Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.2% → 94.7%

Time: 13.0s

Alternatives: 17

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

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 = x + ((y - z) * ((t - x) / (a - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 = x + ((y - z) * ((t - x) / (a - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 94.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-294}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -1e-294)
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (if (<= t_1 0.0)
       (+ t (* x (/ (- y a) z)))
       (+ x (* (- t x) (/ (- y z) (- a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -1e-294) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else if (t_1 <= 0.0) {
		tmp = t + (x * ((y - a) / z));
	} else {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_1 <= (-1d-294)) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else if (t_1 <= 0.0d0) then
        tmp = t + (x * ((y - a) / z))
    else
        tmp = x + ((t - x) * ((y - z) / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -1e-294) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else if (t_1 <= 0.0) {
		tmp = t + (x * ((y - a) / z));
	} else {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_1 <= -1e-294:
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	elif t_1 <= 0.0:
		tmp = t + (x * ((y - a) / z))
	else:
		tmp = x + ((t - x) * ((y - z) / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -1e-294)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(x * Float64(Float64(y - a) / z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_1 <= -1e-294)
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	elseif (t_1 <= 0.0)
		tmp = t + (x * ((y - a) / z));
	else
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-294], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.00000000000000002e-294

   1. Initial program 91.2%

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

      1. clear-num N/A

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

      2. associate-*r/ N/A

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

      3. div-inv N/A

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

      4. times-frac N/A

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

      5. flip-- N/A

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

      6. clear-num N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

      11. --lowering--.f64 N/A

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

      12. --lowering--.f64 N/A

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

      13. --lowering--.f64 95.7%

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

   4. Applied egg-rr 95.7%

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

      1. +-commutative N/A

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

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

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

      3. *-commutative N/A

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

      4. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(t - x\right) \cdot \frac{1}{\frac{a - z}{y - z}}\right), x\right) \]

      5. un-div-inv N/A

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

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

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

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

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

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

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

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

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

      10. --lowering--.f64 96.3%

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

   6. Applied egg-rr 96.3%

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

   if -1.00000000000000002e-294 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.1%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

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

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

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

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

      8. associate-/l* N/A

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

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

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

      10. --lowering--.f64 N/A

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

      11. /-lowering-/.f64 N/A

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

      12. --lowering--.f64 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(-1 \cdot \frac{x \cdot \left(y - a\right)}{z}\right)}\right) \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

      4. mul-1-neg N/A

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

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

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

      6. associate-*r/ N/A

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

      7. distribute-lft-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y - -1 \cdot a}{z}\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y + \left(\mathsf{neg}\left(-1 \cdot a\right)\right)}{z}\right)\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right)}{z}\right)\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y + a}{z}\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{a + -1 \cdot y}{z}\right)\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(a + -1 \cdot y\right), \color{blue}{z}\right)\right)\right) \]

      13. mul-1-neg N/A

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

      14. sub-neg N/A

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

      15. --lowering--.f64 100.0%

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

   8. Simplified 100.0%

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

   if 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 87.2%

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

      1. clear-num N/A

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

      2. associate-*r/ N/A

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

      3. div-inv N/A

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

      4. times-frac N/A

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

      5. flip-- N/A

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

      6. clear-num N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

      11. --lowering--.f64 N/A

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

      12. --lowering--.f64 N/A

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

      13. --lowering--.f64 93.8%

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

   4. Applied egg-rr 93.8%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-294}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-294}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ (- y z) (- a z)))))
        (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_2 -1e-294) t_1 (if (<= t_2 0.0) (+ t (* x (/ (- y a) z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * ((y - z) / (a - z)));
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -1e-294) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + (x * ((y - a) / 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) :: t_2
    real(8) :: tmp
    t_1 = x + ((t - x) * ((y - z) / (a - z)))
    t_2 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_2 <= (-1d-294)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) then
        tmp = t + (x * ((y - a) / 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 = x + ((t - x) * ((y - z) / (a - z)));
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -1e-294) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + (x * ((y - a) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) * ((y - z) / (a - z)))
	t_2 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_2 <= -1e-294:
		tmp = t_1
	elif t_2 <= 0.0:
		tmp = t + (x * ((y - a) / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / Float64(a - z))))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -1e-294)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(x * Float64(Float64(y - a) / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) * ((y - z) / (a - z)));
	t_2 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_2 <= -1e-294)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = t + (x * ((y - a) / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-294], t$95$1, If[LessEqual[t$95$2, 0.0], N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.00000000000000002e-294 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 89.1%

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

      1. clear-num N/A

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

      2. associate-*r/ N/A

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

      3. div-inv N/A

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

      4. times-frac N/A

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

      5. flip-- N/A

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

      6. clear-num N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

      11. --lowering--.f64 N/A

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

      12. --lowering--.f64 N/A

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

      13. --lowering--.f64 94.7%

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

   4. Applied egg-rr 94.7%

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

   if -1.00000000000000002e-294 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.1%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

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

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

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

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

      8. associate-/l* N/A

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

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

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

      10. --lowering--.f64 N/A

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

      11. /-lowering-/.f64 N/A

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

      12. --lowering--.f64 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(-1 \cdot \frac{x \cdot \left(y - a\right)}{z}\right)}\right) \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

      4. mul-1-neg N/A

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

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

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

      6. associate-*r/ N/A

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

      7. distribute-lft-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y - -1 \cdot a}{z}\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y + \left(\mathsf{neg}\left(-1 \cdot a\right)\right)}{z}\right)\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right)}{z}\right)\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y + a}{z}\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{a + -1 \cdot y}{z}\right)\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(a + -1 \cdot y\right), \color{blue}{z}\right)\right)\right) \]

