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

Percentage Accurate: 99.4% → 99.4%

Time: 14.7s

Alternatives: 18

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% 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: 99.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

   2. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   3. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   4. neg-sub0 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   5. associate-+l- N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   6. sub0-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   7. distribute-rgt-neg-out N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   8. distribute-frac-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

   9. distribute-frac-neg2 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

   10. sub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

   11. +-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

   12. distribute-neg-in N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

   13. unsub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

   14. remove-double-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

   15. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

   16. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

   17. --lowering--.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

   18. --lowering--.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

   19. *-lowering-*.f64 99.9%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

3. Simplified 99.9%

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

   1. +-commutative N/A

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

   2. fma-define N/A

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

   3. fma-lowering-fma.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(a, \color{blue}{120}, \left(\frac{60 \cdot \left(y - x\right)}{t - z}\right)\right) \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right)\right) \]

   5. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right)\right) \]

   6. --lowering--.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right)\right) \]

   7. --lowering--.f64 99.9%

      \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right)\right) \]

6. Applied egg-rr 99.9%

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

Alternative 2: 57.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-214}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-303}:\\ \;\;\;\;\frac{x \cdot -60}{t - z}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-232}:\\ \;\;\;\;\frac{y}{\frac{t - z}{60}}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{\frac{t - z}{-60}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.8e-214)
   (* a 120.0)
   (if (<= a 3.2e-303)
     (/ (* x -60.0) (- t z))
     (if (<= a 1.25e-232)
       (/ y (/ (- t z) 60.0))
       (if (<= a 1.9e-84) (/ x (/ (- t z) -60.0)) (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.8e-214) {
		tmp = a * 120.0;
	} else if (a <= 3.2e-303) {
		tmp = (x * -60.0) / (t - z);
	} else if (a <= 1.25e-232) {
		tmp = y / ((t - z) / 60.0);
	} else if (a <= 1.9e-84) {
		tmp = x / ((t - z) / -60.0);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5.8d-214)) then
        tmp = a * 120.0d0
    else if (a <= 3.2d-303) then
        tmp = (x * (-60.0d0)) / (t - z)
    else if (a <= 1.25d-232) then
        tmp = y / ((t - z) / 60.0d0)
    else if (a <= 1.9d-84) then
        tmp = x / ((t - z) / (-60.0d0))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.8e-214) {
		tmp = a * 120.0;
	} else if (a <= 3.2e-303) {
		tmp = (x * -60.0) / (t - z);
	} else if (a <= 1.25e-232) {
		tmp = y / ((t - z) / 60.0);
	} else if (a <= 1.9e-84) {
		tmp = x / ((t - z) / -60.0);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.8e-214:
		tmp = a * 120.0
	elif a <= 3.2e-303:
		tmp = (x * -60.0) / (t - z)
	elif a <= 1.25e-232:
		tmp = y / ((t - z) / 60.0)
	elif a <= 1.9e-84:
		tmp = x / ((t - z) / -60.0)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.8e-214)
		tmp = Float64(a * 120.0);
	elseif (a <= 3.2e-303)
		tmp = Float64(Float64(x * -60.0) / Float64(t - z));
	elseif (a <= 1.25e-232)
		tmp = Float64(y / Float64(Float64(t - z) / 60.0));
	elseif (a <= 1.9e-84)
		tmp = Float64(x / Float64(Float64(t - z) / -60.0));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.8e-214)
		tmp = a * 120.0;
	elseif (a <= 3.2e-303)
		tmp = (x * -60.0) / (t - z);
	elseif (a <= 1.25e-232)
		tmp = y / ((t - z) / 60.0);
	elseif (a <= 1.9e-84)
		tmp = x / ((t - z) / -60.0);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.8e-214], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 3.2e-303], N[(N[(x * -60.0), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.25e-232], N[(y / N[(N[(t - z), $MachinePrecision] / 60.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.9e-84], N[(x / N[(N[(t - z), $MachinePrecision] / -60.0), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.7999999999999997e-214 or 1.89999999999999993e-84 < a

   1. Initial program 99.9%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 72.2%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   7. Simplified 72.2%

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

   if -5.7999999999999997e-214 < a < 3.19999999999999991e-303

   1. Initial program 99.9%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. metadata-eval N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(60\right)\right) \cdot x}{t - z} \]

      3. distribute-lft-neg-in N/A

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

      4. *-commutative N/A

         \[\leadsto \frac{\mathsf{neg}\left(x \cdot 60\right)}{t - z} \]

      5. distribute-lft-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(-1 \cdot x\right) \cdot 60\right), \color{blue}{\left(t - z\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(x\right)\right) \cdot 60\right), \left(t - z\right)\right) \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\mathsf{neg}\left(x \cdot 60\right)\right), \left(\color{blue}{t} - z\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\mathsf{neg}\left(60 \cdot x\right)\right), \left(t - z\right)\right) \]

      11. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(60\right)\right) \cdot x\right), \left(\color{blue}{t} - z\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\left(-60 \cdot x\right), \left(t - z\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-60, x\right), \left(\color{blue}{t} - z\right)\right) \]

      14. --lowering--.f64 61.2%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-60, x\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right) \]

   7. Simplified 61.2%

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

   if 3.19999999999999991e-303 < a < 1.25e-232

   1. Initial program 99.8%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.8%

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

      1. flip-+ N/A

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

      2. associate-/l* N/A

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

      3. fmm-def N/A

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

      4. *-commutative N/A

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

      5. clear-num N/A

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

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\mathsf{fma}\left(60, \frac{y - x}{t - z}, \mathsf{neg}\left(120 \cdot a\right)\right)}{\frac{60 \cdot \left(y - x\right)}{t - z} \cdot \frac{60 \cdot \left(y - x\right)}{t - z} - \left(a \cdot 120\right) \cdot \left(a \cdot 120\right)}\right)}\right) \]

      7. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{\color{blue}{\frac{\frac{60 \cdot \left(y - x\right)}{t - z} \cdot \frac{60 \cdot \left(y - x\right)}{t - z} - \left(a \cdot 120\right) \cdot \left(a \cdot 120\right)}{\mathsf{fma}\left(60, \frac{y - x}{t - z}, \mathsf{neg}\left(120 \cdot a\right)\right)}}}\right)\right) \]

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(60 \cdot y\right), \color{blue}{\left(t - z\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, y\right), \left(\color{blue}{t} - z\right)\right) \]

      4. --lowering--.f64 81.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, y\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right) \]

   9. Simplified 81.9%

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

       1. associate-/l* N/A

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

       2. metadata-eval N/A

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

       3. times-frac N/A

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

       4. *-lft-identity N/A

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

       5. *-commutative N/A

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

       6. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(\left(t - z\right) \cdot \frac{1}{60}\right)}\right) \]

       7. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(y, \left(\left(t - z\right) \cdot \frac{1}{\color{blue}{60}}\right)\right) \]

       8. div-inv N/A

          \[\leadsto \mathsf{/.f64}\left(y, \left(\frac{t - z}{\color{blue}{60}}\right)\right) \]

       9. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(\left(t - z\right), \color{blue}{60}\right)\right) \]

       10. --lowering--.f64 81.9%

           \[\leadsto \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, z\right), 60\right)\right) \]

