179], N[Not[LessEqual[y, 8.5e+220]], $MachinePrecision]], t$95$1, N[(N[(x - y), $MachinePrecision] * t$95$2), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3e57 or 5.2000000000000001e73 < y < 7.0000000000000003e179 or 8.4999999999999996e220 < y

   1. Initial program 97.7%

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

   2. Taylor expanded in x around 0 93.0%

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

   if -1.3e57 < y < 5.2000000000000001e73

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 93.6%

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

      1. associate-*r/ 93.7%

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

      2. associate-*l/ 93.7%

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

      3. *-commutative 93.7%

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

   6. Simplified 93.7%

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

   if 7.0000000000000003e179 < y < 8.4999999999999996e220

   1. Initial program 99.8%

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

      1. associate-*r/ 99.6%

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

      2. fma-def 99.6%

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

   3. Simplified 99.6%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in a around 0 86.0%

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

      1. *-commutative 86.0%

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

      2. metadata-eval 86.0%

         \[\leadsto \frac{x - y}{z - t} \cdot \color{blue}{\frac{1}{0.016666666666666666}} \]

      3. times-frac 86.0%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot 1}{\left(z - t\right) \cdot 0.016666666666666666}} \]

      4. associate-*r/ 85.8%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{1}{\left(z - t\right) \cdot 0.016666666666666666}} \]

      5. *-commutative 85.8%

         \[\leadsto \left(x - y\right) \cdot \frac{1}{\color{blue}{0.016666666666666666 \cdot \left(z - t\right)}} \]

      6. associate-/r* 86.1%

         \[\leadsto \left(x - y\right) \cdot \color{blue}{\frac{\frac{1}{0.016666666666666666}}{z - t}} \]

      7. metadata-eval 86.1%

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

   8. Simplified 86.1%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+57}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+179} \lor \neg \left(y \leq 8.5 \cdot 10^{+220}\right):\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \]

Alternative 3: 75.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+97}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{+75} \lor \neg \left(a \leq -7.6 \cdot 10^{+32}\right) \land a \leq 0.5:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.3e+97)
   (* a 120.0)
   (if (or (<= a -6.2e+75) (and (not (<= a -7.6e+32)) (<= a 0.5)))
     (* 60.0 (/ (- x y) (- z t)))
     (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.3e+97) {
		tmp = a * 120.0;
	} else if ((a <= -6.2e+75) || (!(a <= -7.6e+32) && (a <= 0.5))) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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 <= (-2.3d+97)) then
        tmp = a * 120.0d0
    else if ((a <= (-6.2d+75)) .or. (.not. (a <= (-7.6d+32))) .and. (a <= 0.5d0)) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.3e+97) {
		tmp = a * 120.0;
	} else if ((a <= -6.2e+75) || (!(a <= -7.6e+32) && (a <= 0.5))) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.3e+97:
		tmp = a * 120.0
	elif (a <= -6.2e+75) or (not (a <= -7.6e+32) and (a <= 0.5)):
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.3e+97)
		tmp = Float64(a * 120.0);
	elseif ((a <= -6.2e+75) || (!(a <= -7.6e+32) && (a <= 0.5)))
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.3e+97)
		tmp = a * 120.0;
	elseif ((a <= -6.2e+75) || (~((a <= -7.6e+32)) && (a <= 0.5)))
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.3e+97], N[(a * 120.0), $MachinePrecision], If[Or[LessEqual[a, -6.2e+75], And[N[Not[LessEqual[a, -7.6e+32]], $MachinePrecision], LessEqual[a, 0.5]]], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.30000000000000006e97 or -6.2000000000000002e75 < a < -7.6000000000000006e32 or 0.5 < a

   1. Initial program 98.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 74.7%

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

   if -2.30000000000000006e97 < a < -6.2000000000000002e75 or -7.6000000000000006e32 < a < 0.5

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 75.3%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+97}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{+75} \lor \neg \left(a \leq -7.6 \cdot 10^{+32}\right) \land a \leq 0.5:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 4: 74.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{+97}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -4.3 \cdot 10^{+75}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \leq -2.95 \cdot 10^{+32}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 0.145:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.12e+97)
   (* a 120.0)
   (if (<= a -4.3e+75)
     (* (- x y) (/ 60.0 (- z t)))
     (if (<= a -2.95e+32)
       (* a 120.0)
       (if (<= a 0.145) (* 60.0 (/ (- x y) (- z t))) (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.12e+97) {
		tmp = a * 120.0;
	} else if (a <= -4.3e+75) {
		tmp = (x - y) * (60.0 / (z - t));
	} else if (a <= -2.95e+32) {
		tmp = a * 120.0;
	} else if (a <= 0.145) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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 <= (-1.12d+97)) then
        tmp = a * 120.0d0
    else if (a <= (-4.3d+75)) then
        tmp = (x - y) * (60.0d0 / (z - t))
    else if (a <= (-2.95d+32)) then
        tmp = a * 120.0d0
    else if (a <= 0.145d0) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.12e+97) {
		tmp = a * 120.0;
	} else if (a <= -4.3e+75) {
		tmp = (x - y) * (60.0 / (z - t));
	} else if (a <= -2.95e+32) {
		tmp = a * 120.0;
	} else if (a <= 0.145) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.12e+97:
		tmp = a * 120.0
	elif a <= -4.3e+75:
		tmp = (x - y) * (60.0 / (z - t))
	elif a <= -2.95e+32:
		tmp = a * 120.0
	elif a <= 0.145:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.12e+97)
		tmp = Float64(a * 120.0);
	elseif (a <= -4.3e+75)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	elseif (a <= -2.95e+32)
		tmp = Float64(a * 120.0);
	elseif (a <= 0.145)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.12e+97)
		tmp = a * 120.0;
	elseif (a <= -4.3e+75)
		tmp = (x - y) * (60.0 / (z - t));
	elseif (a <= -2.95e+32)
		tmp = a * 120.0;
	elseif (a <= 0.145)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.12e+97], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -4.3e+75], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.95e+32], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 0.145], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.12e97 or -4.3000000000000001e75 < a < -2.94999999999999983e32 or 0.14499999999999999 < a

   1. Initial program 98.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 74.7%

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

   if -1.12e97 < a < -4.3000000000000001e75

   1. Initial program 100.0%

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

      1. associate-*r/ 100.0%

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

      2. fma-def 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.5%

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

      2. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in a around 0 74.8%

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

      1. *-commutative 74.8%

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

      2. metadata-eval 74.8%

         \[\leadsto \frac{x - y}{z - t} \cdot \color{blue}{\frac{1}{0.016666666666666666}} \]

