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

Percentage Accurate: 99.4% → 99.8%

Time: 11.7s

Alternatives: 19

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

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

   2. lift-/.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. associate-/l* N/A

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

   6. *-commutative N/A

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

   7. lower-fma.f64 N/A

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

   8. lower-/.f64 99.8

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

4. Applied rewrites 99.8%

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

Alternative 2: 60.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+139}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-59}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{y}{z}, a \cdot 120\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+62}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t\_1 \leq 10^{+144}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -5e+139)
     (* (- x y) (/ -60.0 t))
     (if (<= t_1 -2e-59)
       (fma -60.0 (/ y z) (* a 120.0))
       (if (<= t_1 1e+62)
         (* a 120.0)
         (if (<= t_1 1e+144)
           (* 60.0 (/ x (- z t)))
           (/ (* y -60.0) (- z 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 <= -5e+139) {
		tmp = (x - y) * (-60.0 / t);
	} else if (t_1 <= -2e-59) {
		tmp = fma(-60.0, (y / z), (a * 120.0));
	} else if (t_1 <= 1e+62) {
		tmp = a * 120.0;
	} else if (t_1 <= 1e+144) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = (y * -60.0) / (z - 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 <= -5e+139)
		tmp = Float64(Float64(x - y) * Float64(-60.0 / t));
	elseif (t_1 <= -2e-59)
		tmp = fma(-60.0, Float64(y / z), Float64(a * 120.0));
	elseif (t_1 <= 1e+62)
		tmp = Float64(a * 120.0);
	elseif (t_1 <= 1e+144)
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	else
		tmp = Float64(Float64(y * -60.0) / Float64(z - t));
	end
	return 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, -5e+139], N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-59], N[(-60.0 * N[(y / z), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+62], N[(a * 120.0), $MachinePrecision], If[LessEqual[t$95$1, 1e+144], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5.0000000000000003e139

   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

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t} + 120 \cdot a} \]
   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 70.2

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

   5. Applied rewrites 70.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 70.1%

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

   10. Applied rewrites 70.4%

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

   if -5.0000000000000003e139 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -2.0000000000000001e-59

   1. Initial program 99.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 75.3

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

   5. Applied rewrites 75.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 65.6%

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

   if -2.0000000000000001e-59 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.00000000000000004e62

   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 72.9

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

   5. Applied rewrites 72.9%

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

   if 1.00000000000000004e62 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.00000000000000002e144

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf

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

      1. 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. lower-*.f64 N/A

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

      4. lower--.f64 59.3

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

   5. Applied rewrites 59.3%

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

   7. Applied rewrites 59.4%

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

   if 1.00000000000000002e144 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 5.6

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

   5. Applied rewrites 5.6%

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

   6. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 73.5

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

   8. Applied rewrites 73.5%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{+139}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -2 \cdot 10^{-59}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{y}{z}, a \cdot 120\right)\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+62}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+144}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+139}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;t\_1 \leq 10^{+62}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t\_1 \leq 10^{+144}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -5e+139)
     (* (- x y) (/ -60.0 t))
     (if (<= t_1 1e+62)
       (* a 120.0)
       (if (<= t_1 1e+144) (* 60.0 (/ x (- z t))) (/ (* y -60.0) (- z 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 <= -5e+139) {
		tmp = (x - y) * (-60.0 / t);
	} else if (t_1 <= 1e+62) {
		tmp = a * 120.0;
	} else if (t_1 <= 1e+144) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = (y * -60.0) / (z - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-5d+139)) then
        tmp = (x - y) * ((-60.0d0) / t)
    else if (t_1 <= 1d+62) then
        tmp = a * 120.0d0
    else if (t_1 <= 1d+144) then
        tmp = 60.0d0 * (x / (z - t))
    else
        tmp = (y * (-60.0d0)) / (z - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -5e+139) {
		tmp = (x - y) * (-60.0 / t);
	} else if (t_1 <= 1e+62) {
		tmp = a * 120.0;
	} else if (t_1 <= 1e+144) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = (y * -60.0) / (z - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -5e+139:
		tmp = (x - y) * (-60.0 / t)
	elif t_1 <= 1e+62:
		tmp = a * 120.0
	elif t_1 <= 1e+144:
		tmp = 60.0 * (x / (z - t))
	else:
		tmp = (y * -60.0) / (z - 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 <= -5e+139)
		tmp = Float64(Float64(x - y) * Float64(-60.0 / t));
	elseif (t_1 <= 1e+62)
		tmp = Float64(a * 120.0);
	elseif (t_1 <= 1e+144)
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	else
		tmp = Float64(Float64(y * -60.0) / Float64(z - 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 <= -5e+139)
		tmp = (x - y) * (-60.0 / t);
	elseif (t_1 <= 1e+62)
		tmp = a * 120.0;
	elseif (t_1 <= 1e+144)
		tmp = 60.0 * (x / (z - t));
	else
		tmp = (y * -60.0) / (z - 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, -5e+139], N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+62], N[(a * 120.0), $MachinePrecision], If[LessEqual[t$95$1, 1e+144], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5.0000000000000003e139