   11. Applied egg-rr 81.9%

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

   if 1.25e-232 < a < 1.89999999999999993e-84

   1. Initial program 99.7%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.7%

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

      1. +-commutative N/A

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

      2. fma-define N/A

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

      3. fma-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, \color{blue}{120}, \left(\frac{60 \cdot \left(y - x\right)}{t - z}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right)\right) \]

      7. --lowering--.f64 99.6%

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right)\right) \]

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{x}{t - z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(x, \color{blue}{\left(t - z\right)}\right)\right) \]

      3. --lowering--.f64 65.4%

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   9. Simplified 65.4%

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

       1. *-commutative N/A

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

       2. associate-*l/ N/A

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

       3. associate-*r/ N/A

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

       4. clear-num N/A

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

       5. un-div-inv N/A

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

       6. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{t - z}{-60}\right)}\right) \]

       7. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\left(t - z\right), \color{blue}{-60}\right)\right) \]

       8. --lowering--.f64 65.6%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, z\right), -60\right)\right) \]

   11. Applied egg-rr 65.6%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-214}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-303}:\\ \;\;\;\;\frac{x \cdot -60}{t - z}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-232}:\\ \;\;\;\;\frac{y}{\frac{t - z}{60}}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{\frac{t - z}{-60}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 57.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{t - z}{-60}}\\ \mathbf{if}\;a \leq -7.2 \cdot 10^{-214}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-303}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-233}:\\ \;\;\;\;\frac{y}{\frac{t - z}{60}}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-83}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (/ (- t z) -60.0))))
   (if (<= a -7.2e-214)
     (* a 120.0)
     (if (<= a 3.3e-303)
       t_1
       (if (<= a 8e-233)
         (/ y (/ (- t z) 60.0))
         (if (<= a 1.3e-83) t_1 (* a 120.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / ((t - z) / -60.0);
	double tmp;
	if (a <= -7.2e-214) {
		tmp = a * 120.0;
	} else if (a <= 3.3e-303) {
		tmp = t_1;
	} else if (a <= 8e-233) {
		tmp = y / ((t - z) / 60.0);
	} else if (a <= 1.3e-83) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / ((t - z) / (-60.0d0))
    if (a <= (-7.2d-214)) then
        tmp = a * 120.0d0
    else if (a <= 3.3d-303) then
        tmp = t_1
    else if (a <= 8d-233) then
        tmp = y / ((t - z) / 60.0d0)
    else if (a <= 1.3d-83) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x / ((t - z) / -60.0);
	double tmp;
	if (a <= -7.2e-214) {
		tmp = a * 120.0;
	} else if (a <= 3.3e-303) {
		tmp = t_1;
	} else if (a <= 8e-233) {
		tmp = y / ((t - z) / 60.0);
	} else if (a <= 1.3e-83) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / ((t - z) / -60.0)
	tmp = 0
	if a <= -7.2e-214:
		tmp = a * 120.0
	elif a <= 3.3e-303:
		tmp = t_1
	elif a <= 8e-233:
		tmp = y / ((t - z) / 60.0)
	elif a <= 1.3e-83:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(Float64(t - z) / -60.0))
	tmp = 0.0
	if (a <= -7.2e-214)
		tmp = Float64(a * 120.0);
	elseif (a <= 3.3e-303)
		tmp = t_1;
	elseif (a <= 8e-233)
		tmp = Float64(y / Float64(Float64(t - z) / 60.0));
	elseif (a <= 1.3e-83)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / ((t - z) / -60.0);
	tmp = 0.0;
	if (a <= -7.2e-214)
		tmp = a * 120.0;
	elseif (a <= 3.3e-303)
		tmp = t_1;
	elseif (a <= 8e-233)
		tmp = y / ((t - z) / 60.0);
	elseif (a <= 1.3e-83)
		tmp = t_1;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(N[(t - z), $MachinePrecision] / -60.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.2e-214], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 3.3e-303], t$95$1, If[LessEqual[a, 8e-233], N[(y / N[(N[(t - z), $MachinePrecision] / 60.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.3e-83], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.2e-214 or 1.30000000000000004e-83 < a

   1. Initial program 99.9%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 72.2%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   7. Simplified 72.2%

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

   if -7.2e-214 < a < 3.2999999999999997e-303 or 7.99999999999999966e-233 < a < 1.30000000000000004e-83

   1. Initial program 99.8%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.8%

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

      1. +-commutative N/A

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

      2. fma-define N/A

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

      3. fma-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, \color{blue}{120}, \left(\frac{60 \cdot \left(y - x\right)}{t - z}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right)\right) \]

      7. --lowering--.f64 99.7%

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right)\right) \]

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{x}{t - z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(x, \color{blue}{\left(t - z\right)}\right)\right) \]

      3. --lowering--.f64 63.4%

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   9. Simplified 63.4%

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

       1. *-commutative N/A

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

       2. associate-*l/ N/A

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

       3. associate-*r/ N/A

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

       4. clear-num N/A

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

       5. un-div-inv N/A

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

       6. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{t - z}{-60}\right)}\right) \]

       7. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\left(t - z\right), \color{blue}{-60}\right)\right) \]

       8. --lowering--.f64 63.6%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, z\right), -60\right)\right) \]

   11. Applied egg-rr 63.6%

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

   if 3.2999999999999997e-303 < a < 7.99999999999999966e-233

   1. Initial program 99.8%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.8%

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

      1. flip-+ N/A

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

      2. associate-/l* N/A

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

      3. fmm-def N/A

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

      4. *-commutative N/A

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

      5. clear-num N/A

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

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\mathsf{fma}\left(60, \frac{y - x}{t - z}, \mathsf{neg}\left(120 \cdot a\right)\right)}{\frac{60 \cdot \left(y - x\right)}{t - z} \cdot \frac{60 \cdot \left(y - x\right)}{t - z} - \left(a \cdot 120\right) \cdot \left(a \cdot 120\right)}\right)}\right) \]

      7. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{\color{blue}{\frac{\frac{60 \cdot \left(y - x\right)}{t - z} \cdot \frac{60 \cdot \left(y - x\right)}{t - z} - \left(a \cdot 120\right) \cdot \left(a \cdot 120\right)}{\mathsf{fma}\left(60, \frac{y - x}{t - z}, \mathsf{neg}\left(120 \cdot a\right)\right)}}}\right)\right) \]

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(60 \cdot y\right), \color{blue}{\left(t - z\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, y\right), \left(\color{blue}{t} - z\right)\right) \]

      4. --lowering--.f64 81.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, y\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right) \]

   9. Simplified 81.9%

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

       1. associate-/l* N/A

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

       2. metadata-eval N/A

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

       3. times-frac N/A

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

       4. *-lft-identity N/A

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

       5. *-commutative N/A

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

       6. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(\left(t - z\right) \cdot \frac{1}{60}\right)}\right) \]

       7. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(y, \left(\left(t - z\right) \cdot \frac{1}{\color{blue}{60}}\right)\right) \]

       8. div-inv N/A

          \[\leadsto \mathsf{/.f64}\left(y, \left(\frac{t - z}{\color{blue}{60}}\right)\right) \]

       9. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(\left(t - z\right), \color{blue}{60}\right)\right) \]

       10. --lowering--.f64 81.9%

           \[\leadsto \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, z\right), 60\right)\right) \]

