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

Percentage Accurate: 97.8% → 98.6%

Time: 11.1s

Alternatives: 21

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: 97.8% 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: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq 10^{+97}:\\ \;\;\;\;x + y \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t - a}, -z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (<= t_1 1e+97) (+ x (* y t_1)) (fma (/ y (- t a)) (- z) 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 <= 1e+97) {
		tmp = x + (y * t_1);
	} else {
		tmp = fma((y / (t - a)), -z, 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 <= 1e+97)
		tmp = Float64(x + Float64(y * t_1));
	else
		tmp = fma(Float64(y / Float64(t - a)), Float64(-z), 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[LessEqual[t$95$1, 1e+97], N[(x + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision] * (-z) + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 1.0000000000000001e97

   1. Initial program 99.0%

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

   if 1.0000000000000001e97 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 78.8%

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

      1. +-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. frac-2neg N/A

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

      5. associate-/r/ N/A

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

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

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

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

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

      8. neg-sub0 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. associate--r+ N/A

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

      12. neg-sub0 N/A

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

      13. remove-double-neg N/A

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

      14. --lowering--.f64 N/A

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

      15. neg-sub0 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. associate--r+ N/A

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

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. --lowering--.f64 99.7

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 99.7

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

   7. Simplified 99.7%

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

Alternative 2: 97.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := \mathsf{fma}\left(\frac{y}{t - a}, -z, x\right)\\ \mathbf{if}\;t\_1 \leq -40000000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.02:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{t - a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))) (t_2 (fma (/ y (- t a)) (- z) x)))
   (if (<= t_1 -40000000000000.0)
     t_2
     (if (<= t_1 0.02)
       (fma y (/ (- z t) a) x)
       (if (<= t_1 2.0) (fma y (/ t (- t a)) 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 = fma((y / (t - a)), -z, x);
	double tmp;
	if (t_1 <= -40000000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.02) {
		tmp = fma(y, ((z - t) / a), x);
	} else if (t_1 <= 2.0) {
		tmp = fma(y, (t / (t - a)), 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 = fma(Float64(y / Float64(t - a)), Float64(-z), x)
	tmp = 0.0
	if (t_1 <= -40000000000000.0)
		tmp = t_2;
	elseif (t_1 <= 0.02)
		tmp = fma(y, Float64(Float64(z - t) / a), x);
	elseif (t_1 <= 2.0)
		tmp = fma(y, Float64(t / Float64(t - a)), 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[(t - a), $MachinePrecision]), $MachinePrecision] * (-z) + x), $MachinePrecision]}, If[LessEqual[t$95$1, -40000000000000.0], t$95$2, If[LessEqual[t$95$1, 0.02], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -4e13 or 2 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 91.2%

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

      1. +-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. frac-2neg N/A

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

      5. associate-/r/ N/A

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

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

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

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

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

      8. neg-sub0 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. associate--r+ N/A

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

      12. neg-sub0 N/A

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

      13. remove-double-neg N/A

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

      14. --lowering--.f64 N/A

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

      15. neg-sub0 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. associate--r+ N/A

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

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. --lowering--.f64 92.4

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

   4. Applied egg-rr 92.4%

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

   5. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 92.2

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

   7. Simplified 92.2%

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

   if -4e13 < (/.f64 (-.f64 z t) (-.f64 a t)) < 0.0200000000000000004

   1. Initial program 99.7%

      \[x + y \cdot \frac{z - t}{a - t} \]
   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. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 99.4

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

   5. Simplified 99.4%

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

   if 0.0200000000000000004 < (/.f64 (-.f64 z t) (-.f64 a t)) < 2

   1. Initial program 99.9%

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

      1. +-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. frac-2neg N/A

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

      5. associate-/r/ N/A

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

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

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

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

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

      8. neg-sub0 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. associate--r+ N/A

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

      12. neg-sub0 N/A

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

      13. remove-double-neg N/A

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

      14. --lowering--.f64 N/A

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

      15. neg-sub0 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. associate--r+ N/A

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

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. --lowering--.f64 93.4

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

   4. Applied egg-rr 93.4%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

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

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

      6. --lowering--.f64 99.4

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

   7. Simplified 99.4%

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

Alternative 3: 87.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+62}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, -z, x\right)\\ \mathbf{elif}\;t\_1 \leq 0.02:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 50:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{t - a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (<= t_1 -5e+62)
     (fma (/ y t) (- z) x)
     (if (<= t_1 0.02)
       (fma y (/ (- z t) a) x)
       (if (<= t_1 50.0) (fma y (/ t (- t a)) x) (* y (/ z (- a t))))))))

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+62) {
		tmp = fma((y / t), -z, x);
	} else if (t_1 <= 0.02) {
		tmp = fma(y, ((z - t) / a), x);
	} else if (t_1 <= 50.0) {
		tmp = fma(y, (t / (t - a)), x);
	} else {
		tmp = y * (z / (a - t));
	}
	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+62)
		tmp = fma(Float64(y / t), Float64(-z), x);
	elseif (t_1 <= 0.02)
		tmp = fma(y, Float64(Float64(z - t) / a), x);
	elseif (t_1 <= 50.0)
		tmp = fma(y, Float64(t / Float64(t - a)), x);
	else
		tmp = Float64(y * Float64(z / Float64(a - t)));
	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, -5e+62], N[(N[(y / t), $MachinePrecision] * (-z) + x), $MachinePrecision], If[LessEqual[t$95$1, 0.02], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 50.0], N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -5.00000000000000029e62

