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

Percentage Accurate: 99.2% → 99.8%

Time: 17.8s

Alternatives: 18

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: 99.2% 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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. +-commutative 99.8%

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

   2. fma-def 99.8%

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

   3. associate-*l/ 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 71.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60}{z - t} \cdot \left(x - y\right)\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-31}:\\ \;\;\;\;60 \cdot \frac{x}{z} + a \cdot 120\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{-51}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ 60.0 (- z t)) (- x y))) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -5e+87)
     t_1
     (if (<= t_2 -5e-31)
       (+ (* 60.0 (/ x z)) (* a 120.0))
       (if (<= t_2 -2e-117)
         t_1
         (if (<= t_2 5e-51) (* a 120.0) (/ 60.0 (/ (- z t) (- x y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 / (z - t)) * (x - y);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e+87) {
		tmp = t_1;
	} else if (t_2 <= -5e-31) {
		tmp = (60.0 * (x / z)) + (a * 120.0);
	} else if (t_2 <= -2e-117) {
		tmp = t_1;
	} else if (t_2 <= 5e-51) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 / ((z - t) / (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (60.0d0 / (z - t)) * (x - y)
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-5d+87)) then
        tmp = t_1
    else if (t_2 <= (-5d-31)) then
        tmp = (60.0d0 * (x / z)) + (a * 120.0d0)
    else if (t_2 <= (-2d-117)) then
        tmp = t_1
    else if (t_2 <= 5d-51) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 / ((z - t) / (x - y))
    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 / (z - t)) * (x - y);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e+87) {
		tmp = t_1;
	} else if (t_2 <= -5e-31) {
		tmp = (60.0 * (x / z)) + (a * 120.0);
	} else if (t_2 <= -2e-117) {
		tmp = t_1;
	} else if (t_2 <= 5e-51) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 / ((z - t) / (x - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 / (z - t)) * (x - y)
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -5e+87:
		tmp = t_1
	elif t_2 <= -5e-31:
		tmp = (60.0 * (x / z)) + (a * 120.0)
	elif t_2 <= -2e-117:
		tmp = t_1
	elif t_2 <= 5e-51:
		tmp = a * 120.0
	else:
		tmp = 60.0 / ((z - t) / (x - y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y))
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -5e+87)
		tmp = t_1;
	elseif (t_2 <= -5e-31)
		tmp = Float64(Float64(60.0 * Float64(x / z)) + Float64(a * 120.0));
	elseif (t_2 <= -2e-117)
		tmp = t_1;
	elseif (t_2 <= 5e-51)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 / (z - t)) * (x - y);
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -5e+87)
		tmp = t_1;
	elseif (t_2 <= -5e-31)
		tmp = (60.0 * (x / z)) + (a * 120.0);
	elseif (t_2 <= -2e-117)
		tmp = t_1;
	elseif (t_2 <= 5e-51)
		tmp = a * 120.0;
	else
		tmp = 60.0 / ((z - t) / (x - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+87], t$95$1, If[LessEqual[t$95$2, -5e-31], N[(N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -2e-117], t$95$1, If[LessEqual[t$95$2, 5e-51], N[(a * 120.0), $MachinePrecision], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < -4.9999999999999998e87 or -5e-31 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < -2.00000000000000006e-117

   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* 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in a around 0 84.3%

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

      1. *-commutative 84.3%

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

      2. associate-*l/ 84.3%

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

      3. associate-*r/ 84.4%

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

   8. Simplified 84.4%

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

   if -4.9999999999999998e87 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < -5e-31

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-def 99.9%

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

      3. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 77.8%

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

   5. Taylor expanded in y around 0 67.2%

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

   if -2.00000000000000006e-117 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < 5.00000000000000004e-51

   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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 87.3%

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

   if 5.00000000000000004e-51 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t))

   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 78.9%

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

      1. expm1-log1p-u 75.1%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)\right)} \]

      2. expm1-udef 67.7%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)} - 1} \]

      3. associate-*r/ 67.7%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}}\right)} - 1 \]

      4. associate-/l* 67.7%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{60}{\frac{z - t}{x - y}}}\right)} - 1 \]

   6. Applied egg-rr 67.7%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{60}{\frac{z - t}{x - y}}\right)} - 1} \]
   7. Step-by-step derivation

      1. expm1-def 75.0%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{60}{\frac{z - t}{x - y}}\right)\right)} \]

      2. expm1-log1p 79.0%

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

   8. Simplified 79.0%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{+87}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{-31}:\\ \;\;\;\;60 \cdot \frac{x}{z} + a \cdot 120\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -2 \cdot 10^{-117}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 5 \cdot 10^{-51}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \end{array} \]

