Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B

Percentage Accurate: 98.3% → 98.7%

Time: 6.9s

Alternatives: 14

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot \frac{z - t}{a - t} \leq 10^{+251}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - z}{t - a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t - a}, t - z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* y (/ (- z t) (- a t))) 1e+251)
   (fma (/ (- t z) (- t a)) y x)
   (fma (/ y (- t a)) (- t z) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y * ((z - t) / (a - t))) <= 1e+251) {
		tmp = fma(((t - z) / (t - a)), y, x);
	} else {
		tmp = fma((y / (t - a)), (t - z), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(y * Float64(Float64(z - t) / Float64(a - t))) <= 1e+251)
		tmp = fma(Float64(Float64(t - z) / Float64(t - a)), y, x);
	else
		tmp = fma(Float64(y / Float64(t - a)), Float64(t - z), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1e+251], N[(N[(N[(t - z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], N[(N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))) < 1e251

   1. Initial program 98.3%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 98.3

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

      6. lift-/.f64 N/A

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

      7. frac-2neg N/A

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

      8. lower-/.f64 N/A

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

      9. neg-sub0 N/A

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

      10. lift--.f64 N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. associate--r+ N/A

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

      14. neg-sub0 N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. neg-sub0 N/A

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

      18. lift--.f64 N/A

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

      19. sub-neg N/A

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

      20. +-commutative N/A

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

      21. associate--r+ N/A

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

      22. neg-sub0 N/A

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

      23. remove-double-neg N/A

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

      24. lower--.f64 98.3

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

   4. Applied rewrites 98.3%

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

   if 1e251 < (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))

   1. Initial program 73.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. clear-num N/A

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

      6. un-div-inv N/A

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

      7. frac-2neg N/A

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

      8. associate-/r/ N/A

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

      9. lower-fma.f64 N/A

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

   4. Applied rewrites 100.0%

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

Alternative 2: 83.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := \frac{y}{a - t} \cdot z\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+121}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-39}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{elif}\;t\_1 \leq 10^{-14}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-t}{a}, y, x\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+113}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))) (t_2 (* (/ y (- a t)) z)))
   (if (<= t_1 -2e+121)
     t_2
     (if (<= t_1 -2e-39)
       (fma (/ z a) y x)
       (if (<= t_1 1e-14)
         (fma (/ (- t) a) y x)
         (if (<= t_1 4e+113) (+ y x) t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = (y / (a - t)) * z;
	double tmp;
	if (t_1 <= -2e+121) {
		tmp = t_2;
	} else if (t_1 <= -2e-39) {
		tmp = fma((z / a), y, x);
	} else if (t_1 <= 1e-14) {
		tmp = fma((-t / a), y, x);
	} else if (t_1 <= 4e+113) {
		tmp = y + x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	t_2 = Float64(Float64(y / Float64(a - t)) * z)
	tmp = 0.0
	if (t_1 <= -2e+121)
		tmp = t_2;
	elseif (t_1 <= -2e-39)
		tmp = fma(Float64(z / a), y, x);
	elseif (t_1 <= 1e-14)
		tmp = fma(Float64(Float64(-t) / a), y, x);
	elseif (t_1 <= 4e+113)
		tmp = Float64(y + x);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+121], t$95$2, If[LessEqual[t$95$1, -2e-39], N[(N[(z / a), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[t$95$1, 1e-14], N[(N[((-t) / a), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[t$95$1, 4e+113], N[(y + x), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -2.00000000000000007e121 or 4e113 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 84.4%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

      5. lower-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. lower-/.f64 N/A

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

      8. neg-sub0 N/A

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

      9. lift--.f64 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. associate--r+ N/A

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

      13. neg-sub0 N/A

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

      14. remove-double-neg N/A

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

      15. lower--.f64 N/A

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

      16. neg-sub0 N/A

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

      17. lift--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

      20. associate--r+ N/A

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

      21. neg-sub0 N/A

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

      22. remove-double-neg N/A

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

      23. lower--.f64 87.4

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

   4. Applied rewrites 87.4%

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

   5. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. sub-neg N/A

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

      4. distribute-neg-in N/A

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

      5. remove-double-neg N/A

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

      6. +-commutative N/A

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

      7. sub-neg N/A

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

      8. associate-*l/ N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 82.4

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

   7. Applied rewrites 82.4%

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

   if -2.00000000000000007e121 < (/.f64 (-.f64 z t) (-.f64 a t)) < -1.99999999999999986e-39

