Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 81.5% → 95.1%

Time: 13.9s

Alternatives: 19

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: 81.5% 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: 95.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-302}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -1e-302)
     (+ x (* (- t x) (/ (- y z) (- a z))))
     (if (<= t_1 0.0)
       (+ t (* (/ (- t x) z) (- a y)))
       (+ x (/ (- t x) (/ (- a z) (- y 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-302) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else if (t_1 <= 0.0) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = x + ((t - x) / ((a - z) / (y - 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-302)) then
        tmp = x + ((t - x) * ((y - z) / (a - z)))
    else if (t_1 <= 0.0d0) then
        tmp = t + (((t - x) / z) * (a - y))
    else
        tmp = x + ((t - x) / ((a - z) / (y - 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-302) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else if (t_1 <= 0.0) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = x + ((t - x) / ((a - z) / (y - 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-302:
		tmp = x + ((t - x) * ((y - z) / (a - z)))
	elif t_1 <= 0.0:
		tmp = t + (((t - x) / z) * (a - y))
	else:
		tmp = x + ((t - x) / ((a - z) / (y - 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-302)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / Float64(a - z))));
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - 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-302)
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	elseif (t_1 <= 0.0)
		tmp = t + (((t - x) / z) * (a - y));
	else
		tmp = x + ((t - x) / ((a - z) / (y - 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-302], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - 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)))) < -9.9999999999999996e-303

   1. Initial program 91.5%

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

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

   if -9.9999999999999996e-303 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

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

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

      3. associate-/l* N/A

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

      4. associate-/l* N/A

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

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

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

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

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

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

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

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

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

      9. --lowering--.f64 99.9%

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

   8. Simplified 99.9%

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

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

   1. Initial program 85.8%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 92.5%

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

   4. Applied egg-rr 92.5%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. associate-*l/ N/A

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

      5. flip-- N/A

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

      6. +-commutative N/A

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

      7. div-inv N/A

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

      8. frac-times N/A

         \[\leadsto \frac{y - z}{a \cdot a - z \cdot z} \cdot \frac{t - x}{\frac{1}{z + a}} + x \]

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

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

   6. Applied egg-rr 92.6%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-302}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-302}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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-302)
     t_1
     (if (<= t_2 0.0) (+ t (* (/ (- t x) z) (- a y))) 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-302) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + (((t - x) / z) * (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) :: 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-302)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) then
        tmp = t + (((t - x) / z) * (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 = x + ((t - x) * ((y - z) / (a - z)));
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -1e-302) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + (((t - x) / z) * (a - y));
	} 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-302:
		tmp = t_1
	elif t_2 <= 0.0:
		tmp = t + (((t - x) / z) * (a - y))
	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-302)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	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-302)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = t + (((t - x) / z) * (a - y));
	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-302], t$95$1, If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $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)))) < -9.9999999999999996e-303 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 88.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 92.9%

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

   4. Applied egg-rr 92.9%

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

   if -9.9999999999999996e-303 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

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

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

      3. associate-/l* N/A

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

      4. associate-/l* N/A

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

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

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

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

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

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

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

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

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

      9. --lowering--.f64 99.9%

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

   8. Simplified 99.9%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-302}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-192}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-236}:\\ \;\;\;\;t + \frac{t - x}{\frac{z}{a - y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -5e-192)
     t_1
     (if (<= t_1 5e-236) (+ t (/ (- t x) (/ z (- a y)))) 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 <= -5e-192) {
		tmp = t_1;
	} else if (t_1 <= 5e-236) {
		tmp = t + ((t - x) / (z / (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 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_1 <= (-5d-192)) then
        tmp = t_1
    else if (t_1 <= 5d-236) then
        tmp = t + ((t - x) / (z / (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 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -5e-192) {
		tmp = t_1;
	} else if (t_1 <= 5e-236) {
		tmp = t + ((t - x) / (z / (a - y)));
	} 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 <= -5e-192:
		tmp = t_1
	elif t_1 <= 5e-236:
		tmp = t + ((t - x) / (z / (a - y)))
	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 <= -5e-192)
		tmp = t_1;
	elseif (t_1 <= 5e-236)
		tmp = Float64(t + Float64(Float64(t - x) / Float64(z / Float64(a - y))));
	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 <= -5e-192)
		tmp = t_1;
	elseif (t_1 <= 5e-236)
		tmp = t + ((t - x) / (z / (a - y)));
	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, -5e-192], t$95$1, If[LessEqual[t$95$1, 5e-236], N[(t + N[(N[(t - x), $MachinePrecision] / N[(z / N[(a - y), $MachinePrecision]), $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)))) < -5.0000000000000001e-192 or 4.9999999999999998e-236 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.5%

