Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B

Percentage Accurate: 74.9% → 90.5%

Time: 16.6s

Alternatives: 17

Speedup: 0.6×

Specification

Math

\[\begin{array}{l} \\ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    code = (x + ((y * z) / t)) / ((a + 1.0d0) + ((y * b) / t))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
}

Python

def code(x, y, z, t, a, b):
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))

Julia

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

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
end

Wolfram

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

Initial Program: 74.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    code = (x + ((y * z) / t)) / ((a + 1.0d0) + ((y * b) / t))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
}

Python

def code(x, y, z, t, a, b):
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))

Julia

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

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
end

Wolfram

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

Alternative 1: 90.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := x + \frac{y \cdot z}{t}\\ t_3 := 1 + \left(a + t\_1\right)\\ t_4 := \frac{t\_2}{\left(a + 1\right) + t\_1}\\ t_5 := z \cdot \left(\frac{x}{z \cdot t\_3} + \frac{y}{t \cdot t\_3}\right)\\ \mathbf{if}\;t\_4 \leq -1 \cdot 10^{+236}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{t\_2}{\left(a + 1\right) + \left(1 + \left(b \cdot \frac{y}{t} + -1\right)\right)}\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y b) t))
        (t_2 (+ x (/ (* y z) t)))
        (t_3 (+ 1.0 (+ a t_1)))
        (t_4 (/ t_2 (+ (+ a 1.0) t_1)))
        (t_5 (* z (+ (/ x (* z t_3)) (/ y (* t t_3))))))
   (if (<= t_4 -1e+236)
     t_5
     (if (<= t_4 2e+306)
       (/ t_2 (+ (+ a 1.0) (+ 1.0 (+ (* b (/ y t)) -1.0))))
       (if (<= t_4 INFINITY) t_5 (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = x + ((y * z) / t);
	double t_3 = 1.0 + (a + t_1);
	double t_4 = t_2 / ((a + 1.0) + t_1);
	double t_5 = z * ((x / (z * t_3)) + (y / (t * t_3)));
	double tmp;
	if (t_4 <= -1e+236) {
		tmp = t_5;
	} else if (t_4 <= 2e+306) {
		tmp = t_2 / ((a + 1.0) + (1.0 + ((b * (y / t)) + -1.0)));
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_5;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = x + ((y * z) / t);
	double t_3 = 1.0 + (a + t_1);
	double t_4 = t_2 / ((a + 1.0) + t_1);
	double t_5 = z * ((x / (z * t_3)) + (y / (t * t_3)));
	double tmp;
	if (t_4 <= -1e+236) {
		tmp = t_5;
	} else if (t_4 <= 2e+306) {
		tmp = t_2 / ((a + 1.0) + (1.0 + ((b * (y / t)) + -1.0)));
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * b) / t
	t_2 = x + ((y * z) / t)
	t_3 = 1.0 + (a + t_1)
	t_4 = t_2 / ((a + 1.0) + t_1)
	t_5 = z * ((x / (z * t_3)) + (y / (t * t_3)))
	tmp = 0
	if t_4 <= -1e+236:
		tmp = t_5
	elif t_4 <= 2e+306:
		tmp = t_2 / ((a + 1.0) + (1.0 + ((b * (y / t)) + -1.0)))
	elif t_4 <= math.inf:
		tmp = t_5
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * b) / t)
	t_2 = Float64(x + Float64(Float64(y * z) / t))
	t_3 = Float64(1.0 + Float64(a + t_1))
	t_4 = Float64(t_2 / Float64(Float64(a + 1.0) + t_1))
	t_5 = Float64(z * Float64(Float64(x / Float64(z * t_3)) + Float64(y / Float64(t * t_3))))
	tmp = 0.0
	if (t_4 <= -1e+236)
		tmp = t_5;
	elseif (t_4 <= 2e+306)
		tmp = Float64(t_2 / Float64(Float64(a + 1.0) + Float64(1.0 + Float64(Float64(b * Float64(y / t)) + -1.0))));
	elseif (t_4 <= Inf)
		tmp = t_5;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * b) / t;
	t_2 = x + ((y * z) / t);
	t_3 = 1.0 + (a + t_1);
	t_4 = t_2 / ((a + 1.0) + t_1);
	t_5 = z * ((x / (z * t_3)) + (y / (t * t_3)));
	tmp = 0.0;
	if (t_4 <= -1e+236)
		tmp = t_5;
	elseif (t_4 <= 2e+306)
		tmp = t_2 / ((a + 1.0) + (1.0 + ((b * (y / t)) + -1.0)));
	elseif (t_4 <= Inf)
		tmp = t_5;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$2 / N[(N[(a + 1.0), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(z * N[(N[(x / N[(z * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, -1e+236], t$95$5, If[LessEqual[t$95$4, 2e+306], N[(t$95$2 / N[(N[(a + 1.0), $MachinePrecision] + N[(1.0 + N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, Infinity], t$95$5, N[(z / b), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.00000000000000005e236 or 2.00000000000000003e306 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 49.0%

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

      1. +-commutative 49.0%

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

      2. associate-/l* 72.0%

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

      3. fma-define 72.0%

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

      4. +-commutative 72.0%

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

      5. associate-/l* 72.0%

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

      6. fma-define 72.0%

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

   3. Simplified 72.0%

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

   5. Taylor expanded in z around inf 86.7%

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

   if -1.00000000000000005e236 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.00000000000000003e306

   1. Initial program 91.5%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 91.5%

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

      2. associate-/l* 93.4%

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

   4. Applied egg-rr 93.4%

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

      1. expm1-log1p-u 78.7%

         \[\leadsto \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(b \cdot \frac{y}{t}\right)\right)}} \]

      2. expm1-undefine 78.7%

         \[\leadsto \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \color{blue}{\left(e^{\mathsf{log1p}\left(b \cdot \frac{y}{t}\right)} - 1\right)}} \]

      3. log1p-undefine 78.7%

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

      4. add-exp-log 93.4%

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

      5. *-commutative 93.4%

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

   6. Applied egg-rr 93.4%

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

      1. associate--l+ 93.5%

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

      2. *-commutative 93.5%

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

   8. Simplified 93.5%

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

   if +inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 0.0%

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

      1. +-commutative 0.0%

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

      2. associate-/l* 0.2%

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

      3. fma-define 0.2%

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

      4. +-commutative 0.2%

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

      5. associate-/l* 4.4%

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

      6. fma-define 4.4%

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

   3. Simplified 4.4%

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

   5. Taylor expanded in y around inf 96.2%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -1 \cdot 10^{+236}:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)} + \frac{y}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \left(1 + \left(b \cdot \frac{y}{t} + -1\right)\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)} + \frac{y}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 86.9% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 + \mathsf{fma}\left(b, \frac{y}{t}, a\right)\\ \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, \frac{z}{t\_1}, \frac{x}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ 1.0 (fma b (/ y t) a))))
   (if (<= (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))) INFINITY)
     (fma (/ y t) (/ z t_1) (/ x t_1))
     (/ z b))))