Alternative 3: 66.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z - t \leq -5 \cdot 10^{+76}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z - t \leq 10^{+92}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;z - t \leq 5 \cdot 10^{+179}:\\ \;\;\;\;60 \cdot \frac{y}{t} + a \cdot 120\\ \mathbf{elif}\;z - t \leq 4 \cdot 10^{+265}:\\ \;\;\;\;60 \cdot \frac{x}{z} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (- z t) -5e+76)
   (* a 120.0)
   (if (<= (- z t) 1e+92)
     (* (/ 60.0 (- z t)) (- x y))
     (if (<= (- z t) 5e+179)
       (+ (* 60.0 (/ y t)) (* a 120.0))
       (if (<= (- z t) 4e+265)
         (+ (* 60.0 (/ x z)) (* a 120.0))
         (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z - t) <= -5e+76) {
		tmp = a * 120.0;
	} else if ((z - t) <= 1e+92) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else if ((z - t) <= 5e+179) {
		tmp = (60.0 * (y / t)) + (a * 120.0);
	} else if ((z - t) <= 4e+265) {
		tmp = (60.0 * (x / z)) + (a * 120.0);
	} 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 ((z - t) <= (-5d+76)) then
        tmp = a * 120.0d0
    else if ((z - t) <= 1d+92) then
        tmp = (60.0d0 / (z - t)) * (x - y)
    else if ((z - t) <= 5d+179) then
        tmp = (60.0d0 * (y / t)) + (a * 120.0d0)
    else if ((z - t) <= 4d+265) then
        tmp = (60.0d0 * (x / z)) + (a * 120.0d0)
    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 ((z - t) <= -5e+76) {
		tmp = a * 120.0;
	} else if ((z - t) <= 1e+92) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else if ((z - t) <= 5e+179) {
		tmp = (60.0 * (y / t)) + (a * 120.0);
	} else if ((z - t) <= 4e+265) {
		tmp = (60.0 * (x / z)) + (a * 120.0);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z - t) <= -5e+76:
		tmp = a * 120.0
	elif (z - t) <= 1e+92:
		tmp = (60.0 / (z - t)) * (x - y)
	elif (z - t) <= 5e+179:
		tmp = (60.0 * (y / t)) + (a * 120.0)
	elif (z - t) <= 4e+265:
		tmp = (60.0 * (x / z)) + (a * 120.0)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z - t) <= -5e+76)
		tmp = Float64(a * 120.0);
	elseif (Float64(z - t) <= 1e+92)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	elseif (Float64(z - t) <= 5e+179)
		tmp = Float64(Float64(60.0 * Float64(y / t)) + Float64(a * 120.0));
	elseif (Float64(z - t) <= 4e+265)
		tmp = Float64(Float64(60.0 * Float64(x / z)) + Float64(a * 120.0));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z - t) <= -5e+76)
		tmp = a * 120.0;
	elseif ((z - t) <= 1e+92)
		tmp = (60.0 / (z - t)) * (x - y);
	elseif ((z - t) <= 5e+179)
		tmp = (60.0 * (y / t)) + (a * 120.0);
	elseif ((z - t) <= 4e+265)
		tmp = (60.0 * (x / z)) + (a * 120.0);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(z - t), $MachinePrecision], -5e+76], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(z - t), $MachinePrecision], 1e+92], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z - t), $MachinePrecision], 5e+179], N[(N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z - t), $MachinePrecision], 4e+265], N[(N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 z t) < -4.99999999999999991e76 or 4.00000000000000027e265 < (-.f64 z t)

   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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 73.1%

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

   if -4.99999999999999991e76 < (-.f64 z t) < 1e92

   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* 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in a around 0 83.6%

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

      1. *-commutative 83.6%

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

      2. associate-*l/ 83.5%

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

      3. associate-*r/ 83.7%

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

   8. Simplified 83.7%

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

   if 1e92 < (-.f64 z t) < 5e179

   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* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 92.6%