   11. Applied egg-rr 81.9%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{-214}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-303}:\\ \;\;\;\;\frac{x}{\frac{t - z}{-60}}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-233}:\\ \;\;\;\;\frac{y}{\frac{t - z}{60}}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-83}:\\ \;\;\;\;\frac{x}{\frac{t - z}{-60}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 57.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{t - z}{-60}}\\ \mathbf{if}\;a \leq -8 \cdot 10^{-215}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-304}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-232}:\\ \;\;\;\;y \cdot \frac{60}{t - z}\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-84}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (/ (- t z) -60.0))))
   (if (<= a -8e-215)
     (* a 120.0)
     (if (<= a 3.2e-304)
       t_1
       (if (<= a 6.5e-232)
         (* y (/ 60.0 (- t z)))
         (if (<= a 3.7e-84) t_1 (* a 120.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / ((t - z) / -60.0);
	double tmp;
	if (a <= -8e-215) {
		tmp = a * 120.0;
	} else if (a <= 3.2e-304) {
		tmp = t_1;
	} else if (a <= 6.5e-232) {
		tmp = y * (60.0 / (t - z));
	} else if (a <= 3.7e-84) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / ((t - z) / (-60.0d0))
    if (a <= (-8d-215)) then
        tmp = a * 120.0d0
    else if (a <= 3.2d-304) then
        tmp = t_1
    else if (a <= 6.5d-232) then
        tmp = y * (60.0d0 / (t - z))
    else if (a <= 3.7d-84) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x / ((t - z) / -60.0);
	double tmp;
	if (a <= -8e-215) {
		tmp = a * 120.0;
	} else if (a <= 3.2e-304) {
		tmp = t_1;
	} else if (a <= 6.5e-232) {
		tmp = y * (60.0 / (t - z));
	} else if (a <= 3.7e-84) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / ((t - z) / -60.0)
	tmp = 0
	if a <= -8e-215:
		tmp = a * 120.0
	elif a <= 3.2e-304:
		tmp = t_1
	elif a <= 6.5e-232:
		tmp = y * (60.0 / (t - z))
	elif a <= 3.7e-84:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(Float64(t - z) / -60.0))
	tmp = 0.0
	if (a <= -8e-215)
		tmp = Float64(a * 120.0);
	elseif (a <= 3.2e-304)
		tmp = t_1;
	elseif (a <= 6.5e-232)
		tmp = Float64(y * Float64(60.0 / Float64(t - z)));
	elseif (a <= 3.7e-84)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / ((t - z) / -60.0);
	tmp = 0.0;
	if (a <= -8e-215)
		tmp = a * 120.0;
	elseif (a <= 3.2e-304)
		tmp = t_1;
	elseif (a <= 6.5e-232)
		tmp = y * (60.0 / (t - z));
	elseif (a <= 3.7e-84)
		tmp = t_1;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(N[(t - z), $MachinePrecision] / -60.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8e-215], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 3.2e-304], t$95$1, If[LessEqual[a, 6.5e-232], N[(y * N[(60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.7e-84], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.00000000000000033e-215 or 3.6999999999999999e-84 < a

   1. Initial program 99.9%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 72.2%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   7. Simplified 72.2%

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

   if -8.00000000000000033e-215 < a < 3.19999999999999999e-304 or 6.50000000000000007e-232 < a < 3.6999999999999999e-84

   1. Initial program 99.8%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.8%

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

      1. +-commutative N/A

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

      2. fma-define N/A

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

      3. fma-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, \color{blue}{120}, \left(\frac{60 \cdot \left(y - x\right)}{t - z}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right)\right) \]

      7. --lowering--.f64 99.7%

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right)\right) \]

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{x}{t - z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(x, \color{blue}{\left(t - z\right)}\right)\right) \]

      3. --lowering--.f64 63.4%

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   9. Simplified 63.4%

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

       1. *-commutative N/A

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

       2. associate-*l/ N/A

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

       3. associate-*r/ N/A

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

       4. clear-num N/A

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

       5. un-div-inv N/A

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

       6. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{t - z}{-60}\right)}\right) \]

       7. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\left(t - z\right), \color{blue}{-60}\right)\right) \]

       8. --lowering--.f64 63.6%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, z\right), -60\right)\right) \]

   11. Applied egg-rr 63.6%

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

   if 3.19999999999999999e-304 < a < 6.50000000000000007e-232

   1. Initial program 99.8%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf

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

      1. *-lft-identity N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(60 \cdot \frac{1}{t - z}\right)}\right) \]

      6. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(\frac{60 \cdot 1}{\color{blue}{t - z}}\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(\frac{60}{\color{blue}{t} - z}\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(60, \color{blue}{\left(t - z\right)}\right)\right) \]

      9. --lowering--.f64 81.8%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   7. Simplified 81.8%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-215}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-304}:\\ \;\;\;\;\frac{x}{\frac{t - z}{-60}}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-232}:\\ \;\;\;\;y \cdot \frac{60}{t - z}\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{\frac{t - z}{-60}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{x}{t - z}\\ \mathbf{if}\;a \leq -6.5 \cdot 10^{-214}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-306}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-232}:\\ \;\;\;\;y \cdot \frac{60}{t - z}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-84}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ x (- t z)))))
   (if (<= a -6.5e-214)
     (* a 120.0)
     (if (<= a 2.15e-306)
       t_1
       (if (<= a 6.6e-232)
         (* y (/ 60.0 (- t z)))
         (if (<= a 1.7e-84) t_1 (* a 120.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (x / (t - z));
	double tmp;
	if (a <= -6.5e-214) {
		tmp = a * 120.0;
	} else if (a <= 2.15e-306) {
		tmp = t_1;
	} else if (a <= 6.6e-232) {
		tmp = y * (60.0 / (t - z));
	} else if (a <= 1.7e-84) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-60.0d0) * (x / (t - z))
    if (a <= (-6.5d-214)) then
        tmp = a * 120.0d0
    else if (a <= 2.15d-306) then
        tmp = t_1
    else if (a <= 6.6d-232) then
        tmp = y * (60.0d0 / (t - z))
    else if (a <= 1.7d-84) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (x / (t - z));
	double tmp;
	if (a <= -6.5e-214) {
		tmp = a * 120.0;
	} else if (a <= 2.15e-306) {
		tmp = t_1;
	} else if (a <= 6.6e-232) {
		tmp = y * (60.0 / (t - z));
	} else if (a <= 1.7e-84) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (x / (t - z))
	tmp = 0
	if a <= -6.5e-214:
		tmp = a * 120.0
	elif a <= 2.15e-306:
		tmp = t_1
	elif a <= 6.6e-232:
		tmp = y * (60.0 / (t - z))
	elif a <= 1.7e-84:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(x / Float64(t - z)))
	tmp = 0.0
	if (a <= -6.5e-214)
		tmp = Float64(a * 120.0);
	elseif (a <= 2.15e-306)
		tmp = t_1;
	elseif (a <= 6.6e-232)
		tmp = Float64(y * Float64(60.0 / Float64(t - z)));
	elseif (a <= 1.7e-84)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * (x / (t - z));
	tmp = 0.0;
	if (a <= -6.5e-214)
		tmp = a * 120.0;
	elseif (a <= 2.15e-306)
		tmp = t_1;
	elseif (a <= 6.6e-232)
		tmp = y * (60.0 / (t - z));
	elseif (a <= 1.7e-84)
		tmp = t_1;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.5e-214], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 2.15e-306], t$95$1, If[LessEqual[a, 6.6e-232], N[(y * N[(60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.7e-84], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.5000000000000004e-214 or 1.7000000000000001e-84 < a

