Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A

Percentage Accurate: 84.2% → 96.8%

Time: 11.9s

Alternatives: 10

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - z \cdot a\\ t_2 := \mathsf{fma}\left(y, \frac{z}{\mathsf{fma}\left(z, a, -t\right)}, \frac{x}{t\_1}\right)\\ t_3 := \frac{x - y \cdot z}{t\_1}\\ t_4 := \mathsf{fma}\left(y, -z, x\right)\\ \mathbf{if}\;t\_3 \leq -4 \cdot 10^{-272}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{-47}:\\ \;\;\;\;\frac{1}{\mathsf{fma}\left(-z, \frac{a}{t\_4}, \frac{t}{t\_4}\right)}\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* z a)))
        (t_2 (fma y (/ z (fma z a (- t))) (/ x t_1)))
        (t_3 (/ (- x (* y z)) t_1))
        (t_4 (fma y (- z) x)))
   (if (<= t_3 -4e-272)
     t_2
     (if (<= t_3 5e-47)
       (/ 1.0 (fma (- z) (/ a t_4) (/ t t_4)))
       (if (<= t_3 INFINITY) t_2 (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (z * a);
	double t_2 = fma(y, (z / fma(z, a, -t)), (x / t_1));
	double t_3 = (x - (y * z)) / t_1;
	double t_4 = fma(y, -z, x);
	double tmp;
	if (t_3 <= -4e-272) {
		tmp = t_2;
	} else if (t_3 <= 5e-47) {
		tmp = 1.0 / fma(-z, (a / t_4), (t / t_4));
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(z * a))
	t_2 = fma(y, Float64(z / fma(z, a, Float64(-t))), Float64(x / t_1))
	t_3 = Float64(Float64(x - Float64(y * z)) / t_1)
	t_4 = fma(y, Float64(-z), x)
	tmp = 0.0
	if (t_3 <= -4e-272)
		tmp = t_2;
	elseif (t_3 <= 5e-47)
		tmp = Float64(1.0 / fma(Float64(-z), Float64(a / t_4), Float64(t / t_4)));
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(y / a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / N[(z * a + (-t)), $MachinePrecision]), $MachinePrecision] + N[(x / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(y * (-z) + x), $MachinePrecision]}, If[LessEqual[t$95$3, -4e-272], t$95$2, If[LessEqual[t$95$3, 5e-47], N[(1.0 / N[((-z) * N[(a / t$95$4), $MachinePrecision] + N[(t / t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, Infinity], t$95$2, N[(y / a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -3.99999999999999972e-272 or 5.00000000000000011e-47 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < +inf.0

   1. Initial program 96.6%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

   5. Simplified 98.7%

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

   if -3.99999999999999972e-272 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 5.00000000000000011e-47

   1. Initial program 81.4%

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

      1. lift-*.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

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

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

      7. lower-fma.f64 N/A

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

      8. lower-neg.f64 81.4

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

   4. Applied egg-rr 81.4%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-neg.f64 N/A

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

      4. lift-fma.f64 N/A

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

      5. clear-num N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 79.9

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

      8. lift-fma.f64 N/A

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

      9. +-commutative N/A

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

      10. lift-neg.f64 N/A

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

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

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

      12. lift-*.f64 N/A

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

      13. lift--.f64 79.9

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

      14. lift--.f64 N/A

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

      15. sub-neg N/A

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

      16. +-commutative N/A

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

      17. lift-*.f64 N/A

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

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

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

      19. lift-neg.f64 N/A

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

      20. lower-fma.f64 79.8

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

   6. Applied egg-rr 79.8%

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

      1. lift-*.f64 N/A

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

      2. lift-neg.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. div-inv N/A

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

      6. *-commutative N/A

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

      7. lift-fma.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. flip3-+ N/A

         \[\leadsto \frac{1}{\frac{1}{\color{blue}{\frac{{\left(y \cdot \left(\mathsf{neg}\left(z\right)\right)\right)}^{3} + {x}^{3}}{\left(y \cdot \left(\mathsf{neg}\left(z\right)\right)\right) \cdot \left(y \cdot \left(\mathsf{neg}\left(z\right)\right)\right) + \left(x \cdot x - \left(y \cdot \left(\mathsf{neg}\left(z\right)\right)\right) \cdot x\right)}}} \cdot \left(t - z \cdot a\right)} \]