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

   if -5.0000000000000001e-192 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.9999999999999998e-236

   1. Initial program 12.6%

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

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

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 88.7%

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

   7. Applied egg-rr 88.7%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-192}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 5 \cdot 10^{-236}:\\ \;\;\;\;t + \frac{t - x}{\frac{z}{a - y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+50}:\\ \;\;\;\;t + \frac{t - x}{\frac{z}{a - y}}\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-73}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+42}:\\ \;\;\;\;x - y \cdot \frac{t - x}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8e+50)
   (+ t (/ (- t x) (/ z (- a y))))
   (if (<= z -2.35e-73)
     (/ t (/ (- a z) (- y z)))
     (if (<= z 5.8e+42)
       (- x (* y (/ (- t x) (- z a))))
       (+ t (* (/ (- t x) z) (- a y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8e+50) {
		tmp = t + ((t - x) / (z / (a - y)));
	} else if (z <= -2.35e-73) {
		tmp = t / ((a - z) / (y - z));
	} else if (z <= 5.8e+42) {
		tmp = x - (y * ((t - x) / (z - a)));
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8d+50)) then
        tmp = t + ((t - x) / (z / (a - y)))
    else if (z <= (-2.35d-73)) then
        tmp = t / ((a - z) / (y - z))
    else if (z <= 5.8d+42) then
        tmp = x - (y * ((t - x) / (z - a)))
    else
        tmp = t + (((t - x) / z) * (a - y))
    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 <= -8e+50) {
		tmp = t + ((t - x) / (z / (a - y)));
	} else if (z <= -2.35e-73) {
		tmp = t / ((a - z) / (y - z));
	} else if (z <= 5.8e+42) {
		tmp = x - (y * ((t - x) / (z - a)));
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8e+50:
		tmp = t + ((t - x) / (z / (a - y)))
	elif z <= -2.35e-73:
		tmp = t / ((a - z) / (y - z))
	elif z <= 5.8e+42:
		tmp = x - (y * ((t - x) / (z - a)))
	else:
		tmp = t + (((t - x) / z) * (a - y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8e+50)
		tmp = Float64(t + Float64(Float64(t - x) / Float64(z / Float64(a - y))));
	elseif (z <= -2.35e-73)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (z <= 5.8e+42)
		tmp = Float64(x - Float64(y * Float64(Float64(t - x) / Float64(z - a))));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8e+50)
		tmp = t + ((t - x) / (z / (a - y)));
	elseif (z <= -2.35e-73)
		tmp = t / ((a - z) / (y - z));
	elseif (z <= 5.8e+42)
		tmp = x - (y * ((t - x) / (z - a)));
	else
		tmp = t + (((t - x) / z) * (a - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8e+50], N[(t + N[(N[(t - x), $MachinePrecision] / N[(z / N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.35e-73], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e+42], N[(x - N[(y * N[(N[(t - x), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.0000000000000006e50

