Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.0% → 86.7%

Time: 11.1s

Alternatives: 22

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.0% 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: 86.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+111}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-1, t, x\right), \frac{y - a}{z}, t\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+168}:\\ \;\;\;\;x + \frac{y - z}{\frac{z - a}{x - t}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.9e+111)
   (fma (fma -1.0 t x) (/ (- y a) z) t)
   (if (<= z 1.55e+168)
     (+ x (/ (- y z) (/ (- z a) (- x t))))
     (- t (* (/ (- t x) z) (- y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.9e+111) {
		tmp = fma(fma(-1.0, t, x), ((y - a) / z), t);
	} else if (z <= 1.55e+168) {
		tmp = x + ((y - z) / ((z - a) / (x - t)));
	} else {
		tmp = t - (((t - x) / z) * (y - a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.9e+111)
		tmp = fma(fma(-1.0, t, x), Float64(Float64(y - a) / z), t);
	elseif (z <= 1.55e+168)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(z - a) / Float64(x - t))));
	else
		tmp = Float64(t - Float64(Float64(Float64(t - x) / z) * Float64(y - a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.9e+111], N[(N[(-1.0 * t + x), $MachinePrecision] * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] + t), $MachinePrecision], If[LessEqual[z, 1.55e+168], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.89999999999999988e111

   1. Initial program 48.2%

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

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 90.2%

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

   if -1.89999999999999988e111 < z < 1.54999999999999998e168

   1. Initial program 89.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

      5. lower-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. lower-/.f64 N/A

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

      8. neg-sub0 N/A

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

      9. lift--.f64 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. associate--r+ N/A

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

      13. neg-sub0 N/A

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

      14. remove-double-neg N/A

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

      15. lower--.f64 N/A

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

      16. neg-sub0 N/A

          \[\leadsto x + \frac{y - z}{\frac{z - a}{\color{blue}{0 - \left(t - x\right)}}} \]

      17. lift--.f64 N/A

          \[\leadsto x + \frac{y - z}{\frac{z - a}{0 - \color{blue}{\left(t - x\right)}}} \]

      18. sub-neg N/A

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

      19. +-commutative N/A

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

      20. associate--r+ N/A

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

      21. neg-sub0 N/A

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

      22. remove-double-neg N/A

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

      23. lower--.f64 89.7

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

   4. Applied rewrites 89.7%

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

   if 1.54999999999999998e168 < z

   1. Initial program 47.4%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 35.3

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

   5. Applied rewrites 35.3%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 3.0%

      \[\leadsto x + \left(-x\right) \]

   9. Taylor expanded in z around inf

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

       1. associate--l+ N/A

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

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

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

       3. div-sub N/A

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

       4. mul-1-neg N/A

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

       5. unsub-neg N/A

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

       6. lower--.f64 N/A

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

       7. div-sub N/A

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

       8. associate-/l* N/A

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

       9. associate-/l* N/A

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

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

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

       11. lower-*.f64 N/A

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

       12. lower-/.f64 N/A

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

       13. lower--.f64 N/A

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

       14. lower--.f64 93.7

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

   11. Applied rewrites 93.7%

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

Alternative 2: 77.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+15}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-1, t, x\right), \frac{y - a}{z}, t\right)\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-162}:\\ \;\;\;\;x + \frac{y - z}{a} \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+134}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ t (- a z))))))
   (if (<= z -6.5e+15)
     (fma (fma -1.0 t x) (/ (- y a) z) t)
     (if (<= z -4e-74)
       t_1
       (if (<= z 8e-162)
         (+ x (* (/ (- y z) a) (- t x)))
         (if (<= z 6.4e+134) t_1 (- t (* (/ (- t x) z) (- y a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (t / (a - z)));
	double tmp;
	if (z <= -6.5e+15) {
		tmp = fma(fma(-1.0, t, x), ((y - a) / z), t);
	} else if (z <= -4e-74) {
		tmp = t_1;
	} else if (z <= 8e-162) {
		tmp = x + (((y - z) / a) * (t - x));
	} else if (z <= 6.4e+134) {
		tmp = t_1;
	} else {
		tmp = t - (((t - x) / z) * (y - a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))))
	tmp = 0.0
	if (z <= -6.5e+15)
		tmp = fma(fma(-1.0, t, x), Float64(Float64(y - a) / z), t);
	elseif (z <= -4e-74)
		tmp = t_1;
	elseif (z <= 8e-162)
		tmp = Float64(x + Float64(Float64(Float64(y - z) / a) * Float64(t - x)));
	elseif (z <= 6.4e+134)
		tmp = t_1;
	else
		tmp = Float64(t - Float64(Float64(Float64(t - x) / z) * Float64(y - a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+15], N[(N[(-1.0 * t + x), $MachinePrecision] * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] + t), $MachinePrecision], If[LessEqual[z, -4e-74], t$95$1, If[LessEqual[z, 8e-162], N[(x + N[(N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.4e+134], t$95$1, N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.5e15

   1. Initial program 60.8%

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

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 84.9%

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

   if -6.5e15 < z < -3.99999999999999983e-74 or 7.99999999999999963e-162 < z < 6.4000000000000001e134

   1. Initial program 89.7%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 77.5

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

   5. Applied rewrites 77.5%

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

   if -3.99999999999999983e-74 < z < 7.99999999999999963e-162

   1. Initial program 90.6%

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

   3. Taylor expanded in a around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 85.6

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

   5. Applied rewrites 85.6%

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

   if 6.4000000000000001e134 < z

   1. Initial program 54.7%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 32.8

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

   5. Applied rewrites 32.8%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 2.9%

      \[\leadsto x + \left(-x\right) \]