   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

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t} + 120 \cdot a} \]
   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 70.2

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

   5. Applied rewrites 70.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 70.1%

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

   10. Applied rewrites 70.4%

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

   if -5.0000000000000003e139 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.00000000000000004e62

   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 67.8

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

   5. Applied rewrites 67.8%

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

   if 1.00000000000000004e62 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.00000000000000002e144

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf

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

      1. 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. lower-*.f64 N/A

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

      4. lower--.f64 59.3

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

   5. Applied rewrites 59.3%

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

   7. Applied rewrites 59.4%

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

   if 1.00000000000000002e144 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 5.6

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

   5. Applied rewrites 5.6%

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

   6. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 73.5

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

   8. Applied rewrites 73.5%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{+139}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+62}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+144}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+139}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;t\_1 \leq 10^{+62}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t\_1 \leq 10^{+144}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{60}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -5e+139)
     (* (- x y) (/ -60.0 t))
     (if (<= t_1 1e+62)
       (* a 120.0)
       (if (<= t_1 1e+144) (* 60.0 (/ x (- z t))) (* y (/ 60.0 (- t 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 <= -5e+139) {
		tmp = (x - y) * (-60.0 / t);
	} else if (t_1 <= 1e+62) {
		tmp = a * 120.0;
	} else if (t_1 <= 1e+144) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = y * (60.0 / (t - 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 <= (-5d+139)) then
        tmp = (x - y) * ((-60.0d0) / t)
    else if (t_1 <= 1d+62) then
        tmp = a * 120.0d0
    else if (t_1 <= 1d+144) then
        tmp = 60.0d0 * (x / (z - t))
    else
        tmp = y * (60.0d0 / (t - 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 <= -5e+139) {
		tmp = (x - y) * (-60.0 / t);
	} else if (t_1 <= 1e+62) {
		tmp = a * 120.0;
	} else if (t_1 <= 1e+144) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = y * (60.0 / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -5e+139:
		tmp = (x - y) * (-60.0 / t)
	elif t_1 <= 1e+62:
		tmp = a * 120.0
	elif t_1 <= 1e+144:
		tmp = 60.0 * (x / (z - t))
	else:
		tmp = y * (60.0 / (t - 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 <= -5e+139)
		tmp = Float64(Float64(x - y) * Float64(-60.0 / t));
	elseif (t_1 <= 1e+62)
		tmp = Float64(a * 120.0);
	elseif (t_1 <= 1e+144)
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	else
		tmp = Float64(y * Float64(60.0 / Float64(t - 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 <= -5e+139)
		tmp = (x - y) * (-60.0 / t);
	elseif (t_1 <= 1e+62)
		tmp = a * 120.0;
	elseif (t_1 <= 1e+144)
		tmp = 60.0 * (x / (z - t));
	else
		tmp = y * (60.0 / (t - 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, -5e+139], N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+62], N[(a * 120.0), $MachinePrecision], If[LessEqual[t$95$1, 1e+144], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5.0000000000000003e139

   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

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t} + 120 \cdot a} \]
   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 70.2

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

   5. Applied rewrites 70.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 70.1%

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

   10. Applied rewrites 70.4%

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

   if -5.0000000000000003e139 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.00000000000000004e62

   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 67.8

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

   5. Applied rewrites 67.8%

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

   if 1.00000000000000004e62 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.00000000000000002e144

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf

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

      1. 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. lower-*.f64 N/A

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

      4. lower--.f64 59.3

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

   5. Applied rewrites 59.3%

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

   7. Applied rewrites 59.4%

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

   if 1.00000000000000002e144 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.8

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

      5. lift-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

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

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

      11. lower-*.f64 N/A

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

      12. metadata-eval N/A

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

      13. neg-sub0 N/A

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

      14. lift--.f64 N/A

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

      15. sub-neg N/A

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

      16. +-commutative N/A

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

      17. associate--r+ N/A

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

      18. neg-sub0 N/A

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

      19. remove-double-neg N/A

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

      20. lower--.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. associate-*r/ N/A