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

      1. associate-*r/ 92.5%

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

      2. associate-/l* 92.5%

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

   6. Simplified 92.5%

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

   7. Taylor expanded in z around 0 76.3%

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

   if 5e179 < (-.f64 z t) < 4.00000000000000027e265

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-def 99.9%

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

      3. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 88.6%

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

   5. Taylor expanded in y around 0 75.8%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z - t \leq -5 \cdot 10^{+76}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z - t \leq 10^{+92}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;z - t \leq 5 \cdot 10^{+179}:\\ \;\;\;\;60 \cdot \frac{y}{t} + a \cdot 120\\ \mathbf{elif}\;z - t \leq 4 \cdot 10^{+265}:\\ \;\;\;\;60 \cdot \frac{x}{z} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 4: 66.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z - t \leq -5 \cdot 10^{+76}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z - t \leq 10^{+92}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;z - t \leq 5 \cdot 10^{+179}:\\ \;\;\;\;60 \cdot \frac{y}{t} + a \cdot 120\\ \mathbf{elif}\;z - t \leq 4 \cdot 10^{+232}:\\ \;\;\;\;60 \cdot \frac{x}{z} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (- z t) -5e+76)
   (* a 120.0)
   (if (<= (- z t) 1e+92)
     (* (/ 60.0 (- z t)) (- x y))
     (if (<= (- z t) 5e+179)
       (+ (* 60.0 (/ y t)) (* a 120.0))
       (if (<= (- z t) 4e+232)
         (+ (* 60.0 (/ x z)) (* a 120.0))
         (+ (* a 120.0) (/ -60.0 (/ z y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z - t) <= -5e+76) {
		tmp = a * 120.0;
	} else if ((z - t) <= 1e+92) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else if ((z - t) <= 5e+179) {
		tmp = (60.0 * (y / t)) + (a * 120.0);
	} else if ((z - t) <= 4e+232) {
		tmp = (60.0 * (x / z)) + (a * 120.0);
	} else {
		tmp = (a * 120.0) + (-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 ((z - t) <= (-5d+76)) then
        tmp = a * 120.0d0
    else if ((z - t) <= 1d+92) then
        tmp = (60.0d0 / (z - t)) * (x - y)
    else if ((z - t) <= 5d+179) then
        tmp = (60.0d0 * (y / t)) + (a * 120.0d0)
    else if ((z - t) <= 4d+232) then
        tmp = (60.0d0 * (x / z)) + (a * 120.0d0)
    else
        tmp = (a * 120.0d0) + ((-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 ((z - t) <= -5e+76) {
		tmp = a * 120.0;
	} else if ((z - t) <= 1e+92) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else if ((z - t) <= 5e+179) {
		tmp = (60.0 * (y / t)) + (a * 120.0);
	} else if ((z - t) <= 4e+232) {
		tmp = (60.0 * (x / z)) + (a * 120.0);
	} else {
		tmp = (a * 120.0) + (-60.0 / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z - t) <= -5e+76:
		tmp = a * 120.0
	elif (z - t) <= 1e+92:
		tmp = (60.0 / (z - t)) * (x - y)
	elif (z - t) <= 5e+179:
		tmp = (60.0 * (y / t)) + (a * 120.0)
	elif (z - t) <= 4e+232:
		tmp = (60.0 * (x / z)) + (a * 120.0)
	else:
		tmp = (a * 120.0) + (-60.0 / (z / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z - t) <= -5e+76)
		tmp = Float64(a * 120.0);
	elseif (Float64(z - t) <= 1e+92)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	elseif (Float64(z - t) <= 5e+179)
		tmp = Float64(Float64(60.0 * Float64(y / t)) + Float64(a * 120.0));
	elseif (Float64(z - t) <= 4e+232)
		tmp = Float64(Float64(60.0 * Float64(x / z)) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z - t) <= -5e+76)
		tmp = a * 120.0;
	elseif ((z - t) <= 1e+92)
		tmp = (60.0 / (z - t)) * (x - y);
	elseif ((z - t) <= 5e+179)
		tmp = (60.0 * (y / t)) + (a * 120.0);
	elseif ((z - t) <= 4e+232)
		tmp = (60.0 * (x / z)) + (a * 120.0);
	else
		tmp = (a * 120.0) + (-60.0 / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(z - t), $MachinePrecision], -5e+76], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(z - t), $MachinePrecision], 1e+92], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z - t), $MachinePrecision], 5e+179], N[(N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z - t), $MachinePrecision], 4e+232], N[(N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (-.f64 z t) < -4.99999999999999991e76

   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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 69.2%

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

   if -4.99999999999999991e76 < (-.f64 z t) < 1e92

   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* 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in a around 0 83.6%

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

      1. *-commutative 83.6%

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

      2. associate-*l/ 83.5%

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

      3. associate-*r/ 83.7%

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

   8. Simplified 83.7%

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

   if 1e92 < (-.f64 z t) < 5e179

   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* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 92.6%

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

      1. associate-*r/ 92.5%

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

      2. associate-/l* 92.5%

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

   6. Simplified 92.5%

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

   7. Taylor expanded in z around 0 76.3%

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

   if 5e179 < (-.f64 z t) < 4.00000000000000023e232

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-def 99.9%

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

      3. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 91.1%

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

   5. Taylor expanded in y around 0 84.9%

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

   if 4.00000000000000023e232 < (-.f64 z t)

   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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 95.9%

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

      1. associate-*r/ 96.0%

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

      2. associate-/l* 95.9%

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

   6. Simplified 95.9%

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

   7. Taylor expanded in z around inf 88.4%

      \[\leadsto \frac{-60}{\color{blue}{\frac{z}{y}}} + a \cdot 120 \]
3. Recombined 5 regimes into one program.

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z - t \leq -5 \cdot 10^{+76}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z - t \leq 10^{+92}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;z - t \leq 5 \cdot 10^{+179}:\\ \;\;\;\;60 \cdot \frac{y}{t} + a \cdot 120\\ \mathbf{elif}\;z - t \leq 4 \cdot 10^{+232}:\\ \;\;\;\;60 \cdot \frac{x}{z} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{z}{y}}\\ \end{array} \]