   9. Taylor expanded in z around inf

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

       1. associate--l+ N/A

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

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

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

       3. div-sub N/A

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

       4. mul-1-neg N/A

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

       5. unsub-neg N/A

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

       6. lower--.f64 N/A

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

       7. div-sub N/A

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

       8. associate-/l* N/A

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

       9. associate-/l* N/A

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

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

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

       11. lower-*.f64 N/A

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

       12. lower-/.f64 N/A

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

       13. lower--.f64 N/A

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

       14. lower--.f64 90.2

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

   11. Applied rewrites 90.2%

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

Alternative 3: 77.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t}{a - z}\\ t_2 := t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-162}:\\ \;\;\;\;x + \frac{y - z}{a} \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+134}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ t (- a z)))))
        (t_2 (- t (* (/ (- t x) z) (- y a)))))
   (if (<= z -6.5e+15)
     t_2
     (if (<= z -4e-74)
       t_1
       (if (<= z 8e-162)
         (+ x (* (/ (- y z) a) (- t x)))
         (if (<= z 6.4e+134) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (t / (a - z)));
	double t_2 = t - (((t - x) / z) * (y - a));
	double tmp;
	if (z <= -6.5e+15) {
		tmp = t_2;
	} else if (z <= -4e-74) {
		tmp = t_1;
	} else if (z <= 8e-162) {
		tmp = x + (((y - z) / a) * (t - x));
	} else if (z <= 6.4e+134) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 + ((y - z) * (t / (a - z)))
    t_2 = t - (((t - x) / z) * (y - a))
    if (z <= (-6.5d+15)) then
        tmp = t_2
    else if (z <= (-4d-74)) then
        tmp = t_1
    else if (z <= 8d-162) then
        tmp = x + (((y - z) / a) * (t - x))
    else if (z <= 6.4d+134) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (t / (a - z)));
	double t_2 = t - (((t - x) / z) * (y - a));
	double tmp;
	if (z <= -6.5e+15) {
		tmp = t_2;
	} else if (z <= -4e-74) {
		tmp = t_1;
	} else if (z <= 8e-162) {
		tmp = x + (((y - z) / a) * (t - x));
	} else if (z <= 6.4e+134) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * (t / (a - z)))
	t_2 = t - (((t - x) / z) * (y - a))
	tmp = 0
	if z <= -6.5e+15:
		tmp = t_2
	elif z <= -4e-74:
		tmp = t_1
	elif z <= 8e-162:
		tmp = x + (((y - z) / a) * (t - x))
	elif z <= 6.4e+134:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))))
	t_2 = Float64(t - Float64(Float64(Float64(t - x) / z) * Float64(y - a)))
	tmp = 0.0
	if (z <= -6.5e+15)
		tmp = t_2;
	elseif (z <= -4e-74)
		tmp = t_1;
	elseif (z <= 8e-162)
		tmp = Float64(x + Float64(Float64(Float64(y - z) / a) * Float64(t - x)));
	elseif (z <= 6.4e+134)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * (t / (a - z)));
	t_2 = t - (((t - x) / z) * (y - a));
	tmp = 0.0;
	if (z <= -6.5e+15)
		tmp = t_2;
	elseif (z <= -4e-74)
		tmp = t_1;
	elseif (z <= 8e-162)
		tmp = x + (((y - z) / a) * (t - x));
	elseif (z <= 6.4e+134)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+15], t$95$2, If[LessEqual[z, -4e-74], t$95$1, If[LessEqual[z, 8e-162], N[(x + N[(N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.4e+134], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5e15 or 6.4000000000000001e134 < z

   1. Initial program 58.3%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 35.4

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

   5. Applied rewrites 35.4%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 3.2%

      \[\leadsto x + \left(-x\right) \]

   9. Taylor expanded in z around inf

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

       1. associate--l+ N/A

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

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

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

       3. div-sub N/A

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

       4. mul-1-neg N/A

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

       5. unsub-neg N/A

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

       6. lower--.f64 N/A

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

       7. div-sub N/A

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

       8. associate-/l* N/A

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

       9. associate-/l* N/A

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

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

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

       11. lower-*.f64 N/A

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

       12. lower-/.f64 N/A

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

       13. lower--.f64 N/A

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

       14. lower--.f64 87.0

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

   11. Applied rewrites 87.0%

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

   if -6.5e15 < z < -3.99999999999999983e-74 or 7.99999999999999963e-162 < z < 6.4000000000000001e134

   1. Initial program 89.7%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 77.5

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

   5. Applied rewrites 77.5%

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

   if -3.99999999999999983e-74 < z < 7.99999999999999963e-162

   1. Initial program 90.6%

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

   3. Taylor expanded in a around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 85.6

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

   5. Applied rewrites 85.6%

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

Alternative 4: 45.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, \frac{-y}{a}, x\right)\\ \mathbf{if}\;a \leq -9 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-90}:\\ \;\;\;\;\frac{t - x}{a} \cdot y\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-158}:\\ \;\;\;\;\frac{x - t}{z} \cdot y\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+90}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma x (/ (- y) a) x)))
   (if (<= a -9e-15)
     t_1
     (if (<= a -3.1e-90)
       (* (/ (- t x) a) y)
       (if (<= a 1.75e-158)
         (* (/ (- x t) z) y)
         (if (<= a 1.15e+90) (* (- t x) (/ y a)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(x, (-y / a), x);
	double tmp;
	if (a <= -9e-15) {
		tmp = t_1;
	} else if (a <= -3.1e-90) {
		tmp = ((t - x) / a) * y;
	} else if (a <= 1.75e-158) {
		tmp = ((x - t) / z) * y;
	} else if (a <= 1.15e+90) {
		tmp = (t - x) * (y / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(x, Float64(Float64(-y) / a), x)
	tmp = 0.0
	if (a <= -9e-15)
		tmp = t_1;
	elseif (a <= -3.1e-90)
		tmp = Float64(Float64(Float64(t - x) / a) * y);
	elseif (a <= 1.75e-158)
		tmp = Float64(Float64(Float64(x - t) / z) * y);
	elseif (a <= 1.15e+90)
		tmp = Float64(Float64(t - x) * Float64(y / a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[((-y) / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -9e-15], t$95$1, If[LessEqual[a, -3.1e-90], N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[a, 1.75e-158], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[a, 1.15e+90], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.9999999999999995e-15 or 1.15e90 < a

   1. Initial program 88.3%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 88.4

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

      6. lift-/.f64 N/A

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

      7. frac-2neg N/A

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

      8. lower-/.f64 N/A

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

      9. neg-sub0 N/A

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

      10. lift--.f64 N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. associate--r+ N/A

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

      14. neg-sub0 N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. neg-sub0 N/A

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

      18. lift--.f64 N/A

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

      19. sub-neg N/A

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

      20. +-commutative N/A

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

      21. associate--r+ N/A

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

      22. neg-sub0 N/A

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

      23. remove-double-neg N/A

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

      24. lower--.f64 88.4

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

   4. Applied rewrites 88.4%

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

   5. Taylor expanded in x around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. distribute-lft-in N/A

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

      4. *-rgt-identity N/A

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

      5. associate-/l* N/A

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

      6. +-commutative N/A

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

      7. associate-/l* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower--.f64 62.4

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

   7. Applied rewrites 62.4%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 59.8%

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

   if -8.9999999999999995e-15 < a < -3.1000000000000001e-90

   1. Initial program 76.4%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 48.0

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

   5. Applied rewrites 48.0%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 49.3%

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

   if -3.1000000000000001e-90 < a < 1.75000000000000006e-158

   1. Initial program 69.4%

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

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 87.9%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 44.0%