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

      8. metadata-eval N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 73.4

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

   7. Applied rewrites 73.4%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{+139}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+62}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+144}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{60}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+139}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;t\_1 \leq 10^{+62}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t\_1 \leq 10^{+144}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{60}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -5e+139)
     (* (- x y) (/ -60.0 t))
     (if (<= t_1 1e+62)
       (* a 120.0)
       (if (<= t_1 1e+144) (* (/ 60.0 (- z t)) x) (* y (/ 60.0 (- t 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 <= -5e+139) {
		tmp = (x - y) * (-60.0 / t);
	} else if (t_1 <= 1e+62) {
		tmp = a * 120.0;
	} else if (t_1 <= 1e+144) {
		tmp = (60.0 / (z - t)) * x;
	} else {
		tmp = y * (60.0 / (t - 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 <= (-5d+139)) then
        tmp = (x - y) * ((-60.0d0) / t)
    else if (t_1 <= 1d+62) then
        tmp = a * 120.0d0
    else if (t_1 <= 1d+144) then
        tmp = (60.0d0 / (z - t)) * x
    else
        tmp = y * (60.0d0 / (t - 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 <= -5e+139) {
		tmp = (x - y) * (-60.0 / t);
	} else if (t_1 <= 1e+62) {
		tmp = a * 120.0;
	} else if (t_1 <= 1e+144) {
		tmp = (60.0 / (z - t)) * x;
	} else {
		tmp = y * (60.0 / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -5e+139:
		tmp = (x - y) * (-60.0 / t)
	elif t_1 <= 1e+62:
		tmp = a * 120.0
	elif t_1 <= 1e+144:
		tmp = (60.0 / (z - t)) * x
	else:
		tmp = y * (60.0 / (t - 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 <= -5e+139)
		tmp = Float64(Float64(x - y) * Float64(-60.0 / t));
	elseif (t_1 <= 1e+62)
		tmp = Float64(a * 120.0);
	elseif (t_1 <= 1e+144)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * x);
	else
		tmp = Float64(y * Float64(60.0 / Float64(t - 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 <= -5e+139)
		tmp = (x - y) * (-60.0 / t);
	elseif (t_1 <= 1e+62)
		tmp = a * 120.0;
	elseif (t_1 <= 1e+144)
		tmp = (60.0 / (z - t)) * x;
	else
		tmp = y * (60.0 / (t - 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, -5e+139], N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+62], N[(a * 120.0), $MachinePrecision], If[LessEqual[t$95$1, 1e+144], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(y * N[(60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5.0000000000000003e139

   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

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t} + 120 \cdot a} \]
   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 70.2

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

   5. Applied rewrites 70.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 70.1%

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

   10. Applied rewrites 70.4%

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

   if -5.0000000000000003e139 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.00000000000000004e62

   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 67.8

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

   5. Applied rewrites 67.8%

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

   if 1.00000000000000004e62 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.00000000000000002e144

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf

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

      1. 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. lower-*.f64 N/A

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

      4. lower--.f64 59.3

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

   5. Applied rewrites 59.3%

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

   7. Applied rewrites 59.4%

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

   if 1.00000000000000002e144 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.8

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

      5. lift-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

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

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

      11. lower-*.f64 N/A

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

      12. metadata-eval N/A

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

      13. neg-sub0 N/A

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

      14. lift--.f64 N/A

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

      15. sub-neg N/A

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

      16. +-commutative N/A

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

      17. associate--r+ N/A

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

      18. neg-sub0 N/A

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

      19. remove-double-neg N/A

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

      20. lower--.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. associate-*r/ N/A

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

      8. metadata-eval N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 73.4

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

   7. Applied rewrites 73.4%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{+139}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+62}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+144}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{60}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+139}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+76}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{60}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -5e+139)
     (* (- x y) (/ -60.0 t))
     (if (<= t_1 5e+76) (* a 120.0) (* y (/ 60.0 (- t 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 <= -5e+139) {
		tmp = (x - y) * (-60.0 / t);
	} else if (t_1 <= 5e+76) {
		tmp = a * 120.0;
	} else {
		tmp = y * (60.0 / (t - 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 <= (-5d+139)) then
        tmp = (x - y) * ((-60.0d0) / t)
    else if (t_1 <= 5d+76) then
        tmp = a * 120.0d0
    else
        tmp = y * (60.0d0 / (t - 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 <= -5e+139) {
		tmp = (x - y) * (-60.0 / t);
	} else if (t_1 <= 5e+76) {
		tmp = a * 120.0;
	} else {
		tmp = y * (60.0 / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -5e+139:
		tmp = (x - y) * (-60.0 / t)
	elif t_1 <= 5e+76:
		tmp = a * 120.0
	else:
		tmp = y * (60.0 / (t - 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 <= -5e+139)
		tmp = Float64(Float64(x - y) * Float64(-60.0 / t));
	elseif (t_1 <= 5e+76)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(y * Float64(60.0 / Float64(t - 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 <= -5e+139)
		tmp = (x - y) * (-60.0 / t);
	elseif (t_1 <= 5e+76)
		tmp = a * 120.0;
	else
		tmp = y * (60.0 / (t - 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, -5e+139], N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+76], N[(a * 120.0), $MachinePrecision], N[(y * N[(60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5.0000000000000003e139