      13. mul-1-neg N/A

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

      14. sub-neg N/A

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

      15. --lowering--.f64 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-294}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-294}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -1e-294) t_1 (if (<= t_1 0.0) (+ t (* x (/ (- y a) z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -1e-294) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t + (x * ((y - a) / 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 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_1 <= (-1d-294)) then
        tmp = t_1
    else if (t_1 <= 0.0d0) then
        tmp = t + (x * ((y - a) / 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 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -1e-294) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t + (x * ((y - a) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_1 <= -1e-294:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = t + (x * ((y - a) / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -1e-294)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(x * Float64(Float64(y - a) / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_1 <= -1e-294)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = t + (x * ((y - a) / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-294], t$95$1, If[LessEqual[t$95$1, 0.0], N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.00000000000000002e-294 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 89.1%

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

   if -1.00000000000000002e-294 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.1%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

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

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

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

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

      8. associate-/l* N/A

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

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

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

      10. --lowering--.f64 N/A

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

      11. /-lowering-/.f64 N/A

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

      12. --lowering--.f64 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(-1 \cdot \frac{x \cdot \left(y - a\right)}{z}\right)}\right) \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

      4. mul-1-neg N/A

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

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

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

      6. associate-*r/ N/A

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

      7. distribute-lft-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y - -1 \cdot a}{z}\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y + \left(\mathsf{neg}\left(-1 \cdot a\right)\right)}{z}\right)\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right)}{z}\right)\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y + a}{z}\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{a + -1 \cdot y}{z}\right)\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(a + -1 \cdot y\right), \color{blue}{z}\right)\right)\right) \]

      13. mul-1-neg N/A

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

      14. sub-neg N/A

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

      15. --lowering--.f64 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-294}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x \cdot y}{z}\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+172}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (* x y) z))))
   (if (<= z -1.65e+84)
     t_1
     (if (<= z 1.8e-8)
       (+ x (/ (- t x) (/ a y)))
       (if (<= z 3.1e+172) t_1 (- t (* x (/ a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x * y) / z);
	double tmp;
	if (z <= -1.65e+84) {
		tmp = t_1;
	} else if (z <= 1.8e-8) {
		tmp = x + ((t - x) / (a / y));
	} else if (z <= 3.1e+172) {
		tmp = t_1;
	} else {
		tmp = t - (x * (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((x * y) / z)
    if (z <= (-1.65d+84)) then
        tmp = t_1
    else if (z <= 1.8d-8) then
        tmp = x + ((t - x) / (a / y))
    else if (z <= 3.1d+172) then
        tmp = t_1
    else
        tmp = t - (x * (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x * y) / z);
	double tmp;
	if (z <= -1.65e+84) {
		tmp = t_1;
	} else if (z <= 1.8e-8) {
		tmp = x + ((t - x) / (a / y));
	} else if (z <= 3.1e+172) {
		tmp = t_1;
	} else {
		tmp = t - (x * (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((x * y) / z)
	tmp = 0
	if z <= -1.65e+84:
		tmp = t_1
	elif z <= 1.8e-8:
		tmp = x + ((t - x) / (a / y))
	elif z <= 3.1e+172:
		tmp = t_1
	else:
		tmp = t - (x * (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(x * y) / z))
	tmp = 0.0
	if (z <= -1.65e+84)
		tmp = t_1;
	elseif (z <= 1.8e-8)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	elseif (z <= 3.1e+172)
		tmp = t_1;
	else
		tmp = Float64(t - Float64(x * Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((x * y) / z);
	tmp = 0.0;
	if (z <= -1.65e+84)
		tmp = t_1;
	elseif (z <= 1.8e-8)
		tmp = x + ((t - x) / (a / y));
	elseif (z <= 3.1e+172)
		tmp = t_1;
	else
		tmp = t - (x * (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.65e+84], t$95$1, If[LessEqual[z, 1.8e-8], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e+172], t$95$1, N[(t - N[(x * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.65000000000000008e84 or 1.79999999999999991e-8 < z < 3.09999999999999988e172

   1. Initial program 69.1%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

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

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

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

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

      8. associate-/l* N/A

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

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

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

      10. --lowering--.f64 N/A

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

      11. /-lowering-/.f64 N/A

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

      12. --lowering--.f64 73.3%

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

   5. Simplified 73.3%

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

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(-1 \cdot \frac{x \cdot \left(y - a\right)}{z}\right)}\right) \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

      4. mul-1-neg N/A

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

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

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

      6. associate-*r/ N/A

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

      7. distribute-lft-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y - -1 \cdot a}{z}\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y + \left(\mathsf{neg}\left(-1 \cdot a\right)\right)}{z}\right)\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right)}{z}\right)\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y + a}{z}\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{a + -1 \cdot y}{z}\right)\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(a + -1 \cdot y\right), \color{blue}{z}\right)\right)\right) \]

      13. mul-1-neg N/A

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

      14. sub-neg N/A

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

      15. --lowering--.f64 68.8%

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

   8. Simplified 68.8%

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

   9. Taylor expanded in a around 0

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

       1. sub-neg N/A

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

       2. mul-1-neg N/A

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

       3. remove-double-neg N/A

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

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

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

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

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

       6. *-lowering-*.f64 62.2%

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

   11. Simplified 62.2%

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

   if -1.65000000000000008e84 < z < 1.79999999999999991e-8

   1. Initial program 90.5%

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

      1. clear-num N/A

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

      2. associate-*r/ N/A

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

      3. div-inv N/A

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

      4. times-frac N/A

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

      5. flip-- N/A

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

      6. clear-num N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

      11. --lowering--.f64 N/A

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

      12. --lowering--.f64 N/A

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

      13. --lowering--.f64 96.9%

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

   4. Applied egg-rr 96.9%

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

      1. +-commutative N/A

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

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

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

      3. *-commutative N/A

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

      4. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(t - x\right) \cdot \frac{1}{\frac{a - z}{y - z}}\right), x\right) \]

