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

Percentage Accurate: 99.4% → 99.5%

Time: 10.2s

Alternatives: 18

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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: 99.5% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in y around -inf

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

   1. mul-1-neg N/A

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

   2. +-commutative N/A

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

   3. distribute-rgt-in N/A

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

   4. distribute-neg-in N/A

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

   5. sub-neg N/A

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

   6. associate-*r/ N/A

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

   7. associate-*l/ N/A

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

   8. associate-/l* N/A

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

   9. mul-1-neg N/A

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

   10. *-inverses N/A

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

5. Applied rewrites 99.8%

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

6. Final simplification 99.8%

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

Alternative 2: 60.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-60 \cdot y}{z - t}\\ t_2 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+267}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+104}:\\ \;\;\;\;\frac{x}{z - t} \cdot 60\\ \mathbf{elif}\;t\_2 \leq 10^{+128}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* -60.0 y) (- z t))) (t_2 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_2 -1e+267)
     t_1
     (if (<= t_2 -5e+104)
       (* (/ x (- z t)) 60.0)
       (if (<= t_2 1e+128) (* 120.0 a) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (-60.0 * y) / (z - t);
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -1e+267) {
		tmp = t_1;
	} else if (t_2 <= -5e+104) {
		tmp = (x / (z - t)) * 60.0;
	} else if (t_2 <= 1e+128) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((-60.0d0) * y) / (z - t)
    t_2 = ((x - y) * 60.0d0) / (z - t)
    if (t_2 <= (-1d+267)) then
        tmp = t_1
    else if (t_2 <= (-5d+104)) then
        tmp = (x / (z - t)) * 60.0d0
    else if (t_2 <= 1d+128) then
        tmp = 120.0d0 * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (-60.0 * y) / (z - t);
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -1e+267) {
		tmp = t_1;
	} else if (t_2 <= -5e+104) {
		tmp = (x / (z - t)) * 60.0;
	} else if (t_2 <= 1e+128) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (-60.0 * y) / (z - t)
	t_2 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_2 <= -1e+267:
		tmp = t_1
	elif t_2 <= -5e+104:
		tmp = (x / (z - t)) * 60.0
	elif t_2 <= 1e+128:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-60.0 * y) / Float64(z - t))
	t_2 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -1e+267)
		tmp = t_1;
	elseif (t_2 <= -5e+104)
		tmp = Float64(Float64(x / Float64(z - t)) * 60.0);
	elseif (t_2 <= 1e+128)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (-60.0 * y) / (z - t);
	t_2 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_2 <= -1e+267)
		tmp = t_1;
	elseif (t_2 <= -5e+104)
		tmp = (x / (z - t)) * 60.0;
	elseif (t_2 <= 1e+128)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(-60.0 * y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+267], t$95$1, If[LessEqual[t$95$2, -5e+104], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $MachinePrecision], If[LessEqual[t$95$2, 1e+128], N[(120.0 * a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -9.9999999999999997e266 or 1.0000000000000001e128 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.8%

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

   3. Taylor expanded in y around -inf

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

      1. mul-1-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-in N/A

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

      4. distribute-neg-in N/A

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

      5. sub-neg N/A

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

      6. associate-*r/ N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. mul-1-neg N/A

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

      10. *-inverses N/A

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 89.6

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

   8. Applied rewrites 89.6%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 56.5%

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

   if -9.9999999999999997e266 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -4.9999999999999997e104

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 58.5

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

   5. Applied rewrites 58.5%

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

   if -4.9999999999999997e104 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.0000000000000001e128

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 65.8

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

   5. Applied rewrites 65.8%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -1 \cdot 10^{+267}:\\ \;\;\;\;\frac{-60 \cdot y}{z - t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -5 \cdot 10^{+104}:\\ \;\;\;\;\frac{x}{z - t} \cdot 60\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 10^{+128}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{-60 \cdot y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+114}:\\ \;\;\;\;\frac{x - y}{z - t} \cdot 60\\ \mathbf{elif}\;t\_1 \leq 10^{+128}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z - t}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_1 -1e+114)
     (* (/ (- x y) (- z t)) 60.0)
     (if (<= t_1 1e+128)
       (fma (/ x (- z t)) 60.0 (* 120.0 a))
       (* (/ 60.0 (- z t)) (- x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_1 <= -1e+114) {
		tmp = ((x - y) / (z - t)) * 60.0;
	} else if (t_1 <= 1e+128) {
		tmp = fma((x / (z - t)), 60.0, (120.0 * a));
	} else {
		tmp = (60.0 / (z - t)) * (x - y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -1e+114)
		tmp = Float64(Float64(Float64(x - y) / Float64(z - t)) * 60.0);
	elseif (t_1 <= 1e+128)
		tmp = fma(Float64(x / Float64(z - t)), 60.0, Float64(120.0 * a));
	else
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+114], N[(N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $MachinePrecision], If[LessEqual[t$95$1, 1e+128], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1e114