      10. clear-num N/A

          \[\leadsto \frac{1}{\color{blue}{\frac{\left(y \cdot \left(\mathsf{neg}\left(z\right)\right)\right) \cdot \left(y \cdot \left(\mathsf{neg}\left(z\right)\right)\right) + \left(x \cdot x - \left(y \cdot \left(\mathsf{neg}\left(z\right)\right)\right) \cdot x\right)}{{\left(y \cdot \left(\mathsf{neg}\left(z\right)\right)\right)}^{3} + {x}^{3}}} \cdot \left(t - z \cdot a\right)} \]

      11. lift--.f64 N/A

          \[\leadsto \frac{1}{\frac{\left(y \cdot \left(\mathsf{neg}\left(z\right)\right)\right) \cdot \left(y \cdot \left(\mathsf{neg}\left(z\right)\right)\right) + \left(x \cdot x - \left(y \cdot \left(\mathsf{neg}\left(z\right)\right)\right) \cdot x\right)}{{\left(y \cdot \left(\mathsf{neg}\left(z\right)\right)\right)}^{3} + {x}^{3}} \cdot \color{blue}{\left(t - z \cdot a\right)}} \]

      12. sub-neg N/A

          \[\leadsto \frac{1}{\frac{\left(y \cdot \left(\mathsf{neg}\left(z\right)\right)\right) \cdot \left(y \cdot \left(\mathsf{neg}\left(z\right)\right)\right) + \left(x \cdot x - \left(y \cdot \left(\mathsf{neg}\left(z\right)\right)\right) \cdot x\right)}{{\left(y \cdot \left(\mathsf{neg}\left(z\right)\right)\right)}^{3} + {x}^{3}} \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(z \cdot a\right)\right)\right)}} \]

      13. +-commutative N/A

          \[\leadsto \frac{1}{\frac{\left(y \cdot \left(\mathsf{neg}\left(z\right)\right)\right) \cdot \left(y \cdot \left(\mathsf{neg}\left(z\right)\right)\right) + \left(x \cdot x - \left(y \cdot \left(\mathsf{neg}\left(z\right)\right)\right) \cdot x\right)}{{\left(y \cdot \left(\mathsf{neg}\left(z\right)\right)\right)}^{3} + {x}^{3}} \cdot \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot a\right)\right) + t\right)}} \]

      14. distribute-rgt-in N/A

          \[\leadsto \frac{1}{\color{blue}{\left(\mathsf{neg}\left(z \cdot a\right)\right) \cdot \frac{\left(y \cdot \left(\mathsf{neg}\left(z\right)\right)\right) \cdot \left(y \cdot \left(\mathsf{neg}\left(z\right)\right)\right) + \left(x \cdot x - \left(y \cdot \left(\mathsf{neg}\left(z\right)\right)\right) \cdot x\right)}{{\left(y \cdot \left(\mathsf{neg}\left(z\right)\right)\right)}^{3} + {x}^{3}} + t \cdot \frac{\left(y \cdot \left(\mathsf{neg}\left(z\right)\right)\right) \cdot \left(y \cdot \left(\mathsf{neg}\left(z\right)\right)\right) + \left(x \cdot x - \left(y \cdot \left(\mathsf{neg}\left(z\right)\right)\right) \cdot x\right)}{{\left(y \cdot \left(\mathsf{neg}\left(z\right)\right)\right)}^{3} + {x}^{3}}}} \]