C

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

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 + fma(b, Float64(y / t), a))
	tmp = 0.0
	if (Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t))) <= Inf)
		tmp = fma(Float64(y / t), Float64(z / t_1), Float64(x / t_1));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.0 + N[(b * N[(y / t), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(y / t), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision] + N[(x / t$95$1), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 84.8%

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

      1. +-commutative 84.8%

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

      2. associate-/l* 81.8%

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

      3. fma-define 81.8%

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

      4. +-commutative 81.8%

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

      5. associate-/l* 81.4%

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

      6. fma-define 81.4%

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

   3. Simplified 81.4%

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

   5. Taylor expanded in z around 0 84.7%

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

      1. +-commutative 84.7%

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

      2. times-frac 88.3%

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

      3. fma-define 88.3%

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

      4. associate-*r/ 88.1%

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

      5. +-commutative 88.1%

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

      6. fma-define 88.1%

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

      7. associate-*r/ 89.3%

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

      8. +-commutative 89.3%

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

      9. fma-define 89.3%

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

   7. Simplified 89.3%

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

   if +inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 0.0%

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

      1. +-commutative 0.0%

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

      2. associate-/l* 0.2%

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

      3. fma-define 0.2%

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

      4. +-commutative 0.2%

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

      5. associate-/l* 4.4%

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

      6. fma-define 4.4%

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

   3. Simplified 4.4%

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

   5. Taylor expanded in y around inf 96.2%

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

Alternative 3: 87.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t\_1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+236}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{t\_1}{\left(a + 1\right) + \left(1 + \left(b \cdot \frac{y}{t} + -1\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t))) (t_2 (/ t_1 (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= t_2 -1e+236)
     (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t))))
     (if (<= t_2 2e+306)
       (/ t_1 (+ (+ a 1.0) (+ 1.0 (+ (* b (/ y t)) -1.0))))
       (/ (+ z (/ (* x t) y)) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_2 <= -1e+236) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else if (t_2 <= 2e+306) {
		tmp = t_1 / ((a + 1.0) + (1.0 + ((b * (y / t)) + -1.0)));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((y * z) / t)
    t_2 = t_1 / ((a + 1.0d0) + ((y * b) / t))
    if (t_2 <= (-1d+236)) then
        tmp = (x + (y * (z / t))) / ((a + 1.0d0) + (y * (b / t)))
    else if (t_2 <= 2d+306) then
        tmp = t_1 / ((a + 1.0d0) + (1.0d0 + ((b * (y / t)) + (-1.0d0))))
    else
        tmp = (z + ((x * t) / y)) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_2 <= -1e+236) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else if (t_2 <= 2e+306) {
		tmp = t_1 / ((a + 1.0) + (1.0 + ((b * (y / t)) + -1.0)));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * z) / t)
	t_2 = t_1 / ((a + 1.0) + ((y * b) / t))
	tmp = 0
	if t_2 <= -1e+236:
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	elif t_2 <= 2e+306:
		tmp = t_1 / ((a + 1.0) + (1.0 + ((b * (y / t)) + -1.0)))
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	t_2 = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t_2 <= -1e+236)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	elseif (t_2 <= 2e+306)
		tmp = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(1.0 + Float64(Float64(b * Float64(y / t)) + -1.0))));
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((y * z) / t);
	t_2 = t_1 / ((a + 1.0) + ((y * b) / t));
	tmp = 0.0;
	if (t_2 <= -1e+236)
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	elseif (t_2 <= 2e+306)
		tmp = t_1 / ((a + 1.0) + (1.0 + ((b * (y / t)) + -1.0)));
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+236], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+306], N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(1.0 + N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.00000000000000005e236

   1. Initial program 72.3%

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

      1. associate-/l* 86.0%

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

      2. associate-/l* 86.0%

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

   3. Simplified 86.0%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   if -1.00000000000000005e236 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.00000000000000003e306

   1. Initial program 91.5%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 91.5%

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

      2. associate-/l* 93.4%

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

   4. Applied egg-rr 93.4%

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

      1. expm1-log1p-u 78.7%

         \[\leadsto \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(b \cdot \frac{y}{t}\right)\right)}} \]

      2. expm1-undefine 78.7%

         \[\leadsto \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \color{blue}{\left(e^{\mathsf{log1p}\left(b \cdot \frac{y}{t}\right)} - 1\right)}} \]

      3. log1p-undefine 78.7%

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

      4. add-exp-log 93.4%

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

      5. *-commutative 93.4%

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

   6. Applied egg-rr 93.4%

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

      1. associate--l+ 93.5%

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

      2. *-commutative 93.5%

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

   8. Simplified 93.5%

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

   if 2.00000000000000003e306 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 9.0%