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 89.3

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

   5. Applied rewrites 89.3%

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

   if -1e114 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.0000000000000001e128

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 84.6

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

   5. Applied rewrites 84.6%

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

   if 1.0000000000000001e128 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.8%

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

   3. Taylor expanded in y around -inf

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

      1. mul-1-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-in N/A

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

      4. distribute-neg-in N/A

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

      5. sub-neg N/A

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

      6. associate-*r/ N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. mul-1-neg N/A

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

      10. *-inverses N/A

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 87.6

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

   8. Applied rewrites 87.6%

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

   10. Applied rewrites 87.7%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -1 \cdot 10^{+114}:\\ \;\;\;\;\frac{x - y}{z - t} \cdot 60\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 10^{+128}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z - t}, 60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-43}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-58}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z - t} \cdot 60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_1 -5e-43)
     (* (/ 60.0 (- z t)) (- x y))
     (if (<= t_1 2e-58) (* 120.0 a) (* (/ (- x y) (- z t)) 60.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_1 <= -5e-43) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else if (t_1 <= 2e-58) {
		tmp = 120.0 * a;
	} else {
		tmp = ((x - y) / (z - t)) * 60.0;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = ((x - y) * 60.0d0) / (z - t)
    if (t_1 <= (-5d-43)) then
        tmp = (60.0d0 / (z - t)) * (x - y)
    else if (t_1 <= 2d-58) then
        tmp = 120.0d0 * a
    else
        tmp = ((x - y) / (z - t)) * 60.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_1 <= -5e-43) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else if (t_1 <= 2e-58) {
		tmp = 120.0 * a;
	} else {
		tmp = ((x - y) / (z - t)) * 60.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_1 <= -5e-43:
		tmp = (60.0 / (z - t)) * (x - y)
	elif t_1 <= 2e-58:
		tmp = 120.0 * a
	else:
		tmp = ((x - y) / (z - t)) * 60.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -5e-43)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	elseif (t_1 <= 2e-58)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(Float64(x - y) / Float64(z - t)) * 60.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_1 <= -5e-43)
		tmp = (60.0 / (z - t)) * (x - y);
	elseif (t_1 <= 2e-58)
		tmp = 120.0 * a;
	else
		tmp = ((x - y) / (z - t)) * 60.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-43], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-58], N[(120.0 * a), $MachinePrecision], N[(N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5.00000000000000019e-43

   1. Initial program 99.7%

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

   3. Taylor expanded in y around -inf

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

      1. mul-1-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-in N/A

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

      4. distribute-neg-in N/A

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

      5. sub-neg N/A

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

      6. associate-*r/ N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. mul-1-neg N/A

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

      10. *-inverses N/A

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 72.0

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

   8. Applied rewrites 72.0%

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

   10. Applied rewrites 72.1%

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

   if -5.00000000000000019e-43 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2.0000000000000001e-58

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 81.3

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

   5. Applied rewrites 81.3%

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

   if 2.0000000000000001e-58 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 71.3

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

   5. Applied rewrites 71.3%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -5 \cdot 10^{-43}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 2 \cdot 10^{-58}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z - t} \cdot 60\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60}{z - t} \cdot \left(x - y\right)\\ t_2 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-58}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ 60.0 (- z t)) (- x y))) (t_2 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_2 -5e-43) t_1 (if (<= t_2 2e-58) (* 120.0 a) t_1))))

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 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -5e-43) {
		tmp = t_1;
	} else if (t_2 <= 2e-58) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (60.0d0 / (z - t)) * (x - y)
    t_2 = ((x - y) * 60.0d0) / (z - t)
    if (t_2 <= (-5d-43)) then
        tmp = t_1
    else if (t_2 <= 2d-58) then
        tmp = 120.0d0 * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 / (z - t)) * (x - y);
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -5e-43) {
		tmp = t_1;
	} else if (t_2 <= 2e-58) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 / (z - t)) * (x - y)
	t_2 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_2 <= -5e-43:
		tmp = t_1
	elif t_2 <= 2e-58:
		tmp = 120.0 * a
	else:
		tmp = t_1
	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(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -5e-43)
		tmp = t_1;
	elseif (t_2 <= 2e-58)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 / (z - t)) * (x - y);
	t_2 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_2 <= -5e-43)
		tmp = t_1;
	elseif (t_2 <= 2e-58)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-43], t$95$1, If[LessEqual[t$95$2, 2e-58], N[(120.0 * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5.00000000000000019e-43 or 2.0000000000000001e-58 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

   3. Taylor expanded in y around -inf

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

      1. mul-1-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-in N/A

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

      4. distribute-neg-in N/A

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

      5. sub-neg N/A

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

      6. associate-*r/ N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. mul-1-neg N/A

