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

Percentage Accurate: 99.4% → 99.8%

Time: 12.2s

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: 99.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. lift--.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. remove-double-neg N/A

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

   4. lift--.f64 N/A

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

   5. remove-double-neg N/A

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

   6. div-inv N/A

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

   7. lift-*.f64 N/A

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

   8. div-inv N/A

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

   9. lift-*.f64 N/A

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

   10. *-commutative N/A

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

   11. associate-/l* N/A

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

   12. *-commutative N/A

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

   13. lower-fma.f64 N/A

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

   14. lower-/.f64 99.9

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

4. Applied egg-rr 99.9%

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

Alternative 2: 60.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+107}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+84}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+188}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot -60}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -1e+107)
     (* -60.0 (/ y (- z t)))
     (if (<= t_1 2e+84)
       (* a 120.0)
       (if (<= t_1 5e+188) (/ (* (- x y) -60.0) t) (* (- x y) (/ 60.0 z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+107) {
		tmp = -60.0 * (y / (z - t));
	} else if (t_1 <= 2e+84) {
		tmp = a * 120.0;
	} else if (t_1 <= 5e+188) {
		tmp = ((x - y) * -60.0) / t;
	} else {
		tmp = (x - y) * (60.0 / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-1d+107)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (t_1 <= 2d+84) then
        tmp = a * 120.0d0
    else if (t_1 <= 5d+188) then
        tmp = ((x - y) * (-60.0d0)) / t
    else
        tmp = (x - y) * (60.0d0 / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+107) {
		tmp = -60.0 * (y / (z - t));
	} else if (t_1 <= 2e+84) {
		tmp = a * 120.0;
	} else if (t_1 <= 5e+188) {
		tmp = ((x - y) * -60.0) / t;
	} else {
		tmp = (x - y) * (60.0 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -1e+107:
		tmp = -60.0 * (y / (z - t))
	elif t_1 <= 2e+84:
		tmp = a * 120.0
	elif t_1 <= 5e+188:
		tmp = ((x - y) * -60.0) / t
	else:
		tmp = (x - y) * (60.0 / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -1e+107)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (t_1 <= 2e+84)
		tmp = Float64(a * 120.0);
	elseif (t_1 <= 5e+188)
		tmp = Float64(Float64(Float64(x - y) * -60.0) / t);
	else
		tmp = Float64(Float64(x - y) * Float64(60.0 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -1e+107)
		tmp = -60.0 * (y / (z - t));
	elseif (t_1 <= 2e+84)
		tmp = a * 120.0;
	elseif (t_1 <= 5e+188)
		tmp = ((x - y) * -60.0) / t;
	else
		tmp = (x - y) * (60.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+107], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+84], N[(a * 120.0), $MachinePrecision], If[LessEqual[t$95$1, 5e+188], N[(N[(N[(x - y), $MachinePrecision] * -60.0), $MachinePrecision] / t), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(60.0 / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -9.9999999999999997e106

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 55.7

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

   5. Simplified 55.7%

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

   if -9.9999999999999997e106 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2.00000000000000012e84

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 78.9

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

   5. Simplified 78.9%

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

   if 2.00000000000000012e84 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 5.0000000000000001e188

   1. Initial program 99.5%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 82.9

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

   5. Simplified 82.9%

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

   6. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 63.8

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

   8. Simplified 63.8%

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

   if 5.0000000000000001e188 < (/.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. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. remove-double-neg N/A