Alternative 5: 74.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z} + a \cdot 120\\ \mathbf{if}\;z \leq -5 \cdot 10^{-51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-250}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-307}:\\ \;\;\;\;60 \cdot \frac{y}{t} + a \cdot 120\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-238}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-204}:\\ \;\;\;\;-60 \cdot \frac{x}{t} + a \cdot 120\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+16}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* 60.0 (/ (- x y) z)) (* a 120.0))))
   (if (<= z -5e-51)
     t_1
     (if (<= z -1.6e-250)
       (/ 60.0 (/ (- z t) (- x y)))
       (if (<= z -6.2e-307)
         (+ (* 60.0 (/ y t)) (* a 120.0))
         (if (<= z 8e-238)
           (* 60.0 (/ (- x y) (- z t)))
           (if (<= z 8.8e-204)
             (+ (* -60.0 (/ x t)) (* a 120.0))
             (if (<= z 1.2e+16) (* (/ 60.0 (- z t)) (- x y)) t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * ((x - y) / z)) + (a * 120.0);
	double tmp;
	if (z <= -5e-51) {
		tmp = t_1;
	} else if (z <= -1.6e-250) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if (z <= -6.2e-307) {
		tmp = (60.0 * (y / t)) + (a * 120.0);
	} else if (z <= 8e-238) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (z <= 8.8e-204) {
		tmp = (-60.0 * (x / t)) + (a * 120.0);
	} else if (z <= 1.2e+16) {
		tmp = (60.0 / (z - t)) * (x - y);
	} 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 * ((x - y) / z)) + (a * 120.0d0)
    if (z <= (-5d-51)) then
        tmp = t_1
    else if (z <= (-1.6d-250)) then
        tmp = 60.0d0 / ((z - t) / (x - y))
    else if (z <= (-6.2d-307)) then
        tmp = (60.0d0 * (y / t)) + (a * 120.0d0)
    else if (z <= 8d-238) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if (z <= 8.8d-204) then
        tmp = ((-60.0d0) * (x / t)) + (a * 120.0d0)
    else if (z <= 1.2d+16) then
        tmp = (60.0d0 / (z - t)) * (x - y)
    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 * ((x - y) / z)) + (a * 120.0);
	double tmp;
	if (z <= -5e-51) {
		tmp = t_1;
	} else if (z <= -1.6e-250) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if (z <= -6.2e-307) {
		tmp = (60.0 * (y / t)) + (a * 120.0);
	} else if (z <= 8e-238) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (z <= 8.8e-204) {
		tmp = (-60.0 * (x / t)) + (a * 120.0);
	} else if (z <= 1.2e+16) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * ((x - y) / z)) + (a * 120.0)
	tmp = 0
	if z <= -5e-51:
		tmp = t_1
	elif z <= -1.6e-250:
		tmp = 60.0 / ((z - t) / (x - y))
	elif z <= -6.2e-307:
		tmp = (60.0 * (y / t)) + (a * 120.0)
	elif z <= 8e-238:
		tmp = 60.0 * ((x - y) / (z - t))
	elif z <= 8.8e-204:
		tmp = (-60.0 * (x / t)) + (a * 120.0)
	elif z <= 1.2e+16:
		tmp = (60.0 / (z - t)) * (x - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(Float64(x - y) / z)) + Float64(a * 120.0))
	tmp = 0.0
	if (z <= -5e-51)
		tmp = t_1;
	elseif (z <= -1.6e-250)
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	elseif (z <= -6.2e-307)
		tmp = Float64(Float64(60.0 * Float64(y / t)) + Float64(a * 120.0));
	elseif (z <= 8e-238)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (z <= 8.8e-204)
		tmp = Float64(Float64(-60.0 * Float64(x / t)) + Float64(a * 120.0));
	elseif (z <= 1.2e+16)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * ((x - y) / z)) + (a * 120.0);
	tmp = 0.0;
	if (z <= -5e-51)
		tmp = t_1;
	elseif (z <= -1.6e-250)
		tmp = 60.0 / ((z - t) / (x - y));
	elseif (z <= -6.2e-307)
		tmp = (60.0 * (y / t)) + (a * 120.0);
	elseif (z <= 8e-238)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif (z <= 8.8e-204)
		tmp = (-60.0 * (x / t)) + (a * 120.0);
	elseif (z <= 1.2e+16)
		tmp = (60.0 / (z - t)) * (x - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e-51], t$95$1, If[LessEqual[z, -1.6e-250], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.2e-307], N[(N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-238], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.8e-204], N[(N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e+16], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -5.00000000000000004e-51 or 1.2e16 < z

   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* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 89.8%

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

   if -5.00000000000000004e-51 < z < -1.60000000000000002e-250

   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* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 81.2%

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

      1. expm1-log1p-u 43.1%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)\right)} \]

      2. expm1-udef 27.8%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)} - 1} \]

      3. associate-*r/ 27.8%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}}\right)} - 1 \]

      4. associate-/l* 27.8%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{60}{\frac{z - t}{x - y}}}\right)} - 1 \]

   6. Applied egg-rr 27.8%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{60}{\frac{z - t}{x - y}}\right)} - 1} \]
   7. Step-by-step derivation

      1. expm1-def 43.1%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{60}{\frac{z - t}{x - y}}\right)\right)} \]

      2. expm1-log1p 81.3%

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

   8. Simplified 81.3%

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

   if -1.60000000000000002e-250 < z < -6.1999999999999996e-307

   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* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 89.9%

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

      1. associate-*r/ 89.9%

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

      2. associate-/l* 89.7%

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

   6. Simplified 89.7%

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

   7. Taylor expanded in z around 0 89.9%

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

   if -6.1999999999999996e-307 < z < 7.9999999999999999e-238

   1. Initial program 99.5%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in a around 0 99.6%

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

   if 7.9999999999999999e-238 < z < 8.7999999999999993e-204

   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 99.7%

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

      1. associate-*r/ 99.8%

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

      2. *-commutative 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in z around 0 99.7%

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

   if 8.7999999999999993e-204 < z < 1.2e16

   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* 99.7%

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

   3. Simplified 99.7%

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

      1. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in a around 0 70.9%

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

      1. *-commutative 70.9%

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

      2. associate-*l/ 70.8%

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

      3. associate-*r/ 71.0%

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

   8. Simplified 71.0%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-51}:\\ \;\;\;\;60 \cdot \frac{x - y}{z} + a \cdot 120\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-250}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-307}:\\ \;\;\;\;60 \cdot \frac{y}{t} + a \cdot 120\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-238}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-204}:\\ \;\;\;\;-60 \cdot \frac{x}{t} + a \cdot 120\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+16}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z} + a \cdot 120\\ \end{array} \]