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

      10. *-inverses N/A

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 71.6

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

   8. Applied rewrites 71.6%

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

   10. Applied rewrites 71.6%

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

   if -5.00000000000000019e-43 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2.0000000000000001e-58

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 81.3

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

   5. Applied rewrites 81.3%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -5 \cdot 10^{-43}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 2 \cdot 10^{-58}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+104}:\\ \;\;\;\;\frac{x - y}{0.016666666666666666 \cdot \left(-t\right)}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+155}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{-t} \cdot \left(x - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_1 -5e+104)
     (/ (- x y) (* 0.016666666666666666 (- t)))
     (if (<= t_1 5e+155) (* 120.0 a) (* (/ 60.0 (- t)) (- x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_1 <= -5e+104) {
		tmp = (x - y) / (0.016666666666666666 * -t);
	} else if (t_1 <= 5e+155) {
		tmp = 120.0 * a;
	} else {
		tmp = (60.0 / -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) :: tmp
    t_1 = ((x - y) * 60.0d0) / (z - t)
    if (t_1 <= (-5d+104)) then
        tmp = (x - y) / (0.016666666666666666d0 * -t)
    else if (t_1 <= 5d+155) then
        tmp = 120.0d0 * a
    else
        tmp = (60.0d0 / -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 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_1 <= -5e+104) {
		tmp = (x - y) / (0.016666666666666666 * -t);
	} else if (t_1 <= 5e+155) {
		tmp = 120.0 * a;
	} else {
		tmp = (60.0 / -t) * (x - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_1 <= -5e+104:
		tmp = (x - y) / (0.016666666666666666 * -t)
	elif t_1 <= 5e+155:
		tmp = 120.0 * a
	else:
		tmp = (60.0 / -t) * (x - y)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -5e+104)
		tmp = Float64(Float64(x - y) / Float64(0.016666666666666666 * Float64(-t)));
	elseif (t_1 <= 5e+155)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(60.0 / Float64(-t)) * Float64(x - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_1 <= -5e+104)
		tmp = (x - y) / (0.016666666666666666 * -t);
	elseif (t_1 <= 5e+155)
		tmp = 120.0 * a;
	else
		tmp = (60.0 / -t) * (x - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+104], N[(N[(x - y), $MachinePrecision] / N[(0.016666666666666666 * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+155], N[(120.0 * a), $MachinePrecision], N[(N[(60.0 / (-t)), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -4.9999999999999997e104

   1. Initial program 99.7%

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

   3. Taylor expanded in y around -inf

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

      1. mul-1-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-in N/A

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

      4. distribute-neg-in N/A

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

      5. sub-neg N/A

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

      6. associate-*r/ N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. mul-1-neg N/A

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

      10. *-inverses N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 89.7

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

   8. Applied rewrites 89.7%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 59.0%

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

   13. Applied rewrites 59.1%

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

   if -4.9999999999999997e104 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.9999999999999999e155

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 65.0

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

   5. Applied rewrites 65.0%

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

   if 4.9999999999999999e155 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.8%

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

   3. Taylor expanded in y around -inf

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

      1. mul-1-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-in N/A

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

      4. distribute-neg-in N/A

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

      5. sub-neg N/A

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

      6. associate-*r/ N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. mul-1-neg N/A

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

      10. *-inverses N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 89.1

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

   8. Applied rewrites 89.1%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 64.0%

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

   13. Applied rewrites 64.1%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -5 \cdot 10^{+104}:\\ \;\;\;\;\frac{x - y}{0.016666666666666666 \cdot \left(-t\right)}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 5 \cdot 10^{+155}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{-t} \cdot \left(x - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60}{-t} \cdot \left(x - y\right)\\ t_2 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+155}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ 60.0 (- t)) (- x y))) (t_2 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_2 -5e+104) t_1 (if (<= t_2 5e+155) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 / -t) * (x - y);
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -5e+104) {
		tmp = t_1;
	} else if (t_2 <= 5e+155) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (60.0d0 / -t) * (x - y)
    t_2 = ((x - y) * 60.0d0) / (z - t)
    if (t_2 <= (-5d+104)) then
        tmp = t_1
    else if (t_2 <= 5d+155) then
        tmp = 120.0d0 * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 / -t) * (x - y);
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -5e+104) {
		tmp = t_1;
	} else if (t_2 <= 5e+155) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 / -t) * (x - y)
	t_2 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_2 <= -5e+104:
		tmp = t_1
	elif t_2 <= 5e+155:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 / Float64(-t)) * Float64(x - y))
	t_2 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -5e+104)
		tmp = t_1;
	elseif (t_2 <= 5e+155)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 / -t) * (x - y);
	t_2 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_2 <= -5e+104)
		tmp = t_1;
	elseif (t_2 <= 5e+155)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 / (-t)), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+104], t$95$1, If[LessEqual[t$95$2, 5e+155], N[(120.0 * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -4.9999999999999997e104 or 4.9999999999999999e155 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.8%