   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

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t} + 120 \cdot a} \]
   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 70.2

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

   5. Applied rewrites 70.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 70.1%

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

   10. Applied rewrites 70.4%

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

   if -5.0000000000000003e139 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.99999999999999991e76

   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 66.7

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

   5. Applied rewrites 66.7%

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

   if 4.99999999999999991e76 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.7

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

      5. lift-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

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

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

      11. lower-*.f64 N/A

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

      12. metadata-eval N/A

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

      13. neg-sub0 N/A

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

      14. lift--.f64 N/A

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

      15. sub-neg N/A

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

      16. +-commutative N/A

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

      17. associate--r+ N/A

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

      18. neg-sub0 N/A

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

      19. remove-double-neg N/A

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

      20. lower--.f64 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. associate-*r/ N/A

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

      8. metadata-eval N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 59.1

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

   7. Applied rewrites 59.1%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{+139}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 5 \cdot 10^{+76}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{60}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{60}{t - z}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+76}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ 60.0 (- t z)))) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -5e+78) t_1 (if (<= t_2 5e+76) (* 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 - z));
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e+78) {
		tmp = t_1;
	} else if (t_2 <= 5e+76) {
		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 - z))
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-5d+78)) then
        tmp = t_1
    else if (t_2 <= 5d+76) 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 - z));
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e+78) {
		tmp = t_1;
	} else if (t_2 <= 5e+76) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (60.0 / (t - z))
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -5e+78:
		tmp = t_1
	elif t_2 <= 5e+76:
		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 / Float64(t - z)))
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -5e+78)
		tmp = t_1;
	elseif (t_2 <= 5e+76)
		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 - z));
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -5e+78)
		tmp = t_1;
	elseif (t_2 <= 5e+76)
		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 / N[(t - z), $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, -5e+78], t$95$1, If[LessEqual[t$95$2, 5e+76], 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)) < -4.99999999999999984e78 or 4.99999999999999991e76 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.7

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

      5. lift-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

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

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

      11. lower-*.f64 N/A

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

      12. metadata-eval N/A

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

      13. neg-sub0 N/A

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

      14. lift--.f64 N/A

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

      15. sub-neg N/A

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

      16. +-commutative N/A

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

      17. associate--r+ N/A

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

      18. neg-sub0 N/A

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

      19. remove-double-neg N/A

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

      20. lower--.f64 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-*.f64 N/A

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

      7. associate-*r/ N/A

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

      8. metadata-eval N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 52.8

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

   7. Applied rewrites 52.8%

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

   if -4.99999999999999984e78 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.99999999999999991e76

   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 69.4

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

   5. Applied rewrites 69.4%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{+78}:\\ \;\;\;\;y \cdot \frac{60}{t - z}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 5 \cdot 10^{+76}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{60}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+139}:\\ \;\;\;\;y \cdot \frac{60}{t}\\ \mathbf{elif}\;t\_1 \leq 10^{+111}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -5e+139)
     (* y (/ 60.0 t))
     (if (<= t_1 1e+111) (* a 120.0) (/ (* 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 <= -5e+139) {
		tmp = y * (60.0 / t);
	} else if (t_1 <= 1e+111) {
		tmp = a * 120.0;
	} else {
		tmp = (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 <= (-5d+139)) then
        tmp = y * (60.0d0 / t)
    else if (t_1 <= 1d+111) then
        tmp = a * 120.0d0
    else
        tmp = (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 <= -5e+139) {
		tmp = y * (60.0 / t);
	} else if (t_1 <= 1e+111) {
		tmp = a * 120.0;
	} else {
		tmp = (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 <= -5e+139:
		tmp = y * (60.0 / t)
	elif t_1 <= 1e+111:
		tmp = a * 120.0
	else:
		tmp = (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 <= -5e+139)
		tmp = Float64(y * Float64(60.0 / t));
	elseif (t_1 <= 1e+111)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(Float64(y * -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 <= -5e+139)
		tmp = y * (60.0 / t);
	elseif (t_1 <= 1e+111)
		tmp = a * 120.0;
	else
		tmp = (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, -5e+139], N[(y * N[(60.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+111], N[(a * 120.0), $MachinePrecision], N[(N[(y * -60.0), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5.0000000000000003e139