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 63.3

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

   5. Applied rewrites 63.3%

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

   if -1.99999999999999986e-39 < (/.f64 (-.f64 z t) (-.f64 a t)) < 9.99999999999999999e-15

   1. Initial program 97.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 97.4

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

      6. lift-/.f64 N/A

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

      7. frac-2neg N/A

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

      8. lower-/.f64 N/A

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

      9. neg-sub0 N/A

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

      10. lift--.f64 N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. associate--r+ N/A

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

      14. neg-sub0 N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. neg-sub0 N/A

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

      18. lift--.f64 N/A

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

      19. sub-neg N/A

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

      20. +-commutative N/A

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

      21. associate--r+ N/A

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

      22. neg-sub0 N/A

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

      23. remove-double-neg N/A

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

      24. lower--.f64 97.4

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

   4. Applied rewrites 97.4%

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

   5. Taylor expanded in a around inf

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

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. sub-neg N/A

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

      4. distribute-neg-in N/A

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

      5. remove-double-neg N/A

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

      6. +-commutative N/A

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

      7. sub-neg N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 97.2

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

   7. Applied rewrites 97.2%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 86.1%

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

   if 9.99999999999999999e-15 < (/.f64 (-.f64 z t) (-.f64 a t)) < 4e113

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 91.9

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

   5. Applied rewrites 91.9%

      \[\leadsto \color{blue}{y + x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq -2 \cdot 10^{+121}:\\ \;\;\;\;\frac{y}{a - t} \cdot z\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq -2 \cdot 10^{-39}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 10^{-14}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-t}{a}, y, x\right)\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 4 \cdot 10^{+113}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - t} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := \frac{y}{a - t} \cdot z\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+121}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{-14}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a}, y, x\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+113}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))) (t_2 (* (/ y (- a t)) z)))
   (if (<= t_1 -2e+121)
     t_2
     (if (<= t_1 1e-14)
       (fma (/ (- z t) a) y x)
       (if (<= t_1 4e+113) (+ y x) t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = (y / (a - t)) * z;
	double tmp;
	if (t_1 <= -2e+121) {
		tmp = t_2;
	} else if (t_1 <= 1e-14) {
		tmp = fma(((z - t) / a), y, x);
	} else if (t_1 <= 4e+113) {
		tmp = y + x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	t_2 = Float64(Float64(y / Float64(a - t)) * z)
	tmp = 0.0
	if (t_1 <= -2e+121)
		tmp = t_2;
	elseif (t_1 <= 1e-14)
		tmp = fma(Float64(Float64(z - t) / a), y, x);
	elseif (t_1 <= 4e+113)
		tmp = Float64(y + x);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+121], t$95$2, If[LessEqual[t$95$1, 1e-14], N[(N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[t$95$1, 4e+113], N[(y + x), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -2.00000000000000007e121 or 4e113 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 84.4%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

      5. lower-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. lower-/.f64 N/A

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

      8. neg-sub0 N/A

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

      9. lift--.f64 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. associate--r+ N/A

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

      13. neg-sub0 N/A

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

      14. remove-double-neg N/A

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

      15. lower--.f64 N/A

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

      16. neg-sub0 N/A

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

      17. lift--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

      20. associate--r+ N/A

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

      21. neg-sub0 N/A

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

      22. remove-double-neg N/A

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

      23. lower--.f64 87.4

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

   4. Applied rewrites 87.4%

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

   5. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. sub-neg N/A

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

      4. distribute-neg-in N/A

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

      5. remove-double-neg N/A

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

      6. +-commutative N/A

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

      7. sub-neg N/A

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

      8. associate-*l/ N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 82.4

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

   7. Applied rewrites 82.4%

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

   if -2.00000000000000007e121 < (/.f64 (-.f64 z t) (-.f64 a t)) < 9.99999999999999999e-15