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

      1. +-commutative 9.0%

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

      2. associate-/l* 23.1%

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

      3. fma-define 23.1%

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

      4. +-commutative 23.1%

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

      5. associate-/l* 25.6%

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

      6. fma-define 25.6%

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

   3. Simplified 25.6%

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

   5. Taylor expanded in z around 0 18.7%

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

      1. +-commutative 18.7%

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

      2. times-frac 34.9%

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

      3. fma-define 34.9%

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

      4. associate-*r/ 34.7%

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

      5. +-commutative 34.7%

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

      6. fma-define 34.7%

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

      7. associate-*r/ 37.0%

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

      8. +-commutative 37.0%

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

      9. fma-define 37.0%

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

   7. Simplified 37.0%

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

   8. Taylor expanded in b around inf 76.4%

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

      1. *-commutative 76.4%

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

   10. Simplified 76.4%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -1 \cdot 10^{+236}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \left(1 + \left(b \cdot \frac{y}{t} + -1\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t\_1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+236}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{t\_1}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t))) (t_2 (/ t_1 (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= t_2 -1e+236)
     (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t))))
     (if (<= t_2 2e+306)
       (/ t_1 (+ (+ a 1.0) (* b (/ y t))))
       (/ (+ z (/ (* x t) y)) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_2 <= -1e+236) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else if (t_2 <= 2e+306) {
		tmp = t_1 / ((a + 1.0) + (b * (y / t)));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((y * z) / t)
    t_2 = t_1 / ((a + 1.0d0) + ((y * b) / t))
    if (t_2 <= (-1d+236)) then
        tmp = (x + (y * (z / t))) / ((a + 1.0d0) + (y * (b / t)))
    else if (t_2 <= 2d+306) then
        tmp = t_1 / ((a + 1.0d0) + (b * (y / t)))
    else
        tmp = (z + ((x * t) / y)) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_2 <= -1e+236) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else if (t_2 <= 2e+306) {
		tmp = t_1 / ((a + 1.0) + (b * (y / t)));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * z) / t)
	t_2 = t_1 / ((a + 1.0) + ((y * b) / t))
	tmp = 0
	if t_2 <= -1e+236:
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	elif t_2 <= 2e+306:
		tmp = t_1 / ((a + 1.0) + (b * (y / t)))
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	t_2 = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t_2 <= -1e+236)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	elseif (t_2 <= 2e+306)
		tmp = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((y * z) / t);
	t_2 = t_1 / ((a + 1.0) + ((y * b) / t));
	tmp = 0.0;
	if (t_2 <= -1e+236)
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	elseif (t_2 <= 2e+306)
		tmp = t_1 / ((a + 1.0) + (b * (y / t)));
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+236], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+306], N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.00000000000000005e236

   1. Initial program 72.3%

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

      1. associate-/l* 86.0%

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

      2. associate-/l* 86.0%

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

   3. Simplified 86.0%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   if -1.00000000000000005e236 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.00000000000000003e306

   1. Initial program 91.5%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 91.5%

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

      2. associate-/l* 93.4%

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

   4. Applied egg-rr 93.4%

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

   if 2.00000000000000003e306 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 9.0%

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

      1. +-commutative 9.0%

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

      2. associate-/l* 23.1%

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

      3. fma-define 23.1%

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

      4. +-commutative 23.1%

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

      5. associate-/l* 25.6%

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

      6. fma-define 25.6%

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

   3. Simplified 25.6%

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

   5. Taylor expanded in z around 0 18.7%

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

      1. +-commutative 18.7%

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

      2. times-frac 34.9%

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

      3. fma-define 34.9%

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

      4. associate-*r/ 34.7%

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

      5. +-commutative 34.7%

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

      6. fma-define 34.7%

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

      7. associate-*r/ 37.0%

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

      8. +-commutative 37.0%

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

      9. fma-define 37.0%

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

   7. Simplified 37.0%

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

   8. Taylor expanded in b around inf 76.4%

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

      1. *-commutative 76.4%

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

   10. Simplified 76.4%

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

Alternative 5: 74.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a + 1 \leq -200000 \lor \neg \left(a + 1 \leq 1.1\right):\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{1 + y \cdot \frac{b}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ a 1.0) -200000.0) (not (<= (+ a 1.0) 1.1)))
   (/ (+ x (/ (* y z) t)) (+ a (* b (/ y t))))
   (/ (+ x (* y (/ z t))) (+ 1.0 (* y (/ b t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a + 1.0) <= -200000.0) || !((a + 1.0) <= 1.1)) {
		tmp = (x + ((y * z) / t)) / (a + (b * (y / t)));
	} else {
		tmp = (x + (y * (z / t))) / (1.0 + (y * (b / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if (((a + 1.0d0) <= (-200000.0d0)) .or. (.not. ((a + 1.0d0) <= 1.1d0))) then
        tmp = (x + ((y * z) / t)) / (a + (b * (y / t)))
    else
        tmp = (x + (y * (z / t))) / (1.0d0 + (y * (b / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a + 1.0) <= -200000.0) || !((a + 1.0) <= 1.1)) {
		tmp = (x + ((y * z) / t)) / (a + (b * (y / t)));
	} else {
		tmp = (x + (y * (z / t))) / (1.0 + (y * (b / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((a + 1.0) <= -200000.0) or not ((a + 1.0) <= 1.1):
		tmp = (x + ((y * z) / t)) / (a + (b * (y / t)))
	else:
		tmp = (x + (y * (z / t))) / (1.0 + (y * (b / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(a + 1.0) <= -200000.0) || !(Float64(a + 1.0) <= 1.1))
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + Float64(b * Float64(y / t))));
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(1.0 + Float64(y * Float64(b / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((a + 1.0) <= -200000.0) || ~(((a + 1.0) <= 1.1)))
		tmp = (x + ((y * z) / t)) / (a + (b * (y / t)));
	else
		tmp = (x + (y * (z / t))) / (1.0 + (y * (b / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(a + 1.0), $MachinePrecision], -200000.0], N[Not[LessEqual[N[(a + 1.0), $MachinePrecision], 1.1]], $MachinePrecision]], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 a #s(literal 1 binary64)) < -2e5 or 1.1000000000000001 < (+.f64 a #s(literal 1 binary64))

   1. Initial program 74.1%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 74.1%

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

      2. associate-/l* 73.2%

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

   4. Applied egg-rr 73.2%

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

   5. Taylor expanded in a around inf 72.4%

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

   if -2e5 < (+.f64 a #s(literal 1 binary64)) < 1.1000000000000001

   1. Initial program 80.3%

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

      1. associate-/l* 80.2%

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

      2. associate-/l* 79.5%

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

   3. Simplified 79.5%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 79.5%

      \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\color{blue}{1} + y \cdot \frac{b}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a + 1 \leq -200000 \lor \neg \left(a + 1 \leq 1.1\right):\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{1 + y \cdot \frac{b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{t}\\ t_2 := y \cdot \frac{b}{t}\\ \mathbf{if}\;a + 1 \leq -200000 \lor \neg \left(a + 1 \leq 1\right):\\ \;\;\;\;\frac{t\_1}{a + t\_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{1 + t\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z t)))) (t_2 (* y (/ b t))))
   (if (or (<= (+ a 1.0) -200000.0) (not (<= (+ a 1.0) 1.0)))
     (/ t_1 (+ a t_2))
     (/ t_1 (+ 1.0 t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * (z / t));
	double t_2 = y * (b / t);
	double tmp;
	if (((a + 1.0) <= -200000.0) || !((a + 1.0) <= 1.0)) {
		tmp = t_1 / (a + t_2);
	} else {
		tmp = t_1 / (1.0 + t_2);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y * (z / t))
    t_2 = y * (b / t)
    if (((a + 1.0d0) <= (-200000.0d0)) .or. (.not. ((a + 1.0d0) <= 1.0d0))) then
        tmp = t_1 / (a + t_2)
    else
        tmp = t_1 / (1.0d0 + t_2)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * (z / t));
	double t_2 = y * (b / t);
	double tmp;
	if (((a + 1.0) <= -200000.0) || !((a + 1.0) <= 1.0)) {
		tmp = t_1 / (a + t_2);
	} else {
		tmp = t_1 / (1.0 + t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * (z / t))
	t_2 = y * (b / t)
	tmp = 0
	if ((a + 1.0) <= -200000.0) or not ((a + 1.0) <= 1.0):
		tmp = t_1 / (a + t_2)
	else:
		tmp = t_1 / (1.0 + t_2)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * Float64(z / t)))
	t_2 = Float64(y * Float64(b / t))
	tmp = 0.0
	if ((Float64(a + 1.0) <= -200000.0) || !(Float64(a + 1.0) <= 1.0))
		tmp = Float64(t_1 / Float64(a + t_2));
	else
		tmp = Float64(t_1 / Float64(1.0 + t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * (z / t));
	t_2 = y * (b / t);
	tmp = 0.0;
	if (((a + 1.0) <= -200000.0) || ~(((a + 1.0) <= 1.0)))
		tmp = t_1 / (a + t_2);
	else
		tmp = t_1 / (1.0 + t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(a + 1.0), $MachinePrecision], -200000.0], N[Not[LessEqual[N[(a + 1.0), $MachinePrecision], 1.0]], $MachinePrecision]], N[(t$95$1 / N[(a + t$95$2), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / N[(1.0 + t$95$2), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 a #s(literal 1 binary64)) < -2e5 or 1 < (+.f64 a #s(literal 1 binary64))

