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

Percentage Accurate: 85.1% → 93.9%

Time: 15.0s

Alternatives: 14

Speedup: 0.4×

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: 85.1% 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: 93.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - z \cdot a\\ t_2 := \frac{x - y \cdot z}{t_1}\\ t_3 := \frac{x}{t_1}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{+56}:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{y}{\frac{1}{\frac{z}{t_1}}}, t_3\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{-163}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{y}{\frac{t_1}{z}}, t_3\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* z a))) (t_2 (/ (- x (* y z)) t_1)) (t_3 (/ x t_1)))
   (if (<= t_2 -2e+56)
     (fma -1.0 (/ y (/ 1.0 (/ z t_1))) t_3)
     (if (<= t_2 5e-163)
       t_2
       (if (<= t_2 INFINITY) (fma -1.0 (/ y (/ t_1 z)) t_3) (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (z * a);
	double t_2 = (x - (y * z)) / t_1;
	double t_3 = x / t_1;
	double tmp;
	if (t_2 <= -2e+56) {
		tmp = fma(-1.0, (y / (1.0 / (z / t_1))), t_3);
	} else if (t_2 <= 5e-163) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = fma(-1.0, (y / (t_1 / z)), t_3);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(z * a))
	t_2 = Float64(Float64(x - Float64(y * z)) / t_1)
	t_3 = Float64(x / t_1)
	tmp = 0.0
	if (t_2 <= -2e+56)
		tmp = fma(-1.0, Float64(y / Float64(1.0 / Float64(z / t_1))), t_3);
	elseif (t_2 <= 5e-163)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = fma(-1.0, Float64(y / Float64(t_1 / z)), t_3);
	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[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(x / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+56], N[(-1.0 * N[(y / N[(1.0 / N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision], If[LessEqual[t$95$2, 5e-163], t$95$2, If[LessEqual[t$95$2, Infinity], N[(-1.0 * N[(y / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision] + t$95$3), $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))) < -2.00000000000000018e56

   1. Initial program 90.9%

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

      1. *-commutative 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in x around 0 90.9%

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

      1. fma-def 90.9%

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

      2. associate-/l* 99.6%

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

      3. *-commutative 99.6%

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

      4. *-commutative 99.6%

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

   7. Simplified 99.6%

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

      1. clear-num 99.7%

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

      2. inv-pow 99.7%

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

   9. Applied egg-rr 99.7%

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

       1. unpow-1 99.7%

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

       2. *-commutative 99.7%

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

   11. Simplified 99.7%

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

   if -2.00000000000000018e56 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 4.99999999999999977e-163

   1. Initial program 92.7%

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

   if 4.99999999999999977e-163 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < +inf.0

   1. Initial program 92.1%

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

      1. *-commutative 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in x around 0 92.1%

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

      1. fma-def 92.1%

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

      2. associate-/l* 99.9%

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

      3. *-commutative 99.9%

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

      4. *-commutative 99.9%

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

   7. Simplified 99.9%

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

   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. Step-by-step derivation

      1. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around inf 100.0%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -2 \cdot 10^{+56}:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{y}{\frac{1}{\frac{z}{t - z \cdot a}}}, \frac{x}{t - z \cdot a}\right)\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 5 \cdot 10^{-163}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{y}{\frac{t - z \cdot a}{z}}, \frac{x}{t - z \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - z \cdot a\\ t_2 := \mathsf{fma}\left(-1, \frac{y}{\frac{t_1}{z}}, \frac{x}{t_1}\right)\\ t_3 := \frac{x - y \cdot z}{t_1}\\ \mathbf{if}\;t_3 \leq -1.6 \cdot 10^{+43}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq 5 \cdot 10^{-163}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* z a)))
        (t_2 (fma -1.0 (/ y (/ t_1 z)) (/ x t_1)))
        (t_3 (/ (- x (* y z)) t_1)))
   (if (<= t_3 -1.6e+43)
     t_2
     (if (<= t_3 5e-163) t_3 (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(-1.0, (y / (t_1 / z)), (x / t_1));
	double t_3 = (x - (y * z)) / t_1;
	double tmp;
	if (t_3 <= -1.6e+43) {
		tmp = t_2;
	} else if (t_3 <= 5e-163) {
		tmp = t_3;
	} 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(-1.0, Float64(y / Float64(t_1 / z)), Float64(x / t_1))
	t_3 = Float64(Float64(x - Float64(y * z)) / t_1)
	tmp = 0.0
	if (t_3 <= -1.6e+43)
		tmp = t_2;
	elseif (t_3 <= 5e-163)
		tmp = t_3;
	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[(-1.0 * N[(y / N[(t$95$1 / z), $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]}, If[LessEqual[t$95$3, -1.6e+43], t$95$2, If[LessEqual[t$95$3, 5e-163], t$95$3, 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))) < -1.60000000000000007e43 or 4.99999999999999977e-163 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < +inf.0

   1. Initial program 91.8%

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

      1. *-commutative 91.8%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in x around 0 91.8%