   8. Applied egg-rr 93.3%

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

   if +inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 100.0

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

   5. Simplified 100.0%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -4 \cdot 10^{-272}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{\mathsf{fma}\left(z, a, -t\right)}, \frac{x}{t - z \cdot a}\right)\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 5 \cdot 10^{-47}:\\ \;\;\;\;\frac{1}{\mathsf{fma}\left(-z, \frac{a}{\mathsf{fma}\left(y, -z, x\right)}, \frac{t}{\mathsf{fma}\left(y, -z, x\right)}\right)}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{\mathsf{fma}\left(z, a, -t\right)}, \frac{x}{t - z \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot z\\ t_2 := t - z \cdot a\\ t_3 := \frac{t\_1}{t\_2}\\ \mathbf{if}\;t\_3 \leq -1 \cdot 10^{-306}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{\mathsf{fma}\left(z, a, -t\right)}, \frac{x}{t\_2}\right)\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;\frac{\frac{y \cdot z - x}{a}}{z}\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;\frac{t\_1}{\mathsf{fma}\left(-z, a, t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y z))) (t_2 (- t (* z a))) (t_3 (/ t_1 t_2)))
   (if (<= t_3 -1e-306)
     (fma y (/ z (fma z a (- t))) (/ x t_2))
     (if (<= t_3 0.0)
       (/ (/ (- (* y z) x) a) z)
       (if (<= t_3 INFINITY) (/ t_1 (fma (- z) a t)) (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * z);
	double t_2 = t - (z * a);
	double t_3 = t_1 / t_2;
	double tmp;
	if (t_3 <= -1e-306) {
		tmp = fma(y, (z / fma(z, a, -t)), (x / t_2));
	} else if (t_3 <= 0.0) {
		tmp = (((y * z) - x) / a) / z;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_1 / fma(-z, a, t);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * z))
	t_2 = Float64(t - Float64(z * a))
	t_3 = Float64(t_1 / t_2)
	tmp = 0.0
	if (t_3 <= -1e-306)
		tmp = fma(y, Float64(z / fma(z, a, Float64(-t))), Float64(x / t_2));
	elseif (t_3 <= 0.0)
		tmp = Float64(Float64(Float64(Float64(y * z) - x) / a) / z);
	elseif (t_3 <= Inf)
		tmp = Float64(t_1 / fma(Float64(-z), a, t));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 / t$95$2), $MachinePrecision]}, If[LessEqual[t$95$3, -1e-306], N[(y * N[(z / N[(z * a + (-t)), $MachinePrecision]), $MachinePrecision] + N[(x / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 0.0], N[(N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / a), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$3, Infinity], N[(t$95$1 / N[((-z) * a + t), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -1.00000000000000003e-306

   1. Initial program 96.3%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

   5. Simplified 97.3%

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

   if -1.00000000000000003e-306 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 0.0

   1. Initial program 56.7%

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

      1. lift-*.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

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

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

      7. lower-fma.f64 N/A

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

      8. lower-neg.f64 56.7

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

   4. Applied egg-rr 56.7%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-neg.f64 N/A

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

      4. lift-fma.f64 N/A

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

      5. div-inv N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. lift-*.f64 N/A

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

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

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

      12. lift-neg.f64 N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-/.f64 56.7

