Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3

Percentage Accurate: 68.0% → 89.5%

Time: 13.3s

Alternatives: 19

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-207}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;y + \frac{\mathsf{fma}\left(a, \frac{x - y}{t} \cdot \left(z - a\right), \left(y - x\right) \cdot \left(a - z\right)\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- z t) (- a t)) (- y x) x))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 -5e-207)
     t_1
     (if (<= t_2 0.0)
       (+ y (/ (fma a (* (/ (- x y) t) (- z a)) (* (- y x) (- a z))) t))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((z - t) / (a - t)), (y - x), x);
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -5e-207) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = y + (fma(a, (((x - y) / t) * (z - a)), ((y - x) * (a - z))) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(z - t) / Float64(a - t)), Float64(y - x), x)
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -5e-207)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(fma(a, Float64(Float64(Float64(x - y) / t) * Float64(z - a)), Float64(Float64(y - x) * Float64(a - z))) / t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-207], t$95$1, If[LessEqual[t$95$2, 0.0], N[(y + N[(N[(a * N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision] + N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -5.00000000000000014e-207 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 71.3%

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

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

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

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

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

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

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

      8. --lowering--.f64 91.2

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

   4. Applied egg-rr 91.2%

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

   if -5.00000000000000014e-207 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.5%

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

   3. Taylor expanded in t around -inf

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

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

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

      2. associate-*r/ N/A

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

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

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

   5. Simplified 99.8%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -5 \cdot 10^{-207}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\mathsf{fma}\left(a, \frac{x - y}{t} \cdot \left(z - a\right), \left(y - x\right) \cdot \left(a - z\right)\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-207}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- z t) (- a t)) (- y x) x))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 -5e-207)
     t_1
     (if (<= t_2 0.0) (+ y (* (- y x) (/ (- a z) t))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((z - t) / (a - t)), (y - x), x);
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -5e-207) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(z - t) / Float64(a - t)), Float64(y - x), x)
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -5e-207)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-207], t$95$1, If[LessEqual[t$95$2, 0.0], N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -5.00000000000000014e-207 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 71.3%

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

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

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

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

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

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

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

      8. --lowering--.f64 91.2

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

   4. Applied egg-rr 91.2%

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

   if -5.00000000000000014e-207 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.5%

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

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

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

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

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

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

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

      8. --lowering--.f64 4.8

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

   4. Applied egg-rr 4.8%

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

   5. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

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

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

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

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

      8. associate-/l* N/A

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

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

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

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

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

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

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

      12. --lowering--.f64 99.7

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

   7. Simplified 99.7%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -5 \cdot 10^{-207}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.15 \cdot 10^{-175}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{x - y}{a}, x\right)\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-298}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-78}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+116}:\\ \;\;\;\;\frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- 1.0 (/ z t)))))
   (if (<= t -1.15e+104)
     t_1
     (if (<= t -4.15e-175)
       (fma t (/ (- x y) a) x)
       (if (<= t -3e-298)
         (* x (- 1.0 (/ z a)))
         (if (<= t 6.2e-78)
           (fma (/ z a) y x)
           (if (<= t 1.15e+116) (/ (* z (- x y)) t) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (z / t));
	double tmp;
	if (t <= -1.15e+104) {
		tmp = t_1;
	} else if (t <= -4.15e-175) {
		tmp = fma(t, ((x - y) / a), x);
	} else if (t <= -3e-298) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 6.2e-78) {
		tmp = fma((z / a), y, x);
	} else if (t <= 1.15e+116) {
		tmp = (z * (x - y)) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(1.0 - Float64(z / t)))
	tmp = 0.0
	if (t <= -1.15e+104)
		tmp = t_1;
	elseif (t <= -4.15e-175)
		tmp = fma(t, Float64(Float64(x - y) / a), x);
	elseif (t <= -3e-298)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 6.2e-78)
		tmp = fma(Float64(z / a), y, x);
	elseif (t <= 1.15e+116)
		tmp = Float64(Float64(z * Float64(x - y)) / t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e+104], t$95$1, If[LessEqual[t, -4.15e-175], N[(t * N[(N[(x - y), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, -3e-298], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e-78], N[(N[(z / a), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[t, 1.15e+116], N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.14999999999999992e104 or 1.14999999999999997e116 < t

   1. Initial program 33.3%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

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

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

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

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

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

      12. div-sub N/A

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

      13. sub-neg N/A

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

      14. *-inverses N/A

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

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

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

      18. /-lowering-/.f64 50.8

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

   5. Simplified 50.8%

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

   6. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. +-commutative N/A

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

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

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

      9. mul-1-neg N/A

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

      10. unsub-neg N/A

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

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

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

      12. /-lowering-/.f64 53.2

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

   8. Simplified 53.2%

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

   if -1.14999999999999992e104 < t < -4.15000000000000026e-175

   1. Initial program 77.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

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

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

      6. mul-1-neg N/A

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

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

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. unsub-neg N/A

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

      13. remove-double-neg N/A

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

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

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

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

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

      16. --lowering--.f64 54.2

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

   5. Simplified 54.2%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. div-sub N/A

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

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

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

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

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

      5. --lowering--.f64 55.6

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

   8. Simplified 55.6%

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

   if -4.15000000000000026e-175 < t < -2.9999999999999999e-298

   1. Initial program 99.8%

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

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

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

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

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

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

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

      8. --lowering--.f64 96.5

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

   4. Applied egg-rr 96.5%

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

   5. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 92.8

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

   7. Simplified 92.8%

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

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x \cdot z}{a}} \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. *-rgt-identity N/A