   1. Initial program 99.9%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 72.2%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   7. Simplified 72.2%

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

   if -6.5000000000000004e-214 < a < 2.15e-306 or 6.5999999999999997e-232 < a < 1.7000000000000001e-84

   1. Initial program 99.8%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.8%

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

      1. +-commutative N/A

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

      2. fma-define N/A

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

      3. fma-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, \color{blue}{120}, \left(\frac{60 \cdot \left(y - x\right)}{t - z}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right)\right) \]

      7. --lowering--.f64 99.7%

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right)\right) \]

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{x}{t - z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(x, \color{blue}{\left(t - z\right)}\right)\right) \]

      3. --lowering--.f64 63.4%

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   9. Simplified 63.4%

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

   if 2.15e-306 < a < 6.5999999999999997e-232

   1. Initial program 99.8%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf

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

      1. *-lft-identity N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(60 \cdot \frac{1}{t - z}\right)}\right) \]

      6. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(\frac{60 \cdot 1}{\color{blue}{t - z}}\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(\frac{60}{\color{blue}{t} - z}\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(60, \color{blue}{\left(t - z\right)}\right)\right) \]

      9. --lowering--.f64 81.8%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   7. Simplified 81.8%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{-214}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-306}:\\ \;\;\;\;-60 \cdot \frac{x}{t - z}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-232}:\\ \;\;\;\;y \cdot \frac{60}{t - z}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-84}:\\ \;\;\;\;-60 \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot y}{t - z} + a \cdot 120\\ \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-212}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-95}:\\ \;\;\;\;\frac{60 \cdot \left(y - x\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (/ (* 60.0 y) (- t z)) (* a 120.0))))
   (if (<= (* a 120.0) -5e-212)
     t_1
     (if (<= (* a 120.0) 2e-95) (/ (* 60.0 (- y x)) (- t z)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((60.0 * y) / (t - z)) + (a * 120.0);
	double tmp;
	if ((a * 120.0) <= -5e-212) {
		tmp = t_1;
	} else if ((a * 120.0) <= 2e-95) {
		tmp = (60.0 * (y - x)) / (t - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((60.0d0 * y) / (t - z)) + (a * 120.0d0)
    if ((a * 120.0d0) <= (-5d-212)) then
        tmp = t_1
    else if ((a * 120.0d0) <= 2d-95) then
        tmp = (60.0d0 * (y - x)) / (t - z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((60.0 * y) / (t - z)) + (a * 120.0);
	double tmp;
	if ((a * 120.0) <= -5e-212) {
		tmp = t_1;
	} else if ((a * 120.0) <= 2e-95) {
		tmp = (60.0 * (y - x)) / (t - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((60.0 * y) / (t - z)) + (a * 120.0)
	tmp = 0
	if (a * 120.0) <= -5e-212:
		tmp = t_1
	elif (a * 120.0) <= 2e-95:
		tmp = (60.0 * (y - x)) / (t - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(60.0 * y) / Float64(t - z)) + Float64(a * 120.0))
	tmp = 0.0
	if (Float64(a * 120.0) <= -5e-212)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= 2e-95)
		tmp = Float64(Float64(60.0 * Float64(y - x)) / Float64(t - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((60.0 * y) / (t - z)) + (a * 120.0);
	tmp = 0.0;
	if ((a * 120.0) <= -5e-212)
		tmp = t_1;
	elseif ((a * 120.0) <= 2e-95)
		tmp = (60.0 * (y - x)) / (t - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(60.0 * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e-212], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-95], N[(N[(60.0 * N[(y - x), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -5.00000000000000043e-212 or 1.99999999999999998e-95 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.9%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\color{blue}{\left(60 \cdot y\right)}, \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 87.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, y\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   7. Simplified 87.0%

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

   if -5.00000000000000043e-212 < (*.f64 a #s(literal 120 binary64)) < 1.99999999999999998e-95

   1. Initial program 99.8%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \color{blue}{\left(t - z\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(\color{blue}{t} - z\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right) \]

      5. --lowering--.f64 90.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right) \]

   7. Simplified 90.7%

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

Alternative 7: 81.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{60}{t - z} + a \cdot 120\\ \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-212}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-95}:\\ \;\;\;\;\frac{60 \cdot \left(y - x\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* y (/ 60.0 (- t z))) (* a 120.0))))
   (if (<= (* a 120.0) -5e-212)
     t_1
     (if (<= (* a 120.0) 2e-95) (/ (* 60.0 (- y x)) (- t z)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (60.0 / (t - z))) + (a * 120.0);
	double tmp;
	if ((a * 120.0) <= -5e-212) {
		tmp = t_1;
	} else if ((a * 120.0) <= 2e-95) {
		tmp = (60.0 * (y - x)) / (t - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * (60.0d0 / (t - z))) + (a * 120.0d0)
    if ((a * 120.0d0) <= (-5d-212)) then
        tmp = t_1
    else if ((a * 120.0d0) <= 2d-95) then
        tmp = (60.0d0 * (y - x)) / (t - z)
    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))) + (a * 120.0);
	double tmp;
	if ((a * 120.0) <= -5e-212) {
		tmp = t_1;
	} else if ((a * 120.0) <= 2e-95) {
		tmp = (60.0 * (y - x)) / (t - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (60.0 / (t - z))) + (a * 120.0)
	tmp = 0
	if (a * 120.0) <= -5e-212:
		tmp = t_1
	elif (a * 120.0) <= 2e-95:
		tmp = (60.0 * (y - x)) / (t - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(60.0 / Float64(t - z))) + Float64(a * 120.0))
	tmp = 0.0
	if (Float64(a * 120.0) <= -5e-212)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= 2e-95)
		tmp = Float64(Float64(60.0 * Float64(y - x)) / Float64(t - z));
	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))) + (a * 120.0);
	tmp = 0.0;
	if ((a * 120.0) <= -5e-212)
		tmp = t_1;
	elseif ((a * 120.0) <= 2e-95)
		tmp = (60.0 * (y - x)) / (t - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e-212], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-95], N[(N[(60.0 * N[(y - x), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -5.00000000000000043e-212 or 1.99999999999999998e-95 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.9%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(60 \cdot \frac{y}{t - z}\right)}, \mathsf{*.f64}\left(a, 120\right)\right) \]
   6. Step-by-step derivation

      1. *-lft-identity N/A

         \[\leadsto \mathsf{+.f64}\left(\left(60 \cdot \frac{1 \cdot y}{t - z}\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      2. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(60 \cdot \left(\frac{1}{t - z} \cdot y\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(60 \cdot \frac{1}{t - z}\right) \cdot y\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot \left(60 \cdot \frac{1}{t - z}\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(60 \cdot \frac{1}{t - z}\right)\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

      6. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{60 \cdot 1}{t - z}\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{60}{t - z}\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{/.f64}\left(60, \left(t - z\right)\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

      9. --lowering--.f64 86.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(t, z\right)\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   7. Simplified 86.9%

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

   if -5.00000000000000043e-212 < (*.f64 a #s(literal 120 binary64)) < 1.99999999999999998e-95