   1. Initial program 73.7%

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

      1. associate-/l* 69.1%

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

      2. associate-/l* 69.7%

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

   3. Simplified 69.7%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 68.9%

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

   if -2e5 < (+.f64 a #s(literal 1 binary64)) < 1

   1. Initial program 80.8%

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

      1. associate-/l* 80.7%

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

      2. associate-/l* 80.0%

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

   3. Simplified 80.0%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 80.0%

      \[\leadsto \frac{x + y \cdot \frac{z}{t}}{\color{blue}{1} + y \cdot \frac{b}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a + 1 \leq -200000 \lor \neg \left(a + 1 \leq 1\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{1 + y \cdot \frac{b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{b}{t}\\ t_2 := x + y \cdot \frac{z}{t}\\ \mathbf{if}\;a + 1 \leq -200000:\\ \;\;\;\;\frac{t\_2}{a + t\_1}\\ \mathbf{elif}\;a + 1 \leq 1.0000005:\\ \;\;\;\;\frac{t\_2}{1 + t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_2}{a + b \cdot \frac{y}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (/ b t))) (t_2 (+ x (* y (/ z t)))))
   (if (<= (+ a 1.0) -200000.0)
     (/ t_2 (+ a t_1))
     (if (<= (+ a 1.0) 1.0000005)
       (/ t_2 (+ 1.0 t_1))
       (/ t_2 (+ a (* b (/ y t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b / t);
	double t_2 = x + (y * (z / t));
	double tmp;
	if ((a + 1.0) <= -200000.0) {
		tmp = t_2 / (a + t_1);
	} else if ((a + 1.0) <= 1.0000005) {
		tmp = t_2 / (1.0 + t_1);
	} else {
		tmp = t_2 / (a + (b * (y / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (b / t)
    t_2 = x + (y * (z / t))
    if ((a + 1.0d0) <= (-200000.0d0)) then
        tmp = t_2 / (a + t_1)
    else if ((a + 1.0d0) <= 1.0000005d0) then
        tmp = t_2 / (1.0d0 + t_1)
    else
        tmp = t_2 / (a + (b * (y / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b / t);
	double t_2 = x + (y * (z / t));
	double tmp;
	if ((a + 1.0) <= -200000.0) {
		tmp = t_2 / (a + t_1);
	} else if ((a + 1.0) <= 1.0000005) {
		tmp = t_2 / (1.0 + t_1);
	} else {
		tmp = t_2 / (a + (b * (y / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b / t)
	t_2 = x + (y * (z / t))
	tmp = 0
	if (a + 1.0) <= -200000.0:
		tmp = t_2 / (a + t_1)
	elif (a + 1.0) <= 1.0000005:
		tmp = t_2 / (1.0 + t_1)
	else:
		tmp = t_2 / (a + (b * (y / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b / t))
	t_2 = Float64(x + Float64(y * Float64(z / t)))
	tmp = 0.0
	if (Float64(a + 1.0) <= -200000.0)
		tmp = Float64(t_2 / Float64(a + t_1));
	elseif (Float64(a + 1.0) <= 1.0000005)
		tmp = Float64(t_2 / Float64(1.0 + t_1));
	else
		tmp = Float64(t_2 / Float64(a + Float64(b * Float64(y / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b / t);
	t_2 = x + (y * (z / t));
	tmp = 0.0;
	if ((a + 1.0) <= -200000.0)
		tmp = t_2 / (a + t_1);
	elseif ((a + 1.0) <= 1.0000005)
		tmp = t_2 / (1.0 + t_1);
	else
		tmp = t_2 / (a + (b * (y / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a + 1.0), $MachinePrecision], -200000.0], N[(t$95$2 / N[(a + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a + 1.0), $MachinePrecision], 1.0000005], N[(t$95$2 / N[(1.0 + t$95$1), $MachinePrecision]), $MachinePrecision], N[(t$95$2 / N[(a + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 a #s(literal 1 binary64)) < -2e5

   1. Initial program 77.7%

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

      1. associate-/l* 72.4%

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

      2. associate-/l* 73.6%

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

   3. Simplified 73.6%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 72.8%

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

   if -2e5 < (+.f64 a #s(literal 1 binary64)) < 1.0000005000000001

   1. Initial program 80.1%

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

      1. associate-/l* 80.0%

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

      2. associate-/l* 79.3%

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

   3. Simplified 79.3%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 79.3%

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

   if 1.0000005000000001 < (+.f64 a #s(literal 1 binary64))

   1. Initial program 70.6%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 70.6%

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

      2. associate-/l* 72.1%

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

   4. Applied egg-rr 72.1%

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

   5. Taylor expanded in a around inf 71.2%

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

      1. associate-*r/ 67.1%

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

      2. *-commutative 67.1%

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

   7. Applied egg-rr 67.1%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a + 1 \leq -200000:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;a + 1 \leq 1.0000005:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{1 + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + b \cdot \frac{y}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-144} \lor \neg \left(t \leq 1.9 \cdot 10^{-218}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.05e-144) (not (<= t 1.9e-218)))
   (/ (+ x (/ y (/ t z))) (+ (+ a 1.0) (* y (/ b t))))
   (/ (+ z (/ (* x t) y)) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.05e-144) || !(t <= 1.9e-218)) {
		tmp = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.05d-144)) .or. (.not. (t <= 1.9d-218))) then
        tmp = (x + (y / (t / z))) / ((a + 1.0d0) + (y * (b / t)))
    else
        tmp = (z + ((x * t) / y)) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.05e-144) || !(t <= 1.9e-218)) {
		tmp = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.05e-144) or not (t <= 1.9e-218):
		tmp = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)))
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.05e-144) || !(t <= 1.9e-218))
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.05e-144) || ~((t <= 1.9e-218)))
		tmp = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)));
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.05e-144], N[Not[LessEqual[t, 1.9e-218]], $MachinePrecision]], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.0500000000000001e-144 or 1.8999999999999999e-218 < t