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

      4. lift--.f64 N/A

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

      5. remove-double-neg N/A

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

      6. div-inv N/A

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

      7. lift-*.f64 N/A

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

      8. div-inv N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-/.f64 99.9

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 87.2

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

   7. Simplified 87.2%

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

   8. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 82.8

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

   10. Simplified 82.8%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -1 \cdot 10^{+107}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 2 \cdot 10^{+84}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 5 \cdot 10^{+188}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot -60}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+92}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+222}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ y (- z t)))) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -1e+107)
     t_1
     (if (<= t_2 2e+92)
       (* a 120.0)
       (if (<= t_2 5e+222) t_1 (* (- x y) (/ 60.0 z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -1e+107) {
		tmp = t_1;
	} else if (t_2 <= 2e+92) {
		tmp = a * 120.0;
	} else if (t_2 <= 5e+222) {
		tmp = t_1;
	} else {
		tmp = (x - y) * (60.0 / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-60.0d0) * (y / (z - t))
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-1d+107)) then
        tmp = t_1
    else if (t_2 <= 2d+92) then
        tmp = a * 120.0d0
    else if (t_2 <= 5d+222) then
        tmp = t_1
    else
        tmp = (x - y) * (60.0d0 / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -1e+107) {
		tmp = t_1;
	} else if (t_2 <= 2e+92) {
		tmp = a * 120.0;
	} else if (t_2 <= 5e+222) {
		tmp = t_1;
	} else {
		tmp = (x - y) * (60.0 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (y / (z - t))
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -1e+107:
		tmp = t_1
	elif t_2 <= 2e+92:
		tmp = a * 120.0
	elif t_2 <= 5e+222:
		tmp = t_1
	else:
		tmp = (x - y) * (60.0 / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(y / Float64(z - t)))
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -1e+107)
		tmp = t_1;
	elseif (t_2 <= 2e+92)
		tmp = Float64(a * 120.0);
	elseif (t_2 <= 5e+222)
		tmp = t_1;
	else
		tmp = Float64(Float64(x - y) * Float64(60.0 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * (y / (z - t));
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -1e+107)
		tmp = t_1;
	elseif (t_2 <= 2e+92)
		tmp = a * 120.0;
	elseif (t_2 <= 5e+222)
		tmp = t_1;
	else
		tmp = (x - y) * (60.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+107], t$95$1, If[LessEqual[t$95$2, 2e+92], N[(a * 120.0), $MachinePrecision], If[LessEqual[t$95$2, 5e+222], t$95$1, N[(N[(x - y), $MachinePrecision] * N[(60.0 / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -9.9999999999999997e106 or 2.0000000000000001e92 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 5.00000000000000023e222

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 56.4

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

   5. Simplified 56.4%

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

   if -9.9999999999999997e106 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2.0000000000000001e92

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 78.1

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

   5. Simplified 78.1%

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

   if 5.00000000000000023e222 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 100.0%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. remove-double-neg N/A

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

      4. lift--.f64 N/A

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

      5. remove-double-neg N/A

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

      6. div-inv N/A

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

      7. lift-*.f64 N/A

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

      8. div-inv N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-/.f64 99.9

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 89.4

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

   7. Simplified 89.4%

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

   8. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 89.4

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

   10. Simplified 89.4%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -1 \cdot 10^{+107}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 2 \cdot 10^{+92}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 5 \cdot 10^{+222}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60}{z - t} \cdot \left(x - y\right)\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+67}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ 60.0 (- z t)) (- x y))) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -1e+107) t_1 (if (<= t_2 1e+67) (* a 120.0) 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 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -1e+107) {
		tmp = t_1;
	} else if (t_2 <= 1e+67) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (60.0d0 / (z - t)) * (x - y)
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-1d+107)) then
        tmp = t_1
    else if (t_2 <= 1d+67) then
        tmp = a * 120.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 / (z - t)) * (x - y);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -1e+107) {
		tmp = t_1;
	} else if (t_2 <= 1e+67) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 / (z - t)) * (x - y)
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -1e+107:
		tmp = t_1
	elif t_2 <= 1e+67:
		tmp = a * 120.0
	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(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -1e+107)
		tmp = t_1;
	elseif (t_2 <= 1e+67)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 / (z - t)) * (x - y);
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -1e+107)
		tmp = t_1;
	elseif (t_2 <= 1e+67)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+107], t$95$1, If[LessEqual[t$95$2, 1e+67], N[(a * 120.0), $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)) < -9.9999999999999997e106 or 9.99999999999999983e66 < (/.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. 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. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 89.6

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

   5. Simplified 89.6%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-*l/ N/A

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

      4. lift-/.f64 N/A

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

      5. lower-*.f64 89.8

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

   7. Applied egg-rr 89.8%

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

   if -9.9999999999999997e106 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.99999999999999983e66

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 79.6

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

   5. Simplified 79.6%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -1 \cdot 10^{+107}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+67}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+92}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ y (- z t)))) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -1e+107) t_1 (if (<= t_2 2e+92) (* a 120.0) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -1e+107) {
		tmp = t_1;
	} else if (t_2 <= 2e+92) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-60.0d0) * (y / (z - t))
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-1d+107)) then
        tmp = t_1
    else if (t_2 <= 2d+92) then
        tmp = a * 120.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -1e+107) {
		tmp = t_1;
	} else if (t_2 <= 2e+92) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (y / (z - t))
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -1e+107:
		tmp = t_1
	elif t_2 <= 2e+92:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(y / Float64(z - t)))
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -1e+107)
		tmp = t_1;
	elseif (t_2 <= 2e+92)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * (y / (z - t));
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -1e+107)
		tmp = t_1;
	elseif (t_2 <= 2e+92)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+107], t$95$1, If[LessEqual[t$95$2, 2e+92], N[(a * 120.0), $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)) < -9.9999999999999997e106 or 2.0000000000000001e92 < (/.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