      5. un-div-inv N/A

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

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

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

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

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

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

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

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

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

      10. --lowering--.f64 97.3%

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

   6. Applied egg-rr 97.3%

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

   7. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \color{blue}{\left(\frac{a}{y}\right)}\right), x\right) \]
   8. Step-by-step derivation

      1. /-lowering-/.f64 74.7%

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

   9. Simplified 74.7%

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

   if 3.09999999999999988e172 < z

   1. Initial program 57.6%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

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

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

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

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

      8. associate-/l* N/A

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

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

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

      10. --lowering--.f64 N/A

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

      11. /-lowering-/.f64 N/A

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

      12. --lowering--.f64 88.7%

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

   5. Simplified 88.7%

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

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(-1 \cdot \frac{x \cdot \left(y - a\right)}{z}\right)}\right) \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

      4. mul-1-neg N/A

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

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

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

      6. associate-*r/ N/A

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

      7. distribute-lft-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y - -1 \cdot a}{z}\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y + \left(\mathsf{neg}\left(-1 \cdot a\right)\right)}{z}\right)\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right)}{z}\right)\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y + a}{z}\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{a + -1 \cdot y}{z}\right)\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(a + -1 \cdot y\right), \color{blue}{z}\right)\right)\right) \]

      13. mul-1-neg N/A

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

      14. sub-neg N/A

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

      15. --lowering--.f64 81.5%

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

   8. Simplified 81.5%

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

   9. Taylor expanded in a around inf

      \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{a}{z}\right)}\right)\right) \]
   10. Step-by-step derivation

       1. /-lowering-/.f64 81.2%

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

   11. Simplified 81.2%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+84}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+172}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x \cdot y}{z}\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-8}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{+171}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (* x y) z))))
   (if (<= z -8.2e+77)
     t_1
     (if (<= z 1.45e-8)
       (+ x (* (- t x) (/ y a)))
       (if (<= z 5.7e+171) t_1 (- t (* x (/ a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x * y) / z);
	double tmp;
	if (z <= -8.2e+77) {
		tmp = t_1;
	} else if (z <= 1.45e-8) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 5.7e+171) {
		tmp = t_1;
	} else {
		tmp = t - (x * (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((x * y) / z)
    if (z <= (-8.2d+77)) then
        tmp = t_1
    else if (z <= 1.45d-8) then
        tmp = x + ((t - x) * (y / a))
    else if (z <= 5.7d+171) then
        tmp = t_1
    else
        tmp = t - (x * (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x * y) / z);
	double tmp;
	if (z <= -8.2e+77) {
		tmp = t_1;
	} else if (z <= 1.45e-8) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 5.7e+171) {
		tmp = t_1;
	} else {
		tmp = t - (x * (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((x * y) / z)
	tmp = 0
	if z <= -8.2e+77:
		tmp = t_1
	elif z <= 1.45e-8:
		tmp = x + ((t - x) * (y / a))
	elif z <= 5.7e+171:
		tmp = t_1
	else:
		tmp = t - (x * (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(x * y) / z))
	tmp = 0.0
	if (z <= -8.2e+77)
		tmp = t_1;
	elseif (z <= 1.45e-8)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (z <= 5.7e+171)
		tmp = t_1;
	else
		tmp = Float64(t - Float64(x * Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((x * y) / z);
	tmp = 0.0;
	if (z <= -8.2e+77)
		tmp = t_1;
	elseif (z <= 1.45e-8)
		tmp = x + ((t - x) * (y / a));
	elseif (z <= 5.7e+171)
		tmp = t_1;
	else
		tmp = t - (x * (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.2e+77], t$95$1, If[LessEqual[z, 1.45e-8], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.7e+171], t$95$1, N[(t - N[(x * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.2000000000000002e77 or 1.4500000000000001e-8 < z < 5.7e171

   1. Initial program 69.1%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

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

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

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

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

      8. associate-/l* N/A

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

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

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

      10. --lowering--.f64 N/A

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

      11. /-lowering-/.f64 N/A

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

      12. --lowering--.f64 73.3%

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

   5. Simplified 73.3%

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

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(-1 \cdot \frac{x \cdot \left(y - a\right)}{z}\right)}\right) \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

      4. mul-1-neg N/A

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

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

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

      6. associate-*r/ N/A

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

      7. distribute-lft-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y - -1 \cdot a}{z}\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y + \left(\mathsf{neg}\left(-1 \cdot a\right)\right)}{z}\right)\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right)}{z}\right)\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y + a}{z}\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{a + -1 \cdot y}{z}\right)\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(a + -1 \cdot y\right), \color{blue}{z}\right)\right)\right) \]

      13. mul-1-neg N/A

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

      14. sub-neg N/A

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

      15. --lowering--.f64 68.8%

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

   8. Simplified 68.8%

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

   9. Taylor expanded in a around 0

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

       1. sub-neg N/A

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

       2. mul-1-neg N/A

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

       3. remove-double-neg N/A

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

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

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

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

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

       6. *-lowering-*.f64 62.2%

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

   11. Simplified 62.2%

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

   if -8.2000000000000002e77 < z < 1.4500000000000001e-8

   1. Initial program 90.5%

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

      1. clear-num N/A

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

      2. associate-*r/ N/A

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

      3. div-inv N/A

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

      4. times-frac N/A

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

      5. flip-- N/A

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

      6. clear-num N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

      11. --lowering--.f64 N/A

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

      12. --lowering--.f64 N/A

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

      13. --lowering--.f64 96.9%

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

   4. Applied egg-rr 96.9%

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

   5. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 74.7%

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

   7. Simplified 74.7%

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

   if 5.7e171 < z

   1. Initial program 57.6%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

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

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

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

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

      8. associate-/l* N/A

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

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

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

      10. --lowering--.f64 N/A

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

      11. /-lowering-/.f64 N/A

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

      12. --lowering--.f64 88.7%

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

   5. Simplified 88.7%

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

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(-1 \cdot \frac{x \cdot \left(y - a\right)}{z}\right)}\right) \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