   1. Initial program 57.7%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 78.6%

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

   5. Simplified 78.6%

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

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

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 78.7%

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

   7. Applied egg-rr 78.7%

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

   if -8.0000000000000006e50 < z < -2.34999999999999997e-73

   1. Initial program 85.6%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 74.2%

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

   5. Simplified 74.2%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 78.1%

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

   7. Applied egg-rr 78.1%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 78.2%

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

   9. Applied egg-rr 78.2%

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

   if -2.34999999999999997e-73 < z < 5.79999999999999961e42

   1. Initial program 92.0%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 86.2%

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

   if 5.79999999999999961e42 < z

   1. Initial program 65.2%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 77.1%

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

   5. Simplified 77.1%

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

   6. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

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

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

      3. associate-/l* N/A

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

      4. associate-/l* N/A

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

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

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

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

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

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

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

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

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

      9. --lowering--.f64 77.2%

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

   8. Simplified 77.2%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+50}:\\ \;\;\;\;t + \frac{t - x}{\frac{z}{a - y}}\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-73}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+42}:\\ \;\;\;\;x - y \cdot \frac{t - x}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+50}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-73}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+48}:\\ \;\;\;\;x - y \cdot \frac{t - x}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6e+50)
   (+ t (* (- t x) (/ (- a y) z)))
   (if (<= z -3.2e-73)
     (/ t (/ (- a z) (- y z)))
     (if (<= z 1.15e+48)
       (- x (* y (/ (- t x) (- z a))))
       (+ t (* (/ (- t x) z) (- a y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6e+50) {
		tmp = t + ((t - x) * ((a - y) / z));
	} else if (z <= -3.2e-73) {
		tmp = t / ((a - z) / (y - z));
	} else if (z <= 1.15e+48) {
		tmp = x - (y * ((t - x) / (z - a)));
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6d+50)) then
        tmp = t + ((t - x) * ((a - y) / z))
    else if (z <= (-3.2d-73)) then
        tmp = t / ((a - z) / (y - z))
    else if (z <= 1.15d+48) then
        tmp = x - (y * ((t - x) / (z - a)))
    else
        tmp = t + (((t - x) / z) * (a - y))
    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 <= -6e+50) {
		tmp = t + ((t - x) * ((a - y) / z));
	} else if (z <= -3.2e-73) {
		tmp = t / ((a - z) / (y - z));
	} else if (z <= 1.15e+48) {
		tmp = x - (y * ((t - x) / (z - a)));
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6e+50:
		tmp = t + ((t - x) * ((a - y) / z))
	elif z <= -3.2e-73:
		tmp = t / ((a - z) / (y - z))
	elif z <= 1.15e+48:
		tmp = x - (y * ((t - x) / (z - a)))
	else:
		tmp = t + (((t - x) / z) * (a - y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6e+50)
		tmp = Float64(t + Float64(Float64(t - x) * Float64(Float64(a - y) / z)));
	elseif (z <= -3.2e-73)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (z <= 1.15e+48)
		tmp = Float64(x - Float64(y * Float64(Float64(t - x) / Float64(z - a))));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6e+50)
		tmp = t + ((t - x) * ((a - y) / z));
	elseif (z <= -3.2e-73)
		tmp = t / ((a - z) / (y - z));
	elseif (z <= 1.15e+48)
		tmp = x - (y * ((t - x) / (z - a)));
	else
		tmp = t + (((t - x) / z) * (a - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6e+50], N[(t + N[(N[(t - x), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.2e-73], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e+48], N[(x - N[(y * N[(N[(t - x), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.9999999999999996e50

   1. Initial program 57.7%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 78.6%

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

   5. Simplified 78.6%

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

   if -5.9999999999999996e50 < z < -3.19999999999999986e-73

   1. Initial program 85.6%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 74.2%

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

   5. Simplified 74.2%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 78.1%

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

   7. Applied egg-rr 78.1%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 78.2%

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

   9. Applied egg-rr 78.2%

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

   if -3.19999999999999986e-73 < z < 1.15e48

   1. Initial program 92.0%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 86.2%

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

   if 1.15e48 < z

   1. Initial program 65.2%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 77.1%

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

   5. Simplified 77.1%

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

   6. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

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

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

      3. associate-/l* N/A

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

      4. associate-/l* N/A

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

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

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

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

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

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

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

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

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

      9. --lowering--.f64 77.2%

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

   8. Simplified 77.2%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+50}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-73}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+48}:\\ \;\;\;\;x - y \cdot \frac{t - x}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-73}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+55}:\\ \;\;\;\;x - y \cdot \frac{t - x}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (/ (- t x) z) (- a y)))))
   (if (<= z -1.25e+50)
     t_1
     (if (<= z -3.2e-73)
       (/ t (/ (- a z) (- y z)))
       (if (<= z 2.3e+55) (- x (* y (/ (- t x) (- z a)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((t - x) / z) * (a - y));
	double tmp;
	if (z <= -1.25e+50) {
		tmp = t_1;
	} else if (z <= -3.2e-73) {
		tmp = t / ((a - z) / (y - z));
	} else if (z <= 2.3e+55) {
		tmp = x - (y * ((t - x) / (z - 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 + (((t - x) / z) * (a - y))
    if (z <= (-1.25d+50)) then
        tmp = t_1
    else if (z <= (-3.2d-73)) then
        tmp = t / ((a - z) / (y - z))
    else if (z <= 2.3d+55) then
        tmp = x - (y * ((t - x) / (z - 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 + (((t - x) / z) * (a - y));
	double tmp;
	if (z <= -1.25e+50) {
		tmp = t_1;
	} else if (z <= -3.2e-73) {
		tmp = t / ((a - z) / (y - z));
	} else if (z <= 2.3e+55) {
		tmp = x - (y * ((t - x) / (z - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (((t - x) / z) * (a - y))
	tmp = 0
	if z <= -1.25e+50:
		tmp = t_1
	elif z <= -3.2e-73:
		tmp = t / ((a - z) / (y - z))
	elif z <= 2.3e+55:
		tmp = x - (y * ((t - x) / (z - a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)))
	tmp = 0.0
	if (z <= -1.25e+50)
		tmp = t_1;
	elseif (z <= -3.2e-73)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (z <= 2.3e+55)
		tmp = Float64(x - Float64(y * Float64(Float64(t - x) / Float64(z - a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (((t - x) / z) * (a - y));
	tmp = 0.0;
	if (z <= -1.25e+50)
		tmp = t_1;
	elseif (z <= -3.2e-73)
		tmp = t / ((a - z) / (y - z));
	elseif (z <= 2.3e+55)
		tmp = x - (y * ((t - x) / (z - 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[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.25e+50], t$95$1, If[LessEqual[z, -3.2e-73], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e+55], N[(x - N[(y * N[(N[(t - x), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.25e50 or 2.29999999999999987e55 < z