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

      15. lift-fma.f64 N/A

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

      16. +-commutative N/A

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

      17. lift-neg.f64 N/A

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

      18. cancel-sign-sub-inv N/A

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

      19. lift-*.f64 N/A

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

      20. lift--.f64 56.7

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

   6. Applied egg-rr 56.7%

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

   7. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 40.0

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

   9. Simplified 40.0%

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

       1. lift-neg.f64 N/A

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

       2. lift-fma.f64 N/A

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

       3. associate-/r* N/A

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

       4. associate-*r/ N/A

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

       5. lower-/.f64 N/A

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

       6. frac-2neg N/A

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

       7. metadata-eval N/A

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

       8. un-div-inv N/A

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

       9. remove-double-neg N/A

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

       10. frac-2neg N/A

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

       11. lower-/.f64 N/A

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

       12. lift-fma.f64 N/A

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

       13. distribute-neg-in N/A

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

       14. unsub-neg N/A

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

       15. lift-neg.f64 N/A

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

       16. distribute-rgt-neg-out N/A

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

       17. remove-double-neg N/A

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

       18. lower--.f64 N/A

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

       19. lower-*.f64 89.8

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

   11. Applied egg-rr 89.8%

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

   if 0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < +inf.0

   1. Initial program 98.0%

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

      1. lift-*.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

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

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

      7. lower-fma.f64 N/A

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

      8. lower-neg.f64 98.0

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

   4. Applied egg-rr 98.0%

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

   if +inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 100.0

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

   5. Simplified 100.0%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -1 \cdot 10^{-306}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{\mathsf{fma}\left(z, a, -t\right)}, \frac{x}{t - z \cdot a}\right)\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{\frac{y \cdot z - x}{a}}{z}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq \infty:\\ \;\;\;\;\frac{x - y \cdot z}{\mathsf{fma}\left(-z, a, t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot z\\ t_2 := \frac{t\_1}{\mathsf{fma}\left(-z, a, t\right)}\\ t_3 := \frac{t\_1}{t - z \cdot a}\\ \mathbf{if}\;t\_3 \leq -1 \cdot 10^{-306}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;\frac{\frac{y \cdot z - x}{a}}{z}\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y z)))
        (t_2 (/ t_1 (fma (- z) a t)))
        (t_3 (/ t_1 (- t (* z a)))))
   (if (<= t_3 -1e-306)
     t_2
     (if (<= t_3 0.0)
       (/ (/ (- (* y z) x) a) z)
       (if (<= t_3 INFINITY) t_2 (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * z);
	double t_2 = t_1 / fma(-z, a, t);
	double t_3 = t_1 / (t - (z * a));
	double tmp;
	if (t_3 <= -1e-306) {
		tmp = t_2;
	} else if (t_3 <= 0.0) {
		tmp = (((y * z) - x) / a) / z;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * z))
	t_2 = Float64(t_1 / fma(Float64(-z), a, t))
	t_3 = Float64(t_1 / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (t_3 <= -1e-306)
		tmp = t_2;
	elseif (t_3 <= 0.0)
		tmp = Float64(Float64(Float64(Float64(y * z) - x) / a) / z);
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(y / a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[((-z) * a + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -1e-306], t$95$2, If[LessEqual[t$95$3, 0.0], N[(N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / a), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$3, Infinity], t$95$2, N[(y / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -1.00000000000000003e-306 or 0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < +inf.0

   1. Initial program 97.2%

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

      1. lift-*.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

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

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

      7. lower-fma.f64 N/A

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

      8. lower-neg.f64 97.2

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

   4. Applied egg-rr 97.2%

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

   if -1.00000000000000003e-306 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 0.0

   1. Initial program 56.7%

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

      1. lift-*.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

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

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

      7. lower-fma.f64 N/A

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

      8. lower-neg.f64 56.7

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

   4. Applied egg-rr 56.7%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-neg.f64 N/A

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

      4. lift-fma.f64 N/A

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

      5. div-inv N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. lift-*.f64 N/A

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

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

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

      12. lift-neg.f64 N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-/.f64 56.7

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

      15. lift-fma.f64 N/A

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

      16. +-commutative N/A

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

      17. lift-neg.f64 N/A

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

      18. cancel-sign-sub-inv N/A

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

      19. lift-*.f64 N/A

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

      20. lift--.f64 56.7

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

   6. Applied egg-rr 56.7%

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

   7. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 40.0

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

   9. Simplified 40.0%

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

       1. lift-neg.f64 N/A

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

       2. lift-fma.f64 N/A

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

       3. associate-/r* N/A

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

       4. associate-*r/ N/A

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

       5. lower-/.f64 N/A

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

       6. frac-2neg N/A

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

       7. metadata-eval N/A

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

       8. un-div-inv N/A

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

       9. remove-double-neg N/A

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

       10. frac-2neg N/A

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

       11. lower-/.f64 N/A

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

       12. lift-fma.f64 N/A

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

       13. distribute-neg-in N/A

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

       14. unsub-neg N/A

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

       15. lift-neg.f64 N/A

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

       16. distribute-rgt-neg-out N/A

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

       17. remove-double-neg N/A

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

       18. lower--.f64 N/A

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

       19. lower-*.f64 89.8

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

   11. Applied egg-rr 89.8%

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

   if +inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 100.0

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

   5. Simplified 100.0%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -1 \cdot 10^{-306}:\\ \;\;\;\;\frac{x - y \cdot z}{\mathsf{fma}\left(-z, a, t\right)}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{\frac{y \cdot z - x}{a}}{z}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq \infty:\\ \;\;\;\;\frac{x - y \cdot z}{\mathsf{fma}\left(-z, a, t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * z))
	tmp = 0.0
	if (Float64(t_1 / Float64(t - Float64(z * a))) <= Inf)
		tmp = Float64(t_1 / fma(Float64(-z), a, t));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < +inf.0

   1. Initial program 92.4%

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

      1. lift-*.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

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

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

      7. lower-fma.f64 N/A

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

      8. lower-neg.f64 92.4

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

   4. Applied egg-rr 92.4%

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

   if +inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 100.0

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

   5. Simplified 100.0%

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

4. Final simplification 92.7%

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

Alternative 5: 89.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* y z)) (- t (* z a)))))
   (if (<= t_1 INFINITY) t_1 (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / (t - (z * a));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / (t - (z * a));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (y * z)) / (t - (z * a))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - (y * z)) / (t - (z * a));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < +inf.0