      4. mul-1-neg N/A

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

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

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

      6. associate-*r/ N/A

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

      7. distribute-lft-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y - -1 \cdot a}{z}\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y + \left(\mathsf{neg}\left(-1 \cdot a\right)\right)}{z}\right)\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right)}{z}\right)\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y + a}{z}\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{a + -1 \cdot y}{z}\right)\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(a + -1 \cdot y\right), \color{blue}{z}\right)\right)\right) \]

      13. mul-1-neg N/A

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

      14. sub-neg N/A

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

      15. --lowering--.f64 81.5%

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

   8. Simplified 81.5%

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

   9. Taylor expanded in a around inf

      \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{a}{z}\right)}\right)\right) \]
   10. Step-by-step derivation

       1. /-lowering-/.f64 81.2%

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

   11. Simplified 81.2%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+77}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-8}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{+171}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 53.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x \cdot y}{z}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+171}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (* x y) z))))
   (if (<= z -4.2e+45)
     t_1
     (if (<= z 6.4e-10)
       (* x (- 1.0 (/ y a)))
       (if (<= z 4.8e+171) t_1 (- t (* x (/ a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x * y) / z);
	double tmp;
	if (z <= -4.2e+45) {
		tmp = t_1;
	} else if (z <= 6.4e-10) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 4.8e+171) {
		tmp = t_1;
	} else {
		tmp = t - (x * (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((x * y) / z)
    if (z <= (-4.2d+45)) then
        tmp = t_1
    else if (z <= 6.4d-10) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 4.8d+171) then
        tmp = t_1
    else
        tmp = t - (x * (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x * y) / z);
	double tmp;
	if (z <= -4.2e+45) {
		tmp = t_1;
	} else if (z <= 6.4e-10) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 4.8e+171) {
		tmp = t_1;
	} else {
		tmp = t - (x * (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((x * y) / z)
	tmp = 0
	if z <= -4.2e+45:
		tmp = t_1
	elif z <= 6.4e-10:
		tmp = x * (1.0 - (y / a))
	elif z <= 4.8e+171:
		tmp = t_1
	else:
		tmp = t - (x * (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(x * y) / z))
	tmp = 0.0
	if (z <= -4.2e+45)
		tmp = t_1;
	elseif (z <= 6.4e-10)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 4.8e+171)
		tmp = t_1;
	else
		tmp = Float64(t - Float64(x * Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((x * y) / z);
	tmp = 0.0;
	if (z <= -4.2e+45)
		tmp = t_1;
	elseif (z <= 6.4e-10)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 4.8e+171)
		tmp = t_1;
	else
		tmp = t - (x * (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e+45], t$95$1, If[LessEqual[z, 6.4e-10], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e+171], t$95$1, N[(t - N[(x * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.1999999999999999e45 or 6.39999999999999961e-10 < z < 4.79999999999999995e171

   1. Initial program 71.6%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

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

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

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

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

      8. associate-/l* N/A

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

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

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

      10. --lowering--.f64 N/A

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

      11. /-lowering-/.f64 N/A

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

      12. --lowering--.f64 71.3%

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

   5. Simplified 71.3%

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

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(-1 \cdot \frac{x \cdot \left(y - a\right)}{z}\right)}\right) \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

      4. mul-1-neg N/A

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

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

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

      6. associate-*r/ N/A

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

      7. distribute-lft-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y - -1 \cdot a}{z}\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y + \left(\mathsf{neg}\left(-1 \cdot a\right)\right)}{z}\right)\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right)}{z}\right)\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y + a}{z}\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{a + -1 \cdot y}{z}\right)\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(a + -1 \cdot y\right), \color{blue}{z}\right)\right)\right) \]

      13. mul-1-neg N/A

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

      14. sub-neg N/A

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

      15. --lowering--.f64 64.5%

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

   8. Simplified 64.5%

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

   9. Taylor expanded in a around 0

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

       1. sub-neg N/A

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

       2. mul-1-neg N/A

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

       3. remove-double-neg N/A

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

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

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

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

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

       6. *-lowering-*.f64 58.6%

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

   11. Simplified 58.6%

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

   if -4.1999999999999999e45 < z < 6.39999999999999961e-10

   1. Initial program 90.5%

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

   3. Taylor expanded in x around inf

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

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

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

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{y - z}{a - z}\right)\right)\right)\right) \]

      3. unsub-neg N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y - z}{a - z}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 69.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   5. Simplified 69.2%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{a}\right)}\right)\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 61.9%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right)\right) \]

   8. Simplified 61.9%

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

   if 4.79999999999999995e171 < z

   1. Initial program 57.6%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

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

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

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

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

      8. associate-/l* N/A

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

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

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

      10. --lowering--.f64 N/A

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

      11. /-lowering-/.f64 N/A

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

      12. --lowering--.f64 88.7%

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

   5. Simplified 88.7%

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

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(-1 \cdot \frac{x \cdot \left(y - a\right)}{z}\right)}\right) \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

      4. mul-1-neg N/A

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

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

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

      6. associate-*r/ N/A

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

      7. distribute-lft-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y - -1 \cdot a}{z}\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y + \left(\mathsf{neg}\left(-1 \cdot a\right)\right)}{z}\right)\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right)}{z}\right)\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y + a}{z}\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{a + -1 \cdot y}{z}\right)\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(a + -1 \cdot y\right), \color{blue}{z}\right)\right)\right) \]

      13. mul-1-neg N/A

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

      14. sub-neg N/A

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

      15. --lowering--.f64 81.5%

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

   8. Simplified 81.5%

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

   9. Taylor expanded in a around inf

      \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{a}{z}\right)}\right)\right) \]
   10. Step-by-step derivation

