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

Percentage Accurate: 77.8% → 93.7%

Time: 7.6s

Alternatives: 11

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}, y, x\right) \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (fma (- (+ (/ t (- a t)) 1.0) (/ z (- a t))) y x))

C

double code(double x, double y, double z, double t, double a) {
	return fma((((t / (a - t)) + 1.0) - (z / (a - t))), y, x);
}

Julia

function code(x, y, z, t, a)
	return fma(Float64(Float64(Float64(t / Float64(a - t)) + 1.0) - Float64(z / Float64(a - t))), y, x)
end

Wolfram

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

Derivation

1. Initial program 74.7%

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

3. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. lower--.f64 N/A

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

   5. +-commutative N/A

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

   6. lower-+.f64 N/A

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

   7. lower-/.f64 N/A

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

   8. lower--.f64 N/A

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

   9. lower-/.f64 N/A

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

   10. lower--.f64 94.8

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

5. Applied rewrites 94.8%

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

Alternative 2: 92.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.3 \cdot 10^{+121} \lor \neg \left(t \leq 1.6 \cdot 10^{+130}\right):\\ \;\;\;\;\mathsf{fma}\left(a, \frac{-y}{t}, x\right) + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{z - t}{a - t}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5.3e+121) (not (<= t 1.6e+130)))
   (+ (fma a (/ (- y) t) x) (* y (/ z t)))
   (fma (- 1.0 (/ (- z t) (- a t))) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.3e+121) || !(t <= 1.6e+130)) {
		tmp = fma(a, (-y / t), x) + (y * (z / t));
	} else {
		tmp = fma((1.0 - ((z - t) / (a - t))), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5.3e+121) || !(t <= 1.6e+130))
		tmp = Float64(fma(a, Float64(Float64(-y) / t), x) + Float64(y * Float64(z / t)));
	else
		tmp = fma(Float64(1.0 - Float64(Float64(z - t) / Float64(a - t))), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5.3e+121], N[Not[LessEqual[t, 1.6e+130]], $MachinePrecision]], N[(N[(a * N[((-y) / t), $MachinePrecision] + x), $MachinePrecision] + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.30000000000000009e121 or 1.6e130 < t

   1. Initial program 47.4%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 91.9

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

   5. Applied rewrites 91.9%

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

   6. Taylor expanded in t around inf

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. associate-/l* N/A

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

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

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. associate-*r/ N/A

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

      9. lower-/.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 N/A

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

      12. mul-1-neg N/A

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

      13. associate-/l* N/A

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

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

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

      15. mul-1-neg N/A

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

      16. lower-*.f64 N/A

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

      17. mul-1-neg N/A

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

      18. lower-neg.f64 N/A

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

      19. lower-/.f64 92.0

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

   8. Applied rewrites 92.0%

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

   if -5.30000000000000009e121 < t < 1.6e130

   1. Initial program 87.1%

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

   3. Taylor expanded in x around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. *-lft-identity N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. fp-cancel-sub-sign N/A

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

      7. mul-1-neg N/A

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

      8. distribute-rgt-in N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. fp-cancel-sign-sub-inv N/A

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

      12. metadata-eval N/A

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

      13. *-lft-identity N/A

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

      14. lower--.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower--.f64 N/A

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

      17. lower--.f64 94.5

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

   5. Applied rewrites 94.5%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.3 \cdot 10^{+121} \lor \neg \left(t \leq 1.6 \cdot 10^{+130}\right):\\ \;\;\;\;\mathsf{fma}\left(a, \frac{-y}{t}, x\right) + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{z - t}{a - t}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.3 \cdot 10^{+121} \lor \neg \left(t \leq 5 \cdot 10^{+214}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{a - z}{-t}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{z - t}{a - t}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5.3e+121) (not (<= t 5e+214)))
   (fma (/ (- a z) (- t)) y x)
   (fma (- 1.0 (/ (- z t) (- a t))) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.3e+121) || !(t <= 5e+214)) {
		tmp = fma(((a - z) / -t), y, x);
	} else {
		tmp = fma((1.0 - ((z - t) / (a - t))), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5.3e+121) || !(t <= 5e+214))
		tmp = fma(Float64(Float64(a - z) / Float64(-t)), y, x);
	else
		tmp = fma(Float64(1.0 - Float64(Float64(z - t) / Float64(a - t))), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5.3e+121], N[Not[LessEqual[t, 5e+214]], $MachinePrecision]], N[(N[(N[(a - z), $MachinePrecision] / (-t)), $MachinePrecision] * y + x), $MachinePrecision], N[(N[(1.0 - N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.30000000000000009e121 or 4.99999999999999953e214 < t