   1. Initial program 81.4%

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

      1. associate-/l* 81.9%

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

      2. associate-/l* 83.3%

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

   3. Simplified 83.3%

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

      1. clear-num 83.2%

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

      2. un-div-inv 83.7%

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

   6. Applied egg-rr 83.7%

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

   if -1.0500000000000001e-144 < t < 1.8999999999999999e-218

   1. Initial program 56.9%

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

      1. +-commutative 56.9%

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

      2. associate-/l* 40.5%

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

      3. fma-define 40.5%

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

      4. +-commutative 40.5%

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

      5. associate-/l* 34.5%

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

      6. fma-define 34.5%

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

   3. Simplified 34.5%

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

   5. Taylor expanded in z around 0 65.2%

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

      1. +-commutative 65.2%

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

      2. times-frac 60.8%

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

      3. fma-define 60.8%

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

      4. associate-*r/ 58.7%

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

      5. +-commutative 58.7%

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

      6. fma-define 58.7%

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

      7. associate-*r/ 58.8%

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

      8. +-commutative 58.8%

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

      9. fma-define 58.8%

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

   7. Simplified 58.8%

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

   8. Taylor expanded in b around inf 66.0%

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

      1. *-commutative 66.0%

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

   10. Simplified 66.0%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-144} \lor \neg \left(t \leq 1.9 \cdot 10^{-218}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 81.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{-144} \lor \neg \left(t \leq 2.1 \cdot 10^{-218}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.22e-144) (not (<= t 2.1e-218)))
   (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t))))
   (/ (+ z (/ (* x t) y)) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.22e-144) || !(t <= 2.1e-218)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.22d-144)) .or. (.not. (t <= 2.1d-218))) then
        tmp = (x + (y * (z / t))) / ((a + 1.0d0) + (y * (b / t)))
    else
        tmp = (z + ((x * t) / y)) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.22e-144) || !(t <= 2.1e-218)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.22e-144) or not (t <= 2.1e-218):
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.22e-144) || !(t <= 2.1e-218))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.22e-144) || ~((t <= 2.1e-218)))
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.22e-144], N[Not[LessEqual[t, 2.1e-218]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.22e-144 or 2.09999999999999994e-218 < t

   1. Initial program 81.4%

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

      1. associate-/l* 81.9%

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

      2. associate-/l* 83.3%

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

   3. Simplified 83.3%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   if -1.22e-144 < t < 2.09999999999999994e-218

   1. Initial program 56.9%

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

      1. +-commutative 56.9%

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

      2. associate-/l* 40.5%

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

      3. fma-define 40.5%

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

      4. +-commutative 40.5%

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

      5. associate-/l* 34.5%

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

      6. fma-define 34.5%

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

   3. Simplified 34.5%

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

   5. Taylor expanded in z around 0 65.2%

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

      1. +-commutative 65.2%

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

      2. times-frac 60.8%

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

      3. fma-define 60.8%

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

      4. associate-*r/ 58.7%

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

      5. +-commutative 58.7%

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

      6. fma-define 58.7%

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

      7. associate-*r/ 58.8%

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

      8. +-commutative 58.8%

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

      9. fma-define 58.8%

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

   7. Simplified 58.8%

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

   8. Taylor expanded in b around inf 66.0%

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

      1. *-commutative 66.0%

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

   10. Simplified 66.0%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{-144} \lor \neg \left(t \leq 2.1 \cdot 10^{-218}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 77.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+169}:\\ \;\;\;\;\frac{x \cdot \left(\frac{t}{y} + \frac{z}{x}\right)}{b}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+229}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + \left(1 + y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.55e+169)
   (/ (* x (+ (/ t y) (/ z x))) b)
   (if (<= y 5.2e+229)
     (/ (+ x (/ (* y z) t)) (+ a (+ 1.0 (* y (/ b t)))))
     (/ (+ z (/ (* x t) y)) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.55e+169) {
		tmp = (x * ((t / y) + (z / x))) / b;
	} else if (y <= 5.2e+229) {
		tmp = (x + ((y * z) / t)) / (a + (1.0 + (y * (b / t))));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.55d+169)) then
        tmp = (x * ((t / y) + (z / x))) / b
    else if (y <= 5.2d+229) then
        tmp = (x + ((y * z) / t)) / (a + (1.0d0 + (y * (b / t))))
    else
        tmp = (z + ((x * t) / y)) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.55e+169) {
		tmp = (x * ((t / y) + (z / x))) / b;
	} else if (y <= 5.2e+229) {
		tmp = (x + ((y * z) / t)) / (a + (1.0 + (y * (b / t))));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.55e+169:
		tmp = (x * ((t / y) + (z / x))) / b
	elif y <= 5.2e+229:
		tmp = (x + ((y * z) / t)) / (a + (1.0 + (y * (b / t))))
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.55e+169)
		tmp = Float64(Float64(x * Float64(Float64(t / y) + Float64(z / x))) / b);
	elseif (y <= 5.2e+229)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + Float64(1.0 + Float64(y * Float64(b / t)))));
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.55e+169)
		tmp = (x * ((t / y) + (z / x))) / b;
	elseif (y <= 5.2e+229)
		tmp = (x + ((y * z) / t)) / (a + (1.0 + (y * (b / t))));
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.55e+169], N[(N[(x * N[(N[(t / y), $MachinePrecision] + N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 5.2e+229], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.55000000000000004e169