   1. Initial program 99.8%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \color{blue}{\left(t - z\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(\color{blue}{t} - z\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right) \]

      5. --lowering--.f64 90.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right) \]

   7. Simplified 90.7%

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

Alternative 8: 88.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(120 \cdot \frac{a}{x} + \frac{-60}{t - z}\right)\\ \mathbf{if}\;x \leq -8.5 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{-28}:\\ \;\;\;\;\frac{60 \cdot y}{t - z} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (+ (* 120.0 (/ a x)) (/ -60.0 (- t z))))))
   (if (<= x -8.5e-24)
     t_1
     (if (<= x 2.65e-28) (+ (/ (* 60.0 y) (- t z)) (* a 120.0)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((120.0 * (a / x)) + (-60.0 / (t - z)));
	double tmp;
	if (x <= -8.5e-24) {
		tmp = t_1;
	} else if (x <= 2.65e-28) {
		tmp = ((60.0 * y) / (t - z)) + (a * 120.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((120.0d0 * (a / x)) + ((-60.0d0) / (t - z)))
    if (x <= (-8.5d-24)) then
        tmp = t_1
    else if (x <= 2.65d-28) then
        tmp = ((60.0d0 * y) / (t - z)) + (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 = x * ((120.0 * (a / x)) + (-60.0 / (t - z)));
	double tmp;
	if (x <= -8.5e-24) {
		tmp = t_1;
	} else if (x <= 2.65e-28) {
		tmp = ((60.0 * y) / (t - z)) + (a * 120.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((120.0 * (a / x)) + (-60.0 / (t - z)))
	tmp = 0
	if x <= -8.5e-24:
		tmp = t_1
	elif x <= 2.65e-28:
		tmp = ((60.0 * y) / (t - z)) + (a * 120.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(120.0 * Float64(a / x)) + Float64(-60.0 / Float64(t - z))))
	tmp = 0.0
	if (x <= -8.5e-24)
		tmp = t_1;
	elseif (x <= 2.65e-28)
		tmp = Float64(Float64(Float64(60.0 * y) / Float64(t - z)) + Float64(a * 120.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((120.0 * (a / x)) + (-60.0 / (t - z)));
	tmp = 0.0;
	if (x <= -8.5e-24)
		tmp = t_1;
	elseif (x <= 2.65e-28)
		tmp = ((60.0 * y) / (t - z)) + (a * 120.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(120.0 * N[(a / x), $MachinePrecision]), $MachinePrecision] + N[(-60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.5e-24], t$95$1, If[LessEqual[x, 2.65e-28], N[(N[(N[(60.0 * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.5000000000000002e-24 or 2.64999999999999994e-28 < x

   1. Initial program 99.8%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(120 + 60 \cdot \frac{y - x}{a \cdot \left(t - z\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(120, \color{blue}{\left(60 \cdot \frac{y - x}{a \cdot \left(t - z\right)}\right)}\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(120, \left(\frac{60 \cdot \left(y - x\right)}{\color{blue}{a \cdot \left(t - z\right)}}\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(120, \mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \color{blue}{\left(a \cdot \left(t - z\right)\right)}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(\color{blue}{a} \cdot \left(t - z\right)\right)\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(a \cdot \left(t - z\right)\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(\left(t - z\right) \cdot \color{blue}{a}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{*.f64}\left(\left(t - z\right), \color{blue}{a}\right)\right)\right)\right) \]

      9. --lowering--.f64 87.7%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, z\right), a\right)\right)\right)\right) \]

   7. Simplified 87.7%

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

   8. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{a \cdot \left(120 + 60 \cdot \frac{y}{a \cdot \left(t - z\right)}\right)}{x} - 60 \cdot \frac{1}{t - z}\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{a \cdot \left(120 + 60 \cdot \frac{y}{a \cdot \left(t - z\right)}\right)}{x} + \color{blue}{\left(\mathsf{neg}\left(60 \cdot \frac{1}{t - z}\right)\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{a \cdot \left(120 + 60 \cdot \frac{y}{a \cdot \left(t - z\right)}\right)}{x}\right), \color{blue}{\left(\mathsf{neg}\left(60 \cdot \frac{1}{t - z}\right)\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\frac{\left(120 + 60 \cdot \frac{y}{a \cdot \left(t - z\right)}\right) \cdot a}{x}\right), \left(\mathsf{neg}\left(\color{blue}{60} \cdot \frac{1}{t - z}\right)\right)\right)\right) \]

      5. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(120 + 60 \cdot \frac{y}{a \cdot \left(t - z\right)}\right) \cdot \frac{a}{x}\right), \left(\mathsf{neg}\left(\color{blue}{60 \cdot \frac{1}{t - z}}\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(120 + 60 \cdot \frac{y}{a \cdot \left(t - z\right)}\right), \left(\frac{a}{x}\right)\right), \left(\mathsf{neg}\left(\color{blue}{60 \cdot \frac{1}{t - z}}\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(120, \left(60 \cdot \frac{y}{a \cdot \left(t - z\right)}\right)\right), \left(\frac{a}{x}\right)\right), \left(\mathsf{neg}\left(\color{blue}{60} \cdot \frac{1}{t - z}\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(120, \mathsf{*.f64}\left(60, \left(\frac{y}{a \cdot \left(t - z\right)}\right)\right)\right), \left(\frac{a}{x}\right)\right), \left(\mathsf{neg}\left(60 \cdot \frac{1}{t - z}\right)\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(120, \mathsf{*.f64}\left(60, \mathsf{/.f64}\left(y, \left(a \cdot \left(t - z\right)\right)\right)\right)\right), \left(\frac{a}{x}\right)\right), \left(\mathsf{neg}\left(60 \cdot \frac{1}{t - z}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(120, \mathsf{*.f64}\left(60, \mathsf{/.f64}\left(y, \left(\left(t - z\right) \cdot a\right)\right)\right)\right), \left(\frac{a}{x}\right)\right), \left(\mathsf{neg}\left(60 \cdot \frac{1}{t - z}\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(120, \mathsf{*.f64}\left(60, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(\left(t - z\right), a\right)\right)\right)\right), \left(\frac{a}{x}\right)\right), \left(\mathsf{neg}\left(60 \cdot \frac{1}{t - z}\right)\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(120, \mathsf{*.f64}\left(60, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, z\right), a\right)\right)\right)\right), \left(\frac{a}{x}\right)\right), \left(\mathsf{neg}\left(60 \cdot \frac{1}{t - z}\right)\right)\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(120, \mathsf{*.f64}\left(60, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, z\right), a\right)\right)\right)\right), \mathsf{/.f64}\left(a, x\right)\right), \left(\mathsf{neg}\left(60 \cdot \color{blue}{\frac{1}{t - z}}\right)\right)\right)\right) \]

      14. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(120, \mathsf{*.f64}\left(60, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, z\right), a\right)\right)\right)\right), \mathsf{/.f64}\left(a, x\right)\right), \left(\mathsf{neg}\left(\frac{60 \cdot 1}{t - z}\right)\right)\right)\right) \]

   10. Simplified 89.4%

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

   11. Taylor expanded in y around 0

       \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{120}, \mathsf{/.f64}\left(a, x\right)\right), \mathsf{/.f64}\left(-60, \mathsf{\_.f64}\left(t, z\right)\right)\right)\right) \]
   12. Step-by-step derivation