      3. times-frac 74.8%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot 1}{\left(z - t\right) \cdot 0.016666666666666666}} \]

      4. associate-*r/ 74.9%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{1}{\left(z - t\right) \cdot 0.016666666666666666}} \]

      5. *-commutative 74.9%

         \[\leadsto \left(x - y\right) \cdot \frac{1}{\color{blue}{0.016666666666666666 \cdot \left(z - t\right)}} \]

      6. associate-/r* 74.9%

         \[\leadsto \left(x - y\right) \cdot \color{blue}{\frac{\frac{1}{0.016666666666666666}}{z - t}} \]

      7. metadata-eval 74.9%

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

   8. Simplified 74.9%

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

   if -2.94999999999999983e32 < a < 0.14499999999999999

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 75.3%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{+97}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -4.3 \cdot 10^{+75}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \leq -2.95 \cdot 10^{+32}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 0.145:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 5: 73.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{if}\;a \leq -1.05 \cdot 10^{+160}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -6 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{+32}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-40}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* 60.0 (/ y t)))))
   (if (<= a -1.05e+160)
     (* a 120.0)
     (if (<= a -6e+57)
       t_1
       (if (<= a -2.65e+32)
         (* a 120.0)
         (if (<= a 4.4e-40) (* (- x y) (/ 60.0 (- z t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (60.0 * (y / t));
	double tmp;
	if (a <= -1.05e+160) {
		tmp = a * 120.0;
	} else if (a <= -6e+57) {
		tmp = t_1;
	} else if (a <= -2.65e+32) {
		tmp = a * 120.0;
	} else if (a <= 4.4e-40) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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 = (a * 120.0d0) + (60.0d0 * (y / t))
    if (a <= (-1.05d+160)) then
        tmp = a * 120.0d0
    else if (a <= (-6d+57)) then
        tmp = t_1
    else if (a <= (-2.65d+32)) then
        tmp = a * 120.0d0
    else if (a <= 4.4d-40) then
        tmp = (x - y) * (60.0d0 / (z - t))
    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 = (a * 120.0) + (60.0 * (y / t));
	double tmp;
	if (a <= -1.05e+160) {
		tmp = a * 120.0;
	} else if (a <= -6e+57) {
		tmp = t_1;
	} else if (a <= -2.65e+32) {
		tmp = a * 120.0;
	} else if (a <= 4.4e-40) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (60.0 * (y / t))
	tmp = 0
	if a <= -1.05e+160:
		tmp = a * 120.0
	elif a <= -6e+57:
		tmp = t_1
	elif a <= -2.65e+32:
		tmp = a * 120.0
	elif a <= 4.4e-40:
		tmp = (x - y) * (60.0 / (z - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / t)))
	tmp = 0.0
	if (a <= -1.05e+160)
		tmp = Float64(a * 120.0);
	elseif (a <= -6e+57)
		tmp = t_1;
	elseif (a <= -2.65e+32)
		tmp = Float64(a * 120.0);
	elseif (a <= 4.4e-40)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + (60.0 * (y / t));
	tmp = 0.0;
	if (a <= -1.05e+160)
		tmp = a * 120.0;
	elseif (a <= -6e+57)
		tmp = t_1;
	elseif (a <= -2.65e+32)
		tmp = a * 120.0;
	elseif (a <= 4.4e-40)
		tmp = (x - y) * (60.0 / (z - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.05e+160], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -6e+57], t$95$1, If[LessEqual[a, -2.65e+32], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 4.4e-40], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.04999999999999998e160 or -5.9999999999999999e57 < a < -2.65e32

   1. Initial program 97.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 77.6%

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

   if -1.04999999999999998e160 < a < -5.9999999999999999e57 or 4.40000000000000018e-40 < a

   1. Initial program 99.0%

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

   2. Taylor expanded in x around 0 91.0%

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

   3. Taylor expanded in z around 0 75.3%

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

   if -2.65e32 < a < 4.40000000000000018e-40

   1. Initial program 99.6%

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

      1. associate-*r/ 99.6%

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

      2. fma-def 99.6%

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

   3. Simplified 99.6%

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

      1. clear-num 99.6%

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

      2. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in a around 0 76.5%

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

      1. *-commutative 76.5%

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

      2. metadata-eval 76.5%

         \[\leadsto \frac{x - y}{z - t} \cdot \color{blue}{\frac{1}{0.016666666666666666}} \]

      3. times-frac 76.6%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot 1}{\left(z - t\right) \cdot 0.016666666666666666}} \]

      4. associate-*r/ 76.4%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{1}{\left(z - t\right) \cdot 0.016666666666666666}} \]

      5. *-commutative 76.4%

         \[\leadsto \left(x - y\right) \cdot \frac{1}{\color{blue}{0.016666666666666666 \cdot \left(z - t\right)}} \]

      6. associate-/r* 76.5%

         \[\leadsto \left(x - y\right) \cdot \color{blue}{\frac{\frac{1}{0.016666666666666666}}{z - t}} \]