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

      3. associate-/l* N/A

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

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

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

      5. mul-1-neg N/A

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

      6. distribute-lft-in N/A

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

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

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

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

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

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

      11. /-lowering-/.f64 86.2

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

   10. Simplified 86.2%

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

   if -2.9999999999999999e-298 < t < 6.20000000000000035e-78

   1. Initial program 82.8%

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

      1. +-commutative N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

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

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

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

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

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

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

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

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

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

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

      11. --lowering--.f64 96.0

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

   4. Applied egg-rr 96.0%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 83.0%

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

   8. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 77.1

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

   10. Simplified 77.1%

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

   if 6.20000000000000035e-78 < t < 1.14999999999999997e116

   1. Initial program 83.4%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

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

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

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

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

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

      12. div-sub N/A

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

      13. sub-neg N/A

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

      14. *-inverses N/A

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

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

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

      18. /-lowering-/.f64 58.9

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

   5. Simplified 58.9%

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

   6. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 49.7

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

   8. Simplified 49.7%

      \[\leadsto \color{blue}{\frac{z \cdot \left(x - y\right)}{t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+104}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq -4.15 \cdot 10^{-175}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{x - y}{a}, x\right)\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-298}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-78}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+116}:\\ \;\;\;\;\frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;t \leq -3.9 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-94}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y - x}{a}, x\right)\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+168}:\\ \;\;\;\;\mathsf{fma}\left(x - y, \frac{z}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- 1.0 (/ z t)))))
   (if (<= t -3.9e+131)
     t_1
     (if (<= t 3.4e-94)
       (fma z (/ (- y x) a) x)
       (if (<= t 2.1e+168) (fma (- x y) (/ z t) x) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (z / t));
	double tmp;
	if (t <= -3.9e+131) {
		tmp = t_1;
	} else if (t <= 3.4e-94) {
		tmp = fma(z, ((y - x) / a), x);
	} else if (t <= 2.1e+168) {
		tmp = fma((x - y), (z / t), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(1.0 - Float64(z / t)))
	tmp = 0.0
	if (t <= -3.9e+131)
		tmp = t_1;
	elseif (t <= 3.4e-94)
		tmp = fma(z, Float64(Float64(y - x) / a), x);
	elseif (t <= 2.1e+168)
		tmp = fma(Float64(x - y), Float64(z / t), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.9e+131], t$95$1, If[LessEqual[t, 3.4e-94], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 2.1e+168], N[(N[(x - y), $MachinePrecision] * N[(z / t), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.9e131 or 2.10000000000000003e168 < t

   1. Initial program 29.2%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

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

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

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

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

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

      12. div-sub N/A

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

      13. sub-neg N/A

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

      14. *-inverses N/A

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

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

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

      18. /-lowering-/.f64 57.9

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

   5. Simplified 57.9%

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

   6. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. +-commutative N/A

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

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

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

      9. mul-1-neg N/A

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

      10. unsub-neg N/A

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

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

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

      12. /-lowering-/.f64 61.5

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

   8. Simplified 61.5%

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

   if -3.9e131 < t < 3.3999999999999998e-94

   1. Initial program 81.7%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 74.4

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

   5. Simplified 74.4%

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

   if 3.3999999999999998e-94 < t < 2.10000000000000003e168

   1. Initial program 75.4%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

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

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

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

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

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

      12. div-sub N/A

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

      13. sub-neg N/A

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

      14. *-inverses N/A

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

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

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

      18. /-lowering-/.f64 50.0

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

   5. Simplified 50.0%

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

   6. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 55.1

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

   8. Simplified 55.1%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+131}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-94}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y - x}{a}, x\right)\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+168}:\\ \;\;\;\;\mathsf{fma}\left(x - y, \frac{z}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{+144}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+166}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* (- y x) (/ (- a z) t)))))
   (if (<= t -3.7e+144)
     t_1
     (if (<= t 4e+166) (fma (- z t) (/ (- y x) (- a t)) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((y - x) * ((a - z) / t));
	double tmp;
	if (t <= -3.7e+144) {
		tmp = t_1;
	} else if (t <= 4e+166) {
		tmp = fma((z - t), ((y - x) / (a - t)), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)))
	tmp = 0.0
	if (t <= -3.7e+144)
		tmp = t_1;
	elseif (t <= 4e+166)
		tmp = fma(Float64(z - t), Float64(Float64(y - x) / Float64(a - t)), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.7e+144], t$95$1, If[LessEqual[t, 4e+166], N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.6999999999999997e144 or 3.99999999999999976e166 < t

   1. Initial program 29.2%

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

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

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

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

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

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

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

      8. --lowering--.f64 69.3

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

   4. Applied egg-rr 69.3%

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

   5. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

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

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

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

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

      8. associate-/l* N/A

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

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

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

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

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

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

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

      12. --lowering--.f64 89.4

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

   7. Simplified 89.4%

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

   if -3.6999999999999997e144 < t < 3.99999999999999976e166

   1. Initial program 80.0%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

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

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

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

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

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

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

      8. --lowering--.f64 91.5

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

   4. Applied egg-rr 91.5%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+144}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+166}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 54.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;t \leq -2.25 \cdot 10^{+128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-78}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+118}:\\ \;\;\;\;\frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- 1.0 (/ z t)))))
   (if (<= t -2.25e+128)
     t_1
     (if (<= t 7.2e-78)
       (fma (/ z a) y x)
       (if (<= t 9e+118) (/ (* z (- x y)) t) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (z / t));
	double tmp;
	if (t <= -2.25e+128) {
		tmp = t_1;
	} else if (t <= 7.2e-78) {
		tmp = fma((z / a), y, x);
	} else if (t <= 9e+118) {
		tmp = (z * (x - y)) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(1.0 - Float64(z / t)))
	tmp = 0.0
	if (t <= -2.25e+128)
		tmp = t_1;
	elseif (t <= 7.2e-78)
		tmp = fma(Float64(z / a), y, x);
	elseif (t <= 9e+118)
		tmp = Float64(Float64(z * Float64(x - y)) / t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.25e+128], t$95$1, If[LessEqual[t, 7.2e-78], N[(N[(z / a), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[t, 9e+118], N[(N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.2500000000000001e128 or 9.00000000000000004e118 < t