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 53.1

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

   5. Simplified 53.1%

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

   if -9.9999999999999997e106 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2.0000000000000001e92

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 78.1

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

   5. Simplified 78.1%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -1 \cdot 10^{+107}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 2 \cdot 10^{+92}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 54.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+107}:\\ \;\;\;\;\frac{y \cdot -60}{z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+222}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -1e+107)
     (/ (* y -60.0) z)
     (if (<= t_1 5e+222) (* a 120.0) (/ (* 60.0 x) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+107) {
		tmp = (y * -60.0) / z;
	} else if (t_1 <= 5e+222) {
		tmp = a * 120.0;
	} else {
		tmp = (60.0 * x) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-1d+107)) then
        tmp = (y * (-60.0d0)) / z
    else if (t_1 <= 5d+222) then
        tmp = a * 120.0d0
    else
        tmp = (60.0d0 * x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+107) {
		tmp = (y * -60.0) / z;
	} else if (t_1 <= 5e+222) {
		tmp = a * 120.0;
	} else {
		tmp = (60.0 * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -1e+107:
		tmp = (y * -60.0) / z
	elif t_1 <= 5e+222:
		tmp = a * 120.0
	else:
		tmp = (60.0 * x) / z
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -1e+107)
		tmp = Float64(Float64(y * -60.0) / z);
	elseif (t_1 <= 5e+222)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(Float64(60.0 * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -1e+107)
		tmp = (y * -60.0) / z;
	elseif (t_1 <= 5e+222)
		tmp = a * 120.0;
	else
		tmp = (60.0 * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+107], N[(N[(y * -60.0), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 5e+222], N[(a * 120.0), $MachinePrecision], N[(N[(60.0 * x), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -9.9999999999999997e106

   1. Initial program 99.7%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. remove-double-neg N/A

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

      4. lift--.f64 N/A

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

      5. remove-double-neg N/A

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

      6. div-inv N/A

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

      7. lift-*.f64 N/A

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

      8. div-inv N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-/.f64 99.9

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 56.7

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

   7. Simplified 56.7%

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

   8. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 42.5

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

   10. Simplified 42.5%

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

   if -9.9999999999999997e106 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 5.00000000000000023e222

   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 71.8

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

   5. Simplified 71.8%

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

   if 5.00000000000000023e222 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 100.0%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. remove-double-neg N/A

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

      4. lift--.f64 N/A

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

      5. remove-double-neg N/A

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

      6. div-inv N/A

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

      7. lift-*.f64 N/A

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

      8. div-inv N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-/.f64 99.9

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 59.3

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

   7. Simplified 59.3%

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

   8. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 58.7

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

   10. Simplified 58.7%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -1 \cdot 10^{+107}:\\ \;\;\;\;\frac{y \cdot -60}{z}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 5 \cdot 10^{+222}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 54.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot -60}{z}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+103}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y -60.0) z)) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -1e+107) t_1 (if (<= t_2 2e+103) (* a 120.0) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * -60.0) / z;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -1e+107) {
		tmp = t_1;
	} else if (t_2 <= 2e+103) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * (-60.0d0)) / z
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-1d+107)) then
        tmp = t_1
    else if (t_2 <= 2d+103) then
        tmp = a * 120.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * -60.0) / z;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -1e+107) {
		tmp = t_1;
	} else if (t_2 <= 2e+103) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * -60.0) / z
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -1e+107:
		tmp = t_1
	elif t_2 <= 2e+103:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * -60.0) / z)
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -1e+107)
		tmp = t_1;
	elseif (t_2 <= 2e+103)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * -60.0) / z;
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -1e+107)
		tmp = t_1;
	elseif (t_2 <= 2e+103)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * -60.0), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+107], t$95$1, If[LessEqual[t$95$2, 2e+103], N[(a * 120.0), $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)) < -9.9999999999999997e106 or 2e103 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. remove-double-neg N/A