   1. Initial program 37.9%

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

      1. +-commutative 37.9%

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

      2. associate-/l* 38.3%

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

      3. fma-define 38.3%

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

      4. +-commutative 38.3%

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

      5. associate-/l* 46.3%

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

      6. fma-define 46.3%

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

   3. Simplified 46.3%

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

   5. Taylor expanded in b around inf 21.9%

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

   6. Taylor expanded in x around inf 45.9%

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

      1. *-commutative 45.9%

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

      2. *-commutative 45.9%

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

   8. Simplified 45.9%

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

   9. Taylor expanded in b around 0 69.2%

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

   if -2.55000000000000004e169 < y < 5.2e229

   1. Initial program 86.3%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 86.3%

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

      2. associate-/l* 86.7%

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

   4. Applied egg-rr 86.7%

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

      1. associate-+l+ 86.7%

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

      2. *-un-lft-identity 86.7%

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

      3. fma-define 86.7%

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

      4. *-commutative 86.7%

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

   6. Applied egg-rr 86.7%

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

      1. fma-undefine 86.7%

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

      2. *-commutative 86.7%

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

      3. *-rgt-identity 86.7%

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

      4. associate-*l/ 86.3%

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

      5. associate-/l* 83.1%

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

   8. Simplified 83.1%

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

   if 5.2e229 < y

   1. Initial program 37.2%

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

      1. +-commutative 37.2%

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

      2. associate-/l* 44.5%

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

      3. fma-define 44.5%

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

      4. +-commutative 44.5%

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

      5. associate-/l* 45.4%

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

      6. fma-define 45.4%

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

   3. Simplified 45.4%

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

   5. Taylor expanded in z around 0 41.2%

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

      1. +-commutative 41.2%

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

      2. times-frac 41.0%

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

      3. fma-define 41.0%

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

      4. associate-*r/ 40.6%

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

      5. +-commutative 40.6%

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

      6. fma-define 40.6%

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

      7. associate-*r/ 40.6%

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

      8. +-commutative 40.6%

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

      9. fma-define 40.6%

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

   7. Simplified 40.6%

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

   8. Taylor expanded in b around inf 73.8%

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

      1. *-commutative 73.8%

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

   10. Simplified 73.8%

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

Alternative 11: 60.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-16}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+159}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ 1.0 (+ a (/ (* y b) t))))))
   (if (<= t -1.4e-22)
     t_1
     (if (<= t 1.02e-16)
       (/ (+ z (/ (* x t) y)) b)
       (if (<= t 2.25e+159) (* (/ y t) (/ z (+ a 1.0))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + (a + ((y * b) / t)));
	double tmp;
	if (t <= -1.4e-22) {
		tmp = t_1;
	} else if (t <= 1.02e-16) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (t <= 2.25e+159) {
		tmp = (y / t) * (z / (a + 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 + (a + ((y * b) / t)))
    if (t <= (-1.4d-22)) then
        tmp = t_1
    else if (t <= 1.02d-16) then
        tmp = (z + ((x * t) / y)) / b
    else if (t <= 2.25d+159) then
        tmp = (y / t) * (z / (a + 1.0d0))
    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 b) {
	double t_1 = x / (1.0 + (a + ((y * b) / t)));
	double tmp;
	if (t <= -1.4e-22) {
		tmp = t_1;
	} else if (t <= 1.02e-16) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (t <= 2.25e+159) {
		tmp = (y / t) * (z / (a + 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 + (a + ((y * b) / t)))
	tmp = 0
	if t <= -1.4e-22:
		tmp = t_1
	elif t <= 1.02e-16:
		tmp = (z + ((x * t) / y)) / b
	elif t <= 2.25e+159:
		tmp = (y / t) * (z / (a + 1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))))
	tmp = 0.0
	if (t <= -1.4e-22)
		tmp = t_1;
	elseif (t <= 1.02e-16)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	elseif (t <= 2.25e+159)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 + (a + ((y * b) / t)));
	tmp = 0.0;
	if (t <= -1.4e-22)
		tmp = t_1;
	elseif (t <= 1.02e-16)
		tmp = (z + ((x * t) / y)) / b;
	elseif (t <= 2.25e+159)
		tmp = (y / t) * (z / (a + 1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.4e-22], t$95$1, If[LessEqual[t, 1.02e-16], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t, 2.25e+159], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.39999999999999997e-22 or 2.25000000000000013e159 < t

   1. Initial program 86.4%

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

      1. +-commutative 86.4%

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

      2. associate-/l* 89.4%

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

      3. fma-define 89.4%

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

      4. +-commutative 89.4%

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

      5. associate-/l* 94.4%

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

      6. fma-define 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in z around 0 76.1%

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

   if -1.39999999999999997e-22 < t < 1.0200000000000001e-16

   1. Initial program 69.3%

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

      1. +-commutative 69.3%

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

      2. associate-/l* 58.4%

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

      3. fma-define 58.3%

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

      4. +-commutative 58.3%

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

      5. associate-/l* 53.3%

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

      6. fma-define 53.3%

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

   3. Simplified 53.3%

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

   5. Taylor expanded in z around 0 73.8%

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

      1. +-commutative 73.8%

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

      2. times-frac 66.7%

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

      3. fma-define 66.7%

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

      4. associate-*r/ 63.9%

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

      5. +-commutative 63.9%

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

      6. fma-define 63.9%

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

      7. associate-*r/ 63.9%

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

      8. +-commutative 63.9%

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

      9. fma-define 63.9%

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

   7. Simplified 63.9%

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

   8. Taylor expanded in b around inf 61.3%

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

      1. *-commutative 61.3%

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

   10. Simplified 61.3%

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

   if 1.0200000000000001e-16 < t < 2.25000000000000013e159

   1. Initial program 74.7%

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

      1. +-commutative 74.7%

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

      2. associate-/l* 81.3%

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

      3. fma-define 81.3%

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

      4. +-commutative 81.3%

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

      5. associate-/l* 83.7%

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

      6. fma-define 83.7%

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

   3. Simplified 83.7%

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

   5. Taylor expanded in y around 0 63.2%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{t \cdot \left(1 + a\right)} - \frac{b \cdot x}{t \cdot {\left(1 + a\right)}^{2}}\right) + \frac{x}{1 + a}} \]

   6. Taylor expanded in z around inf 37.9%

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

      1. times-frac 53.9%

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

   8. Simplified 53.9%

      \[\leadsto \color{blue}{\frac{y}{t} \cdot \frac{z}{1 + a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-16}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+159}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -1.46 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.26 \cdot 10^{-16}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+159}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -1.46e-21)
     t_1
     (if (<= t 1.26e-16)
       (/ (+ z (/ (* x t) y)) b)
       (if (<= t 2.25e+159) (* (/ y t) (/ z (+ a 1.0))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -1.46e-21) {
		tmp = t_1;
	} else if (t <= 1.26e-16) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (t <= 2.25e+159) {
		tmp = (y / t) * (z / (a + 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-1.46d-21)) then
        tmp = t_1
    else if (t <= 1.26d-16) then
        tmp = (z + ((x * t) / y)) / b
    else if (t <= 2.25d+159) then
        tmp = (y / t) * (z / (a + 1.0d0))
    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 b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -1.46e-21) {
		tmp = t_1;
	} else if (t <= 1.26e-16) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (t <= 2.25e+159) {
		tmp = (y / t) * (z / (a + 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -1.46e-21:
		tmp = t_1
	elif t <= 1.26e-16:
		tmp = (z + ((x * t) / y)) / b
	elif t <= 2.25e+159:
		tmp = (y / t) * (z / (a + 1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -1.46e-21)
		tmp = t_1;
	elseif (t <= 1.26e-16)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	elseif (t <= 2.25e+159)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -1.46e-21)
		tmp = t_1;
	elseif (t <= 1.26e-16)
		tmp = (z + ((x * t) / y)) / b;
	elseif (t <= 2.25e+159)
		tmp = (y / t) * (z / (a + 1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.46e-21], t$95$1, If[LessEqual[t, 1.26e-16], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t, 2.25e+159], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.46000000000000006e-21 or 2.25000000000000013e159 < t