   1. Initial program 61.3%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 77.9%

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

   5. Simplified 77.9%

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

   6. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

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

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

      3. associate-/l* N/A

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

      4. associate-/l* N/A

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

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

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

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

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

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

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

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

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

      9. --lowering--.f64 76.3%

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

   8. Simplified 76.3%

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

   if -1.25e50 < z < -3.19999999999999986e-73

   1. Initial program 85.6%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 74.2%

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

   5. Simplified 74.2%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 78.1%

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

   7. Applied egg-rr 78.1%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 78.2%

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

   9. Applied egg-rr 78.2%

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

   if -3.19999999999999986e-73 < z < 2.29999999999999987e55

   1. Initial program 92.0%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 86.2%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+50}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-73}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+55}:\\ \;\;\;\;x - y \cdot \frac{t - x}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-74}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+46}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (/ (- t x) z) (- a y)))))
   (if (<= z -8.2e+49)
     t_1
     (if (<= z -2.4e-74)
       (/ t (/ (- a z) (- y z)))
       (if (<= z 6e+46) (+ x (* (- t x) (/ y a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((t - x) / z) * (a - y));
	double tmp;
	if (z <= -8.2e+49) {
		tmp = t_1;
	} else if (z <= -2.4e-74) {
		tmp = t / ((a - z) / (y - z));
	} else if (z <= 6e+46) {
		tmp = x + ((t - x) * (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 + (((t - x) / z) * (a - y))
    if (z <= (-8.2d+49)) then
        tmp = t_1
    else if (z <= (-2.4d-74)) then
        tmp = t / ((a - z) / (y - z))
    else if (z <= 6d+46) then
        tmp = x + ((t - x) * (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 + (((t - x) / z) * (a - y));
	double tmp;
	if (z <= -8.2e+49) {
		tmp = t_1;
	} else if (z <= -2.4e-74) {
		tmp = t / ((a - z) / (y - z));
	} else if (z <= 6e+46) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (((t - x) / z) * (a - y))
	tmp = 0
	if z <= -8.2e+49:
		tmp = t_1
	elif z <= -2.4e-74:
		tmp = t / ((a - z) / (y - z))
	elif z <= 6e+46:
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)))
	tmp = 0.0
	if (z <= -8.2e+49)
		tmp = t_1;
	elseif (z <= -2.4e-74)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (z <= 6e+46)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (((t - x) / z) * (a - y));
	tmp = 0.0;
	if (z <= -8.2e+49)
		tmp = t_1;
	elseif (z <= -2.4e-74)
		tmp = t / ((a - z) / (y - z));
	elseif (z <= 6e+46)
		tmp = x + ((t - x) * (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[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.2e+49], t$95$1, If[LessEqual[z, -2.4e-74], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+46], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.2e49 or 6.00000000000000047e46 < z