   1. Initial program 98.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 98.0

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

      6. lift-/.f64 N/A

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

      7. frac-2neg N/A

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

      8. lower-/.f64 N/A

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

      9. neg-sub0 N/A

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

      10. lift--.f64 N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. associate--r+ N/A

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

      14. neg-sub0 N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. neg-sub0 N/A

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

      18. lift--.f64 N/A

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

      19. sub-neg N/A

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

      20. +-commutative N/A

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

      21. associate--r+ N/A

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

      22. neg-sub0 N/A

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

      23. remove-double-neg N/A

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

      24. lower--.f64 98.0

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

   4. Applied rewrites 98.0%

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

   5. Taylor expanded in a around inf

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

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. sub-neg N/A

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

      4. distribute-neg-in N/A

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

      5. remove-double-neg N/A

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

      6. +-commutative N/A

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

      7. sub-neg N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 89.1

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

   7. Applied rewrites 89.1%

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

   if 9.99999999999999999e-15 < (/.f64 (-.f64 z t) (-.f64 a t)) < 4e113

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 91.9

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

   5. Applied rewrites 91.9%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq -2 \cdot 10^{+121}:\\ \;\;\;\;\frac{y}{a - t} \cdot z\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 10^{-14}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a}, y, x\right)\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 4 \cdot 10^{+113}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - t} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := \frac{y}{a - t} \cdot z\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+121}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-27}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+113}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))) (t_2 (* (/ y (- a t)) z)))
   (if (<= t_1 -2e+121)
     t_2
     (if (<= t_1 4e-27) (fma (/ z a) y x) (if (<= t_1 4e+113) (+ y x) t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = (y / (a - t)) * z;
	double tmp;
	if (t_1 <= -2e+121) {
		tmp = t_2;
	} else if (t_1 <= 4e-27) {
		tmp = fma((z / a), y, x);
	} else if (t_1 <= 4e+113) {
		tmp = y + x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	t_2 = Float64(Float64(y / Float64(a - t)) * z)
	tmp = 0.0
	if (t_1 <= -2e+121)
		tmp = t_2;
	elseif (t_1 <= 4e-27)
		tmp = fma(Float64(z / a), y, x);
	elseif (t_1 <= 4e+113)
		tmp = Float64(y + x);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+121], t$95$2, If[LessEqual[t$95$1, 4e-27], N[(N[(z / a), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[t$95$1, 4e+113], N[(y + x), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -2.00000000000000007e121 or 4e113 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 84.4%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

      5. lower-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. lower-/.f64 N/A

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

      8. neg-sub0 N/A

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

      9. lift--.f64 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. associate--r+ N/A

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

      13. neg-sub0 N/A

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

      14. remove-double-neg N/A

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

      15. lower--.f64 N/A

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

      16. neg-sub0 N/A

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

      17. lift--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

      20. associate--r+ N/A

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

      21. neg-sub0 N/A

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

      22. remove-double-neg N/A

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

      23. lower--.f64 87.4

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

   4. Applied rewrites 87.4%

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

   5. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. sub-neg N/A

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

      4. distribute-neg-in N/A

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

      5. remove-double-neg N/A

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

      6. +-commutative N/A

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

      7. sub-neg N/A

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

      8. associate-*l/ N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 82.4

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

   7. Applied rewrites 82.4%

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

   if -2.00000000000000007e121 < (/.f64 (-.f64 z t) (-.f64 a t)) < 4.0000000000000002e-27