   13. Simplified 87.5%

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

   if -8.5000000000000002e-24 < x < 2.64999999999999994e-28

   1. Initial program 99.9%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\color{blue}{\left(60 \cdot y\right)}, \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 98.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, y\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   7. Simplified 98.3%

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

Alternative 9: 73.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+19}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-82}:\\ \;\;\;\;\frac{60 \cdot \left(y - x\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -2e+19)
   (* a 120.0)
   (if (<= (* a 120.0) 2e-82) (/ (* 60.0 (- y x)) (- t z)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e+19) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 2e-82) {
		tmp = (60.0 * (y - x)) / (t - z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-2d+19)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 2d-82) then
        tmp = (60.0d0 * (y - x)) / (t - z)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e+19) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 2e-82) {
		tmp = (60.0 * (y - x)) / (t - z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -2e+19:
		tmp = a * 120.0
	elif (a * 120.0) <= 2e-82:
		tmp = (60.0 * (y - x)) / (t - z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e+19)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 2e-82)
		tmp = Float64(Float64(60.0 * Float64(y - x)) / Float64(t - z));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -2e+19)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 2e-82)
		tmp = (60.0 * (y - x)) / (t - z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e+19], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-82], N[(N[(60.0 * N[(y - x), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -2e19 or 2e-82 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.9%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 80.1%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   7. Simplified 80.1%

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

   if -2e19 < (*.f64 a #s(literal 120 binary64)) < 2e-82

   1. Initial program 99.8%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \color{blue}{\left(t - z\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(\color{blue}{t} - z\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right) \]

      5. --lowering--.f64 81.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right) \]

   7. Simplified 81.5%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+19}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-82}:\\ \;\;\;\;\frac{60 \cdot \left(y - x\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+19}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-82}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{60}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -2e+19)
   (* a 120.0)
   (if (<= (* a 120.0) 2e-82) (* (- y x) (/ 60.0 (- t z))) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e+19) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 2e-82) {
		tmp = (y - x) * (60.0 / (t - z));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-2d+19)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 2d-82) then
        tmp = (y - x) * (60.0d0 / (t - z))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e+19) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 2e-82) {
		tmp = (y - x) * (60.0 / (t - z));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -2e+19:
		tmp = a * 120.0
	elif (a * 120.0) <= 2e-82:
		tmp = (y - x) * (60.0 / (t - z))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e+19)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 2e-82)
		tmp = Float64(Float64(y - x) * Float64(60.0 / Float64(t - z)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -2e+19)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 2e-82)
		tmp = (y - x) * (60.0 / (t - z));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e+19], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-82], N[(N[(y - x), $MachinePrecision] * N[(60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -2e19 or 2e-82 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.9%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 80.1%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   7. Simplified 80.1%

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

   if -2e19 < (*.f64 a #s(literal 120 binary64)) < 2e-82

   1. Initial program 99.8%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \color{blue}{\left(t - z\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(\color{blue}{t} - z\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right) \]

      5. --lowering--.f64 81.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right) \]

   7. Simplified 81.5%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y - x\right), \color{blue}{\left(\frac{60}{t - z}\right)}\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{\color{blue}{60}}{t - z}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(60, \color{blue}{\left(t - z\right)}\right)\right) \]

      6. --lowering--.f64 81.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(60, \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   9. Applied egg-rr 81.4%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+19}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-82}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{60}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -23000000000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-232}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot -60}{z}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{\frac{t - z}{-60}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -23000000000000.0)
   (* a 120.0)
   (if (<= a 5.5e-232)
     (/ (* (- y x) -60.0) z)
     (if (<= a 3.3e-84) (/ x (/ (- t z) -60.0)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -23000000000000.0) {
		tmp = a * 120.0;
	} else if (a <= 5.5e-232) {
		tmp = ((y - x) * -60.0) / z;
	} else if (a <= 3.3e-84) {
		tmp = x / ((t - z) / -60.0);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-23000000000000.0d0)) then
        tmp = a * 120.0d0
    else if (a <= 5.5d-232) then
        tmp = ((y - x) * (-60.0d0)) / z
    else if (a <= 3.3d-84) then
        tmp = x / ((t - z) / (-60.0d0))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -23000000000000.0) {
		tmp = a * 120.0;
	} else if (a <= 5.5e-232) {
		tmp = ((y - x) * -60.0) / z;
	} else if (a <= 3.3e-84) {
		tmp = x / ((t - z) / -60.0);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -23000000000000.0:
		tmp = a * 120.0
	elif a <= 5.5e-232:
		tmp = ((y - x) * -60.0) / z
	elif a <= 3.3e-84:
		tmp = x / ((t - z) / -60.0)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -23000000000000.0)
		tmp = Float64(a * 120.0);
	elseif (a <= 5.5e-232)
		tmp = Float64(Float64(Float64(y - x) * -60.0) / z);
	elseif (a <= 3.3e-84)
		tmp = Float64(x / Float64(Float64(t - z) / -60.0));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -23000000000000.0)
		tmp = a * 120.0;
	elseif (a <= 5.5e-232)
		tmp = ((y - x) * -60.0) / z;
	elseif (a <= 3.3e-84)
		tmp = x / ((t - z) / -60.0);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -23000000000000.0], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 5.5e-232], N[(N[(N[(y - x), $MachinePrecision] * -60.0), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 3.3e-84], N[(x / N[(N[(t - z), $MachinePrecision] / -60.0), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.3e13 or 3.29999999999999984e-84 < a

   1. Initial program 99.9%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 80.1%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   7. Simplified 80.1%

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

   if -2.3e13 < a < 5.50000000000000023e-232

   1. Initial program 99.8%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \color{blue}{\left(t - z\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(\color{blue}{t} - z\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right) \]

      5. --lowering--.f64 80.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right) \]

   7. Simplified 80.7%

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

   8. Taylor expanded in t around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-60 \cdot \left(y - x\right)\right), \color{blue}{z}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(y - x\right) \cdot -60\right), z\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(y - x\right), -60\right), z\right) \]

      5. --lowering--.f64 54.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), -60\right), z\right) \]

   10. Simplified 54.6%

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

   if 5.50000000000000023e-232 < a < 3.29999999999999984e-84

   1. Initial program 99.7%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.7%

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

      1. +-commutative N/A

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

      2. fma-define N/A

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

      3. fma-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, \color{blue}{120}, \left(\frac{60 \cdot \left(y - x\right)}{t - z}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right)\right) \]

      7. --lowering--.f64 99.6%

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right)\right) \]

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{x}{t - z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(x, \color{blue}{\left(t - z\right)}\right)\right) \]

      3. --lowering--.f64 65.4%

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   9. Simplified 65.4%

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

       1. *-commutative N/A

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

       2. associate-*l/ N/A

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

       3. associate-*r/ N/A

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

       4. clear-num N/A

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

       5. un-div-inv N/A

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

       6. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{t - z}{-60}\right)}\right) \]

       7. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\left(t - z\right), \color{blue}{-60}\right)\right) \]

       8. --lowering--.f64 65.6%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, z\right), -60\right)\right) \]