      7. metadata-eval 76.5%

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

   8. Simplified 76.5%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{+160}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -6 \cdot 10^{+57}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{+32}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-40}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 6: 73.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + 60 \cdot \frac{y}{t}\\ t_2 := a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{if}\;a \leq -7.8 \cdot 10^{+157}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{+24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-39}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* 60.0 (/ y t))))
        (t_2 (+ (* a 120.0) (* 60.0 (/ x z)))))
   (if (<= a -7.8e+157)
     t_2
     (if (<= a -6.6e+75)
       t_1
       (if (<= a -3.9e+24)
         t_2
         (if (<= a 1.35e-39) (* (- x y) (/ 60.0 (- z t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (60.0 * (y / t));
	double t_2 = (a * 120.0) + (60.0 * (x / z));
	double tmp;
	if (a <= -7.8e+157) {
		tmp = t_2;
	} else if (a <= -6.6e+75) {
		tmp = t_1;
	} else if (a <= -3.9e+24) {
		tmp = t_2;
	} else if (a <= 1.35e-39) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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 = (a * 120.0d0) + (60.0d0 * (y / t))
    t_2 = (a * 120.0d0) + (60.0d0 * (x / z))
    if (a <= (-7.8d+157)) then
        tmp = t_2
    else if (a <= (-6.6d+75)) then
        tmp = t_1
    else if (a <= (-3.9d+24)) then
        tmp = t_2
    else if (a <= 1.35d-39) then
        tmp = (x - y) * (60.0d0 / (z - t))
    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 = (a * 120.0) + (60.0 * (y / t));
	double t_2 = (a * 120.0) + (60.0 * (x / z));
	double tmp;
	if (a <= -7.8e+157) {
		tmp = t_2;
	} else if (a <= -6.6e+75) {
		tmp = t_1;
	} else if (a <= -3.9e+24) {
		tmp = t_2;
	} else if (a <= 1.35e-39) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (60.0 * (y / t))
	t_2 = (a * 120.0) + (60.0 * (x / z))
	tmp = 0
	if a <= -7.8e+157:
		tmp = t_2
	elif a <= -6.6e+75:
		tmp = t_1
	elif a <= -3.9e+24:
		tmp = t_2
	elif a <= 1.35e-39:
		tmp = (x - y) * (60.0 / (z - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / t)))
	t_2 = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / z)))
	tmp = 0.0
	if (a <= -7.8e+157)
		tmp = t_2;
	elseif (a <= -6.6e+75)
		tmp = t_1;
	elseif (a <= -3.9e+24)
		tmp = t_2;
	elseif (a <= 1.35e-39)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + (60.0 * (y / t));
	t_2 = (a * 120.0) + (60.0 * (x / z));
	tmp = 0.0;
	if (a <= -7.8e+157)
		tmp = t_2;
	elseif (a <= -6.6e+75)
		tmp = t_1;
	elseif (a <= -3.9e+24)
		tmp = t_2;
	elseif (a <= 1.35e-39)
		tmp = (x - y) * (60.0 / (z - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.8e+157], t$95$2, If[LessEqual[a, -6.6e+75], t$95$1, If[LessEqual[a, -3.9e+24], t$95$2, If[LessEqual[a, 1.35e-39], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.79999999999999941e157 or -6.59999999999999996e75 < a < -3.8999999999999998e24

   1. Initial program 97.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 90.2%

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

   5. Taylor expanded in x around inf 79.9%

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

      1. *-commutative 79.9%

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

   7. Simplified 79.9%

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

   if -7.79999999999999941e157 < a < -6.59999999999999996e75 or 1.35e-39 < a

   1. Initial program 98.9%

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

   2. Taylor expanded in x around 0 91.4%

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

   3. Taylor expanded in z around 0 76.6%

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

   if -3.8999999999999998e24 < a < 1.35e-39

   1. Initial program 99.6%

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

      1. associate-*r/ 99.6%

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

      2. fma-def 99.6%

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

   3. Simplified 99.6%

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

      1. clear-num 99.6%

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

      2. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in a around 0 76.6%

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

      1. *-commutative 76.6%

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

      2. metadata-eval 76.6%

         \[\leadsto \frac{x - y}{z - t} \cdot \color{blue}{\frac{1}{0.016666666666666666}} \]

      3. times-frac 76.6%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot 1}{\left(z - t\right) \cdot 0.016666666666666666}} \]

      4. associate-*r/ 76.5%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{1}{\left(z - t\right) \cdot 0.016666666666666666}} \]

      5. *-commutative 76.5%

         \[\leadsto \left(x - y\right) \cdot \frac{1}{\color{blue}{0.016666666666666666 \cdot \left(z - t\right)}} \]

      6. associate-/r* 76.6%

         \[\leadsto \left(x - y\right) \cdot \color{blue}{\frac{\frac{1}{0.016666666666666666}}{z - t}} \]

      7. metadata-eval 76.6%

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

   8. Simplified 76.6%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+157}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{+75}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{+24}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-39}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 7: 73.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + 60 \cdot \frac{y}{t}\\ t_2 := a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{if}\;a \leq -2.9 \cdot 10^{+160}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{+32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-40}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* 60.0 (/ y t))))
        (t_2 (+ (* a 120.0) (* -60.0 (/ y z)))))
   (if (<= a -2.9e+160)
     t_2
     (if (<= a -2.65e+79)
       t_1
       (if (<= a -3.2e+32)
         t_2
         (if (<= a 5e-40) (* (- x y) (/ 60.0 (- z t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (60.0 * (y / t));
	double t_2 = (a * 120.0) + (-60.0 * (y / z));
	double tmp;
	if (a <= -2.9e+160) {
		tmp = t_2;
	} else if (a <= -2.65e+79) {
		tmp = t_1;
	} else if (a <= -3.2e+32) {
		tmp = t_2;
	} else if (a <= 5e-40) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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 = (a * 120.0d0) + (60.0d0 * (y / t))
    t_2 = (a * 120.0d0) + ((-60.0d0) * (y / z))
    if (a <= (-2.9d+160)) then
        tmp = t_2
    else if (a <= (-2.65d+79)) then
        tmp = t_1
    else if (a <= (-3.2d+32)) then
        tmp = t_2
    else if (a <= 5d-40) then
        tmp = (x - y) * (60.0d0 / (z - t))
    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 = (a * 120.0) + (60.0 * (y / t));
	double t_2 = (a * 120.0) + (-60.0 * (y / z));
	double tmp;
	if (a <= -2.9e+160) {
		tmp = t_2;
	} else if (a <= -2.65e+79) {
		tmp = t_1;
	} else if (a <= -3.2e+32) {
		tmp = t_2;
	} else if (a <= 5e-40) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (60.0 * (y / t))
	t_2 = (a * 120.0) + (-60.0 * (y / z))
	tmp = 0
	if a <= -2.9e+160:
		tmp = t_2
	elif a <= -2.65e+79:
		tmp = t_1
	elif a <= -3.2e+32:
		tmp = t_2
	elif a <= 5e-40:
		tmp = (x - y) * (60.0 / (z - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / t)))
	t_2 = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)))
	tmp = 0.0
	if (a <= -2.9e+160)
		tmp = t_2;
	elseif (a <= -2.65e+79)
		tmp = t_1;
	elseif (a <= -3.2e+32)
		tmp = t_2;
	elseif (a <= 5e-40)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + (60.0 * (y / t));
	t_2 = (a * 120.0) + (-60.0 * (y / z));
	tmp = 0.0;
	if (a <= -2.9e+160)
		tmp = t_2;
	elseif (a <= -2.65e+79)
		tmp = t_1;
	elseif (a <= -3.2e+32)
		tmp = t_2;
	elseif (a <= 5e-40)
		tmp = (x - y) * (60.0 / (z - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.9e+160], t$95$2, If[LessEqual[a, -2.65e+79], t$95$1, If[LessEqual[a, -3.2e+32], t$95$2, If[LessEqual[a, 5e-40], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.8999999999999999e160 or -2.64999999999999989e79 < a < -3.1999999999999999e32