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

      1. fma-def 91.8%

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

      2. associate-/l* 99.8%

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

      3. *-commutative 99.8%

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

      4. *-commutative 99.8%

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

   7. Simplified 99.8%

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

   if -1.60000000000000007e43 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 4.99999999999999977e-163

   1. Initial program 92.6%

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

      1. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around inf 100.0%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -1.6 \cdot 10^{+43}:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{y}{\frac{t - z \cdot a}{z}}, \frac{x}{t - z \cdot a}\right)\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 5 \cdot 10^{-163}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{y}{\frac{t - z \cdot a}{z}}, \frac{x}{t - z \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - z \cdot a\\ t_2 := \frac{x - y \cdot z}{t_1}\\ \mathbf{if}\;t_2 \leq 4 \cdot 10^{+271}:\\ \;\;\;\;\frac{x}{t_1} - \frac{y \cdot z}{t_1}\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{y}{\frac{1}{\frac{z}{t_1}}}, \frac{x}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* z a))) (t_2 (/ (- x (* y z)) t_1)))
   (if (<= t_2 4e+271)
     (- (/ x t_1) (/ (* y z) t_1))
     (if (<= t_2 INFINITY)
       (fma -1.0 (/ y (/ 1.0 (/ z t_1))) (/ x t))
       (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (z * a);
	double t_2 = (x - (y * z)) / t_1;
	double tmp;
	if (t_2 <= 4e+271) {
		tmp = (x / t_1) - ((y * z) / t_1);
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = fma(-1.0, (y / (1.0 / (z / t_1))), (x / t));
	} else {
		tmp = y / a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(z * a))
	t_2 = Float64(Float64(x - Float64(y * z)) / t_1)
	tmp = 0.0
	if (t_2 <= 4e+271)
		tmp = Float64(Float64(x / t_1) - Float64(Float64(y * z) / t_1));
	elseif (t_2 <= Inf)
		tmp = fma(-1.0, Float64(y / Float64(1.0 / Float64(z / t_1))), Float64(x / t));
	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[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, 4e+271], N[(N[(x / t$95$1), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], N[(-1.0 * N[(y / N[(1.0 / N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x / t), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 3.99999999999999981e271

   1. Initial program 94.4%

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

      1. *-commutative 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in x around 0 94.4%

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

   if 3.99999999999999981e271 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < +inf.0

   1. Initial program 63.9%

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

      1. *-commutative 63.9%

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

   3. Simplified 63.9%

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

   5. Taylor expanded in x around 0 63.9%

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

      1. fma-def 63.9%

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

      2. associate-/l* 100.0%

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

      3. *-commutative 100.0%

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

      4. *-commutative 100.0%

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

   7. Simplified 100.0%

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

      1. clear-num 99.7%

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

      2. inv-pow 99.7%

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

   9. Applied egg-rr 99.7%

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

       1. unpow-1 99.7%

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

       2. *-commutative 99.7%

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

   11. Simplified 99.7%

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

   12. Taylor expanded in t around inf 89.0%

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

   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. Step-by-step derivation

      1. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around inf 100.0%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 4 \cdot 10^{+271}:\\ \;\;\;\;\frac{x}{t - z \cdot a} - \frac{y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{y}{\frac{1}{\frac{z}{t - z \cdot a}}}, \frac{x}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;a \leq -2.7 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-96}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{t} - \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+21}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{+71}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)))
   (if (<= a -2.7e-15)
     t_1
     (if (<= a -1.3e-96)
       (/ (- x (* y z)) t)
       (if (<= a -1.2e-119)
         t_1
         (if (<= a 3.7e-8)
           (- (/ x t) (/ z (/ t y)))
           (if (<= a 1.85e+21)
             (/ y a)
             (if (<= a 2.15e+71) (/ x (- t (* z a))) t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (a <= -2.7e-15) {
		tmp = t_1;
	} else if (a <= -1.3e-96) {
		tmp = (x - (y * z)) / t;
	} else if (a <= -1.2e-119) {
		tmp = t_1;
	} else if (a <= 3.7e-8) {
		tmp = (x / t) - (z / (t / y));
	} else if (a <= 1.85e+21) {
		tmp = y / a;
	} else if (a <= 2.15e+71) {
		tmp = x / (t - (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 = (y - (x / z)) / a
    if (a <= (-2.7d-15)) then
        tmp = t_1
    else if (a <= (-1.3d-96)) then
        tmp = (x - (y * z)) / t
    else if (a <= (-1.2d-119)) then
        tmp = t_1
    else if (a <= 3.7d-8) then
        tmp = (x / t) - (z / (t / y))
    else if (a <= 1.85d+21) then
        tmp = y / a
    else if (a <= 2.15d+71) then
        tmp = x / (t - (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 = (y - (x / z)) / a;
	double tmp;
	if (a <= -2.7e-15) {
		tmp = t_1;
	} else if (a <= -1.3e-96) {
		tmp = (x - (y * z)) / t;
	} else if (a <= -1.2e-119) {
		tmp = t_1;
	} else if (a <= 3.7e-8) {
		tmp = (x / t) - (z / (t / y));
	} else if (a <= 1.85e+21) {
		tmp = y / a;
	} else if (a <= 2.15e+71) {
		tmp = x / (t - (z * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - (x / z)) / a
	tmp = 0
	if a <= -2.7e-15:
		tmp = t_1
	elif a <= -1.3e-96:
		tmp = (x - (y * z)) / t
	elif a <= -1.2e-119:
		tmp = t_1
	elif a <= 3.7e-8:
		tmp = (x / t) - (z / (t / y))
	elif a <= 1.85e+21:
		tmp = y / a
	elif a <= 2.15e+71:
		tmp = x / (t - (z * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (a <= -2.7e-15)
		tmp = t_1;
	elseif (a <= -1.3e-96)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	elseif (a <= -1.2e-119)
		tmp = t_1;
	elseif (a <= 3.7e-8)
		tmp = Float64(Float64(x / t) - Float64(z / Float64(t / y)));
	elseif (a <= 1.85e+21)
		tmp = Float64(y / a);
	elseif (a <= 2.15e+71)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - (x / z)) / a;
	tmp = 0.0;
	if (a <= -2.7e-15)
		tmp = t_1;
	elseif (a <= -1.3e-96)
		tmp = (x - (y * z)) / t;
	elseif (a <= -1.2e-119)
		tmp = t_1;
	elseif (a <= 3.7e-8)
		tmp = (x / t) - (z / (t / y));
	elseif (a <= 1.85e+21)
		tmp = y / a;
	elseif (a <= 2.15e+71)
		tmp = x / (t - (z * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[a, -2.7e-15], t$95$1, If[LessEqual[a, -1.3e-96], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, -1.2e-119], t$95$1, If[LessEqual[a, 3.7e-8], N[(N[(x / t), $MachinePrecision] - N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.85e+21], N[(y / a), $MachinePrecision], If[LessEqual[a, 2.15e+71], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.70000000000000009e-15 or -1.3000000000000001e-96 < a < -1.20000000000000004e-119 or 2.14999999999999992e71 < a