   1. Initial program 93.6%

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

      1. +-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. frac-2neg N/A

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

      5. associate-/r/ N/A

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

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

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

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

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

      8. neg-sub0 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. associate--r+ N/A

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

      12. neg-sub0 N/A

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

      13. remove-double-neg N/A

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

      14. --lowering--.f64 N/A

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

      15. neg-sub0 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. associate--r+ N/A

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

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. --lowering--.f64 93.1

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

   4. Applied egg-rr 93.1%

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

   5. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 93.1

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

   7. Simplified 93.1%

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

   8. Taylor expanded in t around inf

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

      1. /-lowering-/.f64 76.7

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

   10. Simplified 76.7%

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

   if -5.00000000000000029e62 < (/.f64 (-.f64 z t) (-.f64 a t)) < 0.0200000000000000004

   1. Initial program 99.7%

      \[x + y \cdot \frac{z - t}{a - t} \]
   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. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 97.5

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

   5. Simplified 97.5%

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

   if 0.0200000000000000004 < (/.f64 (-.f64 z t) (-.f64 a t)) < 50

   1. Initial program 99.9%

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

      1. +-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. frac-2neg N/A

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

      5. associate-/r/ N/A

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

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

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

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

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

      8. neg-sub0 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. associate--r+ N/A

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

      12. neg-sub0 N/A

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

      13. remove-double-neg N/A

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

      14. --lowering--.f64 N/A

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

      15. neg-sub0 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. associate--r+ N/A

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

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. --lowering--.f64 93.5

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

   4. Applied egg-rr 93.5%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

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

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

      6. --lowering--.f64 99.4

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

   7. Simplified 99.4%

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

   if 50 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 88.0%

      \[x + y \cdot \frac{z - t}{a - t} \]
   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. *-lowering-*.f64 N/A

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

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

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

      4. --lowering--.f64 73.2

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

   5. Simplified 73.2%

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

Alternative 4: 82.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a - t}\\ t_2 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+62}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, -z, x\right)\\ \mathbf{elif}\;t\_2 \leq -40000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 50:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{t - a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- a t)))) (t_2 (/ (- z t) (- a t))))
   (if (<= t_2 -5e+62)
     (fma (/ y t) (- z) x)
     (if (<= t_2 -40000000000000.0)
       t_1
       (if (<= t_2 50.0) (fma y (/ t (- t a)) x) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (a - t));
	double t_2 = (z - t) / (a - t);
	double tmp;
	if (t_2 <= -5e+62) {
		tmp = fma((y / t), -z, x);
	} else if (t_2 <= -40000000000000.0) {
		tmp = t_1;
	} else if (t_2 <= 50.0) {
		tmp = fma(y, (t / (t - a)), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(a - t)))
	t_2 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if (t_2 <= -5e+62)
		tmp = fma(Float64(y / t), Float64(-z), x);
	elseif (t_2 <= -40000000000000.0)
		tmp = t_1;
	elseif (t_2 <= 50.0)
		tmp = fma(y, Float64(t / Float64(t - a)), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+62], N[(N[(y / t), $MachinePrecision] * (-z) + x), $MachinePrecision], If[LessEqual[t$95$2, -40000000000000.0], t$95$1, If[LessEqual[t$95$2, 50.0], N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -5.00000000000000029e62

   1. Initial program 93.6%

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

      1. +-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. frac-2neg N/A

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

      5. associate-/r/ N/A

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

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

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

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

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

      8. neg-sub0 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. associate--r+ N/A

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

      12. neg-sub0 N/A

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

      13. remove-double-neg N/A

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

      14. --lowering--.f64 N/A

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

      15. neg-sub0 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. associate--r+ N/A

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

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. --lowering--.f64 93.1

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

   4. Applied egg-rr 93.1%

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

   5. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 93.1

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

   7. Simplified 93.1%

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

   8. Taylor expanded in t around inf

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

      1. /-lowering-/.f64 76.7

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

   10. Simplified 76.7%

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

   if -5.00000000000000029e62 < (/.f64 (-.f64 z t) (-.f64 a t)) < -4e13 or 50 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 89.5%

      \[x + y \cdot \frac{z - t}{a - t} \]
   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. *-lowering-*.f64 N/A

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

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

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

      4. --lowering--.f64 76.4

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

   5. Simplified 76.4%

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

   if -4e13 < (/.f64 (-.f64 z t) (-.f64 a t)) < 50

   1. Initial program 99.8%

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

      1. +-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. frac-2neg N/A

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

      5. associate-/r/ N/A

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

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

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

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

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

      8. neg-sub0 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. associate--r+ N/A

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

      12. neg-sub0 N/A

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

      13. remove-double-neg N/A

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

      14. --lowering--.f64 N/A

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

      15. neg-sub0 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. associate--r+ N/A

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

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. --lowering--.f64 95.7

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

   4. Applied egg-rr 95.7%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

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

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

      6. --lowering--.f64 92.5

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

   7. Simplified 92.5%

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

Alternative 5: 83.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+62}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, -z, x\right)\\ \mathbf{elif}\;t\_1 \leq 0.02:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+106}:\\ \;\;\;\;\mathsf{fma}\left(y, 1 - \frac{z}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (<= t_1 -5e+62)
     (fma (/ y t) (- z) x)
     (if (<= t_1 0.02)
       (fma y (/ z a) x)
       (if (<= t_1 1e+106) (fma y (- 1.0 (/ z t)) x) (/ (* y z) (- a t)))))))