   1. Initial program 92.4%

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

   if +inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 100.0

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

   5. Simplified 100.0%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq \infty:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y \cdot z}{t}\\ \mathbf{if}\;t \leq -4 \cdot 10^{-29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-19}:\\ \;\;\;\;\frac{y \cdot z - x}{z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* y z)) t)))
   (if (<= t -4e-29) t_1 (if (<= t 6.2e-19) (/ (- (* y z) x) (* z a)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / t;
	double tmp;
	if (t <= -4e-29) {
		tmp = t_1;
	} else if (t <= 6.2e-19) {
		tmp = ((y * z) - x) / (z * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - (y * z)) / t
    if (t <= (-4d-29)) then
        tmp = t_1
    else if (t <= 6.2d-19) then
        tmp = ((y * z) - x) / (z * a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / t;
	double tmp;
	if (t <= -4e-29) {
		tmp = t_1;
	} else if (t <= 6.2e-19) {
		tmp = ((y * z) - x) / (z * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (y * z)) / t
	tmp = 0
	if t <= -4e-29:
		tmp = t_1
	elif t <= 6.2e-19:
		tmp = ((y * z) - x) / (z * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - Float64(y * z)) / t)
	tmp = 0.0
	if (t <= -4e-29)
		tmp = t_1;
	elseif (t <= 6.2e-19)
		tmp = Float64(Float64(Float64(y * z) - x) / Float64(z * a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - (y * z)) / t;
	tmp = 0.0;
	if (t <= -4e-29)
		tmp = t_1;
	elseif (t <= 6.2e-19)
		tmp = ((y * z) - x) / (z * a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[t, -4e-29], t$95$1, If[LessEqual[t, 6.2e-19], N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(z * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.99999999999999977e-29 or 6.1999999999999998e-19 < t

   1. Initial program 87.5%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 70.4

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

   5. Simplified 70.4%

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

   if -3.99999999999999977e-29 < t < 6.1999999999999998e-19

   1. Initial program 90.1%

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

   3. Taylor expanded in t around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

      4. sub-neg N/A

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

      5. +-commutative N/A

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

      6. distribute-neg-in N/A

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

      7. unsub-neg N/A

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

      8. remove-double-neg N/A

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

      9. lower--.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 69.1

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

   5. Simplified 69.1%

      \[\leadsto \color{blue}{\frac{y \cdot z - x}{z \cdot a}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 64.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t - z \cdot a}\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{-64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-76}:\\ \;\;\;\;\frac{y \cdot z}{\mathsf{fma}\left(z, a, -t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (- t (* z a)))))
   (if (<= x -3.8e-64) t_1 (if (<= x 6e-76) (/ (* y z) (fma z a (- t))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t - (z * a));
	double tmp;
	if (x <= -3.8e-64) {
		tmp = t_1;
	} else if (x <= 6e-76) {
		tmp = (y * z) / fma(z, a, -t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (x <= -3.8e-64)
		tmp = t_1;
	elseif (x <= 6e-76)
		tmp = Float64(Float64(y * z) / fma(z, a, Float64(-t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.8e-64], t$95$1, If[LessEqual[x, 6e-76], N[(N[(y * z), $MachinePrecision] / N[(z * a + (-t)), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.8000000000000002e-64 or 6.00000000000000048e-76 < x

   1. Initial program 86.6%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 66.8

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

   5. Simplified 66.8%

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

   if -3.8000000000000002e-64 < x < 6.00000000000000048e-76

   1. Initial program 92.4%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. associate-*r* N/A

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

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

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

      11. mul-1-neg N/A

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

      12. remove-double-neg N/A

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

      13. *-commutative N/A

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

      14. mul-1-neg N/A

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

      15. lower-fma.f64 N/A

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

      16. mul-1-neg N/A

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

      17. lower-neg.f64 72.8

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

   5. Simplified 72.8%

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

Alternative 8: 66.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+89}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+45}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.3e+89) (/ y a) (if (<= z 1.55e+45) (/ x (- t (* z a))) (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.3e+89) {
		tmp = y / a;
	} else if (z <= 1.55e+45) {
		tmp = x / (t - (z * a));
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.3d+89)) then
        tmp = y / a
    else if (z <= 1.55d+45) then
        tmp = x / (t - (z * a))
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.3e+89) {
		tmp = y / a;
	} else if (z <= 1.55e+45) {
		tmp = x / (t - (z * a));
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.3e+89:
		tmp = y / a
	elif z <= 1.55e+45:
		tmp = x / (t - (z * a))
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.3e+89)
		tmp = Float64(y / a);
	elseif (z <= 1.55e+45)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.3e+89)
		tmp = y / a;
	elseif (z <= 1.55e+45)
		tmp = x / (t - (z * a));
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.3e+89], N[(y / a), $MachinePrecision], If[LessEqual[z, 1.55e+45], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2999999999999999e89 or 1.54999999999999994e45 < z