   1. Initial program 81.5%

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

      1. *-commutative 81.5%

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

   3. Simplified 81.5%

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

   5. Taylor expanded in x around 0 81.5%

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

      1. fma-def 81.5%

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

      2. associate-/l* 81.9%

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

      3. *-commutative 81.9%

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

      4. *-commutative 81.9%

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

   7. Simplified 81.9%

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

   8. Taylor expanded in a around inf 74.0%

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

      1. mul-1-neg 74.0%

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

      2. sub-neg 74.0%

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

   10. Simplified 74.0%

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

   if -2.70000000000000009e-15 < a < -1.3000000000000001e-96

   1. Initial program 87.2%

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

      1. *-commutative 87.2%

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

   3. Simplified 87.2%

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

   5. Taylor expanded in t around inf 68.0%

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

   if -1.20000000000000004e-119 < a < 3.7e-8

   1. Initial program 94.5%

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

      1. *-commutative 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in x around 0 94.5%

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

      1. fma-def 94.5%

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

      2. associate-/l* 96.1%

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

      3. *-commutative 96.1%

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

      4. *-commutative 96.1%

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

   7. Simplified 96.1%

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

   8. Taylor expanded in a around 0 77.4%

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

      1. +-commutative 77.4%

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

      2. mul-1-neg 77.4%

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

      3. *-commutative 77.4%

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

      4. sub-neg 77.4%

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

      5. associate-/l* 79.1%

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

   10. Simplified 79.1%

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

   if 3.7e-8 < a < 1.85e21

   1. Initial program 69.1%

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

      1. *-commutative 69.1%

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

   3. Simplified 69.1%

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

   5. Taylor expanded in z around inf 86.3%

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

   if 1.85e21 < a < 2.14999999999999992e71

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 88.1%

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

      1. *-commutative 88.1%

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

   7. Simplified 88.1%

      \[\leadsto \color{blue}{\frac{x}{t - z \cdot a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{-15}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-96}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-119}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{t} - \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+21}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{+71}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - z \cdot a\\ t_2 := z \cdot \frac{-y}{t_1}\\ t_3 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;a \leq -4.3 \cdot 10^{+23}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-108}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{+23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{+71}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* z a)))
        (t_2 (* z (/ (- y) t_1)))
        (t_3 (/ (- y (/ x z)) a)))
   (if (<= a -4.3e+23)
     t_3
     (if (<= a -6e-36)
       t_2
       (if (<= a 1.7e-108)
         (/ (- x (* y z)) t)
         (if (<= a 5.4e+23) t_2 (if (<= a 7.4e+71) (/ x t_1) t_3)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (z * a);
	double t_2 = z * (-y / t_1);
	double t_3 = (y - (x / z)) / a;
	double tmp;
	if (a <= -4.3e+23) {
		tmp = t_3;
	} else if (a <= -6e-36) {
		tmp = t_2;
	} else if (a <= 1.7e-108) {
		tmp = (x - (y * z)) / t;
	} else if (a <= 5.4e+23) {
		tmp = t_2;
	} else if (a <= 7.4e+71) {
		tmp = x / t_1;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = t - (z * a)
    t_2 = z * (-y / t_1)
    t_3 = (y - (x / z)) / a
    if (a <= (-4.3d+23)) then
        tmp = t_3
    else if (a <= (-6d-36)) then
        tmp = t_2
    else if (a <= 1.7d-108) then
        tmp = (x - (y * z)) / t
    else if (a <= 5.4d+23) then
        tmp = t_2
    else if (a <= 7.4d+71) then
        tmp = x / t_1
    else
        tmp = t_3
    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 - (z * a);
	double t_2 = z * (-y / t_1);
	double t_3 = (y - (x / z)) / a;
	double tmp;
	if (a <= -4.3e+23) {
		tmp = t_3;
	} else if (a <= -6e-36) {
		tmp = t_2;
	} else if (a <= 1.7e-108) {
		tmp = (x - (y * z)) / t;
	} else if (a <= 5.4e+23) {
		tmp = t_2;