       1. /-lowering-/.f64 81.2%

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

   11. Simplified 81.2%

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

Alternative 7: 78.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -3.8 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+54}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ (- y z) (- a z))))))
   (if (<= a -3.8e-80)
     t_1
     (if (<= a 9.2e+54) (+ t (* (- t x) (/ (- a y) z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * ((y - z) / (a - z)));
	double tmp;
	if (a <= -3.8e-80) {
		tmp = t_1;
	} else if (a <= 9.2e+54) {
		tmp = t + ((t - x) * ((a - y) / 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 = x + (t * ((y - z) / (a - z)))
    if (a <= (-3.8d-80)) then
        tmp = t_1
    else if (a <= 9.2d+54) then
        tmp = t + ((t - x) * ((a - y) / 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 = x + (t * ((y - z) / (a - z)));
	double tmp;
	if (a <= -3.8e-80) {
		tmp = t_1;
	} else if (a <= 9.2e+54) {
		tmp = t + ((t - x) * ((a - y) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * ((y - z) / (a - z)))
	tmp = 0
	if a <= -3.8e-80:
		tmp = t_1
	elif a <= 9.2e+54:
		tmp = t + ((t - x) * ((a - y) / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))))
	tmp = 0.0
	if (a <= -3.8e-80)
		tmp = t_1;
	elseif (a <= 9.2e+54)
		tmp = Float64(t + Float64(Float64(t - x) * Float64(Float64(a - y) / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * ((y - z) / (a - z)));
	tmp = 0.0;
	if (a <= -3.8e-80)
		tmp = t_1;
	elseif (a <= 9.2e+54)
		tmp = t + ((t - x) * ((a - y) / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.8e-80], t$95$1, If[LessEqual[a, 9.2e+54], N[(t + N[(N[(t - x), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.79999999999999967e-80 or 9.19999999999999977e54 < a

   1. Initial program 85.9%

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

      1. clear-num N/A

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

      2. associate-*r/ N/A

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

      3. div-inv N/A

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

      4. times-frac N/A

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

      5. flip-- N/A

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

      6. clear-num N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

      11. --lowering--.f64 N/A

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

      12. --lowering--.f64 N/A

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

      13. --lowering--.f64 90.0%

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

   4. Applied egg-rr 90.0%

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

   5. Taylor expanded in t around inf

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

   7. Simplified 78.7%

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

   if -3.79999999999999967e-80 < a < 9.19999999999999977e54

   1. Initial program 71.4%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

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

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

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

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

      8. associate-/l* N/A

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

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

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

      10. --lowering--.f64 N/A

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

      11. /-lowering-/.f64 N/A

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

      12. --lowering--.f64 84.2%

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

   5. Simplified 84.2%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{-80}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+54}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -8 \cdot 10^{-79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+54}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ (- y z) (- a z))))))
   (if (<= a -8e-79) t_1 (if (<= a 8.6e+54) (+ t (* (/ y z) (- x t))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * ((y - z) / (a - z)));
	double tmp;
	if (a <= -8e-79) {
		tmp = t_1;
	} else if (a <= 8.6e+54) {
		tmp = t + ((y / z) * (x - t));
	} 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 + (t * ((y - z) / (a - z)))
    if (a <= (-8d-79)) then
        tmp = t_1
    else if (a <= 8.6d+54) then
        tmp = t + ((y / z) * (x - t))
    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 + (t * ((y - z) / (a - z)));
	double tmp;
	if (a <= -8e-79) {
		tmp = t_1;
	} else if (a <= 8.6e+54) {
		tmp = t + ((y / z) * (x - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * ((y - z) / (a - z)))
	tmp = 0
	if a <= -8e-79:
		tmp = t_1
	elif a <= 8.6e+54:
		tmp = t + ((y / z) * (x - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))))
	tmp = 0.0
	if (a <= -8e-79)
		tmp = t_1;
	elseif (a <= 8.6e+54)
		tmp = Float64(t + Float64(Float64(y / z) * Float64(x - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * ((y - z) / (a - z)));
	tmp = 0.0;
	if (a <= -8e-79)
		tmp = t_1;
	elseif (a <= 8.6e+54)
		tmp = t + ((y / z) * (x - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8e-79], t$95$1, If[LessEqual[a, 8.6e+54], N[(t + N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -8e-79 or 8.59999999999999952e54 < a