   1. Initial program 31.5%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

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

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

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

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

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

      12. div-sub N/A

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

      13. sub-neg N/A

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

      14. *-inverses N/A

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

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

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

      18. /-lowering-/.f64 52.6

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

   5. Simplified 52.6%

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

   6. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. +-commutative N/A

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

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

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

      9. mul-1-neg N/A

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

      10. unsub-neg N/A

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

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

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

      12. /-lowering-/.f64 55.2

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

   8. Simplified 55.2%

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

   if -2.2500000000000001e128 < t < 7.2000000000000005e-78

   1. Initial program 83.3%

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

      1. +-commutative N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

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

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

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

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

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

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

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

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

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

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

      11. --lowering--.f64 92.7

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

   4. Applied egg-rr 92.7%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 75.2%

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

   8. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 61.4

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

   10. Simplified 61.4%

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

   if 7.2000000000000005e-78 < t < 9.00000000000000004e118

   1. Initial program 83.4%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

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

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

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

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

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

      12. div-sub N/A

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

      13. sub-neg N/A

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

      14. *-inverses N/A

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

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

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

      18. /-lowering-/.f64 58.9

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

   5. Simplified 58.9%

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

   6. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 49.7

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

   8. Simplified 49.7%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{+128}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-78}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+118}:\\ \;\;\;\;\frac{z \cdot \left(x - y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+131}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-49}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+168}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.2e+131)
   y
   (if (<= t 6.5e-49)
     (fma (/ z a) y x)
     (if (<= t 3.2e+168) (* x (/ (- z a) t)) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.2e+131) {
		tmp = y;
	} else if (t <= 6.5e-49) {
		tmp = fma((z / a), y, x);
	} else if (t <= 3.2e+168) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.2e+131)
		tmp = y;
	elseif (t <= 6.5e-49)
		tmp = fma(Float64(z / a), y, x);
	elseif (t <= 3.2e+168)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	else
		tmp = y;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.2e+131], y, If[LessEqual[t, 6.5e-49], N[(N[(z / a), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[t, 3.2e+168], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.19999999999999971e131 or 3.2000000000000001e168 < t

   1. Initial program 29.2%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 51.0%

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

   if -4.19999999999999971e131 < t < 6.49999999999999968e-49

   1. Initial program 82.7%

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

      1. +-commutative N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

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

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

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

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

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

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

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

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

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

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

      11. --lowering--.f64 93.0

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

   4. Applied egg-rr 93.0%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 76.2%

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

   8. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 61.0

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

   10. Simplified 61.0%

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

   if 6.49999999999999968e-49 < t < 3.2000000000000001e168

   1. Initial program 70.8%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

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

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

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

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

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

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

   5. Simplified 63.2%

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

   6. Taylor expanded in x around inf

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

      1. div-sub N/A

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

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

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

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

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

      4. --lowering--.f64 39.4

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

   8. Simplified 39.4%

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

Alternative 8: 52.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+131}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-25}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{elif}\;t \leq 10^{+162}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.5e+131)
   y
   (if (<= t 5.5e-25)
     (fma (/ z a) y x)
     (if (<= t 1e+162) (* x (- 1.0 (/ z a))) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.5e+131) {
		tmp = y;
	} else if (t <= 5.5e-25) {
		tmp = fma((z / a), y, x);
	} else if (t <= 1e+162) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.5e+131)
		tmp = y;
	elseif (t <= 5.5e-25)
		tmp = fma(Float64(z / a), y, x);
	elseif (t <= 1e+162)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = y;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.5e+131], y, If[LessEqual[t, 5.5e-25], N[(N[(z / a), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[t, 1e+162], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.4999999999999999e131 or 9.9999999999999994e161 < t

   1. Initial program 30.9%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 48.9%

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

   if -3.4999999999999999e131 < t < 5.50000000000000004e-25

   1. Initial program 82.6%

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

      1. +-commutative N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

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

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

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

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

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

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

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

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

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

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

      11. --lowering--.f64 92.5

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

   4. Applied egg-rr 92.5%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 75.1%

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

   8. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 59.1

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

   10. Simplified 59.1%

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

   if 5.50000000000000004e-25 < t < 9.9999999999999994e161

   1. Initial program 69.7%

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

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

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

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

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

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

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

      8. --lowering--.f64 83.5

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

   4. Applied egg-rr 83.5%

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

   5. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 44.9

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

   7. Simplified 44.9%

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

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x \cdot z}{a}} \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. *-rgt-identity N/A