   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

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t} + 120 \cdot a} \]
   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 70.2

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

   5. Applied rewrites 70.2%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 40.7%

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

   10. Applied rewrites 40.8%

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

   if -5.0000000000000003e139 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 9.99999999999999957e110

   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 63.6

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

   5. Applied rewrites 63.6%

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

   if 9.99999999999999957e110 < (/.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 inf

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

      1. lower-*.f64 7.4

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

   5. Applied rewrites 7.4%

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

   6. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 66.0

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

   8. Applied rewrites 66.0%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 44.0%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{+139}:\\ \;\;\;\;y \cdot \frac{60}{t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+111}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 55.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+139}:\\ \;\;\;\;y \cdot \frac{60}{t}\\ \mathbf{elif}\;t\_1 \leq 10^{+144}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -5e+139)
     (* y (/ 60.0 t))
     (if (<= t_1 1e+144) (* 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 <= -5e+139) {
		tmp = y * (60.0 / t);
	} else if (t_1 <= 1e+144) {
		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 <= (-5d+139)) then
        tmp = y * (60.0d0 / t)
    else if (t_1 <= 1d+144) 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 <= -5e+139) {
		tmp = y * (60.0 / t);
	} else if (t_1 <= 1e+144) {
		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 <= -5e+139:
		tmp = y * (60.0 / t)
	elif t_1 <= 1e+144:
		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 <= -5e+139)
		tmp = Float64(y * Float64(60.0 / t));
	elseif (t_1 <= 1e+144)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(Float64(60.0 * 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 <= -5e+139)
		tmp = y * (60.0 / t);
	elseif (t_1 <= 1e+144)
		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, -5e+139], N[(y * N[(60.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+144], N[(a * 120.0), $MachinePrecision], N[(N[(60.0 * y), $MachinePrecision] / t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5.0000000000000003e139

   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

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t} + 120 \cdot a} \]
   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 70.2

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

   5. Applied rewrites 70.2%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 40.7%

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

   10. Applied rewrites 40.8%

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

   if -5.0000000000000003e139 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.00000000000000002e144

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 62.2

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

   5. Applied rewrites 62.2%

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

   if 1.00000000000000002e144 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.8%

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

   3. Taylor expanded in 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 54.5

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

   5. Applied rewrites 54.5%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 39.1%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{+139}:\\ \;\;\;\;y \cdot \frac{60}{t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+144}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 55.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{60}{t}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+139}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+144}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -5e+139) t_1 (if (<= t_2 1e+144) (* 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 <= -5e+139) {
		tmp = t_1;
	} else if (t_2 <= 1e+144) {
		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 <= (-5d+139)) then
        tmp = t_1
    else if (t_2 <= 1d+144) 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 <= -5e+139) {
		tmp = t_1;
	} else if (t_2 <= 1e+144) {
		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 <= -5e+139:
		tmp = t_1
	elif t_2 <= 1e+144:
		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 <= -5e+139)
		tmp = t_1;
	elseif (t_2 <= 1e+144)
		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 <= -5e+139)
		tmp = t_1;
	elseif (t_2 <= 1e+144)
		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, -5e+139], t$95$1, If[LessEqual[t$95$2, 1e+144], 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)) < -5.0000000000000003e139 or 1.00000000000000002e144 < (/.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

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t} + 120 \cdot a} \]
   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 61.6

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

   5. Applied rewrites 61.6%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 39.8%

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

   10. Applied rewrites 39.8%

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

   if -5.0000000000000003e139 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1.00000000000000002e144

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 62.2

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

   5. Applied rewrites 62.2%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{+139}:\\ \;\;\;\;y \cdot \frac{60}{t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+144}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-60, \frac{y}{z}, a \cdot 120\right)\\ \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{-30}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{elif}\;a \cdot 120 \leq 0.003:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{+130}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x}{z}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma -60.0 (/ y z) (* a 120.0))))
   (if (<= (* a 120.0) -5e+135)
     t_1
     (if (<= (* a 120.0) -4e-30)
       (fma -60.0 (/ (- x y) t) (* a 120.0))
       (if (<= (* a 120.0) 0.003)
         (/ (* 60.0 (- x y)) (- z t))
         (if (<= (* a 120.0) 5e+130) (fma 60.0 (/ x 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, (y / z), (a * 120.0));
	double tmp;
	if ((a * 120.0) <= -5e+135) {
		tmp = t_1;
	} else if ((a * 120.0) <= -4e-30) {
		tmp = fma(-60.0, ((x - y) / t), (a * 120.0));
	} else if ((a * 120.0) <= 0.003) {
		tmp = (60.0 * (x - y)) / (z - t);
	} else if ((a * 120.0) <= 5e+130) {
		tmp = fma(60.0, (x / z), (a * 120.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(-60.0, Float64(y / z), Float64(a * 120.0))
	tmp = 0.0
	if (Float64(a * 120.0) <= -5e+135)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= -4e-30)
		tmp = fma(-60.0, Float64(Float64(x - y) / t), Float64(a * 120.0));
	elseif (Float64(a * 120.0) <= 0.003)
		tmp = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t));
	elseif (Float64(a * 120.0) <= 5e+130)
		tmp = fma(60.0, Float64(x / 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[(y / z), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e+135], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e-30], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 0.003], N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e+130], N[(60.0 * N[(x / z), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -5.00000000000000029e135 or 4.9999999999999996e130 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z} + 120 \cdot a} \]
   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 78.9