   1. Initial program 45.2%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 90.6

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

   5. Applied rewrites 90.6%

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

   6. Taylor expanded in t around -inf

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

   8. Applied rewrites 92.9%

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

   if -5.30000000000000009e121 < t < 4.99999999999999953e214

   1. Initial program 83.6%

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

   3. Taylor expanded in x around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. *-lft-identity N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. fp-cancel-sub-sign N/A

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

      7. mul-1-neg N/A

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

      8. distribute-rgt-in N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. fp-cancel-sign-sub-inv N/A

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

      12. metadata-eval N/A

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

      13. *-lft-identity N/A

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

      14. lower--.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. lower--.f64 N/A

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

      17. lower--.f64 93.7

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

   5. Applied rewrites 93.7%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.3 \cdot 10^{+121} \lor \neg \left(t \leq 5 \cdot 10^{+214}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{a - z}{-t}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{z - t}{a - t}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+120}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a - z}{-t}, y, x\right)\\ \mathbf{elif}\;t \leq 6000000:\\ \;\;\;\;\left(x + y\right) - \frac{z}{a - t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-z}{a - t}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.6e+120)
   (fma (/ (- a z) (- t)) y x)
   (if (<= t 6000000.0)
     (- (+ x y) (* (/ z (- a t)) y))
     (fma (/ (- z) (- a t)) y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.6e+120) {
		tmp = fma(((a - z) / -t), y, x);
	} else if (t <= 6000000.0) {
		tmp = (x + y) - ((z / (a - t)) * y);
	} else {
		tmp = fma((-z / (a - t)), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.6e+120)
		tmp = fma(Float64(Float64(a - z) / Float64(-t)), y, x);
	elseif (t <= 6000000.0)
		tmp = Float64(Float64(x + y) - Float64(Float64(z / Float64(a - t)) * y));
	else
		tmp = fma(Float64(Float64(-z) / Float64(a - t)), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.6e+120], N[(N[(N[(a - z), $MachinePrecision] / (-t)), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[t, 6000000.0], N[(N[(x + y), $MachinePrecision] - N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(N[((-z) / N[(a - t), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.60000000000000016e120

   1. Initial program 49.3%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 89.9

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

   5. Applied rewrites 89.9%

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

   6. Taylor expanded in t around -inf

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

   8. Applied rewrites 90.5%

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

   if -3.60000000000000016e120 < t < 6e6

   1. Initial program 90.2%

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

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 93.5

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

   5. Applied rewrites 93.5%

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

   if 6e6 < t

   1. Initial program 57.8%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 93.7

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

   5. Applied rewrites 93.7%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 86.4%

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

Alternative 5: 87.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+56} \lor \neg \left(a \leq 2.35 \cdot 10^{+36}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{z}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-z}{a - t}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.2e+56) (not (<= a 2.35e+36)))
   (fma (- 1.0 (/ z a)) y x)
   (fma (/ (- z) (- a t)) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.2e+56) || !(a <= 2.35e+36)) {
		tmp = fma((1.0 - (z / a)), y, x);
	} else {
		tmp = fma((-z / (a - t)), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5.2e+56) || !(a <= 2.35e+36))
		tmp = fma(Float64(1.0 - Float64(z / a)), y, x);
	else
		tmp = fma(Float64(Float64(-z) / Float64(a - t)), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5.2e+56], N[Not[LessEqual[a, 2.35e+36]], $MachinePrecision]], N[(N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], N[(N[((-z) / N[(a - t), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.20000000000000022e56 or 2.34999999999999994e36 < a

   1. Initial program 78.5%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 97.4

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

   5. Applied rewrites 97.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 86.9%

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

   if -5.20000000000000022e56 < a < 2.34999999999999994e36

   1. Initial program 72.2%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 93.0

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

   5. Applied rewrites 93.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 88.5%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+56} \lor \neg \left(a \leq 2.35 \cdot 10^{+36}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{z}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-z}{a - t}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-14} \lor \neg \left(a \leq 5.2 \cdot 10^{+36}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{z}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3e-14) (not (<= a 5.2e+36)))
   (fma (- 1.0 (/ z a)) y x)
   (- x (/ (* y (- a z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3e-14) || !(a <= 5.2e+36)) {
		tmp = fma((1.0 - (z / a)), y, x);
	} else {
		tmp = x - ((y * (a - z)) / t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3e-14) || !(a <= 5.2e+36))
		tmp = fma(Float64(1.0 - Float64(z / a)), y, x);
	else
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3e-14], N[Not[LessEqual[a, 5.2e+36]], $MachinePrecision]], N[(N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.9999999999999998e-14 or 5.2000000000000003e36 < a