   1. Initial program 86.4%

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

      1. +-commutative 86.4%

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

      2. associate-/l* 89.4%

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

      3. fma-define 89.4%

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

      4. +-commutative 89.4%

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

      5. associate-/l* 94.4%

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

      6. fma-define 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in y around 0 72.7%

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]

   if -1.46000000000000006e-21 < t < 1.26000000000000001e-16

   1. Initial program 69.3%

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

      1. +-commutative 69.3%

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

      2. associate-/l* 58.4%

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

      3. fma-define 58.3%

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

      4. +-commutative 58.3%

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

      5. associate-/l* 53.3%

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

      6. fma-define 53.3%

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

   3. Simplified 53.3%

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

   5. Taylor expanded in z around 0 73.8%

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

      1. +-commutative 73.8%

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

      2. times-frac 66.7%

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

      3. fma-define 66.7%

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

      4. associate-*r/ 63.9%

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

      5. +-commutative 63.9%

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

      6. fma-define 63.9%

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

      7. associate-*r/ 63.9%

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

      8. +-commutative 63.9%

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

      9. fma-define 63.9%

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

   7. Simplified 63.9%

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

   8. Taylor expanded in b around inf 61.3%

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

      1. *-commutative 61.3%

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

   10. Simplified 61.3%

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

   if 1.26000000000000001e-16 < t < 2.25000000000000013e159

   1. Initial program 74.7%

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

      1. +-commutative 74.7%

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

      2. associate-/l* 81.3%

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

      3. fma-define 81.3%

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

      4. +-commutative 81.3%

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

      5. associate-/l* 83.7%

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

      6. fma-define 83.7%

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

   3. Simplified 83.7%

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

   5. Taylor expanded in y around 0 63.2%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{t \cdot \left(1 + a\right)} - \frac{b \cdot x}{t \cdot {\left(1 + a\right)}^{2}}\right) + \frac{x}{1 + a}} \]

   6. Taylor expanded in z around inf 37.9%

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

      1. times-frac 53.9%

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

   8. Simplified 53.9%

      \[\leadsto \color{blue}{\frac{y}{t} \cdot \frac{z}{1 + a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.46 \cdot 10^{-21}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq 1.26 \cdot 10^{-16}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+159}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 53.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -9.2:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-19}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+159}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -9.2)
     t_1
     (if (<= t 4.5e-19)
       (/ z b)
       (if (<= t 2.25e+159) (* (/ y t) (/ z (+ a 1.0))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -9.2) {
		tmp = t_1;
	} else if (t <= 4.5e-19) {
		tmp = z / b;
	} else if (t <= 2.25e+159) {
		tmp = (y / t) * (z / (a + 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-9.2d0)) then
        tmp = t_1
    else if (t <= 4.5d-19) then
        tmp = z / b
    else if (t <= 2.25d+159) then
        tmp = (y / t) * (z / (a + 1.0d0))
    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 b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -9.2) {
		tmp = t_1;
	} else if (t <= 4.5e-19) {
		tmp = z / b;
	} else if (t <= 2.25e+159) {
		tmp = (y / t) * (z / (a + 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -9.2:
		tmp = t_1
	elif t <= 4.5e-19:
		tmp = z / b
	elif t <= 2.25e+159:
		tmp = (y / t) * (z / (a + 1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -9.2)
		tmp = t_1;
	elseif (t <= 4.5e-19)
		tmp = Float64(z / b);
	elseif (t <= 2.25e+159)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -9.2)
		tmp = t_1;
	elseif (t <= 4.5e-19)
		tmp = z / b;
	elseif (t <= 2.25e+159)
		tmp = (y / t) * (z / (a + 1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.2], t$95$1, If[LessEqual[t, 4.5e-19], N[(z / b), $MachinePrecision], If[LessEqual[t, 2.25e+159], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.1999999999999993 or 2.25000000000000013e159 < t

   1. Initial program 87.0%

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

      1. +-commutative 87.0%

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

      2. associate-/l* 90.1%

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

      3. fma-define 90.1%

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

      4. +-commutative 90.1%

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

      5. associate-/l* 95.2%

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

      6. fma-define 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in y around 0 73.9%

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]

   if -9.1999999999999993 < t < 4.50000000000000013e-19

   1. Initial program 69.0%

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

      1. +-commutative 69.0%

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

      2. associate-/l* 58.2%

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

      3. fma-define 58.2%

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

      4. +-commutative 58.2%

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

      5. associate-/l* 53.2%

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

      6. fma-define 53.2%

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

   3. Simplified 53.2%

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

   5. Taylor expanded in y around inf 53.8%

      \[\leadsto \color{blue}{\frac{z}{b}} \]

   if 4.50000000000000013e-19 < t < 2.25000000000000013e159

   1. Initial program 75.3%

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

      1. +-commutative 75.3%

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

      2. associate-/l* 81.7%

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

      3. fma-define 81.7%

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

      4. +-commutative 81.7%

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

      5. associate-/l* 84.1%

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

      6. fma-define 84.1%

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

   3. Simplified 84.1%

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

   5. Taylor expanded in y around 0 61.8%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{t \cdot \left(1 + a\right)} - \frac{b \cdot x}{t \cdot {\left(1 + a\right)}^{2}}\right) + \frac{x}{1 + a}} \]