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

   5. Applied rewrites 78.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 85.5%

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

   if -5.00000000000000029e135 < (*.f64 a #s(literal 120 binary64)) < -4e-30

   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 81.1

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

   5. Applied rewrites 81.1%

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

   if -4e-30 < (*.f64 a #s(literal 120 binary64)) < 0.0030000000000000001

   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 83.9

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

   5. Applied rewrites 83.9%

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

   if 0.0030000000000000001 < (*.f64 a #s(literal 120 binary64)) < 4.9999999999999996e130

   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

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z} + 120 \cdot a} \]
   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 77.5

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

   5. Applied rewrites 77.5%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 81.1%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+135}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{y}{z}, a \cdot 120\right)\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{-30}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{elif}\;a \cdot 120 \leq 0.003:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{+130}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x}{z}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{y}{z}, a \cdot 120\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 72.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-60, \frac{y}{z}, a \cdot 120\right)\\ \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{-30}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x}{t}, a \cdot 120\right)\\ \mathbf{elif}\;a \cdot 120 \leq 0.003:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{+130}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x}{z}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma -60.0 (/ y z) (* a 120.0))))
   (if (<= (* a 120.0) -5e+135)
     t_1
     (if (<= (* a 120.0) -4e-30)
       (fma -60.0 (/ x t) (* a 120.0))
       (if (<= (* a 120.0) 0.003)
         (/ (* 60.0 (- x y)) (- z t))
         (if (<= (* a 120.0) 5e+130) (fma 60.0 (/ x 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, (y / z), (a * 120.0));
	double tmp;
	if ((a * 120.0) <= -5e+135) {
		tmp = t_1;
	} else if ((a * 120.0) <= -4e-30) {
		tmp = fma(-60.0, (x / t), (a * 120.0));
	} else if ((a * 120.0) <= 0.003) {
		tmp = (60.0 * (x - y)) / (z - t);
	} else if ((a * 120.0) <= 5e+130) {
		tmp = fma(60.0, (x / z), (a * 120.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(-60.0, Float64(y / z), Float64(a * 120.0))
	tmp = 0.0
	if (Float64(a * 120.0) <= -5e+135)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= -4e-30)
		tmp = fma(-60.0, Float64(x / t), Float64(a * 120.0));
	elseif (Float64(a * 120.0) <= 0.003)
		tmp = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t));
	elseif (Float64(a * 120.0) <= 5e+130)
		tmp = fma(60.0, Float64(x / 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[(y / z), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e+135], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e-30], N[(-60.0 * N[(x / t), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 0.003], N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e+130], N[(60.0 * N[(x / z), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -5.00000000000000029e135 or 4.9999999999999996e130 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z} + 120 \cdot a} \]
   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 78.9

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

   5. Applied rewrites 78.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 85.5%

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

   if -5.00000000000000029e135 < (*.f64 a #s(literal 120 binary64)) < -4e-30

   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 81.1

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

   5. Applied rewrites 81.1%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 80.7%

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

   if -4e-30 < (*.f64 a #s(literal 120 binary64)) < 0.0030000000000000001

   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 83.9

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

   5. Applied rewrites 83.9%

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

   if 0.0030000000000000001 < (*.f64 a #s(literal 120 binary64)) < 4.9999999999999996e130

   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

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z} + 120 \cdot a} \]
   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 77.5