   11. Applied egg-rr 65.6%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -23000000000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-232}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot -60}{z}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{\frac{t - z}{-60}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 52.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-229}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-233}:\\ \;\;\;\;\frac{y \cdot -60}{z}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-97}:\\ \;\;\;\;\frac{x \cdot -60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7e-229)
   (* a 120.0)
   (if (<= a 4.8e-233)
     (/ (* y -60.0) z)
     (if (<= a 4.2e-97) (/ (* x -60.0) t) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7e-229) {
		tmp = a * 120.0;
	} else if (a <= 4.8e-233) {
		tmp = (y * -60.0) / z;
	} else if (a <= 4.2e-97) {
		tmp = (x * -60.0) / t;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-7d-229)) then
        tmp = a * 120.0d0
    else if (a <= 4.8d-233) then
        tmp = (y * (-60.0d0)) / z
    else if (a <= 4.2d-97) then
        tmp = (x * (-60.0d0)) / t
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7e-229) {
		tmp = a * 120.0;
	} else if (a <= 4.8e-233) {
		tmp = (y * -60.0) / z;
	} else if (a <= 4.2e-97) {
		tmp = (x * -60.0) / t;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7e-229:
		tmp = a * 120.0
	elif a <= 4.8e-233:
		tmp = (y * -60.0) / z
	elif a <= 4.2e-97:
		tmp = (x * -60.0) / t
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7e-229)
		tmp = Float64(a * 120.0);
	elseif (a <= 4.8e-233)
		tmp = Float64(Float64(y * -60.0) / z);
	elseif (a <= 4.2e-97)
		tmp = Float64(Float64(x * -60.0) / t);
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7e-229)
		tmp = a * 120.0;
	elseif (a <= 4.8e-233)
		tmp = (y * -60.0) / z;
	elseif (a <= 4.2e-97)
		tmp = (x * -60.0) / t;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7e-229], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 4.8e-233], N[(N[(y * -60.0), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 4.2e-97], N[(N[(x * -60.0), $MachinePrecision] / t), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.0000000000000007e-229 or 4.2000000000000002e-97 < a

   1. Initial program 99.9%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 70.2%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   7. Simplified 70.2%

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

   if -7.0000000000000007e-229 < a < 4.7999999999999998e-233

   1. Initial program 99.8%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.8%

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

      1. flip-+ N/A

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

      2. associate-/l* N/A

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

      3. fmm-def N/A

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

      4. *-commutative N/A

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

      5. clear-num N/A

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

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\mathsf{fma}\left(60, \frac{y - x}{t - z}, \mathsf{neg}\left(120 \cdot a\right)\right)}{\frac{60 \cdot \left(y - x\right)}{t - z} \cdot \frac{60 \cdot \left(y - x\right)}{t - z} - \left(a \cdot 120\right) \cdot \left(a \cdot 120\right)}\right)}\right) \]

      7. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{\color{blue}{\frac{\frac{60 \cdot \left(y - x\right)}{t - z} \cdot \frac{60 \cdot \left(y - x\right)}{t - z} - \left(a \cdot 120\right) \cdot \left(a \cdot 120\right)}{\mathsf{fma}\left(60, \frac{y - x}{t - z}, \mathsf{neg}\left(120 \cdot a\right)\right)}}}\right)\right) \]

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(60 \cdot y\right), \color{blue}{\left(t - z\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, y\right), \left(\color{blue}{t} - z\right)\right) \]

      4. --lowering--.f64 53.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, y\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right) \]

   9. Simplified 53.2%

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

   10. Taylor expanded in t around 0

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

       1. associate-*r/ N/A

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

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(-60 \cdot y\right), \color{blue}{z}\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(y \cdot -60\right), z\right) \]

       4. *-lowering-*.f64 42.0%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, -60\right), z\right) \]

   12. Simplified 42.0%

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

   if 4.7999999999999998e-233 < a < 4.2000000000000002e-97

   1. Initial program 99.7%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.7%

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

      1. +-commutative N/A

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

      2. fma-define N/A

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

      3. fma-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, \color{blue}{120}, \left(\frac{60 \cdot \left(y - x\right)}{t - z}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right)\right) \]

      7. --lowering--.f64 99.7%

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right)\right) \]

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{x}{t - z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(x, \color{blue}{\left(t - z\right)}\right)\right) \]

      3. --lowering--.f64 68.6%

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   9. Simplified 68.6%

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

   10. Taylor expanded in t around inf

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

       1. associate-*r/ N/A

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

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(-60 \cdot x\right), \color{blue}{t}\right) \]

       3. *-lowering-*.f64 41.6%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-60, x\right), t\right) \]

   12. Simplified 41.6%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-229}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-233}:\\ \;\;\;\;\frac{y \cdot -60}{z}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-97}:\\ \;\;\;\;\frac{x \cdot -60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 57.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-214}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-83}:\\ \;\;\;\;-60 \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7e-214)
   (* a 120.0)
   (if (<= a 2.5e-83) (* -60.0 (/ x (- t z))) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7e-214) {
		tmp = a * 120.0;
	} else if (a <= 2.5e-83) {
		tmp = -60.0 * (x / (t - z));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-7d-214)) then
        tmp = a * 120.0d0
    else if (a <= 2.5d-83) then
        tmp = (-60.0d0) * (x / (t - z))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7e-214) {
		tmp = a * 120.0;
	} else if (a <= 2.5e-83) {
		tmp = -60.0 * (x / (t - z));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7e-214:
		tmp = a * 120.0
	elif a <= 2.5e-83:
		tmp = -60.0 * (x / (t - z))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7e-214)
		tmp = Float64(a * 120.0);
	elseif (a <= 2.5e-83)
		tmp = Float64(-60.0 * Float64(x / Float64(t - z)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7e-214)
		tmp = a * 120.0;
	elseif (a <= 2.5e-83)
		tmp = -60.0 * (x / (t - z));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7e-214], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 2.5e-83], N[(-60.0 * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -7e-214 or 2.5e-83 < a

   1. Initial program 99.9%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 72.2%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   7. Simplified 72.2%

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

   if -7e-214 < a < 2.5e-83

   1. Initial program 99.8%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.8%

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

      1. +-commutative N/A

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

      2. fma-define N/A

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

      3. fma-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, \color{blue}{120}, \left(\frac{60 \cdot \left(y - x\right)}{t - z}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right)\right) \]

      7. --lowering--.f64 99.8%

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right)\right) \]

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{x}{t - z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(x, \color{blue}{\left(t - z\right)}\right)\right) \]

      3. --lowering--.f64 53.5%

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   9. Simplified 53.5%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-214}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-83}:\\ \;\;\;\;-60 \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 52.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{-216}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-94}:\\ \;\;\;\;\frac{x \cdot -60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.5e-216)
   (* a 120.0)
   (if (<= a 3.3e-94) (/ (* x -60.0) t) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.5e-216) {
		tmp = a * 120.0;
	} else if (a <= 3.3e-94) {
		tmp = (x * -60.0) / t;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-6.5d-216)) then
        tmp = a * 120.0d0
    else if (a <= 3.3d-94) then
        tmp = (x * (-60.0d0)) / t
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.5e-216) {
		tmp = a * 120.0;
	} else if (a <= 3.3e-94) {
		tmp = (x * -60.0) / t;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.5e-216:
		tmp = a * 120.0
	elif a <= 3.3e-94:
		tmp = (x * -60.0) / t
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.5e-216)
		tmp = Float64(a * 120.0);
	elseif (a <= 3.3e-94)
		tmp = Float64(Float64(x * -60.0) / t);
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.5e-216)
		tmp = a * 120.0;
	elseif (a <= 3.3e-94)
		tmp = (x * -60.0) / t;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.5e-216], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 3.3e-94], N[(N[(x * -60.0), $MachinePrecision] / t), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -6.4999999999999999e-216 or 3.3000000000000001e-94 < a