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

      3. associate-/l* N/A

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

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

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

      5. mul-1-neg N/A

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

      6. distribute-lft-in N/A

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

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

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

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

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

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

      11. /-lowering-/.f64 42.8

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

   10. Simplified 42.8%

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

Alternative 9: 74.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{if}\;t \leq -27000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-78}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* (- y x) (/ (- a z) t)))))
   (if (<= t -27000000000.0)
     t_1
     (if (<= t 7.2e-78) (fma z (/ (- y x) a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((y - x) * ((a - z) / t));
	double tmp;
	if (t <= -27000000000.0) {
		tmp = t_1;
	} else if (t <= 7.2e-78) {
		tmp = fma(z, ((y - x) / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)))
	tmp = 0.0
	if (t <= -27000000000.0)
		tmp = t_1;
	elseif (t <= 7.2e-78)
		tmp = fma(z, Float64(Float64(y - x) / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -27000000000.0], t$95$1, If[LessEqual[t, 7.2e-78], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.7e10 or 7.2000000000000005e-78 < t

   1. Initial program 49.4%

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

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

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

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

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

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

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

      8. --lowering--.f64 77.9

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

   4. Applied egg-rr 77.9%

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

   5. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

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

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

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

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

      8. associate-/l* N/A

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

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

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

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

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

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

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

      12. --lowering--.f64 73.5

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

   7. Simplified 73.5%

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

   if -2.7e10 < t < 7.2000000000000005e-78

   1. Initial program 89.0%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 84.0

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

   5. Simplified 84.0%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -27000000000:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-78}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x - y}{t}, z - a, y\right)\\ \mathbf{if}\;t \leq -210000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-78}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- x y) t) (- z a) y)))
   (if (<= t -210000000000.0)
     t_1
     (if (<= t 7e-78) (fma z (/ (- y x) a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((x - y) / t), (z - a), y);
	double tmp;
	if (t <= -210000000000.0) {
		tmp = t_1;
	} else if (t <= 7e-78) {
		tmp = fma(z, ((y - x) / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(x - y) / t), Float64(z - a), y)
	tmp = 0.0
	if (t <= -210000000000.0)
		tmp = t_1;
	elseif (t <= 7e-78)
		tmp = fma(z, Float64(Float64(y - x) / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] * N[(z - a), $MachinePrecision] + y), $MachinePrecision]}, If[LessEqual[t, -210000000000.0], t$95$1, If[LessEqual[t, 7e-78], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.1e11 or 6.9999999999999999e-78 < t

   1. Initial program 49.4%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

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

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

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

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

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

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

   5. Simplified 70.2%

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

   if -2.1e11 < t < 6.9999999999999999e-78

   1. Initial program 89.0%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 84.0

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

   5. Simplified 84.0%

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

Alternative 11: 36.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+126}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-287}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-113}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+30}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.45e+126)
   y
   (if (<= t -3.2e-287)
     x
     (if (<= t 2e-113) (* y (/ z a)) (if (<= t 7.2e+30) x (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.45e+126) {
		tmp = y;
	} else if (t <= -3.2e-287) {
		tmp = x;
	} else if (t <= 2e-113) {
		tmp = y * (z / a);
	} else if (t <= 7.2e+30) {
		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 (t <= (-1.45d+126)) then
        tmp = y
    else if (t <= (-3.2d-287)) then
        tmp = x
    else if (t <= 2d-113) then
        tmp = y * (z / a)
    else if (t <= 7.2d+30) 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 (t <= -1.45e+126) {
		tmp = y;
	} else if (t <= -3.2e-287) {
		tmp = x;
	} else if (t <= 2e-113) {
		tmp = y * (z / a);
	} else if (t <= 7.2e+30) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.45e+126:
		tmp = y
	elif t <= -3.2e-287:
		tmp = x
	elif t <= 2e-113:
		tmp = y * (z / a)
	elif t <= 7.2e+30:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.45e+126)
		tmp = y;
	elseif (t <= -3.2e-287)
		tmp = x;
	elseif (t <= 2e-113)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 7.2e+30)
		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 (t <= -1.45e+126)
		tmp = y;
	elseif (t <= -3.2e-287)
		tmp = x;
	elseif (t <= 2e-113)
		tmp = y * (z / a);
	elseif (t <= 7.2e+30)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.45e+126], y, If[LessEqual[t, -3.2e-287], x, If[LessEqual[t, 2e-113], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e+30], x, N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.44999999999999993e126

   1. Initial program 25.3%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 52.5%

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

   if -1.44999999999999993e126 < t < -3.20000000000000018e-287 or 1.99999999999999996e-113 < t < 7.2000000000000004e30

   1. Initial program 84.6%

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

   3. Taylor expanded in a around inf

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

   5. Simplified 40.0%

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

   if -3.20000000000000018e-287 < t < 1.99999999999999996e-113

   1. Initial program 80.8%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 42.8

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

   5. Simplified 42.8%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 53.3

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

   7. Applied egg-rr 53.3%

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

   8. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 48.0

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

   10. Simplified 48.0%

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

   if 7.2000000000000004e30 < t

   1. Initial program 49.7%

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

      1. +-commutative N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

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

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

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

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

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

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

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

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

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

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

      11. --lowering--.f64 80.8

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

   4. Applied egg-rr 80.8%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 56.2%

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

   8. Taylor expanded in t around inf

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

      1. +-lowering-+.f64 32.9

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

   10. Simplified 32.9%

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

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+126}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-287}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-113}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+30}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 69.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x - y, \frac{z}{t}, y\right)\\ \mathbf{if}\;t \leq -57000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-78}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- x y) (/ z t) y)))
   (if (<= t -57000000000.0)
     t_1
     (if (<= t 7.2e-78) (fma z (/ (- y x) a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x - y), (z / t), y);
	double tmp;
	if (t <= -57000000000.0) {
		tmp = t_1;
	} else if (t <= 7.2e-78) {
		tmp = fma(z, ((y - x) / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x - y), Float64(z / t), y)
	tmp = 0.0
	if (t <= -57000000000.0)
		tmp = t_1;
	elseif (t <= 7.2e-78)
		tmp = fma(z, Float64(Float64(y - x) / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] * N[(z / t), $MachinePrecision] + y), $MachinePrecision]}, If[LessEqual[t, -57000000000.0], t$95$1, If[LessEqual[t, 7.2e-78], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.7e10 or 7.2000000000000005e-78 < t