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

   3. Taylor expanded in y around -inf

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

      1. mul-1-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-in N/A

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

      4. distribute-neg-in N/A

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

      5. sub-neg N/A

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

      6. associate-*r/ N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. mul-1-neg N/A

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

      10. *-inverses N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 89.4

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

   8. Applied rewrites 89.4%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 61.5%

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

   13. Applied rewrites 61.6%

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

   if -4.9999999999999997e104 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.9999999999999999e155

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 65.0

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

   5. Applied rewrites 65.0%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -5 \cdot 10^{+104}:\\ \;\;\;\;\frac{60}{-t} \cdot \left(x - y\right)\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 5 \cdot 10^{+155}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{-t} \cdot \left(x - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 55.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+104}:\\ \;\;\;\;\frac{x}{t} \cdot -60\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+191}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{t} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_1 -5e+104)
     (* (/ x t) -60.0)
     (if (<= t_1 2e+191) (* 120.0 a) (* (/ -60.0 t) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_1 <= -5e+104) {
		tmp = (x / t) * -60.0;
	} else if (t_1 <= 2e+191) {
		tmp = 120.0 * a;
	} else {
		tmp = (-60.0 / t) * x;
	}
	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 = ((x - y) * 60.0d0) / (z - t)
    if (t_1 <= (-5d+104)) then
        tmp = (x / t) * (-60.0d0)
    else if (t_1 <= 2d+191) then
        tmp = 120.0d0 * a
    else
        tmp = ((-60.0d0) / t) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_1 <= -5e+104) {
		tmp = (x / t) * -60.0;
	} else if (t_1 <= 2e+191) {
		tmp = 120.0 * a;
	} else {
		tmp = (-60.0 / t) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_1 <= -5e+104:
		tmp = (x / t) * -60.0
	elif t_1 <= 2e+191:
		tmp = 120.0 * a
	else:
		tmp = (-60.0 / t) * x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -5e+104)
		tmp = Float64(Float64(x / t) * -60.0);
	elseif (t_1 <= 2e+191)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(-60.0 / t) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_1 <= -5e+104)
		tmp = (x / t) * -60.0;
	elseif (t_1 <= 2e+191)
		tmp = 120.0 * a;
	else
		tmp = (-60.0 / t) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+104], N[(N[(x / t), $MachinePrecision] * -60.0), $MachinePrecision], If[LessEqual[t$95$1, 2e+191], N[(120.0 * a), $MachinePrecision], N[(N[(-60.0 / t), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -4.9999999999999997e104

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 48.2

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

   5. Applied rewrites 48.2%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 36.1%

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

   if -4.9999999999999997e104 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2.00000000000000015e191

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 62.8

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

   5. Applied rewrites 62.8%

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

   if 2.00000000000000015e191 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 53.3

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

   5. Applied rewrites 53.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 53.1%

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

   10. Applied rewrites 53.2%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -5 \cdot 10^{+104}:\\ \;\;\;\;\frac{x}{t} \cdot -60\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 2 \cdot 10^{+191}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{t} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 55.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-60}{t} \cdot x\\ t_2 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+191}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ -60.0 t) x)) (t_2 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_2 -5e+104) t_1 (if (<= t_2 2e+191) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (-60.0 / t) * x;
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -5e+104) {
		tmp = t_1;
	} else if (t_2 <= 2e+191) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((-60.0d0) / t) * x
    t_2 = ((x - y) * 60.0d0) / (z - t)
    if (t_2 <= (-5d+104)) then
        tmp = t_1
    else if (t_2 <= 2d+191) then
        tmp = 120.0d0 * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (-60.0 / t) * x;
	double t_2 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_2 <= -5e+104) {
		tmp = t_1;
	} else if (t_2 <= 2e+191) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (-60.0 / t) * x
	t_2 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_2 <= -5e+104:
		tmp = t_1
	elif t_2 <= 2e+191:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-60.0 / t) * x)
	t_2 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -5e+104)
		tmp = t_1;
	elseif (t_2 <= 2e+191)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (-60.0 / t) * x;
	t_2 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_2 <= -5e+104)
		tmp = t_1;
	elseif (t_2 <= 2e+191)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(-60.0 / t), $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+104], t$95$1, If[LessEqual[t$95$2, 2e+191], N[(120.0 * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -4.9999999999999997e104 or 2.00000000000000015e191 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 50.3

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

   5. Applied rewrites 50.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 43.2%

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

   10. Applied rewrites 43.1%

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

   if -4.9999999999999997e104 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2.00000000000000015e191