	} else if (a <= 7.4e+71) {
		tmp = x / t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (z * a)
	t_2 = z * (-y / t_1)
	t_3 = (y - (x / z)) / a
	tmp = 0
	if a <= -4.3e+23:
		tmp = t_3
	elif a <= -6e-36:
		tmp = t_2
	elif a <= 1.7e-108:
		tmp = (x - (y * z)) / t
	elif a <= 5.4e+23:
		tmp = t_2
	elif a <= 7.4e+71:
		tmp = x / t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(z * a))
	t_2 = Float64(z * Float64(Float64(-y) / t_1))
	t_3 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (a <= -4.3e+23)
		tmp = t_3;
	elseif (a <= -6e-36)
		tmp = t_2;
	elseif (a <= 1.7e-108)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	elseif (a <= 5.4e+23)
		tmp = t_2;
	elseif (a <= 7.4e+71)
		tmp = Float64(x / t_1);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (z * a);
	t_2 = z * (-y / t_1);
	t_3 = (y - (x / z)) / a;
	tmp = 0.0;
	if (a <= -4.3e+23)
		tmp = t_3;
	elseif (a <= -6e-36)
		tmp = t_2;
	elseif (a <= 1.7e-108)
		tmp = (x - (y * z)) / t;
	elseif (a <= 5.4e+23)
		tmp = t_2;
	elseif (a <= 7.4e+71)
		tmp = x / t_1;
	else
		tmp = t_3;
	end
	tmp_2 = 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[(z * N[((-y) / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[a, -4.3e+23], t$95$3, If[LessEqual[a, -6e-36], t$95$2, If[LessEqual[a, 1.7e-108], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, 5.4e+23], t$95$2, If[LessEqual[a, 7.4e+71], N[(x / t$95$1), $MachinePrecision], t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.2999999999999999e23 or 7.4e71 < a

   1. Initial program 79.8%

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

      1. *-commutative 79.8%

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

   3. Simplified 79.8%

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

   5. Taylor expanded in x around 0 79.8%

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

      1. fma-def 79.8%

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

      2. associate-/l* 79.4%

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

      3. *-commutative 79.4%

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

      4. *-commutative 79.4%

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

   7. Simplified 79.4%

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

   8. Taylor expanded in a around inf 74.9%

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

      1. mul-1-neg 74.9%

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

      2. sub-neg 74.9%

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

   10. Simplified 74.9%

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

   if -4.2999999999999999e23 < a < -6.0000000000000003e-36 or 1.70000000000000001e-108 < a < 5.3999999999999997e23

   1. Initial program 84.0%

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

      1. *-commutative 84.0%

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

   3. Simplified 84.0%

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

   5. Taylor expanded in x around 0 75.6%

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

      1. mul-1-neg 75.6%

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

      2. associate-/l* 88.7%

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

      3. associate-/r/ 86.3%

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

      4. sub-neg 86.3%

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

      5. +-commutative 86.3%

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

      6. distribute-rgt-neg-in 86.3%

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

      7. fma-udef 86.3%

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

      8. distribute-rgt-neg-in 86.3%

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

      9. fma-udef 86.3%

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

      10. distribute-rgt-neg-in 86.3%

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

      11. +-commutative 86.3%

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

      12. sub-neg 86.3%

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

      13. *-commutative 86.3%

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

   7. Simplified 86.3%

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

   if -6.0000000000000003e-36 < a < 1.70000000000000001e-108

   1. Initial program 95.3%

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

      1. *-commutative 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in t around inf 77.9%

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

   if 5.3999999999999997e23 < a < 7.4e71

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 88.1%

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

      1. *-commutative 88.1%

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

   7. Simplified 88.1%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.3 \cdot 10^{+23}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-36}:\\ \;\;\;\;z \cdot \frac{-y}{t - z \cdot a}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-108}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{+23}:\\ \;\;\;\;z \cdot \frac{-y}{t - z \cdot a}\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{+71}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.9% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], Infinity], N[(N[(x / t$95$1), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / t$95$1), $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 92.1%

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

      1. *-commutative 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in x around 0 92.1%