   1. Initial program 97.6%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 87.5%

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

   5. Taylor expanded in x around 0 82.8%

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

      1. *-commutative 82.8%

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

   7. Simplified 82.8%

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

   if -2.8999999999999999e160 < a < -2.64999999999999989e79 or 4.99999999999999965e-40 < a

   1. Initial program 98.9%

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

   2. Taylor expanded in x around 0 90.2%

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

   3. Taylor expanded in z around 0 76.4%

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

   if -3.1999999999999999e32 < a < 4.99999999999999965e-40

   1. Initial program 99.6%

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

      1. associate-*r/ 99.6%

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

      2. fma-def 99.6%

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

   3. Simplified 99.6%

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

      1. clear-num 99.6%

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

      2. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in a around 0 76.5%

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

      1. *-commutative 76.5%

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

      2. metadata-eval 76.5%

         \[\leadsto \frac{x - y}{z - t} \cdot \color{blue}{\frac{1}{0.016666666666666666}} \]

      3. times-frac 76.6%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot 1}{\left(z - t\right) \cdot 0.016666666666666666}} \]

      4. associate-*r/ 76.4%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{1}{\left(z - t\right) \cdot 0.016666666666666666}} \]

      5. *-commutative 76.4%

         \[\leadsto \left(x - y\right) \cdot \frac{1}{\color{blue}{0.016666666666666666 \cdot \left(z - t\right)}} \]

      6. associate-/r* 76.5%

         \[\leadsto \left(x - y\right) \cdot \color{blue}{\frac{\frac{1}{0.016666666666666666}}{z - t}} \]

      7. metadata-eval 76.5%

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

   8. Simplified 76.5%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{+160}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{+79}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{+32}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-40}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 8: 76.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+49}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-14}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;z \leq 0.0003:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.6e+49)
   (+ (* a 120.0) (* 60.0 (/ x z)))
   (if (<= z -1.1e-14)
     (* 60.0 (/ (- x y) (- z t)))
     (if (<= z 0.0003)
       (+ (* a 120.0) (* -60.0 (/ (- x y) t)))
       (+ (* a 120.0) (* -60.0 (/ y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.6e+49) {
		tmp = (a * 120.0) + (60.0 * (x / z));
	} else if (z <= -1.1e-14) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (z <= 0.0003) {
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	} else {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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 (z <= (-4.6d+49)) then
        tmp = (a * 120.0d0) + (60.0d0 * (x / z))
    else if (z <= (-1.1d-14)) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if (z <= 0.0003d0) then
        tmp = (a * 120.0d0) + ((-60.0d0) * ((x - y) / t))
    else
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.6e+49) {
		tmp = (a * 120.0) + (60.0 * (x / z));
	} else if (z <= -1.1e-14) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (z <= 0.0003) {
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	} else {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.6e+49:
		tmp = (a * 120.0) + (60.0 * (x / z))
	elif z <= -1.1e-14:
		tmp = 60.0 * ((x - y) / (z - t))
	elif z <= 0.0003:
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t))
	else:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.6e+49)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / z)));
	elseif (z <= -1.1e-14)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (z <= 0.0003)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(Float64(x - y) / t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.6e+49)
		tmp = (a * 120.0) + (60.0 * (x / z));
	elseif (z <= -1.1e-14)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif (z <= 0.0003)
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	else
		tmp = (a * 120.0) + (-60.0 * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.6e+49], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.1e-14], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0003], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.60000000000000004e49

   1. Initial program 97.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 85.5%

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

   5. Taylor expanded in x around inf 80.6%

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

      1. *-commutative 80.6%

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

   7. Simplified 80.6%

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

   if -4.60000000000000004e49 < z < -1.1e-14

   1. Initial program 99.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around 0 74.1%

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

   if -1.1e-14 < z < 2.99999999999999974e-4

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 84.4%

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

   if 2.99999999999999974e-4 < z

   1. Initial program 98.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 88.3%

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

   5. Taylor expanded in x around 0 76.9%

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

      1. *-commutative 76.9%

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

   7. Simplified 76.9%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+49}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-14}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;z \leq 0.0003:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \end{array} \]

Alternative 9: 57.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;y \leq -5 \cdot 10^{+155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{-61}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-83}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+182}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ y (- z t)))))
   (if (<= y -5e+155)
     t_1
     (if (<= y -2.25e-61)
       (* a 120.0)
       (if (<= y -3.1e-83)
         (* -60.0 (/ x t))
         (if (<= y 1.65e+182) (* a 120.0) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double tmp;
	if (y <= -5e+155) {
		tmp = t_1;
	} else if (y <= -2.25e-61) {
		tmp = a * 120.0;
	} else if (y <= -3.1e-83) {
		tmp = -60.0 * (x / t);
	} else if (y <= 1.65e+182) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) * (y / (z - t))
    if (y <= (-5d+155)) then
        tmp = t_1
    else if (y <= (-2.25d-61)) then
        tmp = a * 120.0d0
    else if (y <= (-3.1d-83)) then
        tmp = (-60.0d0) * (x / t)
    else if (y <= 1.65d+182) then
        tmp = a * 120.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double tmp;
	if (y <= -5e+155) {
		tmp = t_1;
	} else if (y <= -2.25e-61) {
		tmp = a * 120.0;
	} else if (y <= -3.1e-83) {
		tmp = -60.0 * (x / t);
	} else if (y <= 1.65e+182) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (y / (z - t))
	tmp = 0
	if y <= -5e+155:
		tmp = t_1
	elif y <= -2.25e-61:
		tmp = a * 120.0
	elif y <= -3.1e-83:
		tmp = -60.0 * (x / t)
	elif y <= 1.65e+182:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(y / Float64(z - t)))
	tmp = 0.0
	if (y <= -5e+155)
		tmp = t_1;
	elseif (y <= -2.25e-61)
		tmp = Float64(a * 120.0);
	elseif (y <= -3.1e-83)
		tmp = Float64(-60.0 * Float64(x / t));
	elseif (y <= 1.65e+182)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * (y / (z - t));
	tmp = 0.0;
	if (y <= -5e+155)
		tmp = t_1;
	elseif (y <= -2.25e-61)
		tmp = a * 120.0;
	elseif (y <= -3.1e-83)
		tmp = -60.0 * (x / t);
	elseif (y <= 1.65e+182)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e+155], t$95$1, If[LessEqual[y, -2.25e-61], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, -3.1e-83], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e+182], N[(a * 120.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.9999999999999999e155 or 1.65e182 < y