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 62.8

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

   5. Applied rewrites 62.8%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -5 \cdot 10^{+104}:\\ \;\;\;\;\frac{-60}{t} \cdot x\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 2 \cdot 10^{+191}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{t} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 72.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -1 \cdot 10^{+90}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, -60, 120 \cdot a\right)\\ \mathbf{elif}\;120 \cdot a \leq -2 \cdot 10^{+16}:\\ \;\;\;\;\frac{-60}{z} \cdot y + 120 \cdot a\\ \mathbf{elif}\;120 \cdot a \leq 4 \cdot 10^{-103}:\\ \;\;\;\;\frac{x - y}{z - t} \cdot 60\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{-0.016666666666666666 \cdot z} + 120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* 120.0 a) -1e+90)
   (fma (/ x t) -60.0 (* 120.0 a))
   (if (<= (* 120.0 a) -2e+16)
     (+ (* (/ -60.0 z) y) (* 120.0 a))
     (if (<= (* 120.0 a) 4e-103)
       (* (/ (- x y) (- z t)) 60.0)
       (+ (/ y (* -0.016666666666666666 z)) (* 120.0 a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((120.0 * a) <= -1e+90) {
		tmp = fma((x / t), -60.0, (120.0 * a));
	} else if ((120.0 * a) <= -2e+16) {
		tmp = ((-60.0 / z) * y) + (120.0 * a);
	} else if ((120.0 * a) <= 4e-103) {
		tmp = ((x - y) / (z - t)) * 60.0;
	} else {
		tmp = (y / (-0.016666666666666666 * z)) + (120.0 * a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(120.0 * a) <= -1e+90)
		tmp = fma(Float64(x / t), -60.0, Float64(120.0 * a));
	elseif (Float64(120.0 * a) <= -2e+16)
		tmp = Float64(Float64(Float64(-60.0 / z) * y) + Float64(120.0 * a));
	elseif (Float64(120.0 * a) <= 4e-103)
		tmp = Float64(Float64(Float64(x - y) / Float64(z - t)) * 60.0);
	else
		tmp = Float64(Float64(y / Float64(-0.016666666666666666 * z)) + Float64(120.0 * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(120.0 * a), $MachinePrecision], -1e+90], N[(N[(x / t), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(120.0 * a), $MachinePrecision], -2e+16], N[(N[(N[(-60.0 / z), $MachinePrecision] * y), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(120.0 * a), $MachinePrecision], 4e-103], N[(N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $MachinePrecision], N[(N[(y / N[(-0.016666666666666666 * z), $MachinePrecision]), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -9.99999999999999966e89

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 89.8

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

   5. Applied rewrites 89.8%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\frac{x}{-1 \cdot t}, 60, 120 \cdot a\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 82.0%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 82.0%

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

   if -9.99999999999999966e89 < (*.f64 a #s(literal 120 binary64)) < -2e16

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. associate-*l/ N/A

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

      3. metadata-eval N/A

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

      4. distribute-neg-frac N/A

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

      5. metadata-eval N/A

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

      6. associate-*r/ N/A

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

      7. lower-*.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. distribute-neg-frac N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 95.5

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

   5. Applied rewrites 95.5%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 89.8%

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

   if -2e16 < (*.f64 a #s(literal 120 binary64)) < 3.99999999999999983e-103

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 78.8

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

   5. Applied rewrites 78.8%

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

   if 3.99999999999999983e-103 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. associate-*l/ N/A

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

      3. metadata-eval N/A

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

      4. distribute-neg-frac N/A

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

      5. metadata-eval N/A

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

      6. associate-*r/ N/A

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

      7. lower-*.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. distribute-neg-frac N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 86.2

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

   5. Applied rewrites 86.2%

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

   7. Applied rewrites 86.2%

      \[\leadsto \frac{y}{\color{blue}{\left(z - t\right) \cdot -0.016666666666666666}} + a \cdot 120 \]

   8. Taylor expanded in z around inf

      \[\leadsto \frac{y}{\frac{-1}{60} \cdot \color{blue}{z}} + a \cdot 120 \]
   9. Step-by-step derivation