   1. Initial program 79.1%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 98.5

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

   5. Applied rewrites 98.5%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 85.8%

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

   if -2.9999999999999998e-14 < a < 5.2000000000000003e36

   1. Initial program 71.1%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. *-commutative N/A

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

      5. fp-cancel-sub-sign-inv N/A

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. +-commutative N/A

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

      9. *-lft-identity N/A

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

      10. metadata-eval N/A

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

      11. fp-cancel-sub-sign-inv N/A

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

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

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

      13. mul-1-neg N/A

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

      14. distribute-neg-frac N/A

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

      15. fp-cancel-sub-sign N/A

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

   5. Applied rewrites 83.5%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-14} \lor \neg \left(a \leq 5.2 \cdot 10^{+36}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{z}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{-16} \lor \neg \left(a \leq 9.5 \cdot 10^{+35}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{z}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.5e-16) (not (<= a 9.5e+35)))
   (fma (- 1.0 (/ z a)) y x)
   (fma y (/ z t) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.5e-16) || !(a <= 9.5e+35)) {
		tmp = fma((1.0 - (z / a)), y, x);
	} else {
		tmp = fma(y, (z / t), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5.5e-16) || !(a <= 9.5e+35))
		tmp = fma(Float64(1.0 - Float64(z / a)), y, x);
	else
		tmp = fma(y, Float64(z / t), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5.5e-16], N[Not[LessEqual[a, 9.5e+35]], $MachinePrecision]], N[(N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.49999999999999964e-16 or 9.50000000000000062e35 < a

   1. Initial program 78.5%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 97.6

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

   5. Applied rewrites 97.6%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 85.1%

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

   if -5.49999999999999964e-16 < a < 9.50000000000000062e35

   1. Initial program 71.6%

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

   3. Taylor expanded in a around 0

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

      1. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 62.3

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

   5. Applied rewrites 62.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 79.7%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{-16} \lor \neg \left(a \leq 9.5 \cdot 10^{+35}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{z}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{t}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+56} \lor \neg \left(a \leq 2.35 \cdot 10^{+36}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5e+56) (not (<= a 2.35e+36))) (+ y x) (fma y (/ z t) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5e+56) || !(a <= 2.35e+36)) {
		tmp = y + x;
	} else {
		tmp = fma(y, (z / t), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5e+56) || !(a <= 2.35e+36))
		tmp = Float64(y + x);
	else
		tmp = fma(y, Float64(z / t), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5e+56], N[Not[LessEqual[a, 2.35e+36]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.00000000000000024e56 or 2.34999999999999994e36 < a

   1. Initial program 78.5%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 97.4

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

   5. Applied rewrites 97.4%

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

   6. Taylor expanded in z around -inf

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

   8. Applied rewrites 97.2%

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

   9. Taylor expanded in a around inf

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

       1. +-commutative N/A

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

       2. lower-+.f64 79.2

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

   11. Applied rewrites 79.2%

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

   if -5.00000000000000024e56 < a < 2.34999999999999994e36

   1. Initial program 72.2%

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

   3. Taylor expanded in a around 0

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

      1. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 61.1

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

   5. Applied rewrites 61.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 78.3%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+56} \lor \neg \left(a \leq 2.35 \cdot 10^{+36}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{t}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{-89} \lor \neg \left(a \leq 2.5 \cdot 10^{-187}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -7.8e-89) (not (<= a 2.5e-187))) (+ y x) (/ (* y z) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7.8e-89) || !(a <= 2.5e-187)) {
		tmp = y + x;
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-7.8d-89)) .or. (.not. (a <= 2.5d-187))) then
        tmp = y + x
    else
        tmp = (y * z) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7.8e-89) || !(a <= 2.5e-187)) {
		tmp = y + x;
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -7.8e-89) or not (a <= 2.5e-187):
		tmp = y + x
	else:
		tmp = (y * z) / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -7.8e-89) || !(a <= 2.5e-187))
		tmp = Float64(y + x);
	else
		tmp = Float64(Float64(y * z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -7.8e-89) || ~((a <= 2.5e-187)))
		tmp = y + x;
	else
		tmp = (y * z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -7.8e-89], N[Not[LessEqual[a, 2.5e-187]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.79999999999999957e-89 or 2.4999999999999998e-187 < a