   1. Initial program 61.3%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 77.9%

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

   5. Simplified 77.9%

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

   6. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

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

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

      3. associate-/l* N/A

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

      4. associate-/l* N/A

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

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

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

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

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

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

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

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

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

      9. --lowering--.f64 76.3%

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

   8. Simplified 76.3%

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

   if -8.2e49 < z < -2.3999999999999999e-74

   1. Initial program 86.1%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 75.3%

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

   5. Simplified 75.3%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 79.0%

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

   7. Applied egg-rr 79.0%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 79.1%

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

   9. Applied egg-rr 79.1%

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

   if -2.3999999999999999e-74 < z < 6.00000000000000047e46

   1. Initial program 92.0%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 93.5%

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

   4. Applied egg-rr 93.5%

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

   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 78.4%

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

   7. Simplified 78.4%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+49}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-74}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+46}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.9 \cdot 10^{-148}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 10^{-8}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ t a)))))
   (if (<= a -1.9e+116)
     t_1
     (if (<= a 5.9e-148)
       (* t (/ (- y z) (- a z)))
       (if (<= a 1e-8) (* y (/ (- t x) (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (t / a));
	double tmp;
	if (a <= -1.9e+116) {
		tmp = t_1;
	} else if (a <= 5.9e-148) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 1e-8) {
		tmp = y * ((t - x) / (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 / a))
    if (a <= (-1.9d+116)) then
        tmp = t_1
    else if (a <= 5.9d-148) then
        tmp = t * ((y - z) / (a - z))
    else if (a <= 1d-8) then
        tmp = y * ((t - x) / (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 / a));
	double tmp;
	if (a <= -1.9e+116) {
		tmp = t_1;
	} else if (a <= 5.9e-148) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 1e-8) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * (t / a))
	tmp = 0
	if a <= -1.9e+116:
		tmp = t_1
	elif a <= 5.9e-148:
		tmp = t * ((y - z) / (a - z))
	elif a <= 1e-8:
		tmp = y * ((t - x) / (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(t / a)))
	tmp = 0.0
	if (a <= -1.9e+116)
		tmp = t_1;
	elseif (a <= 5.9e-148)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (a <= 1e-8)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(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 / a));
	tmp = 0.0;
	if (a <= -1.9e+116)
		tmp = t_1;
	elseif (a <= 5.9e-148)
		tmp = t * ((y - z) / (a - z));
	elseif (a <= 1e-8)
		tmp = y * ((t - x) / (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[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.9e+116], t$95$1, If[LessEqual[a, 5.9e-148], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e-8], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.8999999999999999e116 or 1e-8 < a

   1. Initial program 86.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 75.6%

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

   5. Simplified 75.6%

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

   6. Taylor expanded in a around inf

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

   8. Simplified 67.1%

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

   if -1.8999999999999999e116 < a < 5.90000000000000016e-148

   1. Initial program 67.5%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 51.6%

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

   5. Simplified 51.6%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 61.3%

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

   7. Applied egg-rr 61.3%

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

   if 5.90000000000000016e-148 < a < 1e-8

   1. Initial program 81.3%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 68.0%

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

   5. Simplified 68.0%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 71.5%

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

   7. Applied egg-rr 71.5%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+116}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 5.9 \cdot 10^{-148}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 10^{-8}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{a - z}{y - z}}\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{-74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+41}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (/ (- a z) (- y z)))))
   (if (<= z -2.5e-74) t_1 (if (<= z 2.6e+41) (+ x (* (- t x) (/ y a))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / ((a - z) / (y - z));
	double tmp;
	if (z <= -2.5e-74) {
		tmp = t_1;
	} else if (z <= 2.6e+41) {
		tmp = x + ((t - x) * (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 / ((a - z) / (y - z))
    if (z <= (-2.5d-74)) then
        tmp = t_1
    else if (z <= 2.6d+41) then
        tmp = x + ((t - x) * (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 / ((a - z) / (y - z));
	double tmp;
	if (z <= -2.5e-74) {
		tmp = t_1;
	} else if (z <= 2.6e+41) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / ((a - z) / (y - z))
	tmp = 0
	if z <= -2.5e-74:
		tmp = t_1
	elif z <= 2.6e+41:
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(Float64(a - z) / Float64(y - z)))
	tmp = 0.0
	if (z <= -2.5e-74)
		tmp = t_1;
	elseif (z <= 2.6e+41)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t / ((a - z) / (y - z));
	tmp = 0.0;
	if (z <= -2.5e-74)
		tmp = t_1;
	elseif (z <= 2.6e+41)
		tmp = x + ((t - x) * (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[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e-74], t$95$1, If[LessEqual[z, 2.6e+41], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.49999999999999999e-74 or 2.6000000000000001e41 < z