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+62) {
		tmp = fma((y / t), -z, x);
	} else if (t_1 <= 0.02) {
		tmp = fma(y, (z / a), x);
	} else if (t_1 <= 1e+106) {
		tmp = fma(y, (1.0 - (z / t)), x);
	} else {
		tmp = (y * z) / (a - t);
	}
	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+62)
		tmp = fma(Float64(y / t), Float64(-z), x);
	elseif (t_1 <= 0.02)
		tmp = fma(y, Float64(z / a), x);
	elseif (t_1 <= 1e+106)
		tmp = fma(y, Float64(1.0 - Float64(z / t)), x);
	else
		tmp = Float64(Float64(y * z) / Float64(a - t));
	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, -5e+62], N[(N[(y / t), $MachinePrecision] * (-z) + x), $MachinePrecision], If[LessEqual[t$95$1, 0.02], N[(y * N[(z / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 1e+106], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -5.00000000000000029e62

   1. Initial program 93.6%

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

      1. +-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. frac-2neg N/A

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

      5. associate-/r/ N/A

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

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

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

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

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

      8. neg-sub0 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. associate--r+ N/A

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

      12. neg-sub0 N/A

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

      13. remove-double-neg N/A

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

      14. --lowering--.f64 N/A

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

      15. neg-sub0 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. associate--r+ N/A

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

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. --lowering--.f64 93.1

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

   4. Applied egg-rr 93.1%

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

   5. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 93.1

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

   7. Simplified 93.1%

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

   8. Taylor expanded in t around inf

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

      1. /-lowering-/.f64 76.7

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

   10. Simplified 76.7%

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

   if -5.00000000000000029e62 < (/.f64 (-.f64 z t) (-.f64 a t)) < 0.0200000000000000004

   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. accelerator-lowering-fma.f64 N/A

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

      4. /-lowering-/.f64 85.3

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

   5. Simplified 85.3%

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

   if 0.0200000000000000004 < (/.f64 (-.f64 z t) (-.f64 a t)) < 1.00000000000000009e106

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

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

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. *-inverses N/A

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

      8. metadata-eval N/A

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

      9. +-commutative N/A

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

      10. distribute-neg-in N/A

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

      11. metadata-eval N/A

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

      12. mul-1-neg N/A

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

      13. accelerator-lowering-fma.f64 N/A

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

      14. mul-1-neg N/A

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

      15. unsub-neg N/A

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

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

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

      17. /-lowering-/.f64 89.2

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

   5. Simplified 89.2%

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

   if 1.00000000000000009e106 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 76.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   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. *-lowering-*.f64 N/A

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

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

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

      4. --lowering--.f64 72.5

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

   5. Simplified 72.5%

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

      1. associate-*r/ N/A

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

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

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

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

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

      4. --lowering--.f64 86.4

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

   7. Applied egg-rr 86.4%

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

Alternative 6: 80.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+62}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, -z, x\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-68}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 50:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y}{t - a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (<= t_1 -5e+62)
     (fma (/ y t) (- z) x)
     (if (<= t_1 5e-68)
       (fma y (/ z a) x)
       (if (<= t_1 50.0) (fma t (/ y (- t a)) x) (* y (/ z (- a t))))))))

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+62) {
		tmp = fma((y / t), -z, x);
	} else if (t_1 <= 5e-68) {
		tmp = fma(y, (z / a), x);
	} else if (t_1 <= 50.0) {
		tmp = fma(t, (y / (t - a)), x);
	} else {
		tmp = y * (z / (a - t));
	}
	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+62)
		tmp = fma(Float64(y / t), Float64(-z), x);
	elseif (t_1 <= 5e-68)
		tmp = fma(y, Float64(z / a), x);
	elseif (t_1 <= 50.0)
		tmp = fma(t, Float64(y / Float64(t - a)), x);
	else
		tmp = Float64(y * Float64(z / Float64(a - t)));
	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, -5e+62], N[(N[(y / t), $MachinePrecision] * (-z) + x), $MachinePrecision], If[LessEqual[t$95$1, 5e-68], N[(y * N[(z / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 50.0], N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -5.00000000000000029e62

   1. Initial program 93.6%

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

      1. +-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. frac-2neg N/A

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

      5. associate-/r/ N/A

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

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

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

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

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

      8. neg-sub0 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. associate--r+ N/A

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

      12. neg-sub0 N/A

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

      13. remove-double-neg N/A

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

      14. --lowering--.f64 N/A

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

      15. neg-sub0 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. associate--r+ N/A

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

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. --lowering--.f64 93.1

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

   4. Applied egg-rr 93.1%

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

   5. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 93.1

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

   7. Simplified 93.1%

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

   8. Taylor expanded in t around inf

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

      1. /-lowering-/.f64 76.7

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

   10. Simplified 76.7%

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

   if -5.00000000000000029e62 < (/.f64 (-.f64 z t) (-.f64 a t)) < 4.99999999999999971e-68

   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. accelerator-lowering-fma.f64 N/A

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

      4. /-lowering-/.f64 87.1

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

   5. Simplified 87.1%

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

   if 4.99999999999999971e-68 < (/.f64 (-.f64 z t) (-.f64 a t)) < 50

   1. Initial program 99.9%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. frac-2neg N/A

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

      4. div-inv N/A

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

      5. associate-*l* N/A

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

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

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

      7. neg-sub0 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{0 - \left(z - t\right)}, \frac{1}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot y, x\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(0 - \color{blue}{\left(z + \left(\mathsf{neg}\left(t\right)\right)\right)}, \frac{1}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot y, x\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(0 - \color{blue}{\left(\left(\mathsf{neg}\left(t\right)\right) + z\right)}, \frac{1}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot y, x\right) \]