Alternative 6: 67.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z - t \leq -5 \cdot 10^{+76} \lor \neg \left(z - t \leq 10^{+92}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (- z t) -5e+76) (not (<= (- z t) 1e+92)))
   (* a 120.0)
   (* 60.0 (/ (- x y) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z - t) <= -5e+76) || !((z - t) <= 1e+92)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - 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 (((z - t) <= (-5d+76)) .or. (.not. ((z - t) <= 1d+92))) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * ((x - 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 (((z - t) <= -5e+76) || !((z - t) <= 1e+92)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((z - t) <= -5e+76) or not ((z - t) <= 1e+92):
		tmp = a * 120.0
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(z - t) <= -5e+76) || !(Float64(z - t) <= 1e+92))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((z - t) <= -5e+76) || ~(((z - t) <= 1e+92)))
		tmp = a * 120.0;
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(z - t), $MachinePrecision], -5e+76], N[Not[LessEqual[N[(z - t), $MachinePrecision], 1e+92]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 z t) < -4.99999999999999991e76 or 1e92 < (-.f64 z t)

   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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 71.3%

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

   if -4.99999999999999991e76 < (-.f64 z t) < 1e92

   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* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in a around 0 83.6%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z - t \leq -5 \cdot 10^{+76} \lor \neg \left(z - t \leq 10^{+92}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]

Alternative 7: 67.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z - t \leq -5 \cdot 10^{+76} \lor \neg \left(z - t \leq 10^{+92}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (- z t) -5e+76) (not (<= (- z t) 1e+92)))
   (* a 120.0)
   (* (/ 60.0 (- z t)) (- x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z - t) <= -5e+76) || !((z - t) <= 1e+92)) {
		tmp = a * 120.0;
	} else {
		tmp = (60.0 / (z - t)) * (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 - t) <= (-5d+76)) .or. (.not. ((z - t) <= 1d+92))) then
        tmp = a * 120.0d0
    else
        tmp = (60.0d0 / (z - t)) * (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 - t) <= -5e+76) || !((z - t) <= 1e+92)) {
		tmp = a * 120.0;
	} else {
		tmp = (60.0 / (z - t)) * (x - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((z - t) <= -5e+76) or not ((z - t) <= 1e+92):
		tmp = a * 120.0
	else:
		tmp = (60.0 / (z - t)) * (x - y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(z - t) <= -5e+76) || !(Float64(z - t) <= 1e+92))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((z - t) <= -5e+76) || ~(((z - t) <= 1e+92)))
		tmp = a * 120.0;
	else
		tmp = (60.0 / (z - t)) * (x - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(z - t), $MachinePrecision], -5e+76], N[Not[LessEqual[N[(z - t), $MachinePrecision], 1e+92]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 z t) < -4.99999999999999991e76 or 1e92 < (-.f64 z t)

   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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 71.3%

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

   if -4.99999999999999991e76 < (-.f64 z t) < 1e92

   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* 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in a around 0 83.6%

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

      1. *-commutative 83.6%

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

      2. associate-*l/ 83.5%

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

      3. associate-*r/ 83.7%

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

   8. Simplified 83.7%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z - t \leq -5 \cdot 10^{+76} \lor \neg \left(z - t \leq 10^{+92}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \end{array} \]

Alternative 8: 54.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z - t \leq -5 \cdot 10^{+76} \lor \neg \left(z - t \leq 2 \cdot 10^{+68}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (- z t) -5e+76) (not (<= (- z t) 2e+68)))
   (* a 120.0)
   (* -60.0 (/ y (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z - t) <= -5e+76) || !((z - t) <= 2e+68)) {
		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 (((z - t) <= (-5d+76)) .or. (.not. ((z - t) <= 2d+68))) 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 (((z - t) <= -5e+76) || !((z - t) <= 2e+68)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((z - t) <= -5e+76) or not ((z - t) <= 2e+68):
		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 ((Float64(z - t) <= -5e+76) || !(Float64(z - t) <= 2e+68))
		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 (((z - t) <= -5e+76) || ~(((z - t) <= 2e+68)))
		tmp = a * 120.0;
	else
		tmp = -60.0 * (y / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(z - t), $MachinePrecision], -5e+76], N[Not[LessEqual[N[(z - t), $MachinePrecision], 2e+68]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 z t) < -4.99999999999999991e76 or 1.99999999999999991e68 < (-.f64 z t)

   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* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 68.2%

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

   if -4.99999999999999991e76 < (-.f64 z t) < 1.99999999999999991e68

   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* 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in y around inf 47.0%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z - t \leq -5 \cdot 10^{+76} \lor \neg \left(z - t \leq 2 \cdot 10^{+68}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]

Alternative 9: 55.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z - t \leq -5 \cdot 10^{+76} \lor \neg \left(z - t \leq 10^{+77}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (- z t) -5e+76) (not (<= (- z t) 1e+77)))
   (* 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 - t) <= -5e+76) || !((z - t) <= 1e+77)) {
		tmp = a * 120.0;
	} else {
		tmp = -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 - t) <= (-5d+76)) .or. (.not. ((z - t) <= 1d+77))) then
        tmp = a * 120.0d0
    else
        tmp = (-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 - t) <= -5e+76) || !((z - t) <= 1e+77)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * ((x - y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((z - t) <= -5e+76) or not ((z - t) <= 1e+77):
		tmp = a * 120.0
	else:
		tmp = -60.0 * ((x - y) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(z - t) <= -5e+76) || !(Float64(z - t) <= 1e+77))
		tmp = Float64(a * 120.0);
	else
		tmp = 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 - t) <= -5e+76) || ~(((z - t) <= 1e+77)))
		tmp = a * 120.0;
	else
		tmp = -60.0 * ((x - y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(z - t), $MachinePrecision], -5e+76], N[Not[LessEqual[N[(z - t), $MachinePrecision], 1e+77]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 z t) < -4.99999999999999991e76 or 9.99999999999999983e76 < (-.f64 z t)