   1. Initial program 75.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 94.1

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

   5. Applied rewrites 94.1%

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

   6. Taylor expanded in z around -inf

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

   8. Applied rewrites 94.1%

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

   9. Taylor expanded in a around inf

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

       1. +-commutative N/A

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

       2. lower-+.f64 67.4

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

   11. Applied rewrites 67.4%

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

   if -7.79999999999999957e-89 < a < 2.4999999999999998e-187

   1. Initial program 74.0%

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

   3. Taylor expanded in a around 0

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

      1. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 70.8

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

   5. Applied rewrites 70.8%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 48.3%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{-89} \lor \neg \left(a \leq 2.5 \cdot 10^{-187}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.15 \cdot 10^{-15} \lor \neg \left(a \leq 9.5 \cdot 10^{+35}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.15e-15) (not (<= a 9.5e+35))) (+ y x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.15e-15) || !(a <= 9.5e+35)) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-3.15d-15)) .or. (.not. (a <= 9.5d+35))) then
        tmp = y + x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.15e-15) || !(a <= 9.5e+35)) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.15e-15) or not (a <= 9.5e+35):
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.15e-15) || !(a <= 9.5e+35))
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.15e-15) || ~((a <= 9.5e+35)))
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.15e-15], N[Not[LessEqual[a, 9.5e+35]], $MachinePrecision]], N[(y + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -3.14999999999999991e-15 or 9.50000000000000062e35 < a

   1. Initial program 78.5%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 97.6

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

   5. Applied rewrites 97.6%

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

   6. Taylor expanded in z around -inf

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

   8. Applied rewrites 97.5%

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

   9. Taylor expanded in a around inf

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

       1. +-commutative N/A

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

       2. lower-+.f64 77.4

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

   11. Applied rewrites 77.4%

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

   if -3.14999999999999991e-15 < a < 9.50000000000000062e35

   1. Initial program 71.6%

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

   3. Taylor expanded in a around 0

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

      1. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 62.3

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

   5. Applied rewrites 62.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 46.7%

      \[\leadsto \mathsf{fma}\left(0, \color{blue}{y}, x\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 46.7%

       \[\leadsto x \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.15 \cdot 10^{-15} \lor \neg \left(a \leq 9.5 \cdot 10^{+35}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.3% 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 74.7%

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

3. Taylor expanded in a around 0

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

   1. fp-cancel-sub-sign-inv N/A

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

   2. +-commutative N/A

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

   3. metadata-eval N/A

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

   4. *-lft-identity N/A

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

   5. associate-/l* N/A

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

   6. *-commutative N/A

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

   7. lower-fma.f64 N/A

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

   8. lower-/.f64 N/A

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

   9. lower--.f64 N/A

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

   10. +-commutative N/A

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

   11. lower-+.f64 51.0

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

5. Applied rewrites 51.0%

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

6. Taylor expanded in z around 0

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

8. Applied rewrites 45.6%

   \[\leadsto \mathsf{fma}\left(0, \color{blue}{y}, x\right) \]
9. Step-by-step derivation

10. Applied rewrites 45.6%

    \[\leadsto x \]
11. Add Preprocessing

Developer Target 1: 88.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 < -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 < 1.4754293444577233 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (< t_2 -1.3664970889390727e-7)
     t_1
     (if (< t_2 1.4754293444577233e-239)
       (/ (- (* y (- a z)) (* x t)) (- a t))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y + x) - (((z - t) * (1.0d0 / (a - t))) * y)
    t_2 = (x + y) - (((z - t) * y) / (a - t))
    if (t_2 < (-1.3664970889390727d-7)) then
        tmp = t_1
    else if (t_2 < 1.4754293444577233d-239) then
        tmp = ((y * (a - z)) - (x * t)) / (a - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y)
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 < -1.3664970889390727e-7:
		tmp = t_1
	elif t_2 < 1.4754293444577233e-239:
		tmp = ((y * (a - z)) - (x * t)) / (a - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y + x) - Float64(Float64(Float64(z - t) * Float64(1.0 / Float64(a - t))) * y))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = Float64(Float64(Float64(y * Float64(a - z)) - Float64(x * t)) / Float64(a - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -1.3664970889390727e-7], t$95$1, If[Less[t$95$2, 1.4754293444577233e-239], N[(N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024337 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -13664970889390727/100000000000000000000000) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 14754293444577233/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y)))))

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