   1. Initial program 49.4%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

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

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

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

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

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

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

   5. Simplified 70.2%

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

   6. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

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

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

      6. /-lowering-/.f64 64.9

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

   8. Simplified 64.9%

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

   if -5.7e10 < t < 7.2000000000000005e-78

   1. Initial program 89.0%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 84.0

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

   5. Simplified 84.0%

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

Alternative 13: 61.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;t \leq -3.9 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+111}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- 1.0 (/ z t)))))
   (if (<= t -3.9e+131) t_1 (if (<= t 4.6e+111) (fma z (/ (- y x) a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (z / t));
	double tmp;
	if (t <= -3.9e+131) {
		tmp = t_1;
	} else if (t <= 4.6e+111) {
		tmp = fma(z, ((y - x) / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(1.0 - Float64(z / t)))
	tmp = 0.0
	if (t <= -3.9e+131)
		tmp = t_1;
	elseif (t <= 4.6e+111)
		tmp = fma(z, Float64(Float64(y - x) / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.9e+131], t$95$1, If[LessEqual[t, 4.6e+111], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.9e131 or 4.60000000000000004e111 < t

   1. Initial program 33.0%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

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

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

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

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

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

      12. div-sub N/A

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

      13. sub-neg N/A

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

      14. *-inverses N/A

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

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

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

      18. /-lowering-/.f64 53.2

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

   5. Simplified 53.2%

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

   6. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. +-commutative N/A

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

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

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

      9. mul-1-neg N/A

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

      10. unsub-neg N/A

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

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

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

      12. /-lowering-/.f64 54.6

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

   8. Simplified 54.6%

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

   if -3.9e131 < t < 4.60000000000000004e111

   1. Initial program 82.3%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 69.3

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

   5. Simplified 69.3%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+131}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+111}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y - x}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 54.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;t \leq -1.02 \cdot 10^{+126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-78}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- 1.0 (/ z t)))))
   (if (<= t -1.02e+126) t_1 (if (<= t 1.35e-78) (fma (/ z a) y x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (z / t));
	double tmp;
	if (t <= -1.02e+126) {
		tmp = t_1;
	} else if (t <= 1.35e-78) {
		tmp = fma((z / a), y, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(1.0 - Float64(z / t)))
	tmp = 0.0
	if (t <= -1.02e+126)
		tmp = t_1;
	elseif (t <= 1.35e-78)
		tmp = fma(Float64(z / a), y, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.02e+126], t$95$1, If[LessEqual[t, 1.35e-78], N[(N[(z / a), $MachinePrecision] * y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.02e126 or 1.34999999999999997e-78 < t

   1. Initial program 46.8%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

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

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{x} - y, \frac{z - t}{t}, x\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{x - y}, \frac{z - t}{t}, x\right) \]

      12. div-sub N/A

          \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{\frac{z}{t} - \frac{t}{t}}, x\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{\frac{z}{t} + \left(\mathsf{neg}\left(\frac{t}{t}\right)\right)}, x\right) \]

      14. *-inverses N/A

          \[\leadsto \mathsf{fma}\left(x - y, \frac{z}{t} + \left(\mathsf{neg}\left(\color{blue}{1}\right)\right), x\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(x - y, \frac{z}{t} + \color{blue}{-1}, x\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{-1 + \frac{z}{t}}, x\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{-1 + \frac{z}{t}}, x\right) \]

      18. /-lowering-/.f64 54.5

          \[\leadsto \mathsf{fma}\left(x - y, -1 + \color{blue}{\frac{z}{t}}, x\right) \]

   5. Simplified 54.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x - y, -1 + \frac{z}{t}, x\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(\frac{z}{t} - 1\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto -1 \cdot \color{blue}{\left(\left(\frac{z}{t} - 1\right) \cdot y\right)} \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(\frac{z}{t} - 1\right)\right) \cdot y} \]

      3. sub-neg N/A

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\frac{z}{t} + \left(\mathsf{neg}\left(1\right)\right)\right)}\right) \cdot y \]

      4. metadata-eval N/A

         \[\leadsto \left(-1 \cdot \left(\frac{z}{t} + \color{blue}{-1}\right)\right) \cdot y \]

      5. distribute-lft-in N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{z}{t} + -1 \cdot -1\right)} \cdot y \]

      6. metadata-eval N/A

         \[\leadsto \left(-1 \cdot \frac{z}{t} + \color{blue}{1}\right) \cdot y \]

      7. +-commutative N/A

         \[\leadsto \color{blue}{\left(1 + -1 \cdot \frac{z}{t}\right)} \cdot y \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\left(1 + -1 \cdot \frac{z}{t}\right) \cdot y} \]

      9. mul-1-neg N/A

         \[\leadsto \left(1 + \color{blue}{\left(\mathsf{neg}\left(\frac{z}{t}\right)\right)}\right) \cdot y \]

      10. unsub-neg N/A

          \[\leadsto \color{blue}{\left(1 - \frac{z}{t}\right)} \cdot y \]

      11. --lowering--.f64 N/A

          \[\leadsto \color{blue}{\left(1 - \frac{z}{t}\right)} \cdot y \]

      12. /-lowering-/.f64 49.5

          \[\leadsto \left(1 - \color{blue}{\frac{z}{t}}\right) \cdot y \]