   1. Initial program 85.9%

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

      1. clear-num N/A

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

      2. associate-*r/ N/A

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

      3. div-inv N/A

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

      4. times-frac N/A

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

      5. flip-- N/A

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

      6. clear-num N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

      11. --lowering--.f64 N/A

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

      12. --lowering--.f64 N/A

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

      13. --lowering--.f64 90.0%

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

   4. Applied egg-rr 90.0%

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

   5. Taylor expanded in t around inf

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

   7. Simplified 78.7%

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

   if -8e-79 < a < 8.59999999999999952e54

   1. Initial program 71.4%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

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

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

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

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

      8. associate-/l* N/A

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

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

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

      10. --lowering--.f64 N/A

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

      11. /-lowering-/.f64 N/A

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

      12. --lowering--.f64 84.2%

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

   5. Simplified 84.2%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 82.4%

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

   8. Simplified 82.4%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-79}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+54}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{if}\;a \leq -2.2 \cdot 10^{-78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+55}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ t (- a z))))))
   (if (<= a -2.2e-78)
     t_1
     (if (<= a 2.35e+55) (+ t (* (/ y z) (- x t))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (t / (a - z)));
	double tmp;
	if (a <= -2.2e-78) {
		tmp = t_1;
	} else if (a <= 2.35e+55) {
		tmp = t + ((y / z) * (x - t));
	} 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 + ((y - z) * (t / (a - z)))
    if (a <= (-2.2d-78)) then
        tmp = t_1
    else if (a <= 2.35d+55) then
        tmp = t + ((y / z) * (x - t))
    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 + ((y - z) * (t / (a - z)));
	double tmp;
	if (a <= -2.2e-78) {
		tmp = t_1;
	} else if (a <= 2.35e+55) {
		tmp = t + ((y / z) * (x - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * (t / (a - z)))
	tmp = 0
	if a <= -2.2e-78:
		tmp = t_1
	elif a <= 2.35e+55:
		tmp = t + ((y / z) * (x - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))))
	tmp = 0.0
	if (a <= -2.2e-78)
		tmp = t_1;
	elseif (a <= 2.35e+55)
		tmp = Float64(t + Float64(Float64(y / z) * Float64(x - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * (t / (a - z)));
	tmp = 0.0;
	if (a <= -2.2e-78)
		tmp = t_1;
	elseif (a <= 2.35e+55)
		tmp = t + ((y / z) * (x - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.2e-78], t$95$1, If[LessEqual[a, 2.35e+55], N[(t + N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.1999999999999999e-78 or 2.35e55 < a

   1. Initial program 85.9%

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

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \color{blue}{\left(\frac{t}{a - z}\right)}\right)\right) \]
   4. Step-by-step derivation

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

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

      2. --lowering--.f64 76.6%

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

   5. Simplified 76.6%

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

   if -2.1999999999999999e-78 < a < 2.35e55

   1. Initial program 71.4%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

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

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

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

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

      8. associate-/l* N/A

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

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

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

      10. --lowering--.f64 N/A

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

      11. /-lowering-/.f64 N/A

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

      12. --lowering--.f64 84.2%

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

   5. Simplified 84.2%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 82.4%

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

   8. Simplified 82.4%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{-78}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+55}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 70.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{+73}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+59}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.65e+73)
   (+ x (/ (- t x) (/ a y)))
   (if (<= a 1.4e+59) (+ t (* (/ y z) (- x t))) (+ x (* (- t x) (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.65e+73) {
		tmp = x + ((t - x) / (a / y));
	} else if (a <= 1.4e+59) {
		tmp = t + ((y / z) * (x - t));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.65d+73)) then
        tmp = x + ((t - x) / (a / y))
    else if (a <= 1.4d+59) then
        tmp = t + ((y / z) * (x - t))
    else
        tmp = x + ((t - x) * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.65e+73) {
		tmp = x + ((t - x) / (a / y));
	} else if (a <= 1.4e+59) {
		tmp = t + ((y / z) * (x - t));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.65e+73:
		tmp = x + ((t - x) / (a / y))
	elif a <= 1.4e+59:
		tmp = t + ((y / z) * (x - t))
	else:
		tmp = x + ((t - x) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.65e+73)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	elseif (a <= 1.4e+59)
		tmp = Float64(t + Float64(Float64(y / z) * Float64(x - t)));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.65e+73)
		tmp = x + ((t - x) / (a / y));
	elseif (a <= 1.4e+59)
		tmp = t + ((y / z) * (x - t));
	else
		tmp = x + ((t - x) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.65e+73], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.4e+59], N[(t + N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.65000000000000015e73

   1. Initial program 84.3%

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

      1. clear-num N/A

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

      2. associate-*r/ N/A

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

      3. div-inv N/A

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

      4. times-frac N/A

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

      5. flip-- N/A

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

      6. clear-num N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

      11. --lowering--.f64 N/A

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

      12. --lowering--.f64 N/A

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

      13. --lowering--.f64 89.9%

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

   4. Applied egg-rr 89.9%

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

      1. +-commutative N/A

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

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

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

      3. *-commutative N/A

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

      4. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(t - x\right) \cdot \frac{1}{\frac{a - z}{y - z}}\right), x\right) \]

      5. un-div-inv N/A

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

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

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

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

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

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

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

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

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

      10. --lowering--.f64 90.0%

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

   6. Applied egg-rr 90.0%

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

   7. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \color{blue}{\left(\frac{a}{y}\right)}\right), x\right) \]
   8. Step-by-step derivation

      1. /-lowering-/.f64 78.2%

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

   9. Simplified 78.2%

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

   if -1.65000000000000015e73 < a < 1.3999999999999999e59

   1. Initial program 73.3%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

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

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

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

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

      8. associate-/l* N/A

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

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

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

      10. --lowering--.f64 N/A

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

      11. /-lowering-/.f64 N/A

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

      12. --lowering--.f64 80.2%

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

   5. Simplified 80.2%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 78.3%

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

   8. Simplified 78.3%

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

   if 1.3999999999999999e59 < a

   1. Initial program 90.0%

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

      1. clear-num N/A

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

      2. associate-*r/ N/A

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

      3. div-inv N/A

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

      4. times-frac N/A

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

      5. flip-- N/A

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

      6. clear-num N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

      11. --lowering--.f64 N/A

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

      12. --lowering--.f64 N/A

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

      13. --lowering--.f64 93.3%

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

   4. Applied egg-rr 93.3%

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

   5. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 68.0%

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

   7. Simplified 68.0%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{+73}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+59}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 69.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + x \cdot \frac{y - a}{z}\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-11}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* x (/ (- y a) z)))))
   (if (<= z -1.45e+84)
     t_1
     (if (<= z 5.3e-11) (+ x (/ (- t x) (/ a y))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x * ((y - a) / z));
	double tmp;
	if (z <= -1.45e+84) {
		tmp = t_1;
	} else if (z <= 5.3e-11) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (x * ((y - a) / z))
    if (z <= (-1.45d+84)) then
        tmp = t_1
    else if (z <= 5.3d-11) then
        tmp = x + ((t - x) / (a / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x * ((y - a) / z));
	double tmp;
	if (z <= -1.45e+84) {
		tmp = t_1;
	} else if (z <= 5.3e-11) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (x * ((y - a) / z))
	tmp = 0
	if z <= -1.45e+84:
		tmp = t_1
	elif z <= 5.3e-11:
		tmp = x + ((t - x) / (a / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(x * Float64(Float64(y - a) / z)))
	tmp = 0.0
	if (z <= -1.45e+84)
		tmp = t_1;
	elseif (z <= 5.3e-11)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (x * ((y - a) / z));
	tmp = 0.0;
	if (z <= -1.45e+84)
		tmp = t_1;
	elseif (z <= 5.3e-11)
		tmp = x + ((t - x) / (a / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.45e+84], t$95$1, If[LessEqual[z, 5.3e-11], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.44999999999999994e84 or 5.2999999999999998e-11 < z