   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* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 69.8%

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

   if -4.99999999999999991e76 < (-.f64 z t) < 9.99999999999999983e76

   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* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 84.5%

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

   5. Taylor expanded in z around 0 56.7%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z - t \leq -5 \cdot 10^{+76} \lor \neg \left(z - t \leq 10^{+77}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \]

Alternative 10: 83.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{-76} \lor \neg \left(z \leq 3.2 \cdot 10^{+14}\right):\\ \;\;\;\;60 \cdot \frac{x - y}{z} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{t}{x - y}} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.8e-76) (not (<= z 3.2e+14)))
   (+ (* 60.0 (/ (- x y) z)) (* a 120.0))
   (+ (/ -60.0 (/ t (- x y))) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.8e-76) || !(z <= 3.2e+14)) {
		tmp = (60.0 * ((x - y) / z)) + (a * 120.0);
	} else {
		tmp = (-60.0 / (t / (x - y))) + (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 ((z <= (-9.8d-76)) .or. (.not. (z <= 3.2d+14))) then
        tmp = (60.0d0 * ((x - y) / z)) + (a * 120.0d0)
    else
        tmp = ((-60.0d0) / (t / (x - y))) + (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 ((z <= -9.8e-76) || !(z <= 3.2e+14)) {
		tmp = (60.0 * ((x - y) / z)) + (a * 120.0);
	} else {
		tmp = (-60.0 / (t / (x - y))) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.8e-76) or not (z <= 3.2e+14):
		tmp = (60.0 * ((x - y) / z)) + (a * 120.0)
	else:
		tmp = (-60.0 / (t / (x - y))) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.8e-76) || !(z <= 3.2e+14))
		tmp = Float64(Float64(60.0 * Float64(Float64(x - y) / z)) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(-60.0 / Float64(t / Float64(x - y))) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9.8e-76) || ~((z <= 3.2e+14)))
		tmp = (60.0 * ((x - y) / z)) + (a * 120.0);
	else
		tmp = (-60.0 / (t / (x - y))) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.8e-76], N[Not[LessEqual[z, 3.2e+14]], $MachinePrecision]], N[(N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(-60.0 / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.79999999999999944e-76 or 3.2e14 < z

   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* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 89.0%

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

   if -9.79999999999999944e-76 < z < 3.2e14

   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 z around 0 87.4%

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

      1. associate-*r/ 87.5%

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

      2. associate-/l* 87.5%

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

   6. Simplified 87.5%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{-76} \lor \neg \left(z \leq 3.2 \cdot 10^{+14}\right):\\ \;\;\;\;60 \cdot \frac{x - y}{z} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{t}{x - y}} + a \cdot 120\\ \end{array} \]

Alternative 11: 89.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+96} \lor \neg \left(x \leq 1.35 \cdot 10^{+76}\right):\\ \;\;\;\;\frac{x}{\frac{z - t}{60}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -2.4e+96) (not (<= x 1.35e+76)))
   (+ (/ x (/ (- z t) 60.0)) (* a 120.0))
   (+ (/ -60.0 (/ (- z t) y)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2.4e+96) || !(x <= 1.35e+76)) {
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0);
	} else {
		tmp = (-60.0 / ((z - t) / y)) + (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 ((x <= (-2.4d+96)) .or. (.not. (x <= 1.35d+76))) then
        tmp = (x / ((z - t) / 60.0d0)) + (a * 120.0d0)
    else
        tmp = ((-60.0d0) / ((z - t) / y)) + (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 ((x <= -2.4e+96) || !(x <= 1.35e+76)) {
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0);
	} else {
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -2.4e+96) or not (x <= 1.35e+76):
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0)
	else:
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -2.4e+96) || !(x <= 1.35e+76))
		tmp = Float64(Float64(x / Float64(Float64(z - t) / 60.0)) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(-60.0 / Float64(Float64(z - t) / y)) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -2.4e+96) || ~((x <= 1.35e+76)))
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0);
	else
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -2.4e+96], N[Not[LessEqual[x, 1.35e+76]], $MachinePrecision]], N[(N[(x / N[(N[(z - t), $MachinePrecision] / 60.0), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(-60.0 / N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.39999999999999993e96 or 1.34999999999999995e76 < x

   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* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 96.2%

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

      1. associate-*r/ 96.3%

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

      2. *-commutative 96.3%

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

      3. associate-/l* 96.4%

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

   6. Simplified 96.4%

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

   if -2.39999999999999993e96 < x < 1.34999999999999995e76

   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 0 91.3%

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

      1. associate-*r/ 91.4%

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

      2. associate-/l* 91.3%

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

   6. Simplified 91.3%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+96} \lor \neg \left(x \leq 1.35 \cdot 10^{+76}\right):\\ \;\;\;\;\frac{x}{\frac{z - t}{60}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \end{array} \]