      10. associate--r+ N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(0 - \left(\mathsf{neg}\left(t\right)\right)\right) - z}, \frac{1}{\mathsf{neg}\left(\left(a - t\right)\right)} \cdot y, x\right) \]

      11. neg-sub0 N/A

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

      12. remove-double-neg N/A

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

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

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

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

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

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

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

      16. neg-sub0 N/A

          \[\leadsto \mathsf{fma}\left(t - z, \frac{1}{\color{blue}{0 - \left(a - t\right)}} \cdot y, x\right) \]

      17. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(t - z, \frac{1}{0 - \color{blue}{\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)}} \cdot y, x\right) \]

      18. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(t - z, \frac{1}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)}} \cdot y, x\right) \]

      19. associate--r+ N/A

          \[\leadsto \mathsf{fma}\left(t - z, \frac{1}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(t\right)\right)\right) - a}} \cdot y, x\right) \]

      20. neg-sub0 N/A

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

      21. remove-double-neg N/A

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

      22. --lowering--.f64 94.3

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

   4. Applied egg-rr 94.3%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 92.5

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

   7. Simplified 92.5%

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

   if 50 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 88.0%

      \[x + y \cdot \frac{z - t}{a - t} \]
   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. *-lowering-*.f64 N/A

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

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

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

      4. --lowering--.f64 73.2

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

   5. Simplified 73.2%

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

Alternative 7: 82.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+62}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, -z, x\right)\\ \mathbf{elif}\;t\_1 \leq 0.02:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 50:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (<= t_1 -5e+62)
     (fma (/ y t) (- z) x)
     (if (<= t_1 0.02)
       (fma y (/ z a) x)
       (if (<= t_1 50.0) (+ x y) (* y (/ z (- a t))))))))

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+62) {
		tmp = fma((y / t), -z, x);
	} else if (t_1 <= 0.02) {
		tmp = fma(y, (z / a), x);
	} else if (t_1 <= 50.0) {
		tmp = x + y;
	} else {
		tmp = y * (z / (a - t));
	}
	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+62)
		tmp = fma(Float64(y / t), Float64(-z), x);
	elseif (t_1 <= 0.02)
		tmp = fma(y, Float64(z / a), x);
	elseif (t_1 <= 50.0)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(z / Float64(a - t)));
	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, -5e+62], N[(N[(y / t), $MachinePrecision] * (-z) + x), $MachinePrecision], If[LessEqual[t$95$1, 0.02], N[(y * N[(z / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 50.0], N[(x + y), $MachinePrecision], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -5.00000000000000029e62

   1. Initial program 93.6%

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

      1. +-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. frac-2neg N/A

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

      5. associate-/r/ N/A

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

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

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

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

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

      8. neg-sub0 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. associate--r+ N/A

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

      12. neg-sub0 N/A

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

      13. remove-double-neg N/A

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

      14. --lowering--.f64 N/A

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

      15. neg-sub0 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. associate--r+ N/A

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

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. --lowering--.f64 93.1

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

   4. Applied egg-rr 93.1%

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

   5. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 93.1

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

   7. Simplified 93.1%

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

   8. Taylor expanded in t around inf

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

      1. /-lowering-/.f64 76.7

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

   10. Simplified 76.7%

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

   if -5.00000000000000029e62 < (/.f64 (-.f64 z t) (-.f64 a t)) < 0.0200000000000000004

   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. accelerator-lowering-fma.f64 N/A

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

      4. /-lowering-/.f64 85.3

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

   5. Simplified 85.3%

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

   if 0.0200000000000000004 < (/.f64 (-.f64 z t) (-.f64 a t)) < 50

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   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. +-lowering-+.f64 95.8

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

   5. Simplified 95.8%

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

   if 50 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 88.0%

      \[x + y \cdot \frac{z - t}{a - t} \]
   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. *-lowering-*.f64 N/A

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

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

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

      4. --lowering--.f64 73.2

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

   5. Simplified 73.2%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq -5 \cdot 10^{+62}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, -z, x\right)\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 0.02:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a}, x\right)\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 50:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+134}:\\ \;\;\;\;\frac{y \cdot z}{a - t}\\ \mathbf{elif}\;t\_1 \leq 0.02:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 50:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (<= t_1 -5e+134)
     (/ (* y z) (- a t))
     (if (<= t_1 0.02)
       (fma y (/ z a) x)
       (if (<= t_1 50.0) (+ x y) (* y (/ z (- a t))))))))

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+134) {
		tmp = (y * z) / (a - t);
	} else if (t_1 <= 0.02) {
		tmp = fma(y, (z / a), x);
	} else if (t_1 <= 50.0) {
		tmp = x + y;
	} else {
		tmp = y * (z / (a - t));
	}
	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+134)
		tmp = Float64(Float64(y * z) / Float64(a - t));
	elseif (t_1 <= 0.02)
		tmp = fma(y, Float64(z / a), x);
	elseif (t_1 <= 50.0)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(z / Float64(a - t)));
	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, -5e+134], N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.02], N[(y * N[(z / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 50.0], N[(x + y), $MachinePrecision], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -4.99999999999999981e134

   1. Initial program 89.1%

      \[x + y \cdot \frac{z - t}{a - t} \]
   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. *-lowering-*.f64 N/A