   1. Initial program 66.1%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

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

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

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

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

      8. associate-/l* N/A

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

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

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

      10. --lowering--.f64 N/A

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

      11. /-lowering-/.f64 N/A

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

      12. --lowering--.f64 77.4%

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

   5. Simplified 77.4%

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

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(-1 \cdot \frac{x \cdot \left(y - a\right)}{z}\right)}\right) \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

      4. mul-1-neg N/A

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

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

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

      6. associate-*r/ N/A

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

      7. distribute-lft-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y - -1 \cdot a}{z}\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y + \left(\mathsf{neg}\left(-1 \cdot a\right)\right)}{z}\right)\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right)}{z}\right)\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y + a}{z}\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{a + -1 \cdot y}{z}\right)\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(a + -1 \cdot y\right), \color{blue}{z}\right)\right)\right) \]

      13. mul-1-neg N/A

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

      14. sub-neg N/A

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

      15. --lowering--.f64 72.2%

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

   8. Simplified 72.2%

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

   if -1.44999999999999994e84 < z < 5.2999999999999998e-11

   1. Initial program 90.5%

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

      1. clear-num N/A

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

      2. associate-*r/ N/A

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

      3. div-inv N/A

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

      4. times-frac N/A

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

      5. flip-- N/A

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

      6. clear-num N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

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

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

      10. /-lowering-/.f64 N/A

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

      11. --lowering--.f64 N/A

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

      12. --lowering--.f64 N/A

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

      13. --lowering--.f64 96.9%

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

   4. Applied egg-rr 96.9%

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

      1. +-commutative N/A

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

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

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

      3. *-commutative N/A

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

      4. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(t - x\right) \cdot \frac{1}{\frac{a - z}{y - z}}\right), x\right) \]

      5. un-div-inv N/A

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

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

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

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

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

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

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

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

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

      10. --lowering--.f64 97.3%

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

   6. Applied egg-rr 97.3%

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

   7. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \color{blue}{\left(\frac{a}{y}\right)}\right), x\right) \]
   8. Step-by-step derivation

      1. /-lowering-/.f64 74.7%

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

   9. Simplified 74.7%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+84}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-11}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 53.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x \cdot y}{z}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (* x y) z))))
   (if (<= z -1.4e+46) t_1 (if (<= z 7e-10) (* x (- 1.0 (/ y a))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x * y) / z);
	double tmp;
	if (z <= -1.4e+46) {
		tmp = t_1;
	} else if (z <= 7e-10) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((x * y) / z)
    if (z <= (-1.4d+46)) then
        tmp = t_1
    else if (z <= 7d-10) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x * y) / z);
	double tmp;
	if (z <= -1.4e+46) {
		tmp = t_1;
	} else if (z <= 7e-10) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((x * y) / z)
	tmp = 0
	if z <= -1.4e+46:
		tmp = t_1
	elif z <= 7e-10:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(x * y) / z))
	tmp = 0.0
	if (z <= -1.4e+46)
		tmp = t_1;
	elseif (z <= 7e-10)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((x * y) / z);
	tmp = 0.0;
	if (z <= -1.4e+46)
		tmp = t_1;
	elseif (z <= 7e-10)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e+46], t$95$1, If[LessEqual[z, 7e-10], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.40000000000000009e46 or 6.99999999999999961e-10 < z

   1. Initial program 68.2%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

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

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

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

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

      8. associate-/l* N/A

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

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

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

      10. --lowering--.f64 N/A

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

      11. /-lowering-/.f64 N/A

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

      12. --lowering--.f64 75.6%

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

   5. Simplified 75.6%

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

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(-1 \cdot \frac{x \cdot \left(y - a\right)}{z}\right)}\right) \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

      4. mul-1-neg N/A

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

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

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

      6. associate-*r/ N/A

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

      7. distribute-lft-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y - -1 \cdot a}{z}\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y + \left(\mathsf{neg}\left(-1 \cdot a\right)\right)}{z}\right)\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a\right)\right)\right)\right)}{z}\right)\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{-1 \cdot y + a}{z}\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \left(\frac{a + -1 \cdot y}{z}\right)\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(a + -1 \cdot y\right), \color{blue}{z}\right)\right)\right) \]

      13. mul-1-neg N/A

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

      14. sub-neg N/A

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

      15. --lowering--.f64 68.6%

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

   8. Simplified 68.6%

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

   9. Taylor expanded in a around 0

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

       1. sub-neg N/A

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

       2. mul-1-neg N/A

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

       3. remove-double-neg N/A

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

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

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

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

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

       6. *-lowering-*.f64 59.3%

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

   11. Simplified 59.3%

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

   if -1.40000000000000009e46 < z < 6.99999999999999961e-10

   1. Initial program 90.5%

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

   3. Taylor expanded in x around inf

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

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

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

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{y - z}{a - z}\right)\right)\right)\right) \]

      3. unsub-neg N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y - z}{a - z}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 69.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   5. Simplified 69.2%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{a}\right)}\right)\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 61.9%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right)\right) \]