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

   5. Applied rewrites 77.5%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 81.1%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+135}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{y}{z}, a \cdot 120\right)\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{-30}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x}{t}, a \cdot 120\right)\\ \mathbf{elif}\;a \cdot 120 \leq 0.003:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{+130}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x}{z}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{y}{z}, a \cdot 120\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 72.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-60, \frac{y}{z}, a \cdot 120\right)\\ \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{-30}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x}{t}, a \cdot 120\right)\\ \mathbf{elif}\;a \cdot 120 \leq 0.003:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma -60.0 (/ y z) (* a 120.0))))
   (if (<= (* a 120.0) -5e+135)
     t_1
     (if (<= (* a 120.0) -4e-30)
       (fma -60.0 (/ x t) (* a 120.0))
       (if (<= (* a 120.0) 0.003) (/ (* 60.0 (- x y)) (- z t)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(-60.0, (y / z), (a * 120.0));
	double tmp;
	if ((a * 120.0) <= -5e+135) {
		tmp = t_1;
	} else if ((a * 120.0) <= -4e-30) {
		tmp = fma(-60.0, (x / t), (a * 120.0));
	} else if ((a * 120.0) <= 0.003) {
		tmp = (60.0 * (x - y)) / (z - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(-60.0, Float64(y / z), Float64(a * 120.0))
	tmp = 0.0
	if (Float64(a * 120.0) <= -5e+135)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= -4e-30)
		tmp = fma(-60.0, Float64(x / t), Float64(a * 120.0));
	elseif (Float64(a * 120.0) <= 0.003)
		tmp = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(y / z), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e+135], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e-30], N[(-60.0 * N[(x / t), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 0.003], N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -5.00000000000000029e135 or 0.0030000000000000001 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z} + 120 \cdot a} \]
   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 78.5

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

   5. Applied rewrites 78.5%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 78.9%

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

   if -5.00000000000000029e135 < (*.f64 a #s(literal 120 binary64)) < -4e-30

   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 81.1

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

   5. Applied rewrites 81.1%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 80.7%

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

   if -4e-30 < (*.f64 a #s(literal 120 binary64)) < 0.0030000000000000001

   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 83.9

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

   5. Applied rewrites 83.9%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+135}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{y}{z}, a \cdot 120\right)\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{-30}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x}{t}, a \cdot 120\right)\\ \mathbf{elif}\;a \cdot 120 \leq 0.003:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{y}{z}, a \cdot 120\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 72.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-60, \frac{y}{z}, a \cdot 120\right)\\ \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot 120 \leq 0.003:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma -60.0 (/ y z) (* a 120.0))))
   (if (<= (* a 120.0) -5e-52)
     t_1
     (if (<= (* a 120.0) 0.003) (/ (* 60.0 (- x y)) (- z t)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(-60.0, (y / z), (a * 120.0));
	double tmp;
	if ((a * 120.0) <= -5e-52) {
		tmp = t_1;
	} else if ((a * 120.0) <= 0.003) {
		tmp = (60.0 * (x - y)) / (z - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(-60.0, Float64(y / z), Float64(a * 120.0))
	tmp = 0.0
	if (Float64(a * 120.0) <= -5e-52)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= 0.003)
		tmp = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(y / z), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e-52], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], 0.003], N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -5e-52 or 0.0030000000000000001 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z} + 120 \cdot a} \]
   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 75.3

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

   5. Applied rewrites 75.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 74.7%

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

   if -5e-52 < (*.f64 a #s(literal 120 binary64)) < 0.0030000000000000001

   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 84.8

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

   5. Applied rewrites 84.8%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-52}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{y}{z}, a \cdot 120\right)\\ \mathbf{elif}\;a \cdot 120 \leq 0.003:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{y}{z}, a \cdot 120\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 82.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+56}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-116}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{60 \cdot \left(x - y\right)}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.2e+56)
   (fma 60.0 (/ (- x y) z) (* a 120.0))
   (if (<= z 4.5e-116)
     (+ (* a 120.0) (* (- x y) (/ -60.0 t)))
     (fma a 120.0 (/ (* 60.0 (- x y)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e+56) {
		tmp = fma(60.0, ((x - y) / z), (a * 120.0));
	} else if (z <= 4.5e-116) {
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	} else {
		tmp = fma(a, 120.0, ((60.0 * (x - y)) / z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.2e+56)
		tmp = fma(60.0, Float64(Float64(x - y) / z), Float64(a * 120.0));
	elseif (z <= 4.5e-116)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x - y) * Float64(-60.0 / t)));
	else
		tmp = fma(a, 120.0, Float64(Float64(60.0 * Float64(x - y)) / z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.2e+56], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-116], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0 + N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.20000000000000003e56

   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

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z} + 120 \cdot a} \]
   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 88.8