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

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

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

      4. --lowering--.f64 71.8

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

   5. Simplified 71.8%

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

      1. associate-*r/ N/A

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

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

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

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

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

      4. --lowering--.f64 82.4

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

   7. Applied egg-rr 82.4%

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

   if -4.99999999999999981e134 < (/.f64 (-.f64 z t) (-.f64 a t)) < 0.0200000000000000004

   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. accelerator-lowering-fma.f64 N/A

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

      4. /-lowering-/.f64 81.7

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

   5. Simplified 81.7%

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

   if 0.0200000000000000004 < (/.f64 (-.f64 z t) (-.f64 a t)) < 50

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   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. +-lowering-+.f64 95.8

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

   5. Simplified 95.8%

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

   if 50 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 88.0%

      \[x + y \cdot \frac{z - t}{a - t} \]
   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. *-lowering-*.f64 N/A

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

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

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

      4. --lowering--.f64 73.2

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

   5. Simplified 73.2%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq -5 \cdot 10^{+134}:\\ \;\;\;\;\frac{y \cdot z}{a - t}\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 0.02:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a}, x\right)\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 50:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := y \cdot \frac{z}{a - t}\\ \mathbf{if}\;t\_1 \leq -40000000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.02:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 50:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))) (t_2 (* y (/ z (- a t)))))
   (if (<= t_1 -40000000000000.0)
     t_2
     (if (<= t_1 0.02) (fma y (/ z a) x) (if (<= t_1 50.0) (+ x y) 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 * (z / (a - t));
	double tmp;
	if (t_1 <= -40000000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.02) {
		tmp = fma(y, (z / a), x);
	} else if (t_1 <= 50.0) {
		tmp = x + y;
	} 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(y * Float64(z / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -40000000000000.0)
		tmp = t_2;
	elseif (t_1 <= 0.02)
		tmp = fma(y, Float64(z / a), x);
	elseif (t_1 <= 50.0)
		tmp = Float64(x + y);
	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[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -40000000000000.0], t$95$2, If[LessEqual[t$95$1, 0.02], N[(y * N[(z / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 50.0], N[(x + y), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -4e13 or 50 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 91.1%

      \[x + y \cdot \frac{z - t}{a - t} \]
   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. *-lowering-*.f64 N/A

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

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

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

      4. --lowering--.f64 68.9

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

   5. Simplified 68.9%

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

   if -4e13 < (/.f64 (-.f64 z t) (-.f64 a t)) < 0.0200000000000000004

   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. accelerator-lowering-fma.f64 N/A

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

      4. /-lowering-/.f64 86.4

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

   5. Simplified 86.4%

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

   if 0.0200000000000000004 < (/.f64 (-.f64 z t) (-.f64 a t)) < 50

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   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. +-lowering-+.f64 95.8

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

   5. Simplified 95.8%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq -40000000000000:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 0.02:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a}, x\right)\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 50:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 79.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+245}:\\ \;\;\;\;-\frac{y \cdot z}{t}\\ \mathbf{elif}\;t\_1 \leq 0.02:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+74}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (<= t_1 -2e+245)
     (- (/ (* y z) t))
     (if (<= t_1 0.02)
       (fma y (/ z a) x)
       (if (<= t_1 2e+74) (+ x y) (- (* z (/ y t))))))))

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 <= -2e+245) {
		tmp = -((y * z) / t);
	} else if (t_1 <= 0.02) {
		tmp = fma(y, (z / a), x);
	} else if (t_1 <= 2e+74) {
		tmp = x + y;
	} else {
		tmp = -(z * (y / t));
	}
	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 <= -2e+245)
		tmp = Float64(-Float64(Float64(y * z) / t));
	elseif (t_1 <= 0.02)
		tmp = fma(y, Float64(z / a), x);
	elseif (t_1 <= 2e+74)
		tmp = Float64(x + y);
	else
		tmp = Float64(-Float64(z * Float64(y / t)));
	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, -2e+245], (-N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), If[LessEqual[t$95$1, 0.02], N[(y * N[(z / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 2e+74], N[(x + y), $MachinePrecision], (-N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision])]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -2.00000000000000009e245

   1. Initial program 77.3%

      \[x + y \cdot \frac{z - t}{a - t} \]
   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. *-lowering-*.f64 N/A

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

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

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

      4. --lowering--.f64 77.3

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

   5. Simplified 77.3%

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

   6. Taylor expanded in a around 0

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

      1. associate-*r/ N/A

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

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

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

      3. mul-1-neg N/A

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

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

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

      5. mul-1-neg N/A

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

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

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

      7. mul-1-neg N/A

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

      8. neg-lowering-neg.f64 77.3

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

   8. Simplified 77.3%

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

   if -2.00000000000000009e245 < (/.f64 (-.f64 z t) (-.f64 a t)) < 0.0200000000000000004

   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. accelerator-lowering-fma.f64 N/A

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

      4. /-lowering-/.f64 79.9

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

   5. Simplified 79.9%

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

   if 0.0200000000000000004 < (/.f64 (-.f64 z t) (-.f64 a t)) < 1.9999999999999999e74

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   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. +-lowering-+.f64 87.0

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

   5. Simplified 87.0%

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

   if 1.9999999999999999e74 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 81.2%

      \[x + y \cdot \frac{z - t}{a - t} \]
   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. *-lowering-*.f64 N/A