   1. Initial program 97.9%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 77.1

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

   5. Applied rewrites 77.1%

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

   if 4.0000000000000002e-27 < (/.f64 (-.f64 z t) (-.f64 a t)) < 4e113

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 90.5

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

   5. Applied rewrites 90.5%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq -2 \cdot 10^{+121}:\\ \;\;\;\;\frac{y}{a - t} \cdot z\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 4 \cdot 10^{-27}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 4 \cdot 10^{+113}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - t} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq 4 \cdot 10^{-27}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+113}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{t - a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (<= t_1 4e-27)
     (fma (- z t) (/ y a) x)
     (if (<= t_1 4e+113) (fma (/ t (- t a)) y x) (* (/ y (- a t)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= 4e-27) {
		tmp = fma((z - t), (y / a), x);
	} else if (t_1 <= 4e+113) {
		tmp = fma((t / (t - a)), y, x);
	} else {
		tmp = (y / (a - t)) * z;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if (t_1 <= 4e-27)
		tmp = fma(Float64(z - t), Float64(y / a), x);
	elseif (t_1 <= 4e+113)
		tmp = fma(Float64(t / Float64(t - a)), y, x);
	else
		tmp = Float64(Float64(y / Float64(a - t)) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 4e-27], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 4e+113], N[(N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 4.0000000000000002e-27

   1. Initial program 95.1%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 83.6

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

   5. Applied rewrites 83.6%

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

   if 4.0000000000000002e-27 < (/.f64 (-.f64 z t) (-.f64 a t)) < 4e113

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 100.0

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

      6. lift-/.f64 N/A

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

      7. frac-2neg N/A

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

      8. lower-/.f64 N/A

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

      9. neg-sub0 N/A

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

      10. lift--.f64 N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. associate--r+ N/A

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

      14. neg-sub0 N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. neg-sub0 N/A

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

      18. lift--.f64 N/A

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

      19. sub-neg N/A

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

      20. +-commutative N/A

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

      21. associate--r+ N/A

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

      22. neg-sub0 N/A

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

      23. remove-double-neg N/A

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

      24. lower--.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 91.4

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

   7. Applied rewrites 91.4%

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

   if 4e113 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 87.1%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

      5. lower-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. lower-/.f64 N/A

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

      8. neg-sub0 N/A

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

      9. lift--.f64 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. associate--r+ N/A

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

      13. neg-sub0 N/A

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

      14. remove-double-neg N/A

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

      15. lower--.f64 N/A

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

      16. neg-sub0 N/A

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

      17. lift--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

      20. associate--r+ N/A

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

      21. neg-sub0 N/A

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

      22. remove-double-neg N/A

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

      23. lower--.f64 93.0

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

   4. Applied rewrites 93.0%

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

   5. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. sub-neg N/A

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

      4. distribute-neg-in N/A

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

      5. remove-double-neg N/A

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

      6. +-commutative N/A

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

      7. sub-neg N/A

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

      8. associate-*l/ N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 87.1

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

   7. Applied rewrites 87.1%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq 4 \cdot 10^{-27}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{a}, x\right)\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 4 \cdot 10^{+113}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{t - a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - t} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq 10^{-14}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+113}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (<= t_1 1e-14)
     (fma (- z t) (/ y a) x)
     (if (<= t_1 4e+113) (+ y x) (* (/ y (- a t)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= 1e-14) {
		tmp = fma((z - t), (y / a), x);
	} else if (t_1 <= 4e+113) {
		tmp = y + x;
	} else {
		tmp = (y / (a - t)) * z;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if (t_1 <= 1e-14)
		tmp = fma(Float64(z - t), Float64(y / a), x);
	elseif (t_1 <= 4e+113)
		tmp = Float64(y + x);
	else
		tmp = Float64(Float64(y / Float64(a - t)) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e-14], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 4e+113], N[(y + x), $MachinePrecision], N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 9.99999999999999999e-15

   1. Initial program 95.2%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 83.2

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

   5. Applied rewrites 83.2%

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

   if 9.99999999999999999e-15 < (/.f64 (-.f64 z t) (-.f64 a t)) < 4e113

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 91.9

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

   5. Applied rewrites 91.9%

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

   if 4e113 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 87.1%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

      5. lower-/.f64 N/A

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

      6. frac-2neg N/A

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

      7. lower-/.f64 N/A

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

      8. neg-sub0 N/A

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

      9. lift--.f64 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. associate--r+ N/A