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

   if 1.75000000000000006e-158 < a < 1.15e90

   1. Initial program 68.0%

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

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 46.9

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

   5. Applied rewrites 46.9%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 38.0%

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

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{-15}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{-y}{a}, x\right)\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-90}:\\ \;\;\;\;\frac{t - x}{a} \cdot y\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-158}:\\ \;\;\;\;\frac{x - t}{z} \cdot y\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+90}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{-y}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 45.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-z, \frac{t}{a}, x\right)\\ \mathbf{if}\;a \leq -2.7 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-90}:\\ \;\;\;\;\frac{t - x}{a} \cdot y\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-158}:\\ \;\;\;\;\frac{x - t}{z} \cdot y\\ \mathbf{elif}\;a \leq 10^{+99}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- z) (/ t a) x)))
   (if (<= a -2.7e-8)
     t_1
     (if (<= a -3.1e-90)
       (* (/ (- t x) a) y)
       (if (<= a 1.75e-158)
         (* (/ (- x t) z) y)
         (if (<= a 1e+99) (* (- t x) (/ y a)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(-z, (t / a), x);
	double tmp;
	if (a <= -2.7e-8) {
		tmp = t_1;
	} else if (a <= -3.1e-90) {
		tmp = ((t - x) / a) * y;
	} else if (a <= 1.75e-158) {
		tmp = ((x - t) / z) * y;
	} else if (a <= 1e+99) {
		tmp = (t - x) * (y / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(-z), Float64(t / a), x)
	tmp = 0.0
	if (a <= -2.7e-8)
		tmp = t_1;
	elseif (a <= -3.1e-90)
		tmp = Float64(Float64(Float64(t - x) / a) * y);
	elseif (a <= 1.75e-158)
		tmp = Float64(Float64(Float64(x - t) / z) * y);
	elseif (a <= 1e+99)
		tmp = Float64(Float64(t - x) * Float64(y / a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-z) * N[(t / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -2.7e-8], t$95$1, If[LessEqual[a, -3.1e-90], N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[a, 1.75e-158], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[a, 1e+99], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.70000000000000002e-8 or 9.9999999999999997e98 < a

   1. Initial program 89.0%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 77.7

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

   5. Applied rewrites 77.7%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 72.8%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 59.4%

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

   if -2.70000000000000002e-8 < a < -3.1000000000000001e-90

   1. Initial program 76.4%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 48.0

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

   5. Applied rewrites 48.0%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 49.3%

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

   if -3.1000000000000001e-90 < a < 1.75000000000000006e-158

   1. Initial program 69.4%

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

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 87.9%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 44.0%

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

   if 1.75000000000000006e-158 < a < 9.9999999999999997e98

   1. Initial program 67.4%

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

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 45.1

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

   5. Applied rewrites 45.1%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 36.6%

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

Alternative 6: 86.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.72 \cdot 10^{+83}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-1, t, x\right), \frac{y - a}{z}, t\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+168}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.72e+83)
   (fma (fma -1.0 t x) (/ (- y a) z) t)
   (if (<= z 1.55e+168)
     (+ x (* (- y z) (/ (- t x) (- a z))))
     (- t (* (/ (- t x) z) (- y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.72e+83) {
		tmp = fma(fma(-1.0, t, x), ((y - a) / z), t);
	} else if (z <= 1.55e+168) {
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	} else {
		tmp = t - (((t - x) / z) * (y - a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.72e+83)
		tmp = fma(fma(-1.0, t, x), Float64(Float64(y - a) / z), t);
	elseif (z <= 1.55e+168)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))));
	else
		tmp = Float64(t - Float64(Float64(Float64(t - x) / z) * Float64(y - a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.72e+83], N[(N[(-1.0 * t + x), $MachinePrecision] * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] + t), $MachinePrecision], If[LessEqual[z, 1.55e+168], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.72000000000000006e83

   1. Initial program 53.8%

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

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 91.3%

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

   if -1.72000000000000006e83 < z < 1.54999999999999998e168

   1. Initial program 89.3%

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

   if 1.54999999999999998e168 < z

   1. Initial program 47.4%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 35.3

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

   5. Applied rewrites 35.3%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 3.0%

      \[\leadsto x + \left(-x\right) \]

   9. Taylor expanded in z around inf

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

       1. associate--l+ N/A

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

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

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

       3. div-sub N/A

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

       4. mul-1-neg N/A

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

       5. unsub-neg N/A

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

       6. lower--.f64 N/A

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

       7. div-sub N/A

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

       8. associate-/l* N/A

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

       9. associate-/l* N/A

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

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

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

       11. lower-*.f64 N/A

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

       12. lower-/.f64 N/A

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

       13. lower--.f64 N/A

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

       14. lower--.f64 93.7

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

   11. Applied rewrites 93.7%

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

Alternative 7: 86.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.72 \cdot 10^{+83}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-1, t, x\right), \frac{y - a}{z}, t\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+168}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z - a}, y - z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.72e+83)
   (fma (fma -1.0 t x) (/ (- y a) z) t)
   (if (<= z 1.55e+168)
     (fma (/ (- x t) (- z a)) (- y z) x)
     (- t (* (/ (- t x) z) (- y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.72e+83) {
		tmp = fma(fma(-1.0, t, x), ((y - a) / z), t);
	} else if (z <= 1.55e+168) {
		tmp = fma(((x - t) / (z - a)), (y - z), x);
	} else {
		tmp = t - (((t - x) / z) * (y - a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.72e+83)
		tmp = fma(fma(-1.0, t, x), Float64(Float64(y - a) / z), t);
	elseif (z <= 1.55e+168)
		tmp = fma(Float64(Float64(x - t) / Float64(z - a)), Float64(y - z), x);
	else
		tmp = Float64(t - Float64(Float64(Float64(t - x) / z) * Float64(y - a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.72e+83], N[(N[(-1.0 * t + x), $MachinePrecision] * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] + t), $MachinePrecision], If[LessEqual[z, 1.55e+168], N[(N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision], N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.72000000000000006e83

   1. Initial program 53.8%

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

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 91.3%

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

   if -1.72000000000000006e83 < z < 1.54999999999999998e168

   1. Initial program 89.3%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 89.3

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

      6. lift-/.f64 N/A

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

      7. frac-2neg N/A

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

      8. lower-/.f64 N/A

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

      9. neg-sub0 N/A

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

      10. lift--.f64 N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. associate--r+ N/A

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

      14. neg-sub0 N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. neg-sub0 N/A

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

      18. lift--.f64 N/A

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

      19. sub-neg N/A

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

      20. +-commutative N/A

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

      21. associate--r+ N/A

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

      22. neg-sub0 N/A

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

      23. remove-double-neg N/A

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

      24. lower--.f64 89.3

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

   4. Applied rewrites 89.3%

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

   if 1.54999999999999998e168 < z

   1. Initial program 47.4%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 35.3

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

   5. Applied rewrites 35.3%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 3.0%

      \[\leadsto x + \left(-x\right) \]