   10. Applied rewrites 76.1%

       \[\leadsto \frac{y}{-0.016666666666666666 \cdot \color{blue}{z}} + a \cdot 120 \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -1 \cdot 10^{+90}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, -60, 120 \cdot a\right)\\ \mathbf{elif}\;120 \cdot a \leq -2 \cdot 10^{+16}:\\ \;\;\;\;\frac{-60}{z} \cdot y + 120 \cdot a\\ \mathbf{elif}\;120 \cdot a \leq 4 \cdot 10^{-103}:\\ \;\;\;\;\frac{x - y}{z - t} \cdot 60\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{-0.016666666666666666 \cdot z} + 120 \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-60}{z} \cdot y + 120 \cdot a\\ \mathbf{if}\;120 \cdot a \leq -1 \cdot 10^{+90}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, -60, 120 \cdot a\right)\\ \mathbf{elif}\;120 \cdot a \leq -2 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;120 \cdot a \leq 4 \cdot 10^{-103}:\\ \;\;\;\;\frac{x - y}{z - t} \cdot 60\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* (/ -60.0 z) y) (* 120.0 a))))
   (if (<= (* 120.0 a) -1e+90)
     (fma (/ x t) -60.0 (* 120.0 a))
     (if (<= (* 120.0 a) -2e+16)
       t_1
       (if (<= (* 120.0 a) 4e-103) (* (/ (- x y) (- z t)) 60.0) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((-60.0 / z) * y) + (120.0 * a);
	double tmp;
	if ((120.0 * a) <= -1e+90) {
		tmp = fma((x / t), -60.0, (120.0 * a));
	} else if ((120.0 * a) <= -2e+16) {
		tmp = t_1;
	} else if ((120.0 * a) <= 4e-103) {
		tmp = ((x - y) / (z - t)) * 60.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(-60.0 / z) * y) + Float64(120.0 * a))
	tmp = 0.0
	if (Float64(120.0 * a) <= -1e+90)
		tmp = fma(Float64(x / t), -60.0, Float64(120.0 * a));
	elseif (Float64(120.0 * a) <= -2e+16)
		tmp = t_1;
	elseif (Float64(120.0 * a) <= 4e-103)
		tmp = Float64(Float64(Float64(x - y) / Float64(z - t)) * 60.0);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(-60.0 / z), $MachinePrecision] * y), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(120.0 * a), $MachinePrecision], -1e+90], N[(N[(x / t), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(120.0 * a), $MachinePrecision], -2e+16], t$95$1, If[LessEqual[N[(120.0 * a), $MachinePrecision], 4e-103], N[(N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -9.99999999999999966e89

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 89.8

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

   5. Applied rewrites 89.8%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\frac{x}{-1 \cdot t}, 60, 120 \cdot a\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 82.0%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 82.0%

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

   if -9.99999999999999966e89 < (*.f64 a #s(literal 120 binary64)) < -2e16 or 3.99999999999999983e-103 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. associate-*l/ N/A

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

      3. metadata-eval N/A

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

      4. distribute-neg-frac N/A

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

      5. metadata-eval N/A

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

      6. associate-*r/ N/A

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

      7. lower-*.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. distribute-neg-frac N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 88.2

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

   5. Applied rewrites 88.2%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 79.2%

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

   if -2e16 < (*.f64 a #s(literal 120 binary64)) < 3.99999999999999983e-103

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 78.8

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

   5. Applied rewrites 78.8%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -1 \cdot 10^{+90}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, -60, 120 \cdot a\right)\\ \mathbf{elif}\;120 \cdot a \leq -2 \cdot 10^{+16}:\\ \;\;\;\;\frac{-60}{z} \cdot y + 120 \cdot a\\ \mathbf{elif}\;120 \cdot a \leq 4 \cdot 10^{-103}:\\ \;\;\;\;\frac{x - y}{z - t} \cdot 60\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{z} \cdot y + 120 \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 72.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -5 \cdot 10^{-49}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, -60, 120 \cdot a\right)\\ \mathbf{elif}\;120 \cdot a \leq 4 \cdot 10^{-103}:\\ \;\;\;\;\frac{x - y}{z - t} \cdot 60\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, 60, 120 \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* 120.0 a) -5e-49)
   (fma (/ x t) -60.0 (* 120.0 a))
   (if (<= (* 120.0 a) 4e-103)
     (* (/ (- x y) (- z t)) 60.0)
     (fma (/ x z) 60.0 (* 120.0 a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((120.0 * a) <= -5e-49) {
		tmp = fma((x / t), -60.0, (120.0 * a));
	} else if ((120.0 * a) <= 4e-103) {
		tmp = ((x - y) / (z - t)) * 60.0;
	} else {
		tmp = fma((x / z), 60.0, (120.0 * a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(120.0 * a) <= -5e-49)
		tmp = fma(Float64(x / t), -60.0, Float64(120.0 * a));
	elseif (Float64(120.0 * a) <= 4e-103)
		tmp = Float64(Float64(Float64(x - y) / Float64(z - t)) * 60.0);
	else
		tmp = fma(Float64(x / z), 60.0, Float64(120.0 * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(120.0 * a), $MachinePrecision], -5e-49], N[(N[(x / t), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(120.0 * a), $MachinePrecision], 4e-103], N[(N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -4.9999999999999999e-49

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 86.9

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

   5. Applied rewrites 86.9%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\frac{x}{-1 \cdot t}, 60, 120 \cdot a\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 74.5%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 74.5%

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

   if -4.9999999999999999e-49 < (*.f64 a #s(literal 120 binary64)) < 3.99999999999999983e-103