   1. Initial program 98.3%

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

      1. associate-*r/ 99.7%

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

      2. fma-def 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.6%

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

      2. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in y around inf 68.8%

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

   if -4.9999999999999999e155 < y < -2.25e-61 or -3.09999999999999992e-83 < y < 1.65e182

   1. Initial program 99.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 60.5%

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

   if -2.25e-61 < y < -3.09999999999999992e-83

   1. Initial program 99.7%

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

      1. associate-*r/ 100.0%

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

      2. fma-def 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around inf 84.0%

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

      1. associate-*r/ 83.7%

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

   8. Simplified 83.7%

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

   9. Taylor expanded in z around 0 84.7%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+155}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{-61}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-83}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+182}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]

Alternative 10: 56.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+28}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -6.9 \cdot 10^{-84}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+182}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ y (- z t)))))
   (if (<= y -1.55e+155)
     t_1
     (if (<= y -1.3e+28)
       (* a 120.0)
       (if (<= y -6.9e-84)
         (* x (/ 60.0 (- z t)))
         (if (<= y 1.08e+182) (* a 120.0) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double tmp;
	if (y <= -1.55e+155) {
		tmp = t_1;
	} else if (y <= -1.3e+28) {
		tmp = a * 120.0;
	} else if (y <= -6.9e-84) {
		tmp = x * (60.0 / (z - t));
	} else if (y <= 1.08e+182) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) * (y / (z - t))
    if (y <= (-1.55d+155)) then
        tmp = t_1
    else if (y <= (-1.3d+28)) then
        tmp = a * 120.0d0
    else if (y <= (-6.9d-84)) then
        tmp = x * (60.0d0 / (z - t))
    else if (y <= 1.08d+182) then
        tmp = a * 120.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double tmp;
	if (y <= -1.55e+155) {
		tmp = t_1;
	} else if (y <= -1.3e+28) {
		tmp = a * 120.0;
	} else if (y <= -6.9e-84) {
		tmp = x * (60.0 / (z - t));
	} else if (y <= 1.08e+182) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (y / (z - t))
	tmp = 0
	if y <= -1.55e+155:
		tmp = t_1
	elif y <= -1.3e+28:
		tmp = a * 120.0
	elif y <= -6.9e-84:
		tmp = x * (60.0 / (z - t))
	elif y <= 1.08e+182:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(y / Float64(z - t)))
	tmp = 0.0
	if (y <= -1.55e+155)
		tmp = t_1;
	elseif (y <= -1.3e+28)
		tmp = Float64(a * 120.0);
	elseif (y <= -6.9e-84)
		tmp = Float64(x * Float64(60.0 / Float64(z - t)));
	elseif (y <= 1.08e+182)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * (y / (z - t));
	tmp = 0.0;
	if (y <= -1.55e+155)
		tmp = t_1;
	elseif (y <= -1.3e+28)
		tmp = a * 120.0;
	elseif (y <= -6.9e-84)
		tmp = x * (60.0 / (z - t));
	elseif (y <= 1.08e+182)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.55e+155], t$95$1, If[LessEqual[y, -1.3e+28], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, -6.9e-84], N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.08e+182], N[(a * 120.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.54999999999999995e155 or 1.08000000000000003e182 < y

   1. Initial program 98.3%

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

      1. associate-*r/ 99.7%

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

      2. fma-def 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.6%

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

      2. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in y around inf 68.8%

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

   if -1.54999999999999995e155 < y < -1.3000000000000001e28 or -6.89999999999999987e-84 < y < 1.08000000000000003e182

   1. Initial program 99.2%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 63.2%

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

   if -1.3000000000000001e28 < y < -6.89999999999999987e-84

   1. Initial program 99.9%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

      1. associate-/l* 99.9%

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

      2. div-inv 99.8%

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

      3. fma-def 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around inf 56.6%

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

      1. associate-*r/ 56.7%

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

      2. associate-*l/ 56.5%

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

      3. *-commutative 56.5%

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

   8. Simplified 56.5%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+155}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+28}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -6.9 \cdot 10^{-84}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+182}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]

Alternative 11: 55.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;y \leq -5.3 \cdot 10^{+154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{+30}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-83}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+185}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ y (- z t)))))
   (if (<= y -5.3e+154)
     t_1
     (if (<= y -1.05e+30)
       (* a 120.0)
       (if (<= y -3.1e-83)
         (* 60.0 (/ x (- z t)))
         (if (<= y 2.5e+185) (* a 120.0) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double tmp;
	if (y <= -5.3e+154) {
		tmp = t_1;
	} else if (y <= -1.05e+30) {
		tmp = a * 120.0;
	} else if (y <= -3.1e-83) {
		tmp = 60.0 * (x / (z - t));
	} else if (y <= 2.5e+185) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) * (y / (z - t))
    if (y <= (-5.3d+154)) then
        tmp = t_1
    else if (y <= (-1.05d+30)) then
        tmp = a * 120.0d0
    else if (y <= (-3.1d-83)) then
        tmp = 60.0d0 * (x / (z - t))
    else if (y <= 2.5d+185) then
        tmp = a * 120.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double tmp;
	if (y <= -5.3e+154) {
		tmp = t_1;
	} else if (y <= -1.05e+30) {
		tmp = a * 120.0;
	} else if (y <= -3.1e-83) {
		tmp = 60.0 * (x / (z - t));
	} else if (y <= 2.5e+185) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (y / (z - t))
	tmp = 0
	if y <= -5.3e+154:
		tmp = t_1
	elif y <= -1.05e+30:
		tmp = a * 120.0
	elif y <= -3.1e-83:
		tmp = 60.0 * (x / (z - t))
	elif y <= 2.5e+185:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(y / Float64(z - t)))
	tmp = 0.0
	if (y <= -5.3e+154)
		tmp = t_1;
	elseif (y <= -1.05e+30)
		tmp = Float64(a * 120.0);
	elseif (y <= -3.1e-83)
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	elseif (y <= 2.5e+185)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * (y / (z - t));
	tmp = 0.0;
	if (y <= -5.3e+154)
		tmp = t_1;
	elseif (y <= -1.05e+30)
		tmp = a * 120.0;
	elseif (y <= -3.1e-83)
		tmp = 60.0 * (x / (z - t));
	elseif (y <= 2.5e+185)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.3e+154], t$95$1, If[LessEqual[y, -1.05e+30], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, -3.1e-83], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+185], N[(a * 120.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.30000000000000024e154 or 2.49999999999999995e185 < y