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

      4. lift--.f64 N/A

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

      5. remove-double-neg N/A

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

      6. div-inv N/A

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

      7. lift-*.f64 N/A

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

      8. div-inv N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-/.f64 99.8

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 62.3

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

   7. Simplified 62.3%

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

   8. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 38.4

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

   10. Simplified 38.4%

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

   if -9.9999999999999997e106 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2e103

   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 77.7

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

   5. Simplified 77.7%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -1 \cdot 10^{+107}:\\ \;\;\;\;\frac{y \cdot -60}{z}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 2 \cdot 10^{+103}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+213}:\\ \;\;\;\;\frac{x \cdot -60}{t}\\ \mathbf{elif}\;t\_1 \leq 10^{+132}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -2e+213)
     (/ (* x -60.0) t)
     (if (<= t_1 1e+132) (* a 120.0) (* 60.0 (/ y t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -2e+213) {
		tmp = (x * -60.0) / t;
	} else if (t_1 <= 1e+132) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-2d+213)) then
        tmp = (x * (-60.0d0)) / t
    else if (t_1 <= 1d+132) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -2e+213) {
		tmp = (x * -60.0) / t;
	} else if (t_1 <= 1e+132) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -2e+213:
		tmp = (x * -60.0) / t
	elif t_1 <= 1e+132:
		tmp = a * 120.0
	else:
		tmp = 60.0 * (y / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -2e+213)
		tmp = Float64(Float64(x * -60.0) / t);
	elseif (t_1 <= 1e+132)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -2e+213)
		tmp = (x * -60.0) / t;
	elseif (t_1 <= 1e+132)
		tmp = a * 120.0;
	else
		tmp = 60.0 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+213], N[(N[(x * -60.0), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t$95$1, 1e+132], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.99999999999999997e213

   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 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 66.5

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

   5. Simplified 66.5%

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

   6. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 40.5

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

   8. Simplified 40.5%

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

   if -1.99999999999999997e213 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.99999999999999991e131

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 71.5

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

   5. Simplified 71.5%

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

   if 9.99999999999999991e131 < (/.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 z around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 64.6

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

   5. Simplified 64.6%

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

   6. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

         \[\leadsto y \cdot \frac{\color{blue}{60 \cdot 1}}{t} \]

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. associate-*r/ N/A

         \[\leadsto y \cdot \color{blue}{\frac{60 \cdot 1}{t}} \]

      8. metadata-eval N/A

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

      9. lower-/.f64 35.8

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

   8. Simplified 35.8%

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

      1. clear-num N/A

         \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{t}{60}}} \]

      2. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{y \cdot 1}{\frac{t}{60}}} \]

      3. div-inv N/A

         \[\leadsto \frac{y \cdot 1}{\color{blue}{t \cdot \frac{1}{60}}} \]

      4. times-frac N/A

         \[\leadsto \color{blue}{\frac{y}{t} \cdot \frac{1}{\frac{1}{60}}} \]

      5. metadata-eval N/A

         \[\leadsto \frac{y}{t} \cdot \frac{1}{\color{blue}{\frac{1}{60}}} \]

      6. metadata-eval N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 35.8

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

   10. Applied egg-rr 35.8%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -2 \cdot 10^{+213}:\\ \;\;\;\;\frac{x \cdot -60}{t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+132}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+213}:\\ \;\;\;\;x \cdot \frac{-60}{t}\\ \mathbf{elif}\;t\_1 \leq 10^{+132}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -2e+213)
     (* x (/ -60.0 t))
     (if (<= t_1 1e+132) (* a 120.0) (* 60.0 (/ y t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -2e+213) {
		tmp = x * (-60.0 / t);
	} else if (t_1 <= 1e+132) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-2d+213)) then
        tmp = x * ((-60.0d0) / t)
    else if (t_1 <= 1d+132) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -2e+213) {
		tmp = x * (-60.0 / t);
	} else if (t_1 <= 1e+132) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -2e+213:
		tmp = x * (-60.0 / t)
	elif t_1 <= 1e+132:
		tmp = a * 120.0
	else:
		tmp = 60.0 * (y / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -2e+213)
		tmp = Float64(x * Float64(-60.0 / t));
	elseif (t_1 <= 1e+132)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -2e+213)
		tmp = x * (-60.0 / t);
	elseif (t_1 <= 1e+132)
		tmp = a * 120.0;
	else
		tmp = 60.0 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+213], N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+132], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.99999999999999997e213