   8. Simplified 49.5%

      \[\leadsto \color{blue}{\left(1 - \frac{z}{t}\right) \cdot y} \]

   if -1.02e126 < t < 1.34999999999999997e-78

   1. Initial program 83.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{a - t}{\left(y - x\right) \cdot \left(z - t\right)}}} + x \]

      3. associate-/r/ N/A

         \[\leadsto \color{blue}{\frac{1}{a - t} \cdot \left(\left(y - x\right) \cdot \left(z - t\right)\right)} + x \]

      4. *-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(z - t\right) \cdot \left(y - x\right)\right)} + x \]

      5. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\frac{1}{a - t} \cdot \left(z - t\right)\right) \cdot \left(y - x\right)} + x \]

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{a - t} \cdot \left(z - t\right), y - x, x\right)} \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{a - t} \cdot \left(z - t\right)}, y - x, x\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{a - t}} \cdot \left(z - t\right), y - x, x\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{\color{blue}{a - t}} \cdot \left(z - t\right), y - x, x\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{1}{a - t} \cdot \color{blue}{\left(z - t\right)}, y - x, x\right) \]

      11. --lowering--.f64 92.7

          \[\leadsto \mathsf{fma}\left(\frac{1}{a - t} \cdot \left(z - t\right), \color{blue}{y - x}, x\right) \]

   4. Applied egg-rr 92.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{a - t} \cdot \left(z - t\right), y - x, x\right)} \]

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(\frac{1}{a - t} \cdot \left(z - t\right), \color{blue}{y}, x\right) \]
   6. Step-by-step derivation

   7. Simplified 75.2%

      \[\leadsto \mathsf{fma}\left(\frac{1}{a - t} \cdot \left(z - t\right), \color{blue}{y}, x\right) \]

   8. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{z}{a}}, y, x\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 61.4

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{z}{a}}, y, x\right) \]

   10. Simplified 61.4%

       \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{z}{a}}, y, x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+126}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-78}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+131}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+33}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.5e+131) y (if (<= t 1.7e+33) (fma (/ z a) y x) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.5e+131) {
		tmp = y;
	} else if (t <= 1.7e+33) {
		tmp = fma((z / a), y, x);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.5e+131)
		tmp = y;
	elseif (t <= 1.7e+33)
		tmp = fma(Float64(z / a), y, x);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.5e+131], y, If[LessEqual[t, 1.7e+33], N[(N[(z / a), $MachinePrecision] * y + x), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.4999999999999999e131

   1. Initial program 26.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{y} \]
   4. Step-by-step derivation

   5. Simplified 52.6%

      \[\leadsto \color{blue}{y} \]

   if -3.4999999999999999e131 < t < 1.7e33

   1. Initial program 82.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{a - t}{\left(y - x\right) \cdot \left(z - t\right)}}} + x \]

      3. associate-/r/ N/A

         \[\leadsto \color{blue}{\frac{1}{a - t} \cdot \left(\left(y - x\right) \cdot \left(z - t\right)\right)} + x \]

      4. *-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(z - t\right) \cdot \left(y - x\right)\right)} + x \]

      5. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\frac{1}{a - t} \cdot \left(z - t\right)\right) \cdot \left(y - x\right)} + x \]

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{a - t} \cdot \left(z - t\right), y - x, x\right)} \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{a - t} \cdot \left(z - t\right)}, y - x, x\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{a - t}} \cdot \left(z - t\right), y - x, x\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{\color{blue}{a - t}} \cdot \left(z - t\right), y - x, x\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{1}{a - t} \cdot \color{blue}{\left(z - t\right)}, y - x, x\right) \]

      11. --lowering--.f64 91.9

          \[\leadsto \mathsf{fma}\left(\frac{1}{a - t} \cdot \left(z - t\right), \color{blue}{y - x}, x\right) \]

   4. Applied egg-rr 91.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{a - t} \cdot \left(z - t\right), y - x, x\right)} \]

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(\frac{1}{a - t} \cdot \left(z - t\right), \color{blue}{y}, x\right) \]
   6. Step-by-step derivation

   7. Simplified 73.9%

      \[\leadsto \mathsf{fma}\left(\frac{1}{a - t} \cdot \left(z - t\right), \color{blue}{y}, x\right) \]

   8. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{z}{a}}, y, x\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 57.7

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{z}{a}}, y, x\right) \]

   10. Simplified 57.7%

       \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{z}{a}}, y, x\right) \]

   if 1.7e33 < t

   1. Initial program 49.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{a - t}{\left(y - x\right) \cdot \left(z - t\right)}}} + x \]

      3. associate-/r/ N/A

         \[\leadsto \color{blue}{\frac{1}{a - t} \cdot \left(\left(y - x\right) \cdot \left(z - t\right)\right)} + x \]

      4. *-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(z - t\right) \cdot \left(y - x\right)\right)} + x \]

      5. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\frac{1}{a - t} \cdot \left(z - t\right)\right) \cdot \left(y - x\right)} + x \]

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{a - t} \cdot \left(z - t\right), y - x, x\right)} \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{a - t} \cdot \left(z - t\right)}, y - x, x\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{a - t}} \cdot \left(z - t\right), y - x, x\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{\color{blue}{a - t}} \cdot \left(z - t\right), y - x, x\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{1}{a - t} \cdot \color{blue}{\left(z - t\right)}, y - x, x\right) \]

      11. --lowering--.f64 80.8

          \[\leadsto \mathsf{fma}\left(\frac{1}{a - t} \cdot \left(z - t\right), \color{blue}{y - x}, x\right) \]