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

   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. Step-by-step derivation

      1. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around inf 100.0%

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

4. Final simplification 92.5%

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

Alternative 7: 64.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-101}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-191}:\\ \;\;\;\;\frac{y \cdot z - x}{z \cdot a}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-131}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+116}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} - \frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -8.5e-101)
   (/ (- x (* y z)) t)
   (if (<= t 1.3e-191)
     (/ (- (* y z) x) (* z a))
     (if (<= t 1.05e-131)
       (/ x (- t (* z a)))
       (if (<= t 1.1e+116) (/ (- y (/ x z)) a) (- (/ x t) (/ z (/ t y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8.5e-101) {
		tmp = (x - (y * z)) / t;
	} else if (t <= 1.3e-191) {
		tmp = ((y * z) - x) / (z * a);
	} else if (t <= 1.05e-131) {
		tmp = x / (t - (z * a));
	} else if (t <= 1.1e+116) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x / t) - (z / (t / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-8.5d-101)) then
        tmp = (x - (y * z)) / t
    else if (t <= 1.3d-191) then
        tmp = ((y * z) - x) / (z * a)
    else if (t <= 1.05d-131) then
        tmp = x / (t - (z * a))
    else if (t <= 1.1d+116) then
        tmp = (y - (x / z)) / a
    else
        tmp = (x / t) - (z / (t / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8.5e-101) {
		tmp = (x - (y * z)) / t;
	} else if (t <= 1.3e-191) {
		tmp = ((y * z) - x) / (z * a);
	} else if (t <= 1.05e-131) {
		tmp = x / (t - (z * a));
	} else if (t <= 1.1e+116) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x / t) - (z / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -8.5e-101:
		tmp = (x - (y * z)) / t
	elif t <= 1.3e-191:
		tmp = ((y * z) - x) / (z * a)
	elif t <= 1.05e-131:
		tmp = x / (t - (z * a))
	elif t <= 1.1e+116:
		tmp = (y - (x / z)) / a
	else:
		tmp = (x / t) - (z / (t / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -8.5e-101)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	elseif (t <= 1.3e-191)
		tmp = Float64(Float64(Float64(y * z) - x) / Float64(z * a));
	elseif (t <= 1.05e-131)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (t <= 1.1e+116)
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	else
		tmp = Float64(Float64(x / t) - Float64(z / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -8.5e-101)
		tmp = (x - (y * z)) / t;
	elseif (t <= 1.3e-191)
		tmp = ((y * z) - x) / (z * a);
	elseif (t <= 1.05e-131)
		tmp = x / (t - (z * a));
	elseif (t <= 1.1e+116)
		tmp = (y - (x / z)) / a;
	else
		tmp = (x / t) - (z / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -8.5e-101], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 1.3e-191], N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(z * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e-131], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e+116], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / t), $MachinePrecision] - N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -8.49999999999999941e-101

   1. Initial program 83.2%

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

      1. *-commutative 83.2%

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

   3. Simplified 83.2%

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

   5. Taylor expanded in t around inf 70.0%

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

   if -8.49999999999999941e-101 < t < 1.29999999999999993e-191

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in t around 0 80.9%

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

      1. associate-*r/ 80.9%

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

      2. neg-mul-1 80.9%

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

      3. sub-neg 80.9%

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

      4. distribute-rgt-neg-out 80.9%

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

      5. +-commutative 80.9%

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

      6. distribute-neg-in 80.9%

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

      7. distribute-rgt-neg-out 80.9%

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

      8. remove-double-neg 80.9%

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

      9. sub-neg 80.9%

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

      10. *-commutative 80.9%

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

   7. Simplified 80.9%

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

   if 1.29999999999999993e-191 < t < 1.04999999999999999e-131

   1. Initial program 92.6%

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

      1. *-commutative 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in x around inf 81.3%