   1. Initial program 99.9%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. remove-double-neg N/A

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

      4. lift--.f64 N/A

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

      5. remove-double-neg N/A

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

      6. div-inv N/A

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

      7. lift-*.f64 N/A

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

      8. div-inv N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-/.f64 99.9

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 48.5

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

   7. Simplified 48.5%

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

   8. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 40.5

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

   10. Simplified 40.5%

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

       1. associate-/l* N/A

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

       2. *-commutative N/A

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

       3. lower-*.f64 N/A

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

       4. lower-/.f64 40.4

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

   12. Applied egg-rr 40.4%

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

   if -1.99999999999999997e213 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.99999999999999991e131

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 71.5

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

   5. Simplified 71.5%

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

   if 9.99999999999999991e131 < (/.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 z around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 64.6

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

   5. Simplified 64.6%

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

   6. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

         \[\leadsto y \cdot \frac{\color{blue}{60 \cdot 1}}{t} \]

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. associate-*r/ N/A

         \[\leadsto y \cdot \color{blue}{\frac{60 \cdot 1}{t}} \]

      8. metadata-eval N/A

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

      9. lower-/.f64 35.8

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

   8. Simplified 35.8%

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

      1. clear-num N/A

         \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{t}{60}}} \]

      2. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{y \cdot 1}{\frac{t}{60}}} \]

      3. div-inv N/A

         \[\leadsto \frac{y \cdot 1}{\color{blue}{t \cdot \frac{1}{60}}} \]

      4. times-frac N/A

         \[\leadsto \color{blue}{\frac{y}{t} \cdot \frac{1}{\frac{1}{60}}} \]

      5. metadata-eval N/A

         \[\leadsto \frac{y}{t} \cdot \frac{1}{\color{blue}{\frac{1}{60}}} \]

      6. metadata-eval N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 35.8

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

   10. Applied egg-rr 35.8%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -2 \cdot 10^{+213}:\\ \;\;\;\;x \cdot \frac{-60}{t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+132}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 54.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+213}:\\ \;\;\;\;x \cdot \frac{-60}{t}\\ \mathbf{elif}\;t\_1 \leq 10^{+132}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -2e+213)
     (* x (/ -60.0 t))
     (if (<= t_1 1e+132) (* a 120.0) (* y (/ 60.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -2e+213) {
		tmp = x * (-60.0 / t);
	} else if (t_1 <= 1e+132) {
		tmp = a * 120.0;
	} else {
		tmp = y * (60.0 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-2d+213)) then
        tmp = x * ((-60.0d0) / t)
    else if (t_1 <= 1d+132) then
        tmp = a * 120.0d0
    else
        tmp = y * (60.0d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -2e+213) {
		tmp = x * (-60.0 / t);
	} else if (t_1 <= 1e+132) {
		tmp = a * 120.0;
	} else {
		tmp = y * (60.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -2e+213:
		tmp = x * (-60.0 / t)
	elif t_1 <= 1e+132:
		tmp = a * 120.0
	else:
		tmp = y * (60.0 / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -2e+213)
		tmp = Float64(x * Float64(-60.0 / t));
	elseif (t_1 <= 1e+132)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(y * Float64(60.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -2e+213)
		tmp = x * (-60.0 / t);
	elseif (t_1 <= 1e+132)
		tmp = a * 120.0;
	else
		tmp = y * (60.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+213], N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+132], N[(a * 120.0), $MachinePrecision], N[(y * N[(60.0 / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.99999999999999997e213

   1. Initial program 99.9%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. remove-double-neg N/A

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

      4. lift--.f64 N/A

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

      5. remove-double-neg N/A

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

      6. div-inv N/A

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

      7. lift-*.f64 N/A

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

      8. div-inv N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-/.f64 99.9

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 48.5

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

   7. Simplified 48.5%

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

   8. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 40.5

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

   10. Simplified 40.5%

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

       1. associate-/l* N/A

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

       2. *-commutative N/A

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

       3. lower-*.f64 N/A

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

       4. lower-/.f64 40.4

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

   12. Applied egg-rr 40.4%

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

   if -1.99999999999999997e213 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.99999999999999991e131

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 71.5

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

   5. Simplified 71.5%

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

   if 9.99999999999999991e131 < (/.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 z around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 64.6

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

   5. Simplified 64.6%

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

   6. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

         \[\leadsto y \cdot \frac{\color{blue}{60 \cdot 1}}{t} \]

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. associate-*r/ N/A

         \[\leadsto y \cdot \color{blue}{\frac{60 \cdot 1}{t}} \]