   4. Applied egg-rr 80.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{a - t} \cdot \left(z - t\right), y - x, x\right)} \]

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(\frac{1}{a - t} \cdot \left(z - t\right), \color{blue}{y}, x\right) \]
   6. Step-by-step derivation

   7. Simplified 56.2%

      \[\leadsto \mathsf{fma}\left(\frac{1}{a - t} \cdot \left(z - t\right), \color{blue}{y}, x\right) \]

   8. Taylor expanded in t around inf

      \[\leadsto \color{blue}{x + y} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 32.9

         \[\leadsto \color{blue}{x + y} \]

   10. Simplified 32.9%

       \[\leadsto \color{blue}{x + y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 16: 38.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{t}\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 112000000:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ z t))))
   (if (<= z -8.5e+72) t_1 (if (<= z 112000000.0) (+ x y) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (z / t);
	double tmp;
	if (z <= -8.5e+72) {
		tmp = t_1;
	} else if (z <= 112000000.0) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z / t)
    if (z <= (-8.5d+72)) then
        tmp = t_1
    else if (z <= 112000000.0d0) then
        tmp = x + y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (z / t);
	double tmp;
	if (z <= -8.5e+72) {
		tmp = t_1;
	} else if (z <= 112000000.0) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (z / t)
	tmp = 0
	if z <= -8.5e+72:
		tmp = t_1
	elif z <= 112000000.0:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(z / t))
	tmp = 0.0
	if (z <= -8.5e+72)
		tmp = t_1;
	elseif (z <= 112000000.0)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (z / t);
	tmp = 0.0;
	if (z <= -8.5e+72)
		tmp = t_1;
	elseif (z <= 112000000.0)
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e+72], t$95$1, If[LessEqual[z, 112000000.0], N[(x + y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.5000000000000004e72 or 1.12e8 < z

   1. Initial program 67.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(y - x\right) \cdot \left(z - t\right)}{t}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{-1 \cdot \frac{\left(y - x\right) \cdot \left(z - t\right)}{t} + x} \]

      2. associate-/l* N/A

         \[\leadsto -1 \cdot \color{blue}{\left(\left(y - x\right) \cdot \frac{z - t}{t}\right)} + x \]

      3. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(y - x\right)\right) \cdot \frac{z - t}{t}} + x \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(y - x\right), \frac{z - t}{t}, x\right)} \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(\left(y - x\right)\right)}, \frac{z - t}{t}, x\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(y + \left(\mathsf{neg}\left(x\right)\right)\right)}\right), \frac{z - t}{t}, x\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(\left(\mathsf{neg}\left(x\right)\right) + y\right)}\right), \frac{z - t}{t}, x\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) + \left(\mathsf{neg}\left(y\right)\right)}, \frac{z - t}{t}, x\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) - y}, \frac{z - t}{t}, x\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{x} - y, \frac{z - t}{t}, x\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{x - y}, \frac{z - t}{t}, x\right) \]

      12. div-sub N/A

          \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{\frac{z}{t} - \frac{t}{t}}, x\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{\frac{z}{t} + \left(\mathsf{neg}\left(\frac{t}{t}\right)\right)}, x\right) \]

      14. *-inverses N/A

          \[\leadsto \mathsf{fma}\left(x - y, \frac{z}{t} + \left(\mathsf{neg}\left(\color{blue}{1}\right)\right), x\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(x - y, \frac{z}{t} + \color{blue}{-1}, x\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{-1 + \frac{z}{t}}, x\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(x - y, \color{blue}{-1 + \frac{z}{t}}, x\right) \]

      18. /-lowering-/.f64 52.2

          \[\leadsto \mathsf{fma}\left(x - y, -1 + \color{blue}{\frac{z}{t}}, x\right) \]

   5. Simplified 52.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x - y, -1 + \frac{z}{t}, x\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x \cdot z}{t}} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z \cdot x}}{t} \]

      2. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{z}{t} \cdot x} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\frac{z}{t} \cdot x} \]

      4. /-lowering-/.f64 38.7

         \[\leadsto \color{blue}{\frac{z}{t}} \cdot x \]

   8. Simplified 38.7%

      \[\leadsto \color{blue}{\frac{z}{t} \cdot x} \]

   if -8.5000000000000004e72 < z < 1.12e8

   1. Initial program 66.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{a - t}{\left(y - x\right) \cdot \left(z - t\right)}}} + x \]

      3. associate-/r/ N/A

         \[\leadsto \color{blue}{\frac{1}{a - t} \cdot \left(\left(y - x\right) \cdot \left(z - t\right)\right)} + x \]

      4. *-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(z - t\right) \cdot \left(y - x\right)\right)} + x \]

      5. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\frac{1}{a - t} \cdot \left(z - t\right)\right) \cdot \left(y - x\right)} + x \]

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{a - t} \cdot \left(z - t\right), y - x, x\right)} \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{a - t} \cdot \left(z - t\right)}, y - x, x\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{a - t}} \cdot \left(z - t\right), y - x, x\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{\color{blue}{a - t}} \cdot \left(z - t\right), y - x, x\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{1}{a - t} \cdot \color{blue}{\left(z - t\right)}, y - x, x\right) \]

      11. --lowering--.f64 84.3

          \[\leadsto \mathsf{fma}\left(\frac{1}{a - t} \cdot \left(z - t\right), \color{blue}{y - x}, x\right) \]

   4. Applied egg-rr 84.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{a - t} \cdot \left(z - t\right), y - x, x\right)} \]

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(\frac{1}{a - t} \cdot \left(z - t\right), \color{blue}{y}, x\right) \]
   6. Step-by-step derivation