   1. Initial program 98.3%

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

      1. associate-*r/ 99.7%

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

      2. fma-def 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.6%

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

      2. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in y around inf 68.8%

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

   if -5.30000000000000024e154 < y < -1.05e30 or -3.09999999999999992e-83 < y < 2.49999999999999995e185

   1. Initial program 99.2%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 63.2%

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

   if -1.05e30 < y < -3.09999999999999992e-83

   1. Initial program 99.9%

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

      1. associate-*r/ 99.9%

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

      2. fma-def 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in x around inf 56.6%

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

      1. *-commutative 56.6%

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

   8. Simplified 56.6%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+154}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{+30}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-83}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+185}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]

Alternative 12: 55.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+154}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{+28}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-83}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+182}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.9e+154)
   (/ (* y -60.0) (- z t))
   (if (<= y -3.5e+28)
     (* a 120.0)
     (if (<= y -1.5e-83)
       (* 60.0 (/ x (- z t)))
       (if (<= y 7.5e+182) (* a 120.0) (* -60.0 (/ y (- z t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.9e+154) {
		tmp = (y * -60.0) / (z - t);
	} else if (y <= -3.5e+28) {
		tmp = a * 120.0;
	} else if (y <= -1.5e-83) {
		tmp = 60.0 * (x / (z - t));
	} else if (y <= 7.5e+182) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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 <= (-2.9d+154)) then
        tmp = (y * (-60.0d0)) / (z - t)
    else if (y <= (-3.5d+28)) then
        tmp = a * 120.0d0
    else if (y <= (-1.5d-83)) then
        tmp = 60.0d0 * (x / (z - t))
    else if (y <= 7.5d+182) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * (y / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.9e+154) {
		tmp = (y * -60.0) / (z - t);
	} else if (y <= -3.5e+28) {
		tmp = a * 120.0;
	} else if (y <= -1.5e-83) {
		tmp = 60.0 * (x / (z - t));
	} else if (y <= 7.5e+182) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.9e+154:
		tmp = (y * -60.0) / (z - t)
	elif y <= -3.5e+28:
		tmp = a * 120.0
	elif y <= -1.5e-83:
		tmp = 60.0 * (x / (z - t))
	elif y <= 7.5e+182:
		tmp = a * 120.0
	else:
		tmp = -60.0 * (y / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.9e+154)
		tmp = Float64(Float64(y * -60.0) / Float64(z - t));
	elseif (y <= -3.5e+28)
		tmp = Float64(a * 120.0);
	elseif (y <= -1.5e-83)
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	elseif (y <= 7.5e+182)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.9e+154)
		tmp = (y * -60.0) / (z - t);
	elseif (y <= -3.5e+28)
		tmp = a * 120.0;
	elseif (y <= -1.5e-83)
		tmp = 60.0 * (x / (z - t));
	elseif (y <= 7.5e+182)
		tmp = a * 120.0;
	else
		tmp = -60.0 * (y / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.9e+154], N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.5e+28], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, -1.5e-83], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+182], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.89999999999999979e154

   1. Initial program 96.3%

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

      1. associate-*r/ 99.8%

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

      2. fma-def 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around inf 62.9%

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

      1. associate-*r/ 63.0%

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

   8. Applied egg-rr 63.0%

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

   if -2.89999999999999979e154 < y < -3.5e28 or -1.50000000000000005e-83 < y < 7.49999999999999989e182

   1. Initial program 99.2%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 63.2%

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

   if -3.5e28 < y < -1.50000000000000005e-83

   1. Initial program 99.9%

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

      1. associate-*r/ 99.9%

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

      2. fma-def 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in x around inf 56.6%

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

      1. *-commutative 56.6%

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

   8. Simplified 56.6%

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

   if 7.49999999999999989e182 < y

   1. Initial program 99.6%

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

      1. associate-*r/ 99.6%

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

      2. fma-def 99.5%

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

   3. Simplified 99.5%

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

      1. clear-num 99.6%

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

      2. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around inf 72.9%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+154}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{+28}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-83}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+182}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]

Alternative 13: 55.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+154}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+28}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-83}:\\ \;\;\;\;\frac{60 \cdot x}{z - t}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+186}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -4.7e+154)
   (/ (* y -60.0) (- z t))
   (if (<= y -1.3e+28)
     (* a 120.0)
     (if (<= y -3.1e-83)
       (/ (* 60.0 x) (- z t))
       (if (<= y 1.45e+186) (* a 120.0) (* -60.0 (/ y (- z t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.7e+154) {
		tmp = (y * -60.0) / (z - t);
	} else if (y <= -1.3e+28) {
		tmp = a * 120.0;
	} else if (y <= -3.1e-83) {
		tmp = (60.0 * x) / (z - t);
	} else if (y <= 1.45e+186) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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 <= (-4.7d+154)) then
        tmp = (y * (-60.0d0)) / (z - t)
    else if (y <= (-1.3d+28)) then
        tmp = a * 120.0d0
    else if (y <= (-3.1d-83)) then
        tmp = (60.0d0 * x) / (z - t)
    else if (y <= 1.45d+186) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * (y / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.7e+154) {
		tmp = (y * -60.0) / (z - t);
	} else if (y <= -1.3e+28) {
		tmp = a * 120.0;
	} else if (y <= -3.1e-83) {
		tmp = (60.0 * x) / (z - t);
	} else if (y <= 1.45e+186) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -4.7e+154:
		tmp = (y * -60.0) / (z - t)
	elif y <= -1.3e+28:
		tmp = a * 120.0
	elif y <= -3.1e-83:
		tmp = (60.0 * x) / (z - t)
	elif y <= 1.45e+186:
		tmp = a * 120.0
	else:
		tmp = -60.0 * (y / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -4.7e+154)
		tmp = Float64(Float64(y * -60.0) / Float64(z - t));
	elseif (y <= -1.3e+28)
		tmp = Float64(a * 120.0);
	elseif (y <= -3.1e-83)
		tmp = Float64(Float64(60.0 * x) / Float64(z - t));
	elseif (y <= 1.45e+186)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -4.7e+154)
		tmp = (y * -60.0) / (z - t);
	elseif (y <= -1.3e+28)
		tmp = a * 120.0;
	elseif (y <= -3.1e-83)
		tmp = (60.0 * x) / (z - t);
	elseif (y <= 1.45e+186)
		tmp = a * 120.0;
	else
		tmp = -60.0 * (y / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -4.7e+154], N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.3e+28], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, -3.1e-83], N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e+186], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.69999999999999983e154