   9. Taylor expanded in z around inf

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

       1. associate--l+ N/A

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

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

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

       3. div-sub N/A

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

       4. mul-1-neg N/A

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

       5. unsub-neg N/A

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

       6. lower--.f64 N/A

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

       7. div-sub N/A

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

       8. associate-/l* N/A

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

       9. associate-/l* N/A

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

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

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

       11. lower-*.f64 N/A

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

       12. lower-/.f64 N/A

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

       13. lower--.f64 N/A

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

       14. lower--.f64 93.7

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

   11. Applied rewrites 93.7%

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

Alternative 8: 75.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+15} \lor \neg \left(z \leq 3.5 \cdot 10^{+74}\right):\\ \;\;\;\;t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a} \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6e+15) (not (<= z 3.5e+74)))
   (- t (* (/ (- t x) z) (- y a)))
   (+ x (* (/ (- y z) a) (- t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6e+15) || !(z <= 3.5e+74)) {
		tmp = t - (((t - x) / z) * (y - a));
	} else {
		tmp = x + (((y - z) / a) * (t - 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 ((z <= (-6d+15)) .or. (.not. (z <= 3.5d+74))) then
        tmp = t - (((t - x) / z) * (y - a))
    else
        tmp = x + (((y - z) / a) * (t - 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 ((z <= -6e+15) || !(z <= 3.5e+74)) {
		tmp = t - (((t - x) / z) * (y - a));
	} else {
		tmp = x + (((y - z) / a) * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6e+15) or not (z <= 3.5e+74):
		tmp = t - (((t - x) / z) * (y - a))
	else:
		tmp = x + (((y - z) / a) * (t - x))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6e+15) || !(z <= 3.5e+74))
		tmp = Float64(t - Float64(Float64(Float64(t - x) / z) * Float64(y - a)));
	else
		tmp = Float64(x + Float64(Float64(Float64(y - z) / a) * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6e+15) || ~((z <= 3.5e+74)))
		tmp = t - (((t - x) / z) * (y - a));
	else
		tmp = x + (((y - z) / a) * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6e+15], N[Not[LessEqual[z, 3.5e+74]], $MachinePrecision]], N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6e15 or 3.50000000000000014e74 < z

   1. Initial program 59.9%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 34.6

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

   5. Applied rewrites 34.6%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 3.2%

      \[\leadsto x + \left(-x\right) \]

   9. Taylor expanded in z around inf

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

       1. associate--l+ N/A

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

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

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

       3. div-sub N/A

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

       4. mul-1-neg N/A

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

       5. unsub-neg N/A

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

       6. lower--.f64 N/A

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

       7. div-sub N/A

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

       8. associate-/l* N/A

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

       9. associate-/l* N/A

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

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

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

       11. lower-*.f64 N/A

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

       12. lower-/.f64 N/A

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

       13. lower--.f64 N/A

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

       14. lower--.f64 84.6

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

   11. Applied rewrites 84.6%

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

   if -6e15 < z < 3.50000000000000014e74

   1. Initial program 90.9%

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

   3. Taylor expanded in a around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 74.9

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

   5. Applied rewrites 74.9%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+15} \lor \neg \left(z \leq 3.5 \cdot 10^{+74}\right):\\ \;\;\;\;t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a} \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+15} \lor \neg \left(z \leq 3.5 \cdot 10^{+74}\right):\\ \;\;\;\;t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6e+15) (not (<= z 3.5e+74)))
   (- t (* (/ (- t x) z) (- y a)))
   (fma (- y z) (/ (- t x) a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6e+15) || !(z <= 3.5e+74)) {
		tmp = t - (((t - x) / z) * (y - a));
	} else {
		tmp = fma((y - z), ((t - x) / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6e+15) || !(z <= 3.5e+74))
		tmp = Float64(t - Float64(Float64(Float64(t - x) / z) * Float64(y - a)));
	else
		tmp = fma(Float64(y - z), Float64(Float64(t - x) / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6e+15], N[Not[LessEqual[z, 3.5e+74]], $MachinePrecision]], N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6e15 or 3.50000000000000014e74 < z

   1. Initial program 59.9%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 34.6

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

   5. Applied rewrites 34.6%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 3.2%

      \[\leadsto x + \left(-x\right) \]

   9. Taylor expanded in z around inf

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

       1. associate--l+ N/A

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

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

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

       3. div-sub N/A

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

       4. mul-1-neg N/A

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

       5. unsub-neg N/A

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

       6. lower--.f64 N/A

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

       7. div-sub N/A

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

       8. associate-/l* N/A

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

       9. associate-/l* N/A

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

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

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

       11. lower-*.f64 N/A

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

       12. lower-/.f64 N/A

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

       13. lower--.f64 N/A

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

       14. lower--.f64 84.6

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

   11. Applied rewrites 84.6%

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

   if -6e15 < z < 3.50000000000000014e74

   1. Initial program 90.9%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 73.8

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

   5. Applied rewrites 73.8%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+15} \lor \neg \left(z \leq 3.5 \cdot 10^{+74}\right):\\ \;\;\;\;t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+77}:\\ \;\;\;\;\mathsf{fma}\left(-z, \frac{t}{a}, x\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z}, y, t\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+90}:\\ \;\;\;\;\frac{t - x}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{-y}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7.2e+77)
   (fma (- z) (/ t a) x)
   (if (<= a 2.3e+22)
     (fma (/ (- x t) z) y t)
     (if (<= a 1.15e+90) (* (/ (- t x) a) y) (fma x (/ (- y) a) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.2e+77) {
		tmp = fma(-z, (t / a), x);
	} else if (a <= 2.3e+22) {
		tmp = fma(((x - t) / z), y, t);
	} else if (a <= 1.15e+90) {
		tmp = ((t - x) / a) * y;
	} else {
		tmp = fma(x, (-y / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7.2e+77)
		tmp = fma(Float64(-z), Float64(t / a), x);
	elseif (a <= 2.3e+22)
		tmp = fma(Float64(Float64(x - t) / z), y, t);
	elseif (a <= 1.15e+90)
		tmp = Float64(Float64(Float64(t - x) / a) * y);
	else
		tmp = fma(x, Float64(Float64(-y) / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7.2e+77], N[((-z) * N[(t / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[a, 2.3e+22], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * y + t), $MachinePrecision], If[LessEqual[a, 1.15e+90], N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * y), $MachinePrecision], N[(x * N[((-y) / a), $MachinePrecision] + x), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.1999999999999996e77

   1. Initial program 85.9%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 81.0

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

   5. Applied rewrites 81.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 77.8%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 64.3%

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

   if -7.1999999999999996e77 < a < 2.3000000000000002e22

   1. Initial program 71.6%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 74.0%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 70.4%