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

      13. neg-sub0 N/A

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

      14. remove-double-neg N/A

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

      15. lower--.f64 N/A

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

      16. neg-sub0 N/A

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

      17. lift--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

      20. associate--r+ N/A

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

      21. neg-sub0 N/A

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

      22. remove-double-neg N/A

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

      23. lower--.f64 93.0

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

   4. Applied rewrites 93.0%

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

   5. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. sub-neg N/A

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

      4. distribute-neg-in N/A

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

      5. remove-double-neg N/A

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

      6. +-commutative N/A

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

      7. sub-neg N/A

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

      8. associate-*l/ N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 87.1

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

   7. Applied rewrites 87.1%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq 10^{-14}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{a}, x\right)\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 4 \cdot 10^{+113}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - t} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq 4 \cdot 10^{-27}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+113}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a - t} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (<= t_1 4e-27)
     (fma (/ z a) y x)
     (if (<= t_1 4e+113) (+ y x) (* (/ z (- a t)) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= 4e-27) {
		tmp = fma((z / a), y, x);
	} else if (t_1 <= 4e+113) {
		tmp = y + x;
	} else {
		tmp = (z / (a - t)) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if (t_1 <= 4e-27)
		tmp = fma(Float64(z / a), y, x);
	elseif (t_1 <= 4e+113)
		tmp = Float64(y + x);
	else
		tmp = Float64(Float64(z / Float64(a - t)) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 4e-27], N[(N[(z / a), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[t$95$1, 4e+113], N[(y + x), $MachinePrecision], N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 4.0000000000000002e-27

   1. Initial program 95.1%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 72.9

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

   5. Applied rewrites 72.9%

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

   if 4.0000000000000002e-27 < (/.f64 (-.f64 z t) (-.f64 a t)) < 4e113

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 90.5

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

   5. Applied rewrites 90.5%

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

   if 4e113 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 87.1%

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

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 74.3

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

   5. Applied rewrites 74.3%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq 4 \cdot 10^{-27}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 4 \cdot 10^{+113}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a - t} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq 4 \cdot 10^{-27} \lor \neg \left(t\_1 \leq 2\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (or (<= t_1 4e-27) (not (<= t_1 2.0))) (fma (/ z a) y x) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if ((t_1 <= 4e-27) || !(t_1 <= 2.0)) {
		tmp = fma((z / a), y, x);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if ((t_1 <= 4e-27) || !(t_1 <= 2.0))
		tmp = fma(Float64(z / a), y, x);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, 4e-27], N[Not[LessEqual[t$95$1, 2.0]], $MachinePrecision]], N[(N[(z / a), $MachinePrecision] * y + x), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 4.0000000000000002e-27 or 2 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 94.7%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 70.4

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

   5. Applied rewrites 70.4%

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

   if 4.0000000000000002e-27 < (/.f64 (-.f64 z t) (-.f64 a t)) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 97.6

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

   5. Applied rewrites 97.6%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq 4 \cdot 10^{-27} \lor \neg \left(\frac{z - t}{a - t} \leq 2\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+141} \lor \neg \left(t\_1 \leq 4 \cdot 10^{+113}\right):\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (or (<= t_1 -5e+141) (not (<= t_1 4e+113))) (* z (/ y a)) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if ((t_1 <= -5e+141) || !(t_1 <= 4e+113)) {
		tmp = z * (y / a);
	} else {
		tmp = y + 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) :: t_1
    real(8) :: tmp
    t_1 = (z - t) / (a - t)
    if ((t_1 <= (-5d+141)) .or. (.not. (t_1 <= 4d+113))) then
        tmp = z * (y / a)
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if ((t_1 <= -5e+141) || !(t_1 <= 4e+113)) {
		tmp = z * (y / a);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (a - t)
	tmp = 0
	if (t_1 <= -5e+141) or not (t_1 <= 4e+113):
		tmp = z * (y / a)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if ((t_1 <= -5e+141) || !(t_1 <= 4e+113))
		tmp = Float64(z * Float64(y / a));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (a - t);
	tmp = 0.0;
	if ((t_1 <= -5e+141) || ~((t_1 <= 4e+113)))
		tmp = z * (y / a);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+141], N[Not[LessEqual[t$95$1, 4e+113]], $MachinePrecision]], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -5.00000000000000025e141 or 4e113 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 84.1%