   1. Initial program 65.8%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 43.1%

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

   5. Simplified 43.1%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 60.9%

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

   7. Applied egg-rr 60.9%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 60.9%

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

   9. Applied egg-rr 60.9%

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

   if -2.49999999999999999e-74 < z < 2.6000000000000001e41

   1. Initial program 92.0%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 93.5%

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

   4. Applied egg-rr 93.5%

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

   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 78.4%

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

   7. Simplified 78.4%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-74}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+41}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{-74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+46}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -2.5e-74)
     t_1
     (if (<= z 1.02e+46) (+ x (* (- t x) (/ y a))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -2.5e-74) {
		tmp = t_1;
	} else if (z <= 1.02e+46) {
		tmp = x + ((t - x) * (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 * ((y - z) / (a - z))
    if (z <= (-2.5d-74)) then
        tmp = t_1
    else if (z <= 1.02d+46) then
        tmp = x + ((t - x) * (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 * ((y - z) / (a - z));
	double tmp;
	if (z <= -2.5e-74) {
		tmp = t_1;
	} else if (z <= 1.02e+46) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -2.5e-74:
		tmp = t_1
	elif z <= 1.02e+46:
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -2.5e-74)
		tmp = t_1;
	elseif (z <= 1.02e+46)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -2.5e-74)
		tmp = t_1;
	elseif (z <= 1.02e+46)
		tmp = x + ((t - x) * (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[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e-74], t$95$1, If[LessEqual[z, 1.02e+46], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.49999999999999999e-74 or 1.0199999999999999e46 < z

   1. Initial program 65.8%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 43.1%

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

   5. Simplified 43.1%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 60.9%

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

   7. Applied egg-rr 60.9%

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

   if -2.49999999999999999e-74 < z < 1.0199999999999999e46

   1. Initial program 92.0%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 93.5%

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

   4. Applied egg-rr 93.5%

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

   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 78.4%

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

   7. Simplified 78.4%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-74}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+46}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;y \leq -4 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+64}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z)))))
   (if (<= y -4e-19) t_1 (if (<= y 2.5e+64) (* t (/ (- y z) (- a z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -4e-19) {
		tmp = t_1;
	} else if (y <= 2.5e+64) {
		tmp = t * ((y - z) / (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 = y * ((t - x) / (a - z))
    if (y <= (-4d-19)) then
        tmp = t_1
    else if (y <= 2.5d+64) then
        tmp = t * ((y - z) / (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 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -4e-19) {
		tmp = t_1;
	} else if (y <= 2.5e+64) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	tmp = 0
	if y <= -4e-19:
		tmp = t_1
	elif y <= 2.5e+64:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	tmp = 0.0
	if (y <= -4e-19)
		tmp = t_1;
	elseif (y <= 2.5e+64)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / (a - z));
	tmp = 0.0;
	if (y <= -4e-19)
		tmp = t_1;
	elseif (y <= 2.5e+64)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4e-19], t$95$1, If[LessEqual[y, 2.5e+64], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.9999999999999999e-19 or 2.5e64 < y

   1. Initial program 83.4%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 58.5%

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

   5. Simplified 58.5%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 69.9%

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

   7. Applied egg-rr 69.9%

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

   if -3.9999999999999999e-19 < y < 2.5e64

   1. Initial program 74.0%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 42.0%

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

   5. Simplified 42.0%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 53.6%

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

   7. Applied egg-rr 53.6%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-19}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+64}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 56.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+63}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z)))))
   (if (<= y -1.5e-44) t_1 (if (<= y 8.5e+63) (+ x t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -1.5e-44) {
		tmp = t_1;
	} else if (y <= 8.5e+63) {
		tmp = 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 = y * ((t - x) / (a - z))
    if (y <= (-1.5d-44)) then
        tmp = t_1
    else if (y <= 8.5d+63) then
        tmp = 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 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -1.5e-44) {
		tmp = t_1;
	} else if (y <= 8.5e+63) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	tmp = 0
	if y <= -1.5e-44:
		tmp = t_1
	elif y <= 8.5e+63:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	tmp = 0.0
	if (y <= -1.5e-44)
		tmp = t_1;
	elseif (y <= 8.5e+63)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / (a - z));
	tmp = 0.0;
	if (y <= -1.5e-44)
		tmp = t_1;
	elseif (y <= 8.5e+63)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.5e-44], t$95$1, If[LessEqual[y, 8.5e+63], N[(x + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5000000000000001e-44 or 8.5000000000000004e63 < y