   1. Initial program 73.3%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 63.6

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

   5. Simplified 63.6%

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

   if -2.2999999999999999e89 < z < 1.54999999999999994e45

   1. Initial program 98.6%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 71.1

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

   5. Simplified 71.1%

      \[\leadsto \color{blue}{\frac{x}{t - z \cdot a}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 54.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-73}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.5e-73) (/ y a) (if (<= z 3.6e-43) (/ x t) (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e-73) {
		tmp = y / a;
	} else if (z <= 3.6e-43) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.5d-73)) then
        tmp = y / a
    else if (z <= 3.6d-43) then
        tmp = x / t
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e-73) {
		tmp = y / a;
	} else if (z <= 3.6e-43) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.5e-73:
		tmp = y / a
	elif z <= 3.6e-43:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.5e-73)
		tmp = Float64(y / a);
	elseif (z <= 3.6e-43)
		tmp = Float64(x / t);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.5e-73)
		tmp = y / a;
	elseif (z <= 3.6e-43)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.5e-73], N[(y / a), $MachinePrecision], If[LessEqual[z, 3.6e-43], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.50000000000000006e-73 or 3.5999999999999999e-43 < z

   1. Initial program 81.1%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 53.2

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

   5. Simplified 53.2%

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

   if -5.50000000000000006e-73 < z < 3.5999999999999999e-43

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 58.8

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

   5. Simplified 58.8%

      \[\leadsto \color{blue}{\frac{x}{t}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 33.9% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \frac{x}{t} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.8%

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

3. Taylor expanded in z around 0

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

   1. lower-/.f64 34.1

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

5. Simplified 34.1%

   \[\leadsto \color{blue}{\frac{x}{t}} \]
6. Add Preprocessing

Developer Target 1: 97.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - a \cdot z\\ t_2 := \frac{x}{t\_1} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{if}\;z < -32113435955957344:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z < 3.5139522372978296 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* a z))) (t_2 (- (/ x t_1) (/ y (- (/ t z) a)))))
   (if (< z -32113435955957344.0)
     t_2
     (if (< z 3.5139522372978296e-86) (* (- x (* y z)) (/ 1.0 t_1)) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * z);
	double t_2 = (x / t_1) - (y / ((t / z) - a));
	double tmp;
	if (z < -32113435955957344.0) {
		tmp = t_2;
	} else if (z < 3.5139522372978296e-86) {
		tmp = (x - (y * z)) * (1.0 / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t - (a * z)
    t_2 = (x / t_1) - (y / ((t / z) - a))
    if (z < (-32113435955957344.0d0)) then
        tmp = t_2
    else if (z < 3.5139522372978296d-86) then
        tmp = (x - (y * z)) * (1.0d0 / t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * z);
	double t_2 = (x / t_1) - (y / ((t / z) - a));
	double tmp;
	if (z < -32113435955957344.0) {
		tmp = t_2;
	} else if (z < 3.5139522372978296e-86) {
		tmp = (x - (y * z)) * (1.0 / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (a * z)
	t_2 = (x / t_1) - (y / ((t / z) - a))
	tmp = 0
	if z < -32113435955957344.0:
		tmp = t_2
	elif z < 3.5139522372978296e-86:
		tmp = (x - (y * z)) * (1.0 / t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(a * z))
	t_2 = Float64(Float64(x / t_1) - Float64(y / Float64(Float64(t / z) - a)))
	tmp = 0.0
	if (z < -32113435955957344.0)
		tmp = t_2;
	elseif (z < 3.5139522372978296e-86)
		tmp = Float64(Float64(x - Float64(y * z)) * Float64(1.0 / t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (a * z);
	t_2 = (x / t_1) - (y / ((t / z) - a));
	tmp = 0.0;
	if (z < -32113435955957344.0)
		tmp = t_2;
	elseif (z < 3.5139522372978296e-86)
		tmp = (x - (y * z)) * (1.0 / t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / t$95$1), $MachinePrecision] - N[(y / N[(N[(t / z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -32113435955957344.0], t$95$2, If[Less[z, 3.5139522372978296e-86], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024207 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -32113435955957344) (- (/ x (- t (* a z))) (/ y (- (/ t z) a))) (if (< z 4392440296622287/125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* (- x (* y z)) (/ 1 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a))))))

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