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

   if 2.3000000000000002e22 < a < 1.15e90

   1. Initial program 77.6%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 75.3

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

   5. Applied rewrites 75.3%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 60.6%

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

   if 1.15e90 < a

   1. Initial program 90.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 90.8

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

      6. lift-/.f64 N/A

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

      7. frac-2neg N/A

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

      8. lower-/.f64 N/A

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

      9. neg-sub0 N/A

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

      10. lift--.f64 N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. associate--r+ N/A

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

      14. neg-sub0 N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. neg-sub0 N/A

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

      18. lift--.f64 N/A

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

      19. sub-neg N/A

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

      20. +-commutative N/A

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

      21. associate--r+ N/A

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

      22. neg-sub0 N/A

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

      23. remove-double-neg N/A

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

      24. lower--.f64 90.8

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

   4. Applied rewrites 90.8%

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

   5. Taylor expanded in x around inf

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

      1. associate--l+ N/A

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

      2. div-sub N/A

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

      3. distribute-lft-in N/A

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

      4. *-rgt-identity N/A

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

      5. associate-/l* N/A

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

      6. +-commutative N/A

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

      7. associate-/l* N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower--.f64 65.2

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

   7. Applied rewrites 65.2%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 63.1%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+77}:\\ \;\;\;\;\mathsf{fma}\left(-z, \frac{t}{a}, x\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z}, y, t\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+90}:\\ \;\;\;\;\frac{t - x}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{-y}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 38.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right)\\ \mathbf{if}\;z \leq -9 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-67}:\\ \;\;\;\;\frac{x - t}{z} \cdot y\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+140}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (- t x))))
   (if (<= z -9e+92)
     t_1
     (if (<= z -3.5e-67)
       (* (/ (- x t) z) y)
       (if (<= z 1.2e+140) (* (- t x) (/ y a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t - x);
	double tmp;
	if (z <= -9e+92) {
		tmp = t_1;
	} else if (z <= -3.5e-67) {
		tmp = ((x - t) / z) * y;
	} else if (z <= 1.2e+140) {
		tmp = (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 = x + (t - x)
    if (z <= (-9d+92)) then
        tmp = t_1
    else if (z <= (-3.5d-67)) then
        tmp = ((x - t) / z) * y
    else if (z <= 1.2d+140) then
        tmp = (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 = x + (t - x);
	double tmp;
	if (z <= -9e+92) {
		tmp = t_1;
	} else if (z <= -3.5e-67) {
		tmp = ((x - t) / z) * y;
	} else if (z <= 1.2e+140) {
		tmp = (t - x) * (y / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t - x)
	tmp = 0
	if z <= -9e+92:
		tmp = t_1
	elif z <= -3.5e-67:
		tmp = ((x - t) / z) * y
	elif z <= 1.2e+140:
		tmp = (t - x) * (y / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t - x))
	tmp = 0.0
	if (z <= -9e+92)
		tmp = t_1;
	elseif (z <= -3.5e-67)
		tmp = Float64(Float64(Float64(x - t) / z) * y);
	elseif (z <= 1.2e+140)
		tmp = 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 = x + (t - x);
	tmp = 0.0;
	if (z <= -9e+92)
		tmp = t_1;
	elseif (z <= -3.5e-67)
		tmp = ((x - t) / z) * y;
	elseif (z <= 1.2e+140)
		tmp = (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[(x + N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e+92], t$95$1, If[LessEqual[z, -3.5e-67], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[z, 1.2e+140], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.9999999999999998e92 or 1.2e140 < z

   1. Initial program 51.8%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 40.5

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

   5. Applied rewrites 40.5%

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

   if -8.9999999999999998e92 < z < -3.5e-67

   1. Initial program 90.3%

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

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 46.7%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 32.3%

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

   if -3.5e-67 < z < 1.2e140

   1. Initial program 88.9%

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

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 53.8

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

   5. Applied rewrites 53.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 40.4%

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

Alternative 12: 38.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right)\\ \mathbf{if}\;z \leq -9 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-67}:\\ \;\;\;\;\frac{x - t}{z} \cdot y\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+91}:\\ \;\;\;\;\frac{t - x}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (- t x))))
   (if (<= z -9e+92)
     t_1
     (if (<= z -3.5e-67)
       (* (/ (- x t) z) y)
       (if (<= z 5.6e+91) (* (/ (- t x) a) y) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t - x);
	double tmp;
	if (z <= -9e+92) {
		tmp = t_1;
	} else if (z <= -3.5e-67) {
		tmp = ((x - t) / z) * y;
	} else if (z <= 5.6e+91) {
		tmp = ((t - x) / a) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (t - x)
    if (z <= (-9d+92)) then
        tmp = t_1
    else if (z <= (-3.5d-67)) then
        tmp = ((x - t) / z) * y
    else if (z <= 5.6d+91) then
        tmp = ((t - x) / a) * y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t - x);
	double tmp;
	if (z <= -9e+92) {
		tmp = t_1;
	} else if (z <= -3.5e-67) {
		tmp = ((x - t) / z) * y;
	} else if (z <= 5.6e+91) {
		tmp = ((t - x) / a) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t - x)
	tmp = 0
	if z <= -9e+92:
		tmp = t_1
	elif z <= -3.5e-67:
		tmp = ((x - t) / z) * y
	elif z <= 5.6e+91:
		tmp = ((t - x) / a) * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t - x))
	tmp = 0.0
	if (z <= -9e+92)
		tmp = t_1;
	elseif (z <= -3.5e-67)
		tmp = Float64(Float64(Float64(x - t) / z) * y);
	elseif (z <= 5.6e+91)
		tmp = Float64(Float64(Float64(t - x) / 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);
	tmp = 0.0;
	if (z <= -9e+92)
		tmp = t_1;
	elseif (z <= -3.5e-67)
		tmp = ((x - t) / z) * y;
	elseif (z <= 5.6e+91)
		tmp = ((t - x) / a) * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e+92], t$95$1, If[LessEqual[z, -3.5e-67], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[z, 5.6e+91], N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.9999999999999998e92 or 5.5999999999999997e91 < z

   1. Initial program 54.7%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 38.1

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

   5. Applied rewrites 38.1%

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

   if -8.9999999999999998e92 < z < -3.5e-67

   1. Initial program 90.3%

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

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 46.7%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 32.3%