   1. Initial program 83.8%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 57.8%

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

   5. Simplified 57.8%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 68.9%

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

   7. Applied egg-rr 68.9%

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

   if -1.5000000000000001e-44 < y < 8.5000000000000004e63

   1. Initial program 73.5%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 68.4%

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

   5. Simplified 68.4%

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

   6. Taylor expanded in z around inf

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

   8. Simplified 50.0%

      \[\leadsto x + \color{blue}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-44}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+63}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 56.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+64}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- t x) (/ y (- a z)))))
   (if (<= y -1.9e-44) t_1 (if (<= y 5.1e+64) (+ x t) 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 (y <= -1.9e-44) {
		tmp = t_1;
	} else if (y <= 5.1e+64) {
		tmp = 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 = (t - x) * (y / (a - z))
    if (y <= (-1.9d-44)) then
        tmp = t_1
    else if (y <= 5.1d+64) then
        tmp = 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 = (t - x) * (y / (a - z));
	double tmp;
	if (y <= -1.9e-44) {
		tmp = t_1;
	} else if (y <= 5.1e+64) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - x) * (y / (a - z))
	tmp = 0
	if y <= -1.9e-44:
		tmp = t_1
	elif y <= 5.1e+64:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (y <= -1.9e-44)
		tmp = t_1;
	elseif (y <= 5.1e+64)
		tmp = Float64(x + t);
	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 (y <= -1.9e-44)
		tmp = t_1;
	elseif (y <= 5.1e+64)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.9e-44], t$95$1, If[LessEqual[y, 5.1e+64], N[(x + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9e-44 or 5.10000000000000024e64 < y

   1. Initial program 83.8%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 57.8%

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

   5. Simplified 57.8%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 67.9%

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

   7. Applied egg-rr 67.9%

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

   if -1.9e-44 < y < 5.10000000000000024e64

   1. Initial program 73.5%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 68.4%

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

   5. Simplified 68.4%

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

   6. Taylor expanded in z around inf

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

   8. Simplified 50.0%

      \[\leadsto x + \color{blue}{t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 51.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+116}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-36}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.9e+116)
   x
   (if (<= a 1.15e-36) (* t (- 1.0 (/ y z))) (+ x (/ (* y t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.9e+116) {
		tmp = x;
	} else if (a <= 1.15e-36) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + ((y * t) / 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 <= (-1.9d+116)) then
        tmp = x
    else if (a <= 1.15d-36) then
        tmp = t * (1.0d0 - (y / z))
    else
        tmp = x + ((y * t) / 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 <= -1.9e+116) {
		tmp = x;
	} else if (a <= 1.15e-36) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.9e+116:
		tmp = x
	elif a <= 1.15e-36:
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.9e+116)
		tmp = x;
	elseif (a <= 1.15e-36)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.9e+116)
		tmp = x;
	elseif (a <= 1.15e-36)
		tmp = t * (1.0 - (y / z));
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.9e+116], x, If[LessEqual[a, 1.15e-36], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.8999999999999999e116

   1. Initial program 81.7%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 55.1%

      \[\leadsto \color{blue}{x} \]

   if -1.8999999999999999e116 < a < 1.14999999999999998e-36

   1. Initial program 70.4%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 49.2%

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

   5. Simplified 49.2%

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

   6. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

      4. mul-1-neg N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. *-inverses N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

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

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

      13. mul-1-neg N/A

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

      14. unsub-neg N/A

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

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

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

      16. /-lowering-/.f64 51.2%

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

   8. Simplified 51.2%

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

   if 1.14999999999999998e-36 < a

   1. Initial program 86.3%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 74.2%

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

   5. Simplified 74.2%

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

   6. Taylor expanded in z around 0

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

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

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

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

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

      3. *-lowering-*.f64 55.0%

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

   8. Simplified 55.0%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+116}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-36}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 48.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+117}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 0.124:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.15e+117) x (if (<= a 0.124) (* t (- 1.0 (/ y z))) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.15e+117) {
		tmp = x;
	} else if (a <= 0.124) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.15d+117)) then
        tmp = x
    else if (a <= 0.124d0) then
        tmp = t * (1.0d0 - (y / z))
    else
        tmp = x
    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 <= -1.15e+117) {
		tmp = x;
	} else if (a <= 0.124) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.15e+117:
		tmp = x
	elif a <= 0.124:
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.15e+117)
		tmp = x;
	elseif (a <= 0.124)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.15e+117)
		tmp = x;
	elseif (a <= 0.124)
		tmp = t * (1.0 - (y / z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.15e+117], x, If[LessEqual[a, 0.124], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.14999999999999994e117 or 0.124 < a