      8. metadata-eval N/A

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

      9. lower-/.f64 35.8

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

   8. Simplified 35.8%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -2 \cdot 10^{+213}:\\ \;\;\;\;x \cdot \frac{-60}{t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+132}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{60}{t}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+227}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+132}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ 60.0 t))) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -2e+227) t_1 (if (<= t_2 1e+132) (* a 120.0) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (60.0 / t);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -2e+227) {
		tmp = t_1;
	} else if (t_2 <= 1e+132) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (60.0d0 / t)
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-2d+227)) then
        tmp = t_1
    else if (t_2 <= 1d+132) then
        tmp = a * 120.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (60.0 / t);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -2e+227) {
		tmp = t_1;
	} else if (t_2 <= 1e+132) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (60.0 / t)
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -2e+227:
		tmp = t_1
	elif t_2 <= 1e+132:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(60.0 / t))
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -2e+227)
		tmp = t_1;
	elseif (t_2 <= 1e+132)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (60.0 / t);
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -2e+227)
		tmp = t_1;
	elseif (t_2 <= 1e+132)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(60.0 / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+227], t$95$1, If[LessEqual[t$95$2, 1e+132], N[(a * 120.0), $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)) < -2.0000000000000002e227 or 9.99999999999999991e131 < (/.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 z around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 66.6

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

   5. Simplified 66.6%

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

   6. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

         \[\leadsto y \cdot \frac{\color{blue}{60 \cdot 1}}{t} \]

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. associate-*r/ N/A

         \[\leadsto y \cdot \color{blue}{\frac{60 \cdot 1}{t}} \]

      8. metadata-eval N/A

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

      9. lower-/.f64 33.9

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

   8. Simplified 33.9%

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

   if -2.0000000000000002e227 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.99999999999999991e131

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 71.2

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

   5. Simplified 71.2%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -2 \cdot 10^{+227}:\\ \;\;\;\;y \cdot \frac{60}{t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+132}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 77.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+46}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{y}{z}, a \cdot 120\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-107}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-41}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{60}{z}, a \cdot 120\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.45e+46)
   (fma -60.0 (/ y z) (* a 120.0))
   (if (<= z 8.2e-107)
     (fma -60.0 (/ (- x y) t) (* a 120.0))
     (if (<= z 1.15e-41)
       (* (/ 60.0 (- z t)) (- x y))
       (fma x (/ 60.0 z) (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.45e+46) {
		tmp = fma(-60.0, (y / z), (a * 120.0));
	} else if (z <= 8.2e-107) {
		tmp = fma(-60.0, ((x - y) / t), (a * 120.0));
	} else if (z <= 1.15e-41) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else {
		tmp = fma(x, (60.0 / z), (a * 120.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.45e+46)
		tmp = fma(-60.0, Float64(y / z), Float64(a * 120.0));
	elseif (z <= 8.2e-107)
		tmp = fma(-60.0, Float64(Float64(x - y) / t), Float64(a * 120.0));
	elseif (z <= 1.15e-41)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	else
		tmp = fma(x, Float64(60.0 / z), Float64(a * 120.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.45e+46], N[(-60.0 * N[(y / z), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e-107], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e-41], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], N[(x * N[(60.0 / z), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.4500000000000001e46

   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

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

      2. lift-*.f64 N/A

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

      3. remove-double-neg N/A

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

      4. lift--.f64 N/A

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

      5. remove-double-neg N/A

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

      6. div-inv N/A

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

      7. lift-*.f64 N/A

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

      8. div-inv N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-/.f64 99.9

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 94.3

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

   7. Simplified 94.3%

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

   8. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 88.6

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

   10. Simplified 88.6%

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

   if -1.4500000000000001e46 < z < 8.1999999999999998e-107

   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 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 83.9

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

   5. Simplified 83.9%

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

   if 8.1999999999999998e-107 < z < 1.15000000000000005e-41

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 92.2

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

   5. Simplified 92.2%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-*l/ N/A

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

      4. lift-/.f64 N/A

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

      5. lower-*.f64 92.3

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

   7. Applied egg-rr 92.3%

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

   if 1.15000000000000005e-41 < z

   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

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

      2. lift-*.f64 N/A

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

      3. remove-double-neg N/A

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

      4. lift--.f64 N/A

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

      5. remove-double-neg N/A

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

      6. div-inv N/A

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

      7. lift-*.f64 N/A

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

      8. div-inv N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-/.f64 99.9

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 85.7

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

   7. Simplified 85.7%

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

   8. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. metadata-eval N/A

         \[\leadsto x \cdot \frac{\color{blue}{60 \cdot 1}}{z} + 120 \cdot a \]