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

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

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

      4. --lowering--.f64 77.6

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

   5. Simplified 77.6%

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

   6. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 54.9

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

   8. Simplified 54.9%

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

      1. associate-*r/ N/A

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

      2. neg-mul-1 N/A

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

      3. *-commutative N/A

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

      4. times-frac N/A

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

      5. div-inv N/A

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

      6. metadata-eval N/A

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

      7. *-commutative N/A

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

      8. neg-mul-1 N/A

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

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

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

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

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

      11. neg-lowering-neg.f64 65.9

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

   10. Applied egg-rr 65.9%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq -2 \cdot 10^{+245}:\\ \;\;\;\;-\frac{y \cdot z}{t}\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 0.02:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a}, x\right)\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 2 \cdot 10^{+74}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 79.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := -z \cdot \frac{y}{t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+245}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.02:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+74}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))) (t_2 (- (* z (/ y t)))))
   (if (<= t_1 -2e+245)
     t_2
     (if (<= t_1 0.02) (fma y (/ z a) x) (if (<= t_1 2e+74) (+ x y) 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 = -(z * (y / t));
	double tmp;
	if (t_1 <= -2e+245) {
		tmp = t_2;
	} else if (t_1 <= 0.02) {
		tmp = fma(y, (z / a), x);
	} else if (t_1 <= 2e+74) {
		tmp = x + y;
	} 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(z * Float64(y / t)))
	tmp = 0.0
	if (t_1 <= -2e+245)
		tmp = t_2;
	elseif (t_1 <= 0.02)
		tmp = fma(y, Float64(z / a), x);
	elseif (t_1 <= 2e+74)
		tmp = Float64(x + y);
	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[(z * N[(y / t), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[t$95$1, -2e+245], t$95$2, If[LessEqual[t$95$1, 0.02], N[(y * N[(z / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 2e+74], N[(x + y), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -2.00000000000000009e245 or 1.9999999999999999e74 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 80.3%

      \[x + y \cdot \frac{z - t}{a - t} \]
   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. *-lowering-*.f64 N/A

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

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

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

      4. --lowering--.f64 77.5

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

   5. Simplified 77.5%

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

   6. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 58.4

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

   8. Simplified 58.4%

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

      1. associate-*r/ N/A

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

      2. neg-mul-1 N/A

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

      3. *-commutative N/A

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

      4. times-frac N/A

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

      5. div-inv N/A

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

      6. metadata-eval N/A

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

      7. *-commutative N/A

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

      8. neg-mul-1 N/A

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

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

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

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

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

      11. neg-lowering-neg.f64 68.5

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

   10. Applied egg-rr 68.5%

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

   if -2.00000000000000009e245 < (/.f64 (-.f64 z t) (-.f64 a t)) < 0.0200000000000000004

   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. accelerator-lowering-fma.f64 N/A

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

      4. /-lowering-/.f64 79.9

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

   5. Simplified 79.9%

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

   if 0.0200000000000000004 < (/.f64 (-.f64 z t) (-.f64 a t)) < 1.9999999999999999e74

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   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. +-lowering-+.f64 87.0

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

   5. Simplified 87.0%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq -2 \cdot 10^{+245}:\\ \;\;\;\;-z \cdot \frac{y}{t}\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 0.02:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a}, x\right)\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 2 \cdot 10^{+74}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 77.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := y \cdot \frac{z}{-t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+245}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.02:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+19}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))) (t_2 (* y (/ z (- t)))))
   (if (<= t_1 -2e+245)
     t_2
     (if (<= t_1 0.02) (fma y (/ z a) x) (if (<= t_1 2e+19) (+ x y) 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 * (z / -t);
	double tmp;
	if (t_1 <= -2e+245) {
		tmp = t_2;
	} else if (t_1 <= 0.02) {
		tmp = fma(y, (z / a), x);
	} else if (t_1 <= 2e+19) {
		tmp = x + y;
	} 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(y * Float64(z / Float64(-t)))
	tmp = 0.0
	if (t_1 <= -2e+245)
		tmp = t_2;
	elseif (t_1 <= 0.02)
		tmp = fma(y, Float64(z / a), x);
	elseif (t_1 <= 2e+19)
		tmp = Float64(x + y);
	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[(y * N[(z / (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+245], t$95$2, If[LessEqual[t$95$1, 0.02], N[(y * N[(z / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 2e+19], N[(x + y), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -2.00000000000000009e245 or 2e19 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 84.4%

      \[x + y \cdot \frac{z - t}{a - t} \]
   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. *-lowering-*.f64 N/A

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

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

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

      4. --lowering--.f64 74.8

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

   5. Simplified 74.8%

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

   6. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 55.2

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

   8. Simplified 55.2%

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

   if -2.00000000000000009e245 < (/.f64 (-.f64 z t) (-.f64 a t)) < 0.0200000000000000004

   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. accelerator-lowering-fma.f64 N/A

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

      4. /-lowering-/.f64 79.9

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

   5. Simplified 79.9%

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

   if 0.0200000000000000004 < (/.f64 (-.f64 z t) (-.f64 a t)) < 2e19

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   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. +-lowering-+.f64 91.9

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

   5. Simplified 91.9%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq -2 \cdot 10^{+245}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 0.02:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a}, x\right)\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 2 \cdot 10^{+19}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 70.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+157}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{elif}\;t\_1 \leq 50:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (<= t_1 -5e+157)
     (/ (* y z) a)
     (if (<= t_1 2e-91) x (if (<= t_1 50.0) (+ x y) (* y (/ z a)))))))