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

   3. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. div-sub N/A

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

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

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

      4. associate-/l* N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

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

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower--.f64 82.0

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

   5. Applied rewrites 82.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 51.2%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 48.1%

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

   13. Applied rewrites 51.2%

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

   if -5.00000000000000025e141 < (/.f64 (-.f64 z t) (-.f64 a t)) < 4e113

   1. Initial program 99.0%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 71.3

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

   5. Applied rewrites 71.3%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq -5 \cdot 10^{+141} \lor \neg \left(\frac{z - t}{a - t} \leq 4 \cdot 10^{+113}\right):\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+110}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+113}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (<= t_1 -5e+110)
     (/ (* z y) a)
     (if (<= t_1 4e+113) (+ y x) (* (/ z a) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= -5e+110) {
		tmp = (z * y) / a;
	} else if (t_1 <= 4e+113) {
		tmp = y + x;
	} else {
		tmp = (z / a) * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z - t) / (a - t)
    if (t_1 <= (-5d+110)) then
        tmp = (z * y) / a
    else if (t_1 <= 4d+113) then
        tmp = y + x
    else
        tmp = (z / a) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= -5e+110) {
		tmp = (z * y) / a;
	} else if (t_1 <= 4e+113) {
		tmp = y + x;
	} else {
		tmp = (z / a) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (a - t)
	tmp = 0
	if t_1 <= -5e+110:
		tmp = (z * y) / a
	elif t_1 <= 4e+113:
		tmp = y + x
	else:
		tmp = (z / a) * y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if (t_1 <= -5e+110)
		tmp = Float64(Float64(z * y) / a);
	elseif (t_1 <= 4e+113)
		tmp = Float64(y + x);
	else
		tmp = Float64(Float64(z / a) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (a - t);
	tmp = 0.0;
	if (t_1 <= -5e+110)
		tmp = (z * y) / a;
	elseif (t_1 <= 4e+113)
		tmp = y + x;
	else
		tmp = (z / a) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+110], N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t$95$1, 4e+113], N[(y + x), $MachinePrecision], N[(N[(z / a), $MachinePrecision] * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -4.99999999999999978e110

   1. Initial program 82.5%

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

   3. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. div-sub N/A

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

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

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

      4. associate-/l* N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

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

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower--.f64 74.2

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

   5. Applied rewrites 74.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 48.1%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 46.4%

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

   13. Applied rewrites 48.6%

       \[\leadsto \frac{z \cdot y}{a} \]

   if -4.99999999999999978e110 < (/.f64 (-.f64 z t) (-.f64 a t)) < 4e113

   1. Initial program 99.0%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 72.0

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

   5. Applied rewrites 72.0%

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

   if 4e113 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 87.1%

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

   3. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. div-sub N/A

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

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

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

      4. associate-/l* N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

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

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower--.f64 87.1

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

   5. Applied rewrites 87.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 49.9%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 49.9%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq -5 \cdot 10^{+110}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 4 \cdot 10^{+113}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+141}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+113}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (<= t_1 -5e+141)
     (* z (/ y a))
     (if (<= t_1 4e+113) (+ y x) (* (/ z a) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= -5e+141) {
		tmp = z * (y / a);
	} else if (t_1 <= 4e+113) {
		tmp = y + x;
	} else {
		tmp = (z / a) * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z - t) / (a - t)
    if (t_1 <= (-5d+141)) then
        tmp = z * (y / a)
    else if (t_1 <= 4d+113) then
        tmp = y + x
    else
        tmp = (z / a) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= -5e+141) {
		tmp = z * (y / a);
	} else if (t_1 <= 4e+113) {
		tmp = y + x;
	} else {
		tmp = (z / a) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (a - t)
	tmp = 0
	if t_1 <= -5e+141:
		tmp = z * (y / a)
	elif t_1 <= 4e+113:
		tmp = y + x
	else:
		tmp = (z / a) * y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if (t_1 <= -5e+141)
		tmp = Float64(z * Float64(y / a));
	elseif (t_1 <= 4e+113)
		tmp = Float64(y + x);
	else
		tmp = Float64(Float64(z / a) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (a - t);
	tmp = 0.0;
	if (t_1 <= -5e+141)
		tmp = z * (y / a);
	elseif (t_1 <= 4e+113)
		tmp = y + x;
	else
		tmp = (z / a) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+141], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+113], N[(y + x), $MachinePrecision], N[(N[(z / a), $MachinePrecision] * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -5.00000000000000025e141