   1. Initial program 99.9%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 71.6%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   7. Simplified 71.6%

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

   if -6.4999999999999999e-216 < a < 3.3000000000000001e-94

   1. Initial program 99.8%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.8%

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

      1. +-commutative N/A

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

      2. fma-define N/A

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

      3. fma-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, \color{blue}{120}, \left(\frac{60 \cdot \left(y - x\right)}{t - z}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right)\right) \]

      7. --lowering--.f64 99.8%

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right)\right) \]

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{x}{t - z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(x, \color{blue}{\left(t - z\right)}\right)\right) \]

      3. --lowering--.f64 54.3%

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   9. Simplified 54.3%

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

   10. Taylor expanded in t around inf

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

       1. associate-*r/ N/A

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

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(-60 \cdot x\right), \color{blue}{t}\right) \]

       3. *-lowering-*.f64 33.1%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-60, x\right), t\right) \]

   12. Simplified 33.1%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{-216}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-94}:\\ \;\;\;\;\frac{x \cdot -60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 52.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-214}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-93}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.6e-214)
   (* a 120.0)
   (if (<= a 2.6e-93) (* -60.0 (/ x t)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.6e-214) {
		tmp = a * 120.0;
	} else if (a <= 2.6e-93) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.6d-214)) then
        tmp = a * 120.0d0
    else if (a <= 2.6d-93) then
        tmp = (-60.0d0) * (x / t)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.6e-214) {
		tmp = a * 120.0;
	} else if (a <= 2.6e-93) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.6e-214:
		tmp = a * 120.0
	elif a <= 2.6e-93:
		tmp = -60.0 * (x / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.6e-214)
		tmp = Float64(a * 120.0);
	elseif (a <= 2.6e-93)
		tmp = Float64(-60.0 * Float64(x / t));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.6e-214)
		tmp = a * 120.0;
	elseif (a <= 2.6e-93)
		tmp = -60.0 * (x / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.6e-214], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 2.6e-93], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.60000000000000007e-214 or 2.5999999999999998e-93 < a

   1. Initial program 99.9%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 71.6%

         \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

   7. Simplified 71.6%

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

   if -1.60000000000000007e-214 < a < 2.5999999999999998e-93

   1. Initial program 99.8%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      7. distribute-rgt-neg-out N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

      8. distribute-frac-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

      15. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

      18. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

      19. *-lowering-*.f64 99.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

   3. Simplified 99.8%

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

      1. +-commutative N/A

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

      2. fma-define N/A

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

      3. fma-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, \color{blue}{120}, \left(\frac{60 \cdot \left(y - x\right)}{t - z}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right)\right) \]

      7. --lowering--.f64 99.8%

         \[\leadsto \mathsf{fma.f64}\left(a, 120, \mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right)\right) \]

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{x}{t - z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(x, \color{blue}{\left(t - z\right)}\right)\right) \]

      3. --lowering--.f64 54.3%

         \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   9. Simplified 54.3%

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

   10. Taylor expanded in t around inf

       \[\leadsto \mathsf{*.f64}\left(-60, \color{blue}{\left(\frac{x}{t}\right)}\right) \]
   11. Step-by-step derivation

       1. /-lowering-/.f64 33.0%

          \[\leadsto \mathsf{*.f64}\left(-60, \mathsf{/.f64}\left(x, \color{blue}{t}\right)\right) \]

   12. Simplified 33.0%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-214}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-93}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 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]

Derivation

1. Initial program 99.9%

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

Alternative 17: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return (60.0 * ((y - x) / (t - z))) + (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 * ((y - x) / (t - z))) + (a * 120.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

   2. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   3. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   4. neg-sub0 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   5. associate-+l- N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   6. sub0-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   7. distribute-rgt-neg-out N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   8. distribute-frac-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

   9. distribute-frac-neg2 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

   10. sub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

   11. +-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

   12. distribute-neg-in N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

   13. unsub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

   14. remove-double-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

   15. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

   16. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

   17. --lowering--.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

   18. --lowering--.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

   19. *-lowering-*.f64 99.9%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

3. Simplified 99.9%

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

   1. associate-/l* N/A

      \[\leadsto \mathsf{+.f64}\left(\left(60 \cdot \frac{y - x}{t - z}\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

   2. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{y - x}{t - z} \cdot 60\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{y - x}{t - z}\right), 60\right), \mathsf{*.f64}\left(\color{blue}{a}, 120\right)\right) \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - x\right), \left(t - z\right)\right), 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   5. --lowering--.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(t - z\right)\right), 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

   6. --lowering--.f64 99.8%

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(t, z\right)\right), 60\right), \mathsf{*.f64}\left(a, 120\right)\right) \]

6. Applied egg-rr 99.8%

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

7. Final simplification 99.8%

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

Alternative 18: 50.4% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x - y\right)}{z - t}\right), \color{blue}{\left(a \cdot 120\right)}\right) \]

   2. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   3. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   4. neg-sub0 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\left(0 - y\right) + x\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   5. associate-+l- N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(0 - \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   6. sub0-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(\mathsf{neg}\left(\left(y - x\right)\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   7. distribute-rgt-neg-out N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{\mathsf{neg}\left(60 \cdot \left(y - x\right)\right)}{z - t}\right), \left(a \cdot 120\right)\right) \]

   8. distribute-frac-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\frac{60 \cdot \left(y - x\right)}{z - t}\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

   9. distribute-frac-neg2 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

   10. sub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right)}\right), \left(a \cdot 120\right)\right) \]

   11. +-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

   12. distribute-neg-in N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) + \left(\mathsf{neg}\left(z\right)\right)}\right), \left(a \cdot 120\right)\right) \]

   13. unsub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(t\right)\right)\right)\right) - z}\right), \left(a \cdot 120\right)\right) \]

   14. remove-double-neg N/A

       \[\leadsto \mathsf{+.f64}\left(\left(\frac{60 \cdot \left(y - x\right)}{t - z}\right), \left(a \cdot 120\right)\right) \]

   15. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(60 \cdot \left(y - x\right)\right), \left(t - z\right)\right), \left(\color{blue}{a} \cdot 120\right)\right) \]

   16. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \left(y - x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

   17. --lowering--.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \left(t - z\right)\right), \left(a \cdot 120\right)\right) \]

   18. --lowering--.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \left(a \cdot 120\right)\right) \]

   19. *-lowering-*.f64 99.9%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(60, \mathsf{\_.f64}\left(y, x\right)\right), \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{120}\right)\right) \]

3. Simplified 99.9%

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

5. Taylor expanded in t around inf

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

   1. *-lowering-*.f64 55.2%

      \[\leadsto \mathsf{*.f64}\left(120, \color{blue}{a}\right) \]

7. Simplified 55.2%

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

8. Final simplification 55.2%

   \[\leadsto a \cdot 120 \]
9. Add Preprocessing

Developer Target 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024158 
(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)))