      5. associate-*r/ N/A

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

      6. lower-fma.f64 N/A

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

      7. associate-*r/ N/A

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

      8. metadata-eval N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 83.9

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

   10. Simplified 83.9%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+46}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{y}{z}, a \cdot 120\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-107}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-41}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{60}{z}, a \cdot 120\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 84.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-78}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{-60}{t}\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-32}:\\ \;\;\;\;\mathsf{fma}\left(\frac{60}{z}, x - y, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.2e-78)
   (fma a 120.0 (* (- x y) (/ -60.0 t)))
   (if (<= t 2.6e-32)
     (fma (/ 60.0 z) (- x y) (* a 120.0))
     (fma -60.0 (/ (- x y) t) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.2e-78) {
		tmp = fma(a, 120.0, ((x - y) * (-60.0 / t)));
	} else if (t <= 2.6e-32) {
		tmp = fma((60.0 / z), (x - y), (a * 120.0));
	} else {
		tmp = fma(-60.0, ((x - y) / t), (a * 120.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.2e-78)
		tmp = fma(a, 120.0, Float64(Float64(x - y) * Float64(-60.0 / t)));
	elseif (t <= 2.6e-32)
		tmp = fma(Float64(60.0 / z), Float64(x - y), Float64(a * 120.0));
	else
		tmp = fma(-60.0, Float64(Float64(x - y) / t), Float64(a * 120.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.2e-78], N[(a * 120.0 + N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e-32], N[(N[(60.0 / z), $MachinePrecision] * N[(x - y), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.1999999999999999e-78

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 89.2

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

   5. Simplified 89.2%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. +-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 89.3

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 89.4

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

   7. Applied egg-rr 89.4%

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

   if -2.1999999999999999e-78 < t < 2.5999999999999997e-32

   1. Initial program 99.9%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. remove-double-neg N/A

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

      4. lift--.f64 N/A

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

      5. remove-double-neg N/A

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

      6. div-inv N/A

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

      7. lift-*.f64 N/A

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

      8. div-inv N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-/.f64 99.9

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 85.5

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

   7. Simplified 85.5%

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

   if 2.5999999999999997e-32 < 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 z around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 91.9

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

   5. Simplified 91.9%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-78}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{-60}{t}\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-32}:\\ \;\;\;\;\mathsf{fma}\left(\frac{60}{z}, x - y, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 84.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-78}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{-60}{t}\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-32}:\\ \;\;\;\;\mathsf{fma}\left(120, a, \frac{60 \cdot \left(x - y\right)}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.2e-78)
   (fma a 120.0 (* (- x y) (/ -60.0 t)))
   (if (<= t 2.6e-32)
     (fma 120.0 a (/ (* 60.0 (- x y)) z))
     (fma -60.0 (/ (- x y) t) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.2e-78) {
		tmp = fma(a, 120.0, ((x - y) * (-60.0 / t)));
	} else if (t <= 2.6e-32) {
		tmp = fma(120.0, a, ((60.0 * (x - y)) / z));
	} else {
		tmp = fma(-60.0, ((x - y) / t), (a * 120.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.2e-78)
		tmp = fma(a, 120.0, Float64(Float64(x - y) * Float64(-60.0 / t)));
	elseif (t <= 2.6e-32)
		tmp = fma(120.0, a, Float64(Float64(60.0 * Float64(x - y)) / z));
	else
		tmp = fma(-60.0, Float64(Float64(x - y) / t), Float64(a * 120.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.2e-78], N[(a * 120.0 + N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e-32], N[(120.0 * a + N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.1999999999999999e-78

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 89.2

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

   5. Simplified 89.2%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. +-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 89.3

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 89.4

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

   7. Applied egg-rr 89.4%

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

   if -2.1999999999999999e-78 < t < 2.5999999999999997e-32

   1. Initial program 99.9%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. remove-double-neg N/A

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

      4. lift--.f64 N/A

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

      5. remove-double-neg N/A

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

      6. div-inv N/A

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

      7. lift-*.f64 N/A

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

      8. div-inv N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-/.f64 99.9

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 85.5

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

   7. Simplified 85.5%

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

   if 2.5999999999999997e-32 < 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 z around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 91.9