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

   if -3.5e-67 < z < 5.5999999999999997e91

   1. Initial program 90.1%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 75.3

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

   5. Applied rewrites 75.3%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 41.6%

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

Alternative 13: 34.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right)\\ \mathbf{if}\;z \leq -9 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{+15}:\\ \;\;\;\;\frac{x - t}{z} \cdot y\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+91}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (- t x))))
   (if (<= z -9e+92)
     t_1
     (if (<= z -4.1e+15)
       (* (/ (- x t) z) y)
       (if (<= z 5.6e+91) (* t (/ y (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t - x);
	double tmp;
	if (z <= -9e+92) {
		tmp = t_1;
	} else if (z <= -4.1e+15) {
		tmp = ((x - t) / z) * y;
	} else if (z <= 5.6e+91) {
		tmp = t * (y / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (t - x)
    if (z <= (-9d+92)) then
        tmp = t_1
    else if (z <= (-4.1d+15)) then
        tmp = ((x - t) / z) * y
    else if (z <= 5.6d+91) then
        tmp = t * (y / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t - x);
	double tmp;
	if (z <= -9e+92) {
		tmp = t_1;
	} else if (z <= -4.1e+15) {
		tmp = ((x - t) / z) * y;
	} else if (z <= 5.6e+91) {
		tmp = t * (y / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t - x)
	tmp = 0
	if z <= -9e+92:
		tmp = t_1
	elif z <= -4.1e+15:
		tmp = ((x - t) / z) * y
	elif z <= 5.6e+91:
		tmp = t * (y / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t - x))
	tmp = 0.0
	if (z <= -9e+92)
		tmp = t_1;
	elseif (z <= -4.1e+15)
		tmp = Float64(Float64(Float64(x - t) / z) * y);
	elseif (z <= 5.6e+91)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t - x);
	tmp = 0.0;
	if (z <= -9e+92)
		tmp = t_1;
	elseif (z <= -4.1e+15)
		tmp = ((x - t) / z) * y;
	elseif (z <= 5.6e+91)
		tmp = t * (y / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e+92], t$95$1, If[LessEqual[z, -4.1e+15], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[z, 5.6e+91], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.9999999999999998e92 or 5.5999999999999997e91 < z

   1. Initial program 54.7%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 38.1

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

   5. Applied rewrites 38.1%

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

   if -8.9999999999999998e92 < z < -4.1e15

   1. Initial program 87.5%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 69.9%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 51.4%

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

   if -4.1e15 < z < 5.5999999999999997e91

   1. Initial program 90.4%

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

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 50.3

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

   5. Applied rewrites 50.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 33.9%

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

Alternative 14: 74.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{+30} \lor \neg \left(a \leq 1.15 \cdot 10^{-38}\right):\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-1, t, x\right), \frac{y}{z}, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.65e+30) (not (<= a 1.15e-38)))
   (fma (- y z) (/ (- t x) a) x)
   (fma (fma -1.0 t x) (/ y z) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.65e+30) || !(a <= 1.15e-38)) {
		tmp = fma((y - z), ((t - x) / a), x);
	} else {
		tmp = fma(fma(-1.0, t, x), (y / z), t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.65e+30) || !(a <= 1.15e-38))
		tmp = fma(Float64(y - z), Float64(Float64(t - x) / a), x);
	else
		tmp = fma(fma(-1.0, t, x), Float64(y / z), t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.65e+30], N[Not[LessEqual[a, 1.15e-38]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], N[(N[(-1.0 * t + x), $MachinePrecision] * N[(y / z), $MachinePrecision] + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.65000000000000013e30 or 1.15000000000000001e-38 < a

   1. Initial program 86.5%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 76.5

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

   5. Applied rewrites 76.5%

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

   if -1.65000000000000013e30 < a < 1.15000000000000001e-38

   1. Initial program 69.7%

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

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 76.9%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 74.6%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-1, t, x\right), \frac{y}{\color{blue}{z}}, t\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{+30} \lor \neg \left(a \leq 1.15 \cdot 10^{-38}\right):\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-1, t, x\right), \frac{y}{z}, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 73.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{+30} \lor \neg \left(a \leq 1.15 \cdot 10^{-38}\right):\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z}, y, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.65e+30) (not (<= a 1.15e-38)))
   (fma (- y z) (/ (- t x) a) x)
   (fma (/ (- x t) z) y t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.65e+30) || !(a <= 1.15e-38)) {
		tmp = fma((y - z), ((t - x) / a), x);
	} else {
		tmp = fma(((x - t) / z), y, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.65e+30) || !(a <= 1.15e-38))
		tmp = fma(Float64(y - z), Float64(Float64(t - x) / a), x);
	else
		tmp = fma(Float64(Float64(x - t) / z), y, t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.65e+30], N[Not[LessEqual[a, 1.15e-38]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * y + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.65000000000000013e30 or 1.15000000000000001e-38 < a

   1. Initial program 86.5%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 76.5

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

   5. Applied rewrites 76.5%

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

   if -1.65000000000000013e30 < a < 1.15000000000000001e-38

   1. Initial program 69.7%

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

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 76.9%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 72.9%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{+30} \lor \neg \left(a \leq 1.15 \cdot 10^{-38}\right):\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z}, y, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 68.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+77} \lor \neg \left(a \leq 3.1 \cdot 10^{+21}\right):\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z}, y, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -6.5e+77) (not (<= a 3.1e+21)))
   (fma (- y z) (/ t a) x)
   (fma (/ (- x t) z) y t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6.5e+77) || !(a <= 3.1e+21)) {
		tmp = fma((y - z), (t / a), x);
	} else {
		tmp = fma(((x - t) / z), y, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -6.5e+77) || !(a <= 3.1e+21))
		tmp = fma(Float64(y - z), Float64(t / a), x);
	else
		tmp = fma(Float64(Float64(x - t) / z), y, t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -6.5e+77], N[Not[LessEqual[a, 3.1e+21]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * y + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.5e77 or 3.1e21 < a

   1. Initial program 86.9%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 80.5

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

   5. Applied rewrites 80.5%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 75.5%

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

   if -6.5e77 < a < 3.1e21

   1. Initial program 71.6%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 74.0%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 70.4%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+77} \lor \neg \left(a \leq 3.1 \cdot 10^{+21}\right):\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z}, y, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 68.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+77}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t}{a}, x\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-38}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z}, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{a}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.5e+77)
   (fma (- y z) (/ t a) x)
   (if (<= a 1.15e-38) (fma (/ (- x t) z) y t) (fma (/ (- t x) a) y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.5e+77) {
		tmp = fma((y - z), (t / a), x);
	} else if (a <= 1.15e-38) {
		tmp = fma(((x - t) / z), y, t);
	} else {
		tmp = fma(((t - x) / a), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.5e+77)
		tmp = fma(Float64(y - z), Float64(t / a), x);
	elseif (a <= 1.15e-38)
		tmp = fma(Float64(Float64(x - t) / z), y, t);
	else
		tmp = fma(Float64(Float64(t - x) / a), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.5e+77], N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[a, 1.15e-38], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * y + t), $MachinePrecision], N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * y + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.5e77