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

   5. Applied rewrites 88.8%

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

   if -3.20000000000000003e56 < z < 4.50000000000000012e-116

   1. Initial program 99.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 81.5

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

   7. Applied rewrites 81.5%

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

   if 4.50000000000000012e-116 < z

   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

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.9

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

      5. lift-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

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

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

      11. lower-*.f64 N/A

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

      12. metadata-eval N/A

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

      13. neg-sub0 N/A

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

      14. lift--.f64 N/A

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

      15. sub-neg N/A

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

      16. +-commutative N/A

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

      17. associate--r+ N/A

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

      18. neg-sub0 N/A

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

      19. remove-double-neg N/A

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

      20. lower--.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in t around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 87.8

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

   7. Applied rewrites 87.8%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+56}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-116}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{60 \cdot \left(x - y\right)}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 82.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+56}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-116}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{60 \cdot \left(x - y\right)}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.2e+56)
   (fma 60.0 (/ (- x y) z) (* a 120.0))
   (if (<= z 4.5e-116)
     (fma -60.0 (/ (- x y) t) (* a 120.0))
     (fma a 120.0 (/ (* 60.0 (- x y)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e+56) {
		tmp = fma(60.0, ((x - y) / z), (a * 120.0));
	} else if (z <= 4.5e-116) {
		tmp = fma(-60.0, ((x - y) / t), (a * 120.0));
	} else {
		tmp = fma(a, 120.0, ((60.0 * (x - y)) / z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.2e+56)
		tmp = fma(60.0, Float64(Float64(x - y) / z), Float64(a * 120.0));
	elseif (z <= 4.5e-116)
		tmp = fma(-60.0, Float64(Float64(x - y) / t), Float64(a * 120.0));
	else
		tmp = fma(a, 120.0, Float64(Float64(60.0 * Float64(x - y)) / z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.2e+56], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-116], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(a * 120.0 + N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.20000000000000003e56

   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

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z} + 120 \cdot a} \]
   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 88.8

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

   5. Applied rewrites 88.8%

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

   if -3.20000000000000003e56 < z < 4.50000000000000012e-116

   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

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t} + 120 \cdot a} \]
   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 81.5

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

   5. Applied rewrites 81.5%

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

   if 4.50000000000000012e-116 < z

   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

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.9

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

      5. lift-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

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

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

      11. lower-*.f64 N/A

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

      12. metadata-eval N/A

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

      13. neg-sub0 N/A

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

      14. lift--.f64 N/A

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

      15. sub-neg N/A

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

      16. +-commutative N/A

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

      17. associate--r+ N/A

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

      18. neg-sub0 N/A

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

      19. remove-double-neg N/A

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

      20. lower--.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in t around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 87.8

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

   7. Applied rewrites 87.8%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+56}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-116}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{60 \cdot \left(x - y\right)}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 82.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-116}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma 60.0 (/ (- x y) z) (* a 120.0))))
   (if (<= z -3.2e+56)
     t_1
     (if (<= z 4.5e-116) (fma -60.0 (/ (- x y) t) (* 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) / z), (a * 120.0));
	double tmp;
	if (z <= -3.2e+56) {
		tmp = t_1;
	} else if (z <= 4.5e-116) {
		tmp = fma(-60.0, ((x - y) / t), (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) / z), Float64(a * 120.0))
	tmp = 0.0
	if (z <= -3.2e+56)
		tmp = t_1;
	elseif (z <= 4.5e-116)
		tmp = fma(-60.0, Float64(Float64(x - y) / t), 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] / z), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e+56], t$95$1, If[LessEqual[z, 4.5e-116], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.20000000000000003e56 or 4.50000000000000012e-116 < z

   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 88.2

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

   5. Applied rewrites 88.2%

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

   if -3.20000000000000003e56 < z < 4.50000000000000012e-116

   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

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t} + 120 \cdot a} \]
   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 81.5

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

   5. Applied rewrites 81.5%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+56}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-116}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, a \cdot 120\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x - y}{z}, a \cdot 120\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 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

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lower-fma.f64 99.8

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

   5. lift-/.f64 N/A

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

   6. frac-2neg N/A

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

   7. lower-/.f64 N/A

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

   8. lift-*.f64 N/A

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

   9. *-commutative N/A

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

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

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

   11. lower-*.f64 N/A

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

   12. metadata-eval N/A

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

   13. neg-sub0 N/A

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

   14. lift--.f64 N/A

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

   15. sub-neg N/A

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

   16. +-commutative N/A

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

   17. associate--r+ N/A

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

   18. neg-sub0 N/A

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

   19. remove-double-neg N/A

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

   20. lower--.f64 99.8

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

4. Applied rewrites 99.8%

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

Alternative 19: 51.6% 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 47.3

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

5. Applied rewrites 47.3%

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

6. Final simplification 47.3%

   \[\leadsto a \cdot 120 \]
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 2024226 
(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)))