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

      1. *-commutative 81.3%

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

   7. Simplified 81.3%

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

   if 1.04999999999999999e-131 < t < 1.1e116

   1. Initial program 83.8%

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

      1. *-commutative 83.8%

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

   3. Simplified 83.8%

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

   5. Taylor expanded in x around 0 83.8%

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

      1. fma-def 83.8%

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

      2. associate-/l* 89.2%

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

      3. *-commutative 89.2%

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

      4. *-commutative 89.2%

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

   7. Simplified 89.2%

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

   8. Taylor expanded in a around inf 68.6%

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

      1. mul-1-neg 68.6%

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

      2. sub-neg 68.6%

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

   10. Simplified 68.6%

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

   if 1.1e116 < t

   1. Initial program 81.1%

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

      1. *-commutative 81.1%

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

   3. Simplified 81.1%

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

   5. Taylor expanded in x around 0 81.1%

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

      1. fma-def 81.1%

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

      2. associate-/l* 81.6%

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

      3. *-commutative 81.6%

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

      4. *-commutative 81.6%

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

   7. Simplified 81.6%

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

   8. Taylor expanded in a around 0 68.4%

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

      1. +-commutative 68.4%

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

      2. mul-1-neg 68.4%

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

      3. *-commutative 68.4%

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

      4. sub-neg 68.4%

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

      5. associate-/l* 74.0%

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

   10. Simplified 74.0%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-101}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-191}:\\ \;\;\;\;\frac{y \cdot z - x}{z \cdot a}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-131}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+116}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} - \frac{z}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{-8}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{-8}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;a \leq 2.85 \cdot 10^{+23} \lor \neg \left(a \leq 2 \cdot 10^{+72}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.25e-8)
   (/ y a)
   (if (<= a 5.7e-8)
     (/ (- x (* y z)) t)
     (if (or (<= a 2.85e+23) (not (<= a 2e+72)))
       (/ y a)
       (/ x (- t (* z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.25e-8) {
		tmp = y / a;
	} else if (a <= 5.7e-8) {
		tmp = (x - (y * z)) / t;
	} else if ((a <= 2.85e+23) || !(a <= 2e+72)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.25d-8)) then
        tmp = y / a
    else if (a <= 5.7d-8) then
        tmp = (x - (y * z)) / t
    else if ((a <= 2.85d+23) .or. (.not. (a <= 2d+72))) then
        tmp = y / a
    else
        tmp = x / (t - (z * 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 (a <= -1.25e-8) {
		tmp = y / a;
	} else if (a <= 5.7e-8) {
		tmp = (x - (y * z)) / t;
	} else if ((a <= 2.85e+23) || !(a <= 2e+72)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.25e-8:
		tmp = y / a
	elif a <= 5.7e-8:
		tmp = (x - (y * z)) / t
	elif (a <= 2.85e+23) or not (a <= 2e+72):
		tmp = y / a
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.25e-8)
		tmp = Float64(y / a);
	elseif (a <= 5.7e-8)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	elseif ((a <= 2.85e+23) || !(a <= 2e+72))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.25e-8)
		tmp = y / a;
	elseif (a <= 5.7e-8)
		tmp = (x - (y * z)) / t;
	elseif ((a <= 2.85e+23) || ~((a <= 2e+72)))
		tmp = y / a;
	else
		tmp = x / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.25e-8], N[(y / a), $MachinePrecision], If[LessEqual[a, 5.7e-8], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[Or[LessEqual[a, 2.85e+23], N[Not[LessEqual[a, 2e+72]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.2499999999999999e-8 or 5.70000000000000009e-8 < a < 2.85e23 or 1.99999999999999989e72 < a

   1. Initial program 79.7%

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

      1. *-commutative 79.7%

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

   3. Simplified 79.7%

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

   5. Taylor expanded in z around inf 59.5%

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

   if -1.2499999999999999e-8 < a < 5.70000000000000009e-8

   1. Initial program 93.9%

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

      1. *-commutative 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in t around inf 74.0%

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

   if 2.85e23 < a < 1.99999999999999989e72

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 88.1%

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

      1. *-commutative 88.1%

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

   7. Simplified 88.1%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{-8}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{-8}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;a \leq 2.85 \cdot 10^{+23} \lor \neg \left(a \leq 2 \cdot 10^{+72}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 56.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t - z \cdot a}\\ \mathbf{if}\;x \leq -0.0026:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-175}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;x \leq -3.35 \cdot 10^{-299}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-44}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (- t (* z a)))))
   (if (<= x -0.0026)
     t_1
     (if (<= x -4.2e-175)
       (/ y a)
       (if (<= x -3.35e-299)
         (/ (* y (- z)) t)
         (if (<= x 5.5e-44) (/ y a) 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 <= -0.0026) {
		tmp = t_1;
	} else if (x <= -4.2e-175) {
		tmp = y / a;
	} else if (x <= -3.35e-299) {
		tmp = (y * -z) / t;
	} else if (x <= 5.5e-44) {
		tmp = y / 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 / (t - (z * a))
    if (x <= (-0.0026d0)) then
        tmp = t_1
    else if (x <= (-4.2d-175)) then
        tmp = y / a
    else if (x <= (-3.35d-299)) then
        tmp = (y * -z) / t
    else if (x <= 5.5d-44) then
        tmp = y / 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 / (t - (z * a));
	double tmp;
	if (x <= -0.0026) {
		tmp = t_1;
	} else if (x <= -4.2e-175) {
		tmp = y / a;
	} else if (x <= -3.35e-299) {
		tmp = (y * -z) / t;
	} else if (x <= 5.5e-44) {
		tmp = y / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (t - (z * a))
	tmp = 0
	if x <= -0.0026:
		tmp = t_1
	elif x <= -4.2e-175:
		tmp = y / a
	elif x <= -3.35e-299:
		tmp = (y * -z) / t
	elif x <= 5.5e-44:
		tmp = y / a
	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 <= -0.0026)
		tmp = t_1;
	elseif (x <= -4.2e-175)
		tmp = Float64(y / a);
	elseif (x <= -3.35e-299)
		tmp = Float64(Float64(y * Float64(-z)) / t);
	elseif (x <= 5.5e-44)
		tmp = Float64(y / a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (t - (z * a));
	tmp = 0.0;
	if (x <= -0.0026)
		tmp = t_1;
	elseif (x <= -4.2e-175)
		tmp = y / a;
	elseif (x <= -3.35e-299)
		tmp = (y * -z) / t;
	elseif (x <= 5.5e-44)
		tmp = y / a;
	else
		tmp = t_1;
	end
	tmp_2 = 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, -0.0026], t$95$1, If[LessEqual[x, -4.2e-175], N[(y / a), $MachinePrecision], If[LessEqual[x, -3.35e-299], N[(N[(y * (-z)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[x, 5.5e-44], N[(y / a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.0025999999999999999 or 5.49999999999999993e-44 < x