Alternative 12: 89.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+98} \lor \neg \left(x \leq 5.5 \cdot 10^{+74}\right):\\ \;\;\;\;\frac{x}{\frac{z - t}{60}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -3.6e+98) (not (<= x 5.5e+74)))
   (+ (/ x (/ (- z t) 60.0)) (* a 120.0))
   (+ (/ (* y -60.0) (- z t)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -3.6e+98) || !(x <= 5.5e+74)) {
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0);
	} else {
		tmp = ((y * -60.0) / (z - t)) + (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 ((x <= (-3.6d+98)) .or. (.not. (x <= 5.5d+74))) then
        tmp = (x / ((z - t) / 60.0d0)) + (a * 120.0d0)
    else
        tmp = ((y * (-60.0d0)) / (z - t)) + (a * 120.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -3.6e+98) || !(x <= 5.5e+74)) {
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0);
	} else {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -3.6e+98) or not (x <= 5.5e+74):
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0)
	else:
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -3.6e+98) || !(x <= 5.5e+74))
		tmp = Float64(Float64(x / Float64(Float64(z - t) / 60.0)) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(Float64(y * -60.0) / Float64(z - t)) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -3.6e+98) || ~((x <= 5.5e+74)))
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0);
	else
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -3.6e+98], N[Not[LessEqual[x, 5.5e+74]], $MachinePrecision]], N[(N[(x / N[(N[(z - t), $MachinePrecision] / 60.0), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.59999999999999981e98 or 5.5000000000000003e74 < x

   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* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 96.2%

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

      1. associate-*r/ 96.3%

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

      2. *-commutative 96.3%

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

      3. associate-/l* 96.4%

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

   6. Simplified 96.4%

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

   if -3.59999999999999981e98 < x < 5.5000000000000003e74

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 91.4%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+98} \lor \neg \left(x \leq 5.5 \cdot 10^{+74}\right):\\ \;\;\;\;\frac{x}{\frac{z - t}{60}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \end{array} \]

Alternative 13: 89.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+95}:\\ \;\;\;\;\frac{x}{\frac{z - t}{60}} + a \cdot 120\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+70}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.3e+95)
   (+ (/ x (/ (- z t) 60.0)) (* a 120.0))
   (if (<= x 3.5e+70)
     (+ (/ (* y -60.0) (- z t)) (* a 120.0))
     (+ (/ (* 60.0 x) (- z t)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.3e+95) {
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0);
	} else if (x <= 3.5e+70) {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	} else {
		tmp = ((60.0 * x) / (z - t)) + (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 (x <= (-1.3d+95)) then
        tmp = (x / ((z - t) / 60.0d0)) + (a * 120.0d0)
    else if (x <= 3.5d+70) then
        tmp = ((y * (-60.0d0)) / (z - t)) + (a * 120.0d0)
    else
        tmp = ((60.0d0 * x) / (z - t)) + (a * 120.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.3e+95) {
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0);
	} else if (x <= 3.5e+70) {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	} else {
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.3e+95:
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0)
	elif x <= 3.5e+70:
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0)
	else:
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.3e+95)
		tmp = Float64(Float64(x / Float64(Float64(z - t) / 60.0)) + Float64(a * 120.0));
	elseif (x <= 3.5e+70)
		tmp = Float64(Float64(Float64(y * -60.0) / Float64(z - t)) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(Float64(60.0 * x) / Float64(z - t)) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.3e+95)
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0);
	elseif (x <= 3.5e+70)
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	else
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.3e+95], N[(N[(x / N[(N[(z - t), $MachinePrecision] / 60.0), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.5e+70], N[(N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.29999999999999995e95

   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* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 99.7%

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

      1. associate-*r/ 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   if -1.29999999999999995e95 < x < 3.50000000000000002e70

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 91.4%

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

   if 3.50000000000000002e70 < x

   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* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around inf 93.5%

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

      1. associate-*r/ 93.6%

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

      2. *-commutative 93.6%

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

   6. Simplified 93.6%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+95}:\\ \;\;\;\;\frac{x}{\frac{z - t}{60}} + a \cdot 120\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+70}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \end{array} \]

Alternative 14: 47.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-106} \lor \neg \left(z \leq 3.9 \cdot 10^{-237}\right) \land \left(z \leq 2.2 \cdot 10^{-206} \lor \neg \left(z \leq 2 \cdot 10^{-80}\right)\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{-t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8e-106)
         (and (not (<= z 3.9e-237)) (or (<= z 2.2e-206) (not (<= z 2e-80)))))
   (* a 120.0)
   (/ -60.0 (/ (- t) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8e-106) || (!(z <= 3.9e-237) && ((z <= 2.2e-206) || !(z <= 2e-80)))) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 / (-t / 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 <= (-8d-106)) .or. (.not. (z <= 3.9d-237)) .and. (z <= 2.2d-206) .or. (.not. (z <= 2d-80))) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) / (-t / 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 <= -8e-106) || (!(z <= 3.9e-237) && ((z <= 2.2e-206) || !(z <= 2e-80)))) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 / (-t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8e-106) or (not (z <= 3.9e-237) and ((z <= 2.2e-206) or not (z <= 2e-80))):
		tmp = a * 120.0
	else:
		tmp = -60.0 / (-t / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8e-106) || (!(z <= 3.9e-237) && ((z <= 2.2e-206) || !(z <= 2e-80))))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 / Float64(Float64(-t) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8e-106) || (~((z <= 3.9e-237)) && ((z <= 2.2e-206) || ~((z <= 2e-80)))))
		tmp = a * 120.0;
	else
		tmp = -60.0 / (-t / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8e-106], And[N[Not[LessEqual[z, 3.9e-237]], $MachinePrecision], Or[LessEqual[z, 2.2e-206], N[Not[LessEqual[z, 2e-80]], $MachinePrecision]]]], N[(a * 120.0), $MachinePrecision], N[(-60.0 / N[((-t) / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.99999999999999953e-106 or 3.8999999999999998e-237 < z < 2.1999999999999999e-206 or 1.99999999999999992e-80 < z