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+157) {
		tmp = (y * z) / a;
	} else if (t_1 <= 2e-91) {
		tmp = x;
	} else if (t_1 <= 50.0) {
		tmp = x + y;
	} else {
		tmp = y * (z / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z - t) / (a - t)
    if (t_1 <= (-5d+157)) then
        tmp = (y * z) / a
    else if (t_1 <= 2d-91) then
        tmp = x
    else if (t_1 <= 50.0d0) then
        tmp = x + y
    else
        tmp = y * (z / a)
    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+157) {
		tmp = (y * z) / a;
	} else if (t_1 <= 2e-91) {
		tmp = x;
	} else if (t_1 <= 50.0) {
		tmp = x + y;
	} else {
		tmp = y * (z / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (a - t)
	tmp = 0
	if t_1 <= -5e+157:
		tmp = (y * z) / a
	elif t_1 <= 2e-91:
		tmp = x
	elif t_1 <= 50.0:
		tmp = x + y
	else:
		tmp = y * (z / a)
	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+157)
		tmp = Float64(Float64(y * z) / a);
	elseif (t_1 <= 2e-91)
		tmp = x;
	elseif (t_1 <= 50.0)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(z / a));
	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+157)
		tmp = (y * z) / a;
	elseif (t_1 <= 2e-91)
		tmp = x;
	elseif (t_1 <= 50.0)
		tmp = x + y;
	else
		tmp = y * (z / a);
	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+157], N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t$95$1, 2e-91], x, If[LessEqual[t$95$1, 50.0], N[(x + y), $MachinePrecision], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -4.99999999999999976e157

   1. Initial program 86.0%

      \[x + y \cdot \frac{z - t}{a - t} \]
   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. *-lowering-*.f64 N/A

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

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

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

      4. --lowering--.f64 78.4

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

   5. Simplified 78.4%

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

   6. Taylor expanded in a around inf

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

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

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

      2. *-lowering-*.f64 40.6

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

   8. Simplified 40.6%

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

   if -4.99999999999999976e157 < (/.f64 (-.f64 z t) (-.f64 a t)) < 2.00000000000000004e-91

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 73.1%

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

   if 2.00000000000000004e-91 < (/.f64 (-.f64 z t) (-.f64 a t)) < 50

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   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. +-lowering-+.f64 86.8

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

   5. Simplified 86.8%

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

   if 50 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 88.0%

      \[x + y \cdot \frac{z - t}{a - t} \]
   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. *-lowering-*.f64 N/A

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

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

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

      4. --lowering--.f64 73.2

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

   5. Simplified 73.2%

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

   6. Taylor expanded in a around inf

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

   8. Simplified 40.1%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq -5 \cdot 10^{+157}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 2 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 50:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 81.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq 0.02:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 2000000:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (<= t_1 0.02)
     (fma y (/ z a) x)
     (if (<= t_1 2000000.0) (+ x y) (fma z (/ y a) 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 <= 0.02) {
		tmp = fma(y, (z / a), x);
	} else if (t_1 <= 2000000.0) {
		tmp = x + y;
	} else {
		tmp = fma(z, (y / a), 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 <= 0.02)
		tmp = fma(y, Float64(z / a), x);
	elseif (t_1 <= 2000000.0)
		tmp = Float64(x + y);
	else
		tmp = fma(z, Float64(y / a), 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[LessEqual[t$95$1, 0.02], N[(y * N[(z / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 2000000.0], N[(x + y), $MachinePrecision], N[(z * N[(y / a), $MachinePrecision] + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 0.0200000000000000004

   1. Initial program 98.4%

      \[x + y \cdot \frac{z - t}{a - t} \]
   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. accelerator-lowering-fma.f64 N/A

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

      4. /-lowering-/.f64 76.1

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

   5. Simplified 76.1%

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

   if 0.0200000000000000004 < (/.f64 (-.f64 z t) (-.f64 a t)) < 2e6

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   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. +-lowering-+.f64 94.8

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

   5. Simplified 94.8%

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

   if 2e6 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 87.7%

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

      1. +-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. frac-2neg N/A

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

      5. associate-/r/ N/A

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

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

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

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

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

      8. neg-sub0 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. associate--r+ N/A

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

      12. neg-sub0 N/A

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

      13. remove-double-neg N/A

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

      14. --lowering--.f64 N/A

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

      15. neg-sub0 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. associate--r+ N/A

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

      19. neg-sub0 N/A

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

      20. remove-double-neg N/A

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

      21. --lowering--.f64 95.2

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

   4. Applied egg-rr 95.2%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

      5. /-lowering-/.f64 46.7

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

   7. Simplified 46.7%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq 0.02:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a}, x\right)\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 2000000:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 81.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := \mathsf{fma}\left(y, \frac{z}{a}, x\right)\\ \mathbf{if}\;t\_1 \leq 0.02:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))) (t_2 (fma y (/ z a) x)))
   (if (<= t_1 0.02) t_2 (if (<= t_1 2.0) (+ x y) 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 = fma(y, (z / a), x);
	double tmp;
	if (t_1 <= 0.02) {
		tmp = t_2;
	} else if (t_1 <= 2.0) {
		tmp = x + y;
	} 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 = fma(y, Float64(z / a), x)
	tmp = 0.0
	if (t_1 <= 0.02)
		tmp = t_2;
	elseif (t_1 <= 2.0)
		tmp = Float64(x + y);
	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[(y * N[(z / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t$95$1, 0.02], t$95$2, If[LessEqual[t$95$1, 2.0], N[(x + y), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 0.0200000000000000004 or 2 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 95.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   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. accelerator-lowering-fma.f64 N/A