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 81.5

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

   5. Applied rewrites 81.5%

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

   if 3.99999999999999983e-103 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 82.2

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

   5. Applied rewrites 82.2%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 70.8%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -5 \cdot 10^{-49}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, -60, 120 \cdot a\right)\\ \mathbf{elif}\;120 \cdot a \leq 4 \cdot 10^{-103}:\\ \;\;\;\;\frac{x - y}{z - t} \cdot 60\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, 60, 120 \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 72.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -5 \cdot 10^{-49}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, -60, 120 \cdot a\right)\\ \mathbf{elif}\;120 \cdot a \leq 4 \cdot 10^{-103}:\\ \;\;\;\;\frac{x - y}{z - t} \cdot 60\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x}{z} \cdot 60\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* 120.0 a) -5e-49)
   (fma (/ x t) -60.0 (* 120.0 a))
   (if (<= (* 120.0 a) 4e-103)
     (* (/ (- x y) (- z t)) 60.0)
     (fma a 120.0 (* (/ x z) 60.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((120.0 * a) <= -5e-49) {
		tmp = fma((x / t), -60.0, (120.0 * a));
	} else if ((120.0 * a) <= 4e-103) {
		tmp = ((x - y) / (z - t)) * 60.0;
	} else {
		tmp = fma(a, 120.0, ((x / z) * 60.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(120.0 * a) <= -5e-49)
		tmp = fma(Float64(x / t), -60.0, Float64(120.0 * a));
	elseif (Float64(120.0 * a) <= 4e-103)
		tmp = Float64(Float64(Float64(x - y) / Float64(z - t)) * 60.0);
	else
		tmp = fma(a, 120.0, Float64(Float64(x / z) * 60.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(120.0 * a), $MachinePrecision], -5e-49], N[(N[(x / t), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(120.0 * a), $MachinePrecision], 4e-103], N[(N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $MachinePrecision], N[(a * 120.0 + N[(N[(x / z), $MachinePrecision] * 60.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -4.9999999999999999e-49

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 86.9

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

   5. Applied rewrites 86.9%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\frac{x}{-1 \cdot t}, 60, 120 \cdot a\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 74.5%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 74.5%

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

   if -4.9999999999999999e-49 < (*.f64 a #s(literal 120 binary64)) < 3.99999999999999983e-103

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 81.5

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

   5. Applied rewrites 81.5%

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

   if 3.99999999999999983e-103 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 82.2

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

   5. Applied rewrites 82.2%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 70.8%

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

   10. Applied rewrites 70.8%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -5 \cdot 10^{-49}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, -60, 120 \cdot a\right)\\ \mathbf{elif}\;120 \cdot a \leq 4 \cdot 10^{-103}:\\ \;\;\;\;\frac{x - y}{z - t} \cdot 60\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{x}{z} \cdot 60\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 58.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -2 \cdot 10^{-111}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;120 \cdot a \leq 2 \cdot 10^{-121}:\\ \;\;\;\;\frac{x}{z - t} \cdot 60\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* 120.0 a) -2e-111)
   (* 120.0 a)
   (if (<= (* 120.0 a) 2e-121) (* (/ x (- z t)) 60.0) (* 120.0 a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((120.0 * a) <= -2e-111) {
		tmp = 120.0 * a;
	} else if ((120.0 * a) <= 2e-121) {
		tmp = (x / (z - t)) * 60.0;
	} else {
		tmp = 120.0 * a;
	}
	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 ((120.0d0 * a) <= (-2d-111)) then
        tmp = 120.0d0 * a
    else if ((120.0d0 * a) <= 2d-121) then
        tmp = (x / (z - t)) * 60.0d0
    else
        tmp = 120.0d0 * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((120.0 * a) <= -2e-111) {
		tmp = 120.0 * a;
	} else if ((120.0 * a) <= 2e-121) {
		tmp = (x / (z - t)) * 60.0;
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (120.0 * a) <= -2e-111:
		tmp = 120.0 * a
	elif (120.0 * a) <= 2e-121:
		tmp = (x / (z - t)) * 60.0
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(120.0 * a) <= -2e-111)
		tmp = Float64(120.0 * a);
	elseif (Float64(120.0 * a) <= 2e-121)
		tmp = Float64(Float64(x / Float64(z - t)) * 60.0);
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((120.0 * a) <= -2e-111)
		tmp = 120.0 * a;
	elseif ((120.0 * a) <= 2e-121)
		tmp = (x / (z - t)) * 60.0;
	else
		tmp = 120.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(120.0 * a), $MachinePrecision], -2e-111], N[(120.0 * a), $MachinePrecision], If[LessEqual[N[(120.0 * a), $MachinePrecision], 2e-121], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -2.00000000000000018e-111 or 2e-121 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 66.2