   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 inf 59.8%

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

   if -7.99999999999999953e-106 < z < 3.8999999999999998e-237 or 2.1999999999999999e-206 < z < 1.99999999999999992e-80

   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* 99.7%

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

   3. Simplified 99.7%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in y around inf 48.5%

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

      1. associate-*r/ 48.5%

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

      2. associate-/l* 48.5%

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

   8. Applied egg-rr 48.5%

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

   9. Taylor expanded in z around 0 46.7%

      \[\leadsto \frac{-60}{\color{blue}{-1 \cdot \frac{t}{y}}} \]
   10. Step-by-step derivation

       1. mul-1-neg 46.7%

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

       2. distribute-neg-frac 46.7%

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

   11. Simplified 46.7%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-106} \lor \neg \left(z \leq 3.9 \cdot 10^{-237}\right) \land \left(z \leq 2.2 \cdot 10^{-206} \lor \neg \left(z \leq 2 \cdot 10^{-80}\right)\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{-t}{y}}\\ \end{array} \]

Alternative 15: 47.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-106} \lor \neg \left(z \leq 2.2 \cdot 10^{-237}\right) \land \left(z \leq 1.52 \cdot 10^{-207} \lor \neg \left(z \leq 5.2 \cdot 10^{-85}\right)\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.9e-106)
         (and (not (<= z 2.2e-237))
              (or (<= z 1.52e-207) (not (<= z 5.2e-85)))))
   (* a 120.0)
   (* 60.0 (/ y t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.9e-106) || (!(z <= 2.2e-237) && ((z <= 1.52e-207) || !(z <= 5.2e-85)))) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (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 <= (-1.9d-106)) .or. (.not. (z <= 2.2d-237)) .and. (z <= 1.52d-207) .or. (.not. (z <= 5.2d-85))) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * (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 <= -1.9e-106) || (!(z <= 2.2e-237) && ((z <= 1.52e-207) || !(z <= 5.2e-85)))) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.9e-106) or (not (z <= 2.2e-237) and ((z <= 1.52e-207) or not (z <= 5.2e-85))):
		tmp = a * 120.0
	else:
		tmp = 60.0 * (y / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.9e-106) || (!(z <= 2.2e-237) && ((z <= 1.52e-207) || !(z <= 5.2e-85))))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.9e-106) || (~((z <= 2.2e-237)) && ((z <= 1.52e-207) || ~((z <= 5.2e-85)))))
		tmp = a * 120.0;
	else
		tmp = 60.0 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.9e-106], And[N[Not[LessEqual[z, 2.2e-237]], $MachinePrecision], Or[LessEqual[z, 1.52e-207], N[Not[LessEqual[z, 5.2e-85]], $MachinePrecision]]]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9e-106 or 2.19999999999999998e-237 < z < 1.52000000000000005e-207 or 5.20000000000000023e-85 < z

   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 inf 59.8%

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

   if -1.9e-106 < z < 2.19999999999999998e-237 or 1.52000000000000005e-207 < z < 5.20000000000000023e-85

   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* 99.7%

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

   3. Simplified 99.7%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in y around inf 48.5%

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

   7. Taylor expanded in z around 0 46.7%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-106} \lor \neg \left(z \leq 2.2 \cdot 10^{-237}\right) \land \left(z \leq 1.52 \cdot 10^{-207} \lor \neg \left(z \leq 5.2 \cdot 10^{-85}\right)\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 16: 99.8% accurate, 1.0× speedup

Math

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

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(Float64(60.0 / 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[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Derivation

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. Step-by-step derivation

   1. associate-/r/ 99.8%

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

5. Applied egg-rr 99.8%

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

6. Final simplification 99.8%

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

Alternative 17: 52.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+247} \lor \neg \left(y \leq 10^{+188}\right):\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -5.8e+247) (not (<= y 1e+188))) (* -60.0 (/ y z)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5.8e+247) || !(y <= 1e+188)) {
		tmp = -60.0 * (y / z);
	} 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 <= (-5.8d+247)) .or. (.not. (y <= 1d+188))) then
        tmp = (-60.0d0) * (y / z)
    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 <= -5.8e+247) || !(y <= 1e+188)) {
		tmp = -60.0 * (y / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -5.8e+247) or not (y <= 1e+188):
		tmp = -60.0 * (y / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -5.8e+247) || !(y <= 1e+188))
		tmp = Float64(-60.0 * Float64(y / z));
	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 <= -5.8e+247) || ~((y <= 1e+188)))
		tmp = -60.0 * (y / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -5.8e+247], N[Not[LessEqual[y, 1e+188]], $MachinePrecision]], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.8000000000000004e247 or 1e188 < y

   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* 99.8%

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

   3. Simplified 99.8%

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

      1. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in y around inf 82.7%

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

   7. Taylor expanded in z around inf 51.0%

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

   if -5.8000000000000004e247 < y < 1e188

   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 inf 51.8%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+247} \lor \neg \left(y \leq 10^{+188}\right):\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 18: 50.9% 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 99.8%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
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 inf 46.5%

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

5. Final simplification 46.5%

   \[\leadsto a \cdot 120 \]

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 2023326 
(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)))