   1. Initial program 80.7%

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

   3. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. div-sub N/A

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

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

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

      4. associate-/l* N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

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

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower--.f64 76.4

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

   5. Applied rewrites 76.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 52.7%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 46.1%

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

   13. Applied rewrites 52.7%

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

   if -5.00000000000000025e141 < (/.f64 (-.f64 z t) (-.f64 a t)) < 4e113

   1. Initial program 99.0%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 71.3

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

   5. Applied rewrites 71.3%

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

   if 4e113 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 87.1%

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

   3. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. div-sub N/A

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

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

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

      4. associate-/l* N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

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

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower--.f64 87.1

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

   5. Applied rewrites 87.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 49.9%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 49.9%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq -5 \cdot 10^{+141}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 4 \cdot 10^{+113}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 98.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{\frac{t - a}{t - z}} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return x + (y / ((t - a) / (t - 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 / ((t - a) / (t - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.6%

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

   1. lift-*.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. clear-num N/A

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

   4. un-div-inv N/A

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

   5. lower-/.f64 N/A

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

   6. frac-2neg N/A

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

   7. lower-/.f64 N/A

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

   8. neg-sub0 N/A

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

   9. lift--.f64 N/A

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

   10. sub-neg N/A

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

   11. +-commutative N/A

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

   12. associate--r+ N/A

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

   13. neg-sub0 N/A

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

   14. remove-double-neg N/A

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

   15. lower--.f64 N/A

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

   16. neg-sub0 N/A

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

   17. lift--.f64 N/A

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

   18. sub-neg N/A

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

   19. +-commutative N/A

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

   20. associate--r+ N/A

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

   21. neg-sub0 N/A

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

   22. remove-double-neg N/A

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

   23. lower--.f64 97.1

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

4. Applied rewrites 97.1%

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

Alternative 13: 95.7% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.6%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lift-/.f64 N/A

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

   5. clear-num N/A

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

   6. un-div-inv N/A

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

   7. frac-2neg N/A

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

   8. associate-/r/ N/A

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

   9. lower-fma.f64 N/A

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

4. Applied rewrites 96.3%

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

Alternative 14: 61.4% accurate, 6.5× speedup

Math

\[\begin{array}{l} \\ y + x \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return y + 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 = y + x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(y + x), $MachinePrecision]

Derivation

1. Initial program 96.6%

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

3. Taylor expanded in t around inf

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

   1. +-commutative N/A

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

   2. lower-+.f64 62.6

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

5. Applied rewrites 62.6%

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

6. Final simplification 62.6%

   \[\leadsto y + x \]
7. Add Preprocessing

Developer Target 1: 99.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y < -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) (- a t))))))
   (if (< y -8.508084860551241e-17)
     t_1
     (if (< y 2.894426862792089e-49)
       (+ x (* (* y (- z t)) (/ 1.0 (- a t))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((z - t) / (a - t)))
    if (y < (-8.508084860551241d-17)) then
        tmp = t_1
    else if (y < 2.894426862792089d-49) then
        tmp = x + ((y * (z - t)) * (1.0d0 / (a - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / (a - t)))
	tmp = 0
	if y < -8.508084860551241e-17:
		tmp = t_1
	elif y < 2.894426862792089e-49:
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) * Float64(1.0 / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / (a - t)));
	tmp = 0.0;
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -8.508084860551241e-17], t$95$1, If[Less[y, 2.894426862792089e-49], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024324 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y -8508084860551241/100000000000000000000000000000000) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2894426862792089/10000000000000000000000000000000000000000000000000000000000000000) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t)))))))

  (+ x (* y (/ (- z t) (- a t)))))