   1. Initial program 86.7%

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

      1. *-commutative 86.7%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in x around inf 67.1%

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

      1. *-commutative 67.1%

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

   7. Simplified 67.1%

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

   if -0.0025999999999999999 < x < -4.2e-175 or -3.34999999999999999e-299 < x < 5.49999999999999993e-44

   1. Initial program 86.1%

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

      1. *-commutative 86.1%

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

   3. Simplified 86.1%

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

   5. Taylor expanded in z around inf 57.3%

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

   if -4.2e-175 < x < -3.34999999999999999e-299

   1. Initial program 95.9%

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

      1. *-commutative 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in t around inf 69.5%

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

   6. Taylor expanded in x around 0 69.6%

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

      1. mul-1-neg 69.6%

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

      2. *-commutative 69.6%

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

      3. distribute-rgt-neg-in 69.6%

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

   8. Simplified 69.6%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0026:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-175}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;x \leq -3.35 \cdot 10^{-299}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-44}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;a \leq -3.3 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-8}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+20}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+72}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)))
   (if (<= a -3.3e-15)
     t_1
     (if (<= a 2.7e-8)
       (/ (- x (* y z)) t)
       (if (<= a 7.2e+20)
         (/ y a)
         (if (<= a 5.6e+72) (/ x (- t (* z a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (a <= -3.3e-15) {
		tmp = t_1;
	} else if (a <= 2.7e-8) {
		tmp = (x - (y * z)) / t;
	} else if (a <= 7.2e+20) {
		tmp = y / a;
	} else if (a <= 5.6e+72) {
		tmp = x / (t - (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 = (y - (x / z)) / a
    if (a <= (-3.3d-15)) then
        tmp = t_1
    else if (a <= 2.7d-8) then
        tmp = (x - (y * z)) / t
    else if (a <= 7.2d+20) then
        tmp = y / a
    else if (a <= 5.6d+72) then
        tmp = x / (t - (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 = (y - (x / z)) / a;
	double tmp;
	if (a <= -3.3e-15) {
		tmp = t_1;
	} else if (a <= 2.7e-8) {
		tmp = (x - (y * z)) / t;
	} else if (a <= 7.2e+20) {
		tmp = y / a;
	} else if (a <= 5.6e+72) {
		tmp = x / (t - (z * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - (x / z)) / a
	tmp = 0
	if a <= -3.3e-15:
		tmp = t_1
	elif a <= 2.7e-8:
		tmp = (x - (y * z)) / t
	elif a <= 7.2e+20:
		tmp = y / a
	elif a <= 5.6e+72:
		tmp = x / (t - (z * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (a <= -3.3e-15)
		tmp = t_1;
	elseif (a <= 2.7e-8)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	elseif (a <= 7.2e+20)
		tmp = Float64(y / a);
	elseif (a <= 5.6e+72)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - (x / z)) / a;
	tmp = 0.0;
	if (a <= -3.3e-15)
		tmp = t_1;
	elseif (a <= 2.7e-8)
		tmp = (x - (y * z)) / t;
	elseif (a <= 7.2e+20)
		tmp = y / a;
	elseif (a <= 5.6e+72)
		tmp = x / (t - (z * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[a, -3.3e-15], t$95$1, If[LessEqual[a, 2.7e-8], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, 7.2e+20], N[(y / a), $MachinePrecision], If[LessEqual[a, 5.6e+72], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.3e-15 or 5.5999999999999998e72 < a

   1. Initial program 80.2%

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

      1. *-commutative 80.2%

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

   3. Simplified 80.2%

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

   5. Taylor expanded in x around 0 80.2%

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

      1. fma-def 80.2%

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

      2. associate-/l* 80.7%

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

      3. *-commutative 80.7%

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

      4. *-commutative 80.7%

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

   7. Simplified 80.7%

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

   8. Taylor expanded in a around inf 74.0%

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

      1. mul-1-neg 74.0%

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

      2. sub-neg 74.0%

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

   10. Simplified 74.0%

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

   if -3.3e-15 < a < 2.70000000000000002e-8

   1. Initial program 93.9%

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

      1. *-commutative 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in t around inf 74.0%

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

   if 2.70000000000000002e-8 < a < 7.2e20

   1. Initial program 69.1%

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

      1. *-commutative 69.1%

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

   3. Simplified 69.1%

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

   5. Taylor expanded in z around inf 86.3%

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

   if 7.2e20 < a < 5.5999999999999998e72

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 88.1%

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

      1. *-commutative 88.1%

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

   7. Simplified 88.1%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{-15}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-8}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+20}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+72}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 89.2% accurate, 0.4× 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 92.1%