   1. Initial program 86.4%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 46.8%

      \[\leadsto \color{blue}{x} \]

   if -1.14999999999999994e117 < a < 0.124

   1. Initial program 70.3%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

      4. mul-1-neg N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. *-inverses N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

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

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

      13. mul-1-neg N/A

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

      14. unsub-neg N/A

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

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

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

      16. /-lowering-/.f64 49.3%

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

   8. Simplified 49.3%

      \[\leadsto \color{blue}{t \cdot \left(1 - \frac{y}{z}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 39.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;y \leq -5.4 \cdot 10^{+123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 10^{+139}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= y -5.4e+123) t_1 (if (<= y 1e+139) (+ x t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (y <= -5.4e+123) {
		tmp = t_1;
	} else if (y <= 1e+139) {
		tmp = 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 = t * (y / a)
    if (y <= (-5.4d+123)) then
        tmp = t_1
    else if (y <= 1d+139) then
        tmp = 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 = t * (y / a);
	double tmp;
	if (y <= -5.4e+123) {
		tmp = t_1;
	} else if (y <= 1e+139) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if y <= -5.4e+123:
		tmp = t_1
	elif y <= 1e+139:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (y <= -5.4e+123)
		tmp = t_1;
	elseif (y <= 1e+139)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (y <= -5.4e+123)
		tmp = t_1;
	elseif (y <= 1e+139)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.4e+123], t$95$1, If[LessEqual[y, 1e+139], N[(x + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.40000000000000026e123 or 1.00000000000000003e139 < y

   1. Initial program 87.3%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 36.1%

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

   5. Simplified 36.1%

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

   6. Taylor expanded in y around inf

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

   8. Simplified 30.6%

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

   9. Taylor expanded in a around inf

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

       1. associate-/l* N/A

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

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

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

       3. /-lowering-/.f64 34.1%

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

   11. Simplified 34.1%

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

   if -5.40000000000000026e123 < y < 1.00000000000000003e139

   1. Initial program 74.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 65.7%

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

   5. Simplified 65.7%

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

   6. Taylor expanded in z around inf

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

   8. Simplified 47.1%

      \[\leadsto x + \color{blue}{t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 38.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+116}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 0.115:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.9e+116) x (if (<= a 0.115) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.9e+116) {
		tmp = x;
	} else if (a <= 0.115) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.9d+116)) then
        tmp = x
    else if (a <= 0.115d0) then
        tmp = t
    else
        tmp = x
    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 <= -1.9e+116) {
		tmp = x;
	} else if (a <= 0.115) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.9e+116:
		tmp = x
	elif a <= 0.115:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.9e+116)
		tmp = x;
	elseif (a <= 0.115)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.9e+116)
		tmp = x;
	elseif (a <= 0.115)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.9e+116], x, If[LessEqual[a, 0.115], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.8999999999999999e116 or 0.115000000000000005 < a

   1. Initial program 86.4%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 46.8%

      \[\leadsto \color{blue}{x} \]

   if -1.8999999999999999e116 < a < 0.115000000000000005

   1. Initial program 70.3%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Simplified 38.0%

      \[\leadsto \color{blue}{t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 24.9% 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 78.0%

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

3. Taylor expanded in z around inf

   \[\leadsto \color{blue}{t} \]
4. Step-by-step derivation

5. Simplified 27.8%

   \[\leadsto \color{blue}{t} \]
6. Add Preprocessing

Alternative 19: 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 78.0%

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

3. Taylor expanded in t around 0

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

   1. mul-1-neg N/A

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

   2. distribute-neg-frac2 N/A

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

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

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

   4. *-commutative N/A

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

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

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

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

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

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

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

   8. --lowering--.f64 38.7%

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

5. Simplified 38.7%

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

6. Taylor expanded in z around inf

   \[\leadsto \color{blue}{x + -1 \cdot x} \]
7. Step-by-step derivation

   1. distribute-rgt1-in N/A

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

   2. metadata-eval N/A

      \[\leadsto 0 \cdot x \]

   3. mul0-lft 2.9%

      \[\leadsto 0 \]

8. Simplified 2.9%

   \[\leadsto \color{blue}{0} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024152 
(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)))))