   1. Initial program 85.9%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 81.0

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

   5. Applied rewrites 81.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 77.8%

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

   if -6.5e77 < a < 1.15000000000000001e-38

   1. Initial program 70.9%

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

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 75.6%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 71.8%

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

   if 1.15000000000000001e-38 < a

   1. Initial program 86.6%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 72.7

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

   5. Applied rewrites 72.7%

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

Alternative 18: 33.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-80} \lor \neg \left(x \leq 5.4 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{y - a}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -3.2e-80) (not (<= x 5.4e+20)))
   (* (/ (- y a) z) x)
   (* t (/ y (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -3.2e-80) || !(x <= 5.4e+20)) {
		tmp = ((y - a) / z) * x;
	} else {
		tmp = t * (y / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-3.2d-80)) .or. (.not. (x <= 5.4d+20))) then
        tmp = ((y - a) / z) * x
    else
        tmp = t * (y / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -3.2e-80) || !(x <= 5.4e+20)) {
		tmp = ((y - a) / z) * x;
	} else {
		tmp = t * (y / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -3.2e-80) or not (x <= 5.4e+20):
		tmp = ((y - a) / z) * x
	else:
		tmp = t * (y / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -3.2e-80) || !(x <= 5.4e+20))
		tmp = Float64(Float64(Float64(y - a) / z) * x);
	else
		tmp = Float64(t * Float64(y / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -3.2e-80) || ~((x <= 5.4e+20)))
		tmp = ((y - a) / z) * x;
	else
		tmp = t * (y / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -3.2e-80], N[Not[LessEqual[x, 5.4e+20]], $MachinePrecision]], N[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.1999999999999999e-80 or 5.4e20 < x

   1. Initial program 74.3%

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

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 56.9%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 32.4%

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

   if -3.1999999999999999e-80 < x < 5.4e20

   1. Initial program 82.3%

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

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 48.2

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

   5. Applied rewrites 48.2%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 41.5%

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

4. Final simplification 36.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-80} \lor \neg \left(x \leq 5.4 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{y - a}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 34.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+15} \lor \neg \left(z \leq 5.6 \cdot 10^{+91}\right):\\ \;\;\;\;x + \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.5e+15) (not (<= z 5.6e+91)))
   (+ x (- t x))
   (* t (/ y (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.5e+15) || !(z <= 5.6e+91)) {
		tmp = x + (t - x);
	} else {
		tmp = t * (y / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-6.5d+15)) .or. (.not. (z <= 5.6d+91))) then
        tmp = x + (t - x)
    else
        tmp = t * (y / (a - z))
    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 <= -6.5e+15) || !(z <= 5.6e+91)) {
		tmp = x + (t - x);
	} else {
		tmp = t * (y / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.5e+15) or not (z <= 5.6e+91):
		tmp = x + (t - x)
	else:
		tmp = t * (y / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.5e+15) || !(z <= 5.6e+91))
		tmp = Float64(x + Float64(t - x));
	else
		tmp = Float64(t * Float64(y / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6.5e+15) || ~((z <= 5.6e+91)))
		tmp = x + (t - x);
	else
		tmp = t * (y / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.5e+15], N[Not[LessEqual[z, 5.6e+91]], $MachinePrecision]], N[(x + N[(t - x), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5e15 or 5.5999999999999997e91 < z

   1. Initial program 59.7%

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

   3. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
   4. Step-by-step derivation

      1. lower--.f64 35.5

         \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   5. Applied rewrites 35.5%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   if -6.5e15 < z < 5.5999999999999997e91

   1. Initial program 90.4%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

      2. associate-/l* N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a - z}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(t - x\right) \cdot y}}{a - z} \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y}{a - z}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y}{a - z}} \]

      6. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(t - x\right)} \cdot \frac{y}{a - z} \]

      7. lower-/.f64 N/A

         \[\leadsto \left(t - x\right) \cdot \color{blue}{\frac{y}{a - z}} \]

      8. lower--.f64 50.3

         \[\leadsto \left(t - x\right) \cdot \frac{y}{\color{blue}{a - z}} \]

   5. Applied rewrites 50.3%

      \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y}{a - z}} \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{t \cdot y}{\color{blue}{a - z}} \]
   7. Step-by-step derivation

   8. Applied rewrites 33.9%

      \[\leadsto t \cdot \color{blue}{\frac{y}{a - z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+15} \lor \neg \left(z \leq 5.6 \cdot 10^{+91}\right):\\ \;\;\;\;x + \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-90} \lor \neg \left(z \leq 1.2 \cdot 10^{+140}\right):\\ \;\;\;\;x + \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.4e-90) (not (<= z 1.2e+140))) (+ x (- t x)) (* t (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.4e-90) || !(z <= 1.2e+140)) {
		tmp = x + (t - x);
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.4d-90)) .or. (.not. (z <= 1.2d+140))) then
        tmp = x + (t - x)
    else
        tmp = t * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.4e-90) || !(z <= 1.2e+140)) {
		tmp = x + (t - x);
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.4e-90) or not (z <= 1.2e+140):
		tmp = x + (t - x)
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.4e-90) || !(z <= 1.2e+140))
		tmp = Float64(x + Float64(t - x));
	else
		tmp = Float64(t * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.4e-90) || ~((z <= 1.2e+140)))
		tmp = x + (t - x);
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.4e-90], N[Not[LessEqual[z, 1.2e+140]], $MachinePrecision]], N[(x + N[(t - x), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.39999999999999994e-90 or 1.2e140 < z

   1. Initial program 65.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
   4. Step-by-step derivation

      1. lower--.f64 32.4

         \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   5. Applied rewrites 32.4%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   if -3.39999999999999994e-90 < z < 1.2e140

   1. Initial program 89.2%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

      2. associate-/l* N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(t - x\right)}{a - z}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(t - x\right) \cdot y}}{a - z} \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y}{a - z}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y}{a - z}} \]

      6. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(t - x\right)} \cdot \frac{y}{a - z} \]

      7. lower-/.f64 N/A

         \[\leadsto \left(t - x\right) \cdot \color{blue}{\frac{y}{a - z}} \]

      8. lower--.f64 54.3

         \[\leadsto \left(t - x\right) \cdot \frac{y}{\color{blue}{a - z}} \]

   5. Applied rewrites 54.3%

      \[\leadsto \color{blue}{\left(t - x\right) \cdot \frac{y}{a - z}} \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{t \cdot y}{\color{blue}{a - z}} \]
   7. Step-by-step derivation

   8. Applied rewrites 35.0%

      \[\leadsto t \cdot \color{blue}{\frac{y}{a - z}} \]