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

      1. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around inf 100.0%

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

4. Final simplification 92.5%

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

Alternative 12: 55.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+73}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-9}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-50} \lor \neg \left(z \leq 2.7 \cdot 10^{-68}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.6e+73)
   (/ y a)
   (if (<= z -6.2e-9)
     (* y (/ (- z) t))
     (if (or (<= z -8.2e-50) (not (<= z 2.7e-68))) (/ y a) (/ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.6e+73) {
		tmp = y / a;
	} else if (z <= -6.2e-9) {
		tmp = y * (-z / t);
	} else if ((z <= -8.2e-50) || !(z <= 2.7e-68)) {
		tmp = y / a;
	} else {
		tmp = x / 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 (z <= (-7.6d+73)) then
        tmp = y / a
    else if (z <= (-6.2d-9)) then
        tmp = y * (-z / t)
    else if ((z <= (-8.2d-50)) .or. (.not. (z <= 2.7d-68))) then
        tmp = y / a
    else
        tmp = x / 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 (z <= -7.6e+73) {
		tmp = y / a;
	} else if (z <= -6.2e-9) {
		tmp = y * (-z / t);
	} else if ((z <= -8.2e-50) || !(z <= 2.7e-68)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.6e+73:
		tmp = y / a
	elif z <= -6.2e-9:
		tmp = y * (-z / t)
	elif (z <= -8.2e-50) or not (z <= 2.7e-68):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.6e+73)
		tmp = Float64(y / a);
	elseif (z <= -6.2e-9)
		tmp = Float64(y * Float64(Float64(-z) / t));
	elseif ((z <= -8.2e-50) || !(z <= 2.7e-68))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.6e+73)
		tmp = y / a;
	elseif (z <= -6.2e-9)
		tmp = y * (-z / t);
	elseif ((z <= -8.2e-50) || ~((z <= 2.7e-68)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.6e+73], N[(y / a), $MachinePrecision], If[LessEqual[z, -6.2e-9], N[(y * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -8.2e-50], N[Not[LessEqual[z, 2.7e-68]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.60000000000000044e73 or -6.2000000000000001e-9 < z < -8.19999999999999971e-50 or 2.7000000000000002e-68 < z

   1. Initial program 78.7%

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

      1. *-commutative 78.7%

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

   3. Simplified 78.7%

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

   5. Taylor expanded in z around inf 56.4%

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

   if -7.60000000000000044e73 < z < -6.2000000000000001e-9

   1. Initial program 79.6%

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

      1. *-commutative 79.6%

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

   3. Simplified 79.6%

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

   5. Taylor expanded in t around inf 58.5%

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

   6. Taylor expanded in x around 0 38.7%

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

      1. mul-1-neg 38.7%

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

      2. associate-/l* 56.2%

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

      3. distribute-neg-frac 56.2%

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

   8. Simplified 56.2%

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

   9. Taylor expanded in y around 0 38.7%

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

       1. mul-1-neg 38.7%

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

       2. associate-*r/ 56.3%

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

       3. distribute-rgt-neg-in 56.3%

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

       4. distribute-neg-frac 56.3%

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

   11. Simplified 56.3%

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

   if -8.19999999999999971e-50 < z < 2.7000000000000002e-68

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 57.9%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+73}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-9}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-50} \lor \neg \left(z \leq 2.7 \cdot 10^{-68}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 55.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-49} \lor \neg \left(z \leq 1.6 \cdot 10^{-68}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.4e-49) (not (<= z 1.6e-68))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.4e-49) || !(z <= 1.6e-68)) {
		tmp = y / a;
	} else {
		tmp = x / 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 ((z <= (-1.4d-49)) .or. (.not. (z <= 1.6d-68))) then
        tmp = y / a
    else
        tmp = x / 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 ((z <= -1.4e-49) || !(z <= 1.6e-68)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.4e-49) or not (z <= 1.6e-68):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.4e-49) || !(z <= 1.6e-68))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.4e-49) || ~((z <= 1.6e-68)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.4e-49], N[Not[LessEqual[z, 1.6e-68]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.39999999999999999e-49 or 1.5999999999999999e-68 < z

   1. Initial program 78.8%

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

      1. *-commutative 78.8%

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

   3. Simplified 78.8%

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

   5. Taylor expanded in z around inf 52.7%

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

   if -1.39999999999999999e-49 < z < 1.5999999999999999e-68

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 57.9%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-49} \lor \neg \left(z \leq 1.6 \cdot 10^{-68}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 36.3% accurate, 3.7× 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 87.4%

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

   1. *-commutative 87.4%

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

3. Simplified 87.4%

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

5. Taylor expanded in z around 0 30.8%

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

6. Final simplification 30.8%

   \[\leadsto \frac{x}{t} \]
7. Add Preprocessing

Developer target: 97.3% accurate, 0.4× 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 2024021 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< z -32113435955957344.0) (- (/ x (- t (* a z))) (/ y (- (/ t z) a))) (if (< z 3.5139522372978296e-86) (* (- x (* y z)) (/ 1.0 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a)))))

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