   8. Simplified 61.9%

      \[\leadsto x \cdot \left(1 - \color{blue}{\frac{y}{a}}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 49.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+45}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+100}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.8e+45) t (if (<= z 1.65e+100) (* x (- 1.0 (/ y a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.8e+45) {
		tmp = t;
	} else if (z <= 1.65e+100) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8.8d+45)) then
        tmp = t
    else if (z <= 1.65d+100) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.8e+45) {
		tmp = t;
	} else if (z <= 1.65e+100) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.8e+45:
		tmp = t
	elif z <= 1.65e+100:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.8e+45)
		tmp = t;
	elseif (z <= 1.65e+100)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.8e+45)
		tmp = t;
	elseif (z <= 1.65e+100)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.8e+45], t, If[LessEqual[z, 1.65e+100], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -8.8000000000000001e45 or 1.6500000000000001e100 < z

   1. Initial program 65.5%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Simplified 55.0%

      \[\leadsto \color{blue}{t} \]

   if -8.8000000000000001e45 < z < 1.6500000000000001e100

   1. Initial program 88.7%

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

   3. Taylor expanded in x around inf

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

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

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

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{y - z}{a - z}\right)\right)\right)\right) \]

      3. unsub-neg N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y - z}{a - z}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 64.9%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   5. Simplified 64.9%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{a}\right)}\right)\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 58.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right)\right) \]

   8. Simplified 58.2%

      \[\leadsto x \cdot \left(1 - \color{blue}{\frac{y}{a}}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 38.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+60}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(\frac{z}{a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.4e+60) t (if (<= z 4.3e-9) (* x (+ (/ z a) 1.0)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.4e+60) {
		tmp = t;
	} else if (z <= 4.3e-9) {
		tmp = x * ((z / a) + 1.0);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.4d+60)) then
        tmp = t
    else if (z <= 4.3d-9) then
        tmp = x * ((z / a) + 1.0d0)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.4e+60) {
		tmp = t;
	} else if (z <= 4.3e-9) {
		tmp = x * ((z / a) + 1.0);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.4e+60:
		tmp = t
	elif z <= 4.3e-9:
		tmp = x * ((z / a) + 1.0)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.4e+60)
		tmp = t;
	elseif (z <= 4.3e-9)
		tmp = Float64(x * Float64(Float64(z / a) + 1.0));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.4e+60)
		tmp = t;
	elseif (z <= 4.3e-9)
		tmp = x * ((z / a) + 1.0);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.4e+60], t, If[LessEqual[z, 4.3e-9], N[(x * N[(N[(z / a), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -5.3999999999999999e60 or 4.29999999999999963e-9 < z

   1. Initial program 67.4%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Simplified 51.5%

      \[\leadsto \color{blue}{t} \]

   if -5.3999999999999999e60 < z < 4.29999999999999963e-9

   1. Initial program 90.2%

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

   3. Taylor expanded in x around inf

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

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

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

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{y - z}{a - z}\right)\right)\right)\right) \]

      3. unsub-neg N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y - z}{a - z}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 67.7%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   5. Simplified 67.7%

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

   6. Taylor expanded in y around 0

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + \frac{z}{a - z}\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{z}{a - z}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{\left(a - z\right)}\right)\right)\right) \]

      4. --lowering--.f64 33.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(z, \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 33.2%

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

   9. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + \frac{z}{a}\right)}\right) \]
   10. Step-by-step derivation

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

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{z}{a}\right)}\right)\right) \]

       2. /-lowering-/.f64 36.4%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(z, \color{blue}{a}\right)\right)\right) \]

   11. Simplified 36.4%

       \[\leadsto x \cdot \color{blue}{\left(1 + \frac{z}{a}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+60}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(\frac{z}{a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 38.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+60}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 0.00106:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.5e+60) t (if (<= z 0.00106) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.5e+60) {
		tmp = t;
	} else if (z <= 0.00106) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.5d+60)) then
        tmp = t
    else if (z <= 0.00106d0) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.5e+60) {
		tmp = t;
	} else if (z <= 0.00106) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.5e+60:
		tmp = t
	elif z <= 0.00106:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.5e+60)
		tmp = t;
	elseif (z <= 0.00106)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.5e+60)
		tmp = t;
	elseif (z <= 0.00106)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.5e+60], t, If[LessEqual[z, 0.00106], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -4.50000000000000013e60 or 0.00105999999999999996 < z

   1. Initial program 67.1%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Simplified 51.9%

      \[\leadsto \color{blue}{t} \]

   if -4.50000000000000013e60 < z < 0.00105999999999999996

   1. Initial program 90.2%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 33.5%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 25.3% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

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

C

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

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 = t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := t

Derivation

1. Initial program 79.0%

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

3. Taylor expanded in z around inf

   \[\leadsto \color{blue}{t} \]
4. Step-by-step derivation

5. Simplified 28.0%

   \[\leadsto \color{blue}{t} \]
6. Add Preprocessing

Alternative 17: 2.8% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 0.0)

C

double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

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 = 0.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Python

def code(x, y, z, t, a):
	return 0.0

Julia

function code(x, y, z, t, a)
	return 0.0
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := 0.0

Derivation

1. Initial program 79.0%

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

3. Taylor expanded in x around inf

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

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

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

   2. mul-1-neg N/A

      \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{y - z}{a - z}\right)\right)\right)\right) \]

   3. unsub-neg N/A

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

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

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y - z}{a - z}\right)}\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right)\right)\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right)\right)\right) \]

   7. --lowering--.f64 45.0%

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

5. Simplified 45.0%

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

6. Taylor expanded in z around inf

   \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{1}\right)\right) \]
7. Step-by-step derivation

8. Simplified 2.8%

   \[\leadsto x \cdot \left(1 - \color{blue}{1}\right) \]
9. Step-by-step derivation

   1. metadata-eval N/A

      \[\leadsto x \cdot 0 \]

   2. mul0-rgt 2.8%

      \[\leadsto 0 \]

10. Applied egg-rr 2.8%

    \[\leadsto \color{blue}{0} \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2024138 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))