   1. Initial program 96.3%

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

      1. associate-*r/ 99.8%

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

      2. fma-def 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around inf 62.9%

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

      1. associate-*r/ 63.0%

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

   8. Applied egg-rr 63.0%

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

   if -4.69999999999999983e154 < y < -1.3000000000000001e28 or -3.09999999999999992e-83 < y < 1.45e186

   1. Initial program 99.2%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 63.2%

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

   if -1.3000000000000001e28 < y < -3.09999999999999992e-83

   1. Initial program 99.9%

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

      1. associate-*r/ 99.9%

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

      2. fma-def 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in x around inf 56.6%

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

      1. associate-*r/ 56.7%

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

   8. Simplified 56.7%

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

   if 1.45e186 < y

   1. Initial program 99.6%

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

      1. associate-*r/ 99.6%

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

      2. fma-def 99.5%

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

   3. Simplified 99.5%

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

      1. clear-num 99.6%

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

      2. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around inf 72.9%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+154}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+28}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-83}:\\ \;\;\;\;\frac{60 \cdot x}{z - t}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+186}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]

Alternative 14: 84.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-20} \lor \neg \left(z \leq 5.3 \cdot 10^{-33}\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.5e-20) (not (<= z 5.3e-33)))
   (+ (* a 120.0) (* 60.0 (/ (- x y) z)))
   (+ (* a 120.0) (* -60.0 (/ (- x y) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.5e-20) || !(z <= 5.3e-33)) {
		tmp = (a * 120.0) + (60.0 * ((x - y) / z));
	} else {
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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 ((z <= (-2.5d-20)) .or. (.not. (z <= 5.3d-33))) then
        tmp = (a * 120.0d0) + (60.0d0 * ((x - y) / z))
    else
        tmp = (a * 120.0d0) + ((-60.0d0) * ((x - y) / 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 ((z <= -2.5e-20) || !(z <= 5.3e-33)) {
		tmp = (a * 120.0) + (60.0 * ((x - y) / z));
	} else {
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.5e-20) or not (z <= 5.3e-33):
		tmp = (a * 120.0) + (60.0 * ((x - y) / z))
	else:
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.5e-20) || !(z <= 5.3e-33))
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(Float64(x - y) / z)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(Float64(x - y) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.5e-20) || ~((z <= 5.3e-33)))
		tmp = (a * 120.0) + (60.0 * ((x - y) / z));
	else
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.5e-20], N[Not[LessEqual[z, 5.3e-33]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4999999999999999e-20 or 5.29999999999999968e-33 < z

   1. Initial program 98.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 85.6%

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

   if -2.4999999999999999e-20 < z < 5.29999999999999968e-33

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 85.5%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-20} \lor \neg \left(z \leq 5.3 \cdot 10^{-33}\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \end{array} \]

Alternative 15: 84.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-16}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;z \leq 0.09:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z}{x - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.5e-16)
   (+ (* a 120.0) (* 60.0 (/ (- x y) z)))
   (if (<= z 0.09)
     (+ (* a 120.0) (* -60.0 (/ (- x y) t)))
     (+ (* a 120.0) (/ 60.0 (/ z (- x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e-16) {
		tmp = (a * 120.0) + (60.0 * ((x - y) / z));
	} else if (z <= 0.09) {
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	} else {
		tmp = (a * 120.0) + (60.0 / (z / (x - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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 (z <= (-8.5d-16)) then
        tmp = (a * 120.0d0) + (60.0d0 * ((x - y) / z))
    else if (z <= 0.09d0) then
        tmp = (a * 120.0d0) + ((-60.0d0) * ((x - y) / t))
    else
        tmp = (a * 120.0d0) + (60.0d0 / (z / (x - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e-16) {
		tmp = (a * 120.0) + (60.0 * ((x - y) / z));
	} else if (z <= 0.09) {
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	} else {
		tmp = (a * 120.0) + (60.0 / (z / (x - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.5e-16:
		tmp = (a * 120.0) + (60.0 * ((x - y) / z))
	elif z <= 0.09:
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t))
	else:
		tmp = (a * 120.0) + (60.0 / (z / (x - y)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.5e-16)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(Float64(x - y) / z)));
	elseif (z <= 0.09)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(Float64(x - y) / t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(z / Float64(x - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.5e-16)
		tmp = (a * 120.0) + (60.0 * ((x - y) / z));
	elseif (z <= 0.09)
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	else
		tmp = (a * 120.0) + (60.0 / (z / (x - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.5e-16], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.09], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.5000000000000001e-16

   1. Initial program 97.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 82.7%

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

   if -8.5000000000000001e-16 < z < 0.089999999999999997

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 84.6%

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

   if 0.089999999999999997 < z

   1. Initial program 98.6%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 89.6%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-16}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;z \leq 0.09:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z}{x - y}}\\ \end{array} \]

Alternative 16: 51.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-61}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-83}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+185}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.25e-61)
   (* a 120.0)
   (if (<= y -3.1e-83)
     (* -60.0 (/ x t))
     (if (<= y 4.9e+185) (* a 120.0) (* -60.0 (/ y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.25e-61) {
		tmp = a * 120.0;
	} else if (y <= -3.1e-83) {
		tmp = -60.0 * (x / t);
	} else if (y <= 4.9e+185) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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 <= (-2.25d-61)) then
        tmp = a * 120.0d0
    else if (y <= (-3.1d-83)) then
        tmp = (-60.0d0) * (x / t)
    else if (y <= 4.9d+185) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * (y / z)
    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 <= -2.25e-61) {
		tmp = a * 120.0;
	} else if (y <= -3.1e-83) {
		tmp = -60.0 * (x / t);
	} else if (y <= 4.9e+185) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.25e-61:
		tmp = a * 120.0
	elif y <= -3.1e-83:
		tmp = -60.0 * (x / t)
	elif y <= 4.9e+185:
		tmp = a * 120.0
	else:
		tmp = -60.0 * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.25e-61)
		tmp = Float64(a * 120.0);
	elseif (y <= -3.1e-83)
		tmp = Float64(-60.0 * Float64(x / t));
	elseif (y <= 4.9e+185)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.25e-61)
		tmp = a * 120.0;
	elseif (y <= -3.1e-83)
		tmp = -60.0 * (x / t);
	elseif (y <= 4.9e+185)
		tmp = a * 120.0;
	else
		tmp = -60.0 * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.25e-61], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, -3.1e-83], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.9e+185], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.25e-61 or -3.09999999999999992e-83 < y < 4.89999999999999984e185