   7. Simplified 80.3%

      \[\leadsto \mathsf{fma}\left(\frac{1}{a - t} \cdot \left(z - t\right), \color{blue}{y}, x\right) \]

   8. Taylor expanded in t around inf

      \[\leadsto \color{blue}{x + y} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 46.7

         \[\leadsto \color{blue}{x + y} \]

   10. Simplified 46.7%

       \[\leadsto \color{blue}{x + y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 112000000:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 36.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+127}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.8e+127) y (if (<= t 1.85e+32) x (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.8e+127) {
		tmp = y;
	} else if (t <= 1.85e+32) {
		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 (t <= (-6.8d+127)) then
        tmp = y
    else if (t <= 1.85d+32) 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 (t <= -6.8e+127) {
		tmp = y;
	} else if (t <= 1.85e+32) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.8e+127:
		tmp = y
	elif t <= 1.85e+32:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.8e+127)
		tmp = y;
	elseif (t <= 1.85e+32)
		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 (t <= -6.8e+127)
		tmp = y;
	elseif (t <= 1.85e+32)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.8e+127], y, If[LessEqual[t, 1.85e+32], x, N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.79999999999999955e127

   1. Initial program 25.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{y} \]
   4. Step-by-step derivation

   5. Simplified 52.5%

      \[\leadsto \color{blue}{y} \]

   if -6.79999999999999955e127 < t < 1.85e32

   1. Initial program 83.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 37.1%

      \[\leadsto \color{blue}{x} \]

   if 1.85e32 < t

   1. Initial program 49.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{a - t}{\left(y - x\right) \cdot \left(z - t\right)}}} + x \]

      3. associate-/r/ N/A

         \[\leadsto \color{blue}{\frac{1}{a - t} \cdot \left(\left(y - x\right) \cdot \left(z - t\right)\right)} + x \]

      4. *-commutative N/A

         \[\leadsto \frac{1}{a - t} \cdot \color{blue}{\left(\left(z - t\right) \cdot \left(y - x\right)\right)} + x \]

      5. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\frac{1}{a - t} \cdot \left(z - t\right)\right) \cdot \left(y - x\right)} + x \]

      6. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{a - t} \cdot \left(z - t\right), y - x, x\right)} \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{a - t} \cdot \left(z - t\right)}, y - x, x\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{a - t}} \cdot \left(z - t\right), y - x, x\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{\color{blue}{a - t}} \cdot \left(z - t\right), y - x, x\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{1}{a - t} \cdot \color{blue}{\left(z - t\right)}, y - x, x\right) \]

      11. --lowering--.f64 80.8

          \[\leadsto \mathsf{fma}\left(\frac{1}{a - t} \cdot \left(z - t\right), \color{blue}{y - x}, x\right) \]

   4. Applied egg-rr 80.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{a - t} \cdot \left(z - t\right), y - x, x\right)} \]

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(\frac{1}{a - t} \cdot \left(z - t\right), \color{blue}{y}, x\right) \]
   6. Step-by-step derivation

   7. Simplified 56.2%

      \[\leadsto \mathsf{fma}\left(\frac{1}{a - t} \cdot \left(z - t\right), \color{blue}{y}, x\right) \]

   8. Taylor expanded in t around inf

      \[\leadsto \color{blue}{x + y} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 32.9

         \[\leadsto \color{blue}{x + y} \]

   10. Simplified 32.9%

       \[\leadsto \color{blue}{x + y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 18: 38.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+126}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.5e+126) y (if (<= t 2e+33) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.5e+126) {
		tmp = y;
	} else if (t <= 2e+33) {
		tmp = x;
	} else {
		tmp = 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 (t <= (-1.5d+126)) then
        tmp = y
    else if (t <= 2d+33) then
        tmp = x
    else
        tmp = 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 (t <= -1.5e+126) {
		tmp = y;
	} else if (t <= 2e+33) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.5e+126:
		tmp = y
	elif t <= 2e+33:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.5e+126)
		tmp = y;
	elseif (t <= 2e+33)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.5e+126)
		tmp = y;
	elseif (t <= 2e+33)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.5e+126], y, If[LessEqual[t, 2e+33], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -1.5000000000000001e126 or 1.9999999999999999e33 < t

   1. Initial program 38.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{y} \]
   4. Step-by-step derivation

   5. Simplified 41.1%

      \[\leadsto \color{blue}{y} \]

   if -1.5000000000000001e126 < t < 1.9999999999999999e33

   1. Initial program 83.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 37.1%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 19: 24.8% accurate, 29.0× 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 66.9%

   \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
2. Add Preprocessing

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 27.0%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 86.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))
   (if (< a -1.6153062845442575e-142)
     t_1
     (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} 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 - x) / 1.0d0) * ((z - t) / (a - t)))
    if (a < (-1.6153062845442575d-142)) then
        tmp = t_1
    else if (a < 3.774403170083174d-182) then
        tmp = y - ((z / t) * (y - x))
    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 - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)))
	tmp = 0
	if a < -1.6153062845442575e-142:
		tmp = t_1
	elif a < 3.774403170083174e-182:
		tmp = y - ((z / t) * (y - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) / 1.0) * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = Float64(y - Float64(Float64(z / t) * Float64(y - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = y - ((z / t) * (y - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[a, -1.6153062845442575e-142], t$95$1, If[Less[a, 3.774403170083174e-182], N[(y - N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024195 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< a -646122513817703/4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t)))) (if (< a 1887201585041587/50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t)))))))

  (+ x (/ (* (- y x) (- z t)) (- a t))))