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

      4. /-lowering-/.f64 68.9

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

   5. Simplified 68.9%

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

   if 0.0200000000000000004 < (/.f64 (-.f64 z t) (-.f64 a t)) < 2

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   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. +-lowering-+.f64 95.7

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

   5. Simplified 95.7%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq 0.02:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a}, x\right)\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 2:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 68.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{elif}\;t\_1 \leq 50:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (<= t_1 2e-91) x (if (<= t_1 50.0) (+ x y) (* y (/ z a))))))

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 <= 2e-91) {
		tmp = x;
	} else if (t_1 <= 50.0) {
		tmp = x + y;
	} else {
		tmp = y * (z / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z - t) / (a - t)
    if (t_1 <= 2d-91) then
        tmp = x
    else if (t_1 <= 50.0d0) then
        tmp = x + y
    else
        tmp = y * (z / a)
    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 <= 2e-91) {
		tmp = x;
	} else if (t_1 <= 50.0) {
		tmp = x + y;
	} else {
		tmp = y * (z / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (a - t)
	tmp = 0
	if t_1 <= 2e-91:
		tmp = x
	elif t_1 <= 50.0:
		tmp = x + y
	else:
		tmp = y * (z / a)
	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 <= 2e-91)
		tmp = x;
	elseif (t_1 <= 50.0)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(z / a));
	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 <= 2e-91)
		tmp = x;
	elseif (t_1 <= 50.0)
		tmp = x + y;
	else
		tmp = y * (z / a);
	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, 2e-91], x, If[LessEqual[t$95$1, 50.0], N[(x + y), $MachinePrecision], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 2.00000000000000004e-91

   1. Initial program 98.1%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 65.7%

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

   if 2.00000000000000004e-91 < (/.f64 (-.f64 z t) (-.f64 a t)) < 50

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   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. +-lowering-+.f64 86.8

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

   5. Simplified 86.8%

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

   if 50 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 88.0%

      \[x + y \cdot \frac{z - t}{a - t} \]
   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. *-lowering-*.f64 N/A

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

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

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

      4. --lowering--.f64 73.2

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

   5. Simplified 73.2%

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

   6. Taylor expanded in a around inf

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

   8. Simplified 40.1%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq 2 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z - t}{a - t} \leq 50:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 98.0% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

   1. clear-num N/A

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

   2. un-div-inv N/A

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

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

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

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

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

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

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

   6. --lowering--.f64 97.8

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

4. Applied egg-rr 97.8%

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

Alternative 18: 53.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot \frac{z - t}{a - t} \leq -5 \cdot 10^{+118}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* y (/ (- z t) (- a t))) -5e+118) y x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y * ((z - t) / (a - t))) <= -5e+118) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y * ((z - t) / (a - t))) <= (-5d+118)) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y * ((z - t) / (a - t))) <= -5e+118) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y * ((z - t) / (a - t))) <= -5e+118:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(y * Float64(Float64(z - t) / Float64(a - t))) <= -5e+118)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y * ((z - t) / (a - t))) <= -5e+118)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -5e+118], y, x]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))) < -4.99999999999999972e118

   1. Initial program 89.2%

      \[x + y \cdot \frac{z - t}{a - t} \]
   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. +-lowering-+.f64 50.0

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

   5. Simplified 50.0%

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

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y} \]
   7. Step-by-step derivation

   8. Simplified 38.3%

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

   if -4.99999999999999972e118 < (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))

   1. Initial program 98.9%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 62.4%

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

Alternative 19: 67.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq 5 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (/ (- z t) (- a t)) 5e-87) x (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z - t) / (a - t)) <= 5e-87) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((z - t) / (a - t)) <= 5d-87) then
        tmp = x
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z - t) / (a - t)) <= 5e-87) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((z - t) / (a - t)) <= 5e-87:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(z - t) / Float64(a - t)) <= 5e-87)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((z - t) / (a - t)) <= 5e-87)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], 5e-87], x, N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 5.00000000000000042e-87

   1. Initial program 98.1%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 65.7%

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

   if 5.00000000000000042e-87 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 96.5%

      \[x + y \cdot \frac{z - t}{a - t} \]
   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. +-lowering-+.f64 68.9

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

   5. Simplified 68.9%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq 5 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 96.1% 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 97.2%

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

   1. +-commutative N/A

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

   2. clear-num N/A

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

   3. un-div-inv N/A

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

   4. frac-2neg N/A

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

   5. associate-/r/ N/A

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

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

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

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

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

   8. neg-sub0 N/A

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

   9. sub-neg N/A

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

   10. +-commutative N/A

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

   11. associate--r+ N/A

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

   12. neg-sub0 N/A

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

   13. remove-double-neg N/A

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

   14. --lowering--.f64 N/A

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

   15. neg-sub0 N/A

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

   16. sub-neg N/A

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

   17. +-commutative N/A

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

   18. associate--r+ N/A

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

   19. neg-sub0 N/A

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

   20. remove-double-neg N/A

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

   21. --lowering--.f64 94.7

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

4. Applied egg-rr 94.7%

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

Alternative 21: 50.9% accurate, 26.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 97.2%

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

3. Taylor expanded in x around inf

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

5. Simplified 53.9%

   \[\leadsto \color{blue}{x} \]
6. 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 2024198 
(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)))))