   1. Initial program 98.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 56.7%

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

   if -2.25e-61 < y < -3.09999999999999992e-83

   1. Initial program 99.7%

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

      1. associate-*r/ 100.0%

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

      2. fma-def 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around inf 84.0%

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

      1. associate-*r/ 83.7%

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

   8. Simplified 83.7%

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

   9. Taylor expanded in z around 0 84.7%

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

   if 4.89999999999999984e185 < y

   1. Initial program 99.6%

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

      1. associate-*r/ 99.6%

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

      2. fma-def 99.5%

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

   3. Simplified 99.5%

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

      1. clear-num 99.6%

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

      2. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around inf 72.9%

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

   7. Taylor expanded in z around inf 44.6%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-61}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-83}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+185}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \end{array} \]

Alternative 17: 51.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-61}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-83}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+187}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.4e-61)
   (* a 120.0)
   (if (<= y -3.1e-83)
     (* -60.0 (/ x t))
     (if (<= y 1.4e+187) (* a 120.0) (/ -60.0 (/ z y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.4e-61) {
		tmp = a * 120.0;
	} else if (y <= -3.1e-83) {
		tmp = -60.0 * (x / t);
	} else if (y <= 1.4e+187) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 / (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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 <= (-2.4d-61)) then
        tmp = a * 120.0d0
    else if (y <= (-3.1d-83)) then
        tmp = (-60.0d0) * (x / t)
    else if (y <= 1.4d+187) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) / (z / y)
    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 <= -2.4e-61) {
		tmp = a * 120.0;
	} else if (y <= -3.1e-83) {
		tmp = -60.0 * (x / t);
	} else if (y <= 1.4e+187) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.4e-61:
		tmp = a * 120.0
	elif y <= -3.1e-83:
		tmp = -60.0 * (x / t)
	elif y <= 1.4e+187:
		tmp = a * 120.0
	else:
		tmp = -60.0 / (z / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.4e-61)
		tmp = Float64(a * 120.0);
	elseif (y <= -3.1e-83)
		tmp = Float64(-60.0 * Float64(x / t));
	elseif (y <= 1.4e+187)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.4e-61)
		tmp = a * 120.0;
	elseif (y <= -3.1e-83)
		tmp = -60.0 * (x / t);
	elseif (y <= 1.4e+187)
		tmp = a * 120.0;
	else
		tmp = -60.0 / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.4e-61], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, -3.1e-83], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e+187], N[(a * 120.0), $MachinePrecision], N[(-60.0 / N[(z / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4000000000000001e-61 or -3.09999999999999992e-83 < y < 1.39999999999999995e187

   1. Initial program 98.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 56.7%

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

   if -2.4000000000000001e-61 < y < -3.09999999999999992e-83

   1. Initial program 99.7%

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

      1. associate-*r/ 100.0%

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

      2. fma-def 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around inf 84.0%

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

      1. associate-*r/ 83.7%

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

   8. Simplified 83.7%

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

   9. Taylor expanded in z around 0 84.7%

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

   if 1.39999999999999995e187 < y

   1. Initial program 99.6%

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

      1. associate-*r/ 99.6%

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

      2. fma-def 99.5%

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

   3. Simplified 99.5%

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

      1. clear-num 99.6%

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

      2. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around inf 72.9%

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

   7. Taylor expanded in z around inf 44.6%

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

      1. associate-*r/ 44.5%

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

      2. associate-/l* 44.7%

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

   9. Simplified 44.7%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-61}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-83}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+187}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{z}{y}}\\ \end{array} \]

Alternative 18: 50.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-61}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-83}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.25e-61)
   (* a 120.0)
   (if (<= y -3.1e-83) (* -60.0 (/ x t)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.25e-61) {
		tmp = a * 120.0;
	} else if (y <= -3.1e-83) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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 <= (-2.25d-61)) then
        tmp = a * 120.0d0
    else if (y <= (-3.1d-83)) then
        tmp = (-60.0d0) * (x / t)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.25e-61) {
		tmp = a * 120.0;
	} else if (y <= -3.1e-83) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.25e-61:
		tmp = a * 120.0
	elif y <= -3.1e-83:
		tmp = -60.0 * (x / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.25e-61)
		tmp = Float64(a * 120.0);
	elseif (y <= -3.1e-83)
		tmp = Float64(-60.0 * Float64(x / t));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.25e-61)
		tmp = a * 120.0;
	elseif (y <= -3.1e-83)
		tmp = -60.0 * (x / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.25e-61], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, -3.1e-83], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.25e-61 or -3.09999999999999992e-83 < y

   1. Initial program 99.0%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 50.2%

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

   if -2.25e-61 < y < -3.09999999999999992e-83

   1. Initial program 99.7%

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

      1. associate-*r/ 100.0%

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

      2. fma-def 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around inf 84.0%

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

      1. associate-*r/ 83.7%

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

   8. Simplified 83.7%

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

   9. Taylor expanded in z around 0 84.7%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-61}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-83}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 19: 51.4% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (* a 120.0))

C

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

Fortran

real(8) function code(x, y, z, t, a)
    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 = a * 120.0d0
end function

Java

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

Python

def code(x, y, z, t, a):
	return a * 120.0

Julia

function code(x, y, z, t, a)
	return Float64(a * 120.0)
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(a * 120.0), $MachinePrecision]

Derivation

1. Initial program 99.0%

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

   1. associate-/l* 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in z around inf 49.1%

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

5. Final simplification 49.1%

   \[\leadsto a \cdot 120 \]

Developer target: 99.8% accurate, 1.0× 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

real(8) function code(x, y, z, t, a)
    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 2023229 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

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

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