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

   5. Simplified 91.9%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-78}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \left(x - y\right) \cdot \frac{-60}{t}\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-32}:\\ \;\;\;\;\mathsf{fma}\left(120, a, \frac{60 \cdot \left(x - y\right)}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 84.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{-78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-32}:\\ \;\;\;\;\mathsf{fma}\left(120, a, \frac{60 \cdot \left(x - y\right)}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma -60.0 (/ (- x y) t) (* a 120.0))))
   (if (<= t -2.2e-78)
     t_1
     (if (<= t 2.6e-32) (fma 120.0 a (/ (* 60.0 (- x y)) z)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(-60.0, ((x - y) / t), (a * 120.0));
	double tmp;
	if (t <= -2.2e-78) {
		tmp = t_1;
	} else if (t <= 2.6e-32) {
		tmp = fma(120.0, a, ((60.0 * (x - y)) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(-60.0, Float64(Float64(x - y) / t), Float64(a * 120.0))
	tmp = 0.0
	if (t <= -2.2e-78)
		tmp = t_1;
	elseif (t <= 2.6e-32)
		tmp = fma(120.0, a, Float64(Float64(60.0 * Float64(x - y)) / z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.2e-78], t$95$1, If[LessEqual[t, 2.6e-32], N[(120.0 * a + N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.1999999999999999e-78 or 2.5999999999999997e-32 < 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 z around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 90.5

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

   5. Simplified 90.5%

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

   if -2.1999999999999999e-78 < t < 2.5999999999999997e-32

   1. Initial program 99.9%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. remove-double-neg N/A

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

      4. lift--.f64 N/A

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

      5. remove-double-neg N/A

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

      6. div-inv N/A

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

      7. lift-*.f64 N/A

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

      8. div-inv N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-/.f64 99.9

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 85.5

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

   7. Simplified 85.5%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-78}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-32}:\\ \;\;\;\;\mathsf{fma}\left(120, a, \frac{60 \cdot \left(x - y\right)}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 84.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{-78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-32}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma -60.0 (/ (- x y) t) (* a 120.0))))
   (if (<= t -2.2e-78)
     t_1
     (if (<= t 2.6e-32) (fma 60.0 (/ (- x y) z) (* a 120.0)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(-60.0, ((x - y) / t), (a * 120.0));
	double tmp;
	if (t <= -2.2e-78) {
		tmp = t_1;
	} else if (t <= 2.6e-32) {
		tmp = fma(60.0, ((x - y) / z), (a * 120.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(-60.0, Float64(Float64(x - y) / t), Float64(a * 120.0))
	tmp = 0.0
	if (t <= -2.2e-78)
		tmp = t_1;
	elseif (t <= 2.6e-32)
		tmp = fma(60.0, Float64(Float64(x - y) / z), Float64(a * 120.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.2e-78], t$95$1, If[LessEqual[t, 2.6e-32], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.1999999999999999e-78 or 2.5999999999999997e-32 < 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 z around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 90.5

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

   5. Simplified 90.5%

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

   if -2.1999999999999999e-78 < t < 2.5999999999999997e-32

   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

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 85.5

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

   5. Simplified 85.5%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-78}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-32}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 99.4% accurate, 1.1× speedup

Math

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

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(Float64(x - y) * -60.0) / Float64(t - z)))
end

Wolfram

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

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

   2. lift-*.f64 N/A

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

   3. remove-double-neg N/A

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

   4. lift--.f64 N/A

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

   5. remove-double-neg N/A

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

   6. lift-/.f64 N/A

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

   7. lift-*.f64 N/A

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

   8. +-commutative N/A

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

   9. lift-*.f64 N/A

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

   10. lower-fma.f64 99.9

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

   11. lift-/.f64 N/A

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

   12. frac-2neg N/A

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

   13. lower-/.f64 N/A

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

   14. lift-*.f64 N/A

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

   15. *-commutative N/A

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

   16. distribute-rgt-neg-in N/A

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

   17. lower-*.f64 N/A

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

   18. metadata-eval N/A

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

   19. neg-sub0 N/A

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

   20. lift--.f64 N/A

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

   21. sub-neg N/A

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

   22. +-commutative N/A

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

   23. associate--r+ N/A

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

   24. neg-sub0 N/A

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

   25. remove-double-neg N/A

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

   26. lower--.f64 99.9

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

4. Applied egg-rr 99.9%

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

Alternative 18: 50.6% accurate, 5.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in z around inf

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

   1. lower-*.f64 57.7

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

5. Simplified 57.7%

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

6. Final simplification 57.7%

   \[\leadsto a \cdot 120 \]
7. 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 2024208 
(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)))