   9. Taylor expanded in z around 0

      \[\leadsto \frac{t \cdot y}{a} \]
   10. Step-by-step derivation

   11. Applied rewrites 29.4%

       \[\leadsto t \cdot \frac{y}{\color{blue}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 30.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-90} \lor \neg \left(z \leq 1.2 \cdot 10^{+140}\right):\\ \;\;\;\;x + \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 19.9% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ x + \left(t - x\right) \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (- t x)))

C

double code(double x, double y, double z, double t, double a) {
	return x + (t - x);
}

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 + (t - x)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (t - x);
}

Python

def code(x, y, z, t, a):
	return x + (t - x)

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(t - x))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (t - x);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(t - x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 77.8%

   \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
2. Add Preprocessing

3. Taylor expanded in z around inf

   \[\leadsto x + \color{blue}{\left(t - x\right)} \]
4. Step-by-step derivation

   1. lower--.f64 19.8

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

5. Applied rewrites 19.8%

   \[\leadsto x + \color{blue}{\left(t - x\right)} \]
6. Add Preprocessing

Alternative 22: 2.8% accurate, 29.0× 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 77.8%

   \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-+.f64 N/A

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]

   3. lift-*.f64 N/A

      \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} + x \]

   4. *-commutative N/A

      \[\leadsto \color{blue}{\frac{t - x}{a - z} \cdot \left(y - z\right)} + x \]

   5. lower-fma.f64 77.8

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t - x}{a - z}, y - z, x\right)} \]

   6. lift-/.f64 N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{t - x}{a - z}}, y - z, x\right) \]

   7. frac-2neg N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{\mathsf{neg}\left(\left(t - x\right)\right)}{\mathsf{neg}\left(\left(a - z\right)\right)}}, y - z, x\right) \]

   8. lower-/.f64 N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{\mathsf{neg}\left(\left(t - x\right)\right)}{\mathsf{neg}\left(\left(a - z\right)\right)}}, y - z, x\right) \]

   9. neg-sub0 N/A

      \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{0 - \left(t - x\right)}}{\mathsf{neg}\left(\left(a - z\right)\right)}, y - z, x\right) \]

   10. lift--.f64 N/A

       \[\leadsto \mathsf{fma}\left(\frac{0 - \color{blue}{\left(t - x\right)}}{\mathsf{neg}\left(\left(a - z\right)\right)}, y - z, x\right) \]

   11. sub-neg N/A

       \[\leadsto \mathsf{fma}\left(\frac{0 - \color{blue}{\left(t + \left(\mathsf{neg}\left(x\right)\right)\right)}}{\mathsf{neg}\left(\left(a - z\right)\right)}, y - z, x\right) \]

   12. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(\frac{0 - \color{blue}{\left(\left(\mathsf{neg}\left(x\right)\right) + t\right)}}{\mathsf{neg}\left(\left(a - z\right)\right)}, y - z, x\right) \]

   13. associate--r+ N/A

       \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\left(0 - \left(\mathsf{neg}\left(x\right)\right)\right) - t}}{\mathsf{neg}\left(\left(a - z\right)\right)}, y - z, x\right) \]

   14. neg-sub0 N/A

       \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right)} - t}{\mathsf{neg}\left(\left(a - z\right)\right)}, y - z, x\right) \]

   15. remove-double-neg N/A

       \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{x} - t}{\mathsf{neg}\left(\left(a - z\right)\right)}, y - z, x\right) \]

   16. lower--.f64 N/A

       \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{x - t}}{\mathsf{neg}\left(\left(a - z\right)\right)}, y - z, x\right) \]

   17. neg-sub0 N/A

       \[\leadsto \mathsf{fma}\left(\frac{x - t}{\color{blue}{0 - \left(a - z\right)}}, y - z, x\right) \]

   18. lift--.f64 N/A

       \[\leadsto \mathsf{fma}\left(\frac{x - t}{0 - \color{blue}{\left(a - z\right)}}, y - z, x\right) \]

   19. sub-neg N/A

       \[\leadsto \mathsf{fma}\left(\frac{x - t}{0 - \color{blue}{\left(a + \left(\mathsf{neg}\left(z\right)\right)\right)}}, y - z, x\right) \]

   20. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(\frac{x - t}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) + a\right)}}, y - z, x\right) \]

   21. associate--r+ N/A

       \[\leadsto \mathsf{fma}\left(\frac{x - t}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(z\right)\right)\right) - a}}, y - z, x\right) \]

   22. neg-sub0 N/A

       \[\leadsto \mathsf{fma}\left(\frac{x - t}{\color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right)} - a}, y - z, x\right) \]

   23. remove-double-neg N/A

       \[\leadsto \mathsf{fma}\left(\frac{x - t}{\color{blue}{z} - a}, y - z, x\right) \]

   24. lower--.f64 77.8

       \[\leadsto \mathsf{fma}\left(\frac{x - t}{\color{blue}{z - a}}, y - z, x\right) \]

4. Applied rewrites 77.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x - t}{z - a}, y - z, x\right)} \]

5. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x \cdot \left(\left(1 + \frac{y}{z - a}\right) - \frac{z}{z - a}\right)} \]
6. Step-by-step derivation

   1. associate--l+ N/A

      \[\leadsto x \cdot \color{blue}{\left(1 + \left(\frac{y}{z - a} - \frac{z}{z - a}\right)\right)} \]

   2. div-sub N/A

      \[\leadsto x \cdot \left(1 + \color{blue}{\frac{y - z}{z - a}}\right) \]

   3. distribute-lft-in N/A

      \[\leadsto \color{blue}{x \cdot 1 + x \cdot \frac{y - z}{z - a}} \]

   4. *-rgt-identity N/A

      \[\leadsto \color{blue}{x} + x \cdot \frac{y - z}{z - a} \]

   5. associate-/l* N/A

      \[\leadsto x + \color{blue}{\frac{x \cdot \left(y - z\right)}{z - a}} \]

   6. +-commutative N/A

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - z\right)}{z - a} + x} \]

   7. associate-/l* N/A

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{z - a}} + x \]

   8. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{y - z}{z - a}, x\right)} \]

   9. lower-/.f64 N/A

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{\frac{y - z}{z - a}}, x\right) \]

   10. lower--.f64 N/A

       \[\leadsto \mathsf{fma}\left(x, \frac{\color{blue}{y - z}}{z - a}, x\right) \]

   11. lower--.f64 43.0

       \[\leadsto \mathsf{fma}\left(x, \frac{y - z}{\color{blue}{z - a}}, x\right) \]

7. Applied rewrites 43.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{y - z}{z - a}, x\right)} \]

8. Taylor expanded in z around inf

   \[\leadsto x + \color{blue}{-1 \cdot x} \]
9. Step-by-step derivation

10. Applied rewrites 2.9%

    \[\leadsto 0 \]

11. Final simplification 2.9%

    \[\leadsto 0 \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024324 
(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)))))