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

   5. Applied rewrites 66.2%

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

   if -2.00000000000000018e-111 < (*.f64 a #s(literal 120 binary64)) < 2e-121

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 48.4

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

   5. Applied rewrites 48.4%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;120 \cdot a \leq -2 \cdot 10^{-111}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;120 \cdot a \leq 2 \cdot 10^{-121}:\\ \;\;\;\;\frac{x}{z - t} \cdot 60\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 90.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x}{z - t}, 60, 120 \cdot a\right)\\ \mathbf{if}\;x \leq -5.9 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z - t}, -60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ x (- z t)) 60.0 (* 120.0 a))))
   (if (<= x -5.9e+16)
     t_1
     (if (<= x 4.6e+24) (fma (/ y (- z t)) -60.0 (* 120.0 a)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x / (z - t)), 60.0, (120.0 * a));
	double tmp;
	if (x <= -5.9e+16) {
		tmp = t_1;
	} else if (x <= 4.6e+24) {
		tmp = fma((y / (z - t)), -60.0, (120.0 * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x / Float64(z - t)), 60.0, Float64(120.0 * a))
	tmp = 0.0
	if (x <= -5.9e+16)
		tmp = t_1;
	elseif (x <= 4.6e+24)
		tmp = fma(Float64(y / Float64(z - t)), -60.0, Float64(120.0 * a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.9e+16], t$95$1, If[LessEqual[x, 4.6e+24], N[(N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.9e16 or 4.5999999999999998e24 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 87.7

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

   5. Applied rewrites 87.7%

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

   if -5.9e16 < x < 4.5999999999999998e24

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 93.2

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

   5. Applied rewrites 93.2%

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

Alternative 16: 62.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-60 \cdot y}{z - t}\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{+143}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{+166}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{t}, -60, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* -60.0 y) (- z t))))
   (if (<= y -1.35e+143)
     t_1
     (if (<= y 1.36e+166) (fma (/ x t) -60.0 (* 120.0 a)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (-60.0 * y) / (z - t);
	double tmp;
	if (y <= -1.35e+143) {
		tmp = t_1;
	} else if (y <= 1.36e+166) {
		tmp = fma((x / t), -60.0, (120.0 * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-60.0 * y) / Float64(z - t))
	tmp = 0.0
	if (y <= -1.35e+143)
		tmp = t_1;
	elseif (y <= 1.36e+166)
		tmp = fma(Float64(x / t), -60.0, Float64(120.0 * a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(-60.0 * y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.35e+143], t$95$1, If[LessEqual[y, 1.36e+166], N[(N[(x / t), $MachinePrecision] * -60.0 + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3500000000000001e143 or 1.36000000000000004e166 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around -inf

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

      1. mul-1-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-in N/A

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

      4. distribute-neg-in N/A

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

      5. sub-neg N/A

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

      6. associate-*r/ N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. mul-1-neg N/A

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

      10. *-inverses N/A

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 73.3

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

   8. Applied rewrites 73.3%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 69.0%

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

   if -1.3500000000000001e143 < y < 1.36000000000000004e166

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 88.3

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

   5. Applied rewrites 88.3%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\frac{x}{-1 \cdot t}, 60, 120 \cdot a\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 63.2%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 63.2%

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

Alternative 17: 99.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lower-fma.f64 99.8

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

   5. lift-/.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. *-commutative N/A

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

   8. associate-/l* N/A

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

   9. *-commutative N/A

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

   10. lower-*.f64 N/A

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

   11. frac-2neg N/A

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

   12. lower-/.f64 N/A

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

   13. metadata-eval N/A

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

   14. neg-sub0 N/A

       \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{\color{blue}{0 - \left(z - t\right)}} \cdot \left(x - y\right)\right) \]

   15. lift--.f64 N/A

       \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{0 - \color{blue}{\left(z - t\right)}} \cdot \left(x - y\right)\right) \]

   16. sub-neg N/A

       \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{0 - \color{blue}{\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)}} \cdot \left(x - y\right)\right) \]

   17. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)}} \cdot \left(x - y\right)\right) \]

   18. associate--r+ N/A

       \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(t\right)\right)\right) - z}} \cdot \left(x - y\right)\right) \]

   19. neg-sub0 N/A

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

   20. remove-double-neg N/A

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

   21. lower--.f64 99.8

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

4. Applied rewrites 99.8%

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

5. Final simplification 99.8%

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

Alternative 18: 50.9% accurate, 5.2× speedup

Math

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

FPCore

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

C

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

Fortran

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 = 120.0d0 * a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in z around inf

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

   1. lower-*.f64 50.1

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

5. Applied rewrites 50.1%

   \[\leadsto \color{blue}{120 \cdot a} \]
6. Add Preprocessing

Developer Target 1: 99.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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 2024325 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (/ 60 (/ (- z t) (- x y))) (* a 120)))

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