   6. Taylor expanded in z around inf 37.1%

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

      1. times-frac 52.7%

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

   8. Simplified 52.7%

      \[\leadsto \color{blue}{\frac{y}{t} \cdot \frac{z}{1 + a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-19}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+159}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 67.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{+29} \lor \neg \left(b \leq 1.35 \cdot 10^{+102}\right):\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.7e+29) (not (<= b 1.35e+102)))
   (+ (/ z b) (* t (/ (/ x b) y)))
   (/ (+ x (/ (* y z) t)) (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.7e+29) || !(b <= 1.35e+102)) {
		tmp = (z / b) + (t * ((x / b) / y));
	} else {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.7d+29)) .or. (.not. (b <= 1.35d+102))) then
        tmp = (z / b) + (t * ((x / b) / y))
    else
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.7e+29) || !(b <= 1.35e+102)) {
		tmp = (z / b) + (t * ((x / b) / y));
	} else {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.7e+29) or not (b <= 1.35e+102):
		tmp = (z / b) + (t * ((x / b) / y))
	else:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.7e+29) || !(b <= 1.35e+102))
		tmp = Float64(Float64(z / b) + Float64(t * Float64(Float64(x / b) / y)));
	else
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.7e+29) || ~((b <= 1.35e+102)))
		tmp = (z / b) + (t * ((x / b) / y));
	else
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.7e+29], N[Not[LessEqual[b, 1.35e+102]], $MachinePrecision]], N[(N[(z / b), $MachinePrecision] + N[(t * N[(N[(x / b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.69999999999999991e29 or 1.3500000000000001e102 < b

   1. Initial program 60.8%

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

      1. +-commutative 60.8%

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

      2. associate-/l* 56.3%

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

      3. fma-define 56.3%

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

      4. +-commutative 56.3%

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

      5. associate-/l* 56.4%

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

      6. fma-define 56.4%

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

   3. Simplified 56.4%

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

   5. Taylor expanded in b around inf 34.6%

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

   6. Taylor expanded in x around inf 50.9%

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

      1. *-commutative 50.9%

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

      2. *-commutative 50.9%

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

   8. Simplified 50.9%

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

   9. Taylor expanded in x around 0 61.8%

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

       1. associate-/l* 67.5%

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

       2. associate-/r* 71.4%

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

   11. Simplified 71.4%

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

   if -1.69999999999999991e29 < b < 1.3500000000000001e102

   1. Initial program 84.8%

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

      1. +-commutative 84.8%

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

      2. associate-/l* 83.0%

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

      3. fma-define 83.0%

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

      4. +-commutative 83.0%

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

      5. associate-/l* 83.0%

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

      6. fma-define 83.0%

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

   3. Simplified 83.0%

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

   5. Taylor expanded in b around 0 73.2%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z}{t}}{1 + a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{+29} \lor \neg \left(b \leq 1.35 \cdot 10^{+102}\right):\\ \;\;\;\;\frac{z}{b} + t \cdot \frac{\frac{x}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 55.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.44 \lor \neg \left(t \leq 2.6 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -0.44) (not (<= t 2.6e+53))) (/ x (+ a 1.0)) (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -0.44) || !(t <= 2.6e+53)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-0.44d0)) .or. (.not. (t <= 2.6d+53))) then
        tmp = x / (a + 1.0d0)
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -0.44) || !(t <= 2.6e+53)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -0.44) or not (t <= 2.6e+53):
		tmp = x / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -0.44) || !(t <= 2.6e+53))
		tmp = Float64(x / Float64(a + 1.0));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -0.44) || ~((t <= 2.6e+53)))
		tmp = x / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -0.44], N[Not[LessEqual[t, 2.6e+53]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -0.440000000000000002 or 2.59999999999999998e53 < t

   1. Initial program 83.4%

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

      1. +-commutative 83.4%

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

      2. associate-/l* 88.1%

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

      3. fma-define 88.1%

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

      4. +-commutative 88.1%

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

      5. associate-/l* 93.0%

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

      6. fma-define 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in y around 0 67.4%

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]

   if -0.440000000000000002 < t < 2.59999999999999998e53

   1. Initial program 70.9%

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

      1. +-commutative 70.9%

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

      2. associate-/l* 61.6%

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

      3. fma-define 61.5%

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

      4. +-commutative 61.5%

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

      5. associate-/l* 57.3%

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

      6. fma-define 57.3%

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

   3. Simplified 57.3%

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

   5. Taylor expanded in y around inf 51.4%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.44 \lor \neg \left(t \leq 2.6 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 42.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -14 \lor \neg \left(t \leq 7 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -14.0) (not (<= t 7e+56))) (/ x a) (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -14.0) || !(t <= 7e+56)) {
		tmp = x / a;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-14.0d0)) .or. (.not. (t <= 7d+56))) then
        tmp = x / a
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -14.0) || !(t <= 7e+56)) {
		tmp = x / a;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -14.0) or not (t <= 7e+56):
		tmp = x / a
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -14.0) || !(t <= 7e+56))
		tmp = Float64(x / a);
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -14.0) || ~((t <= 7e+56)))
		tmp = x / a;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -14.0], N[Not[LessEqual[t, 7e+56]], $MachinePrecision]], N[(x / a), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -14 or 6.99999999999999999e56 < t

   1. Initial program 83.9%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 83.9%

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

      2. associate-/l* 87.9%

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

   4. Applied egg-rr 87.9%

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

   5. Taylor expanded in a around inf 55.6%

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

   6. Taylor expanded in y around 0 40.5%

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

   if -14 < t < 6.99999999999999999e56

   1. Initial program 70.6%

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

      1. +-commutative 70.6%

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

      2. associate-/l* 61.4%

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

      3. fma-define 61.4%

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

      4. +-commutative 61.4%

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

      5. associate-/l* 57.9%

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

      6. fma-define 57.9%

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

   3. Simplified 57.9%

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

   5. Taylor expanded in y around inf 51.0%

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

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -14 \lor \neg \left(t \leq 7 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 25.3% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 76.8%

   \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. *-commutative 76.8%

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

   2. associate-/l* 76.6%

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

4. Applied egg-rr 76.6%

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

5. Taylor expanded in a around inf 51.9%

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

6. Taylor expanded in y around 0 25.5%

   \[\leadsto \color{blue}{\frac{x}{a}} \]
7. Add Preprocessing

Developer Target 1: 79.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{if}\;t < -1.3659085366310088 \cdot 10^{-271}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < 3.036967103737246 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b)))))))
   (if (< t -1.3659085366310088e-271)
     t_1
     (if (< t 3.036967103737246e-130) (/ z b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))));
	double tmp;
	if (t < -1.3659085366310088e-271) {
		tmp = t_1;
	} else if (t < 3.036967103737246e-130) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 * ((x + ((y / t) * z)) * (1.0d0 / ((a + 1.0d0) + ((y / t) * b))))
    if (t < (-1.3659085366310088d-271)) then
        tmp = t_1
    else if (t < 3.036967103737246d-130) then
        tmp = z / b
    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 b) {
	double t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))));
	double tmp;
	if (t < -1.3659085366310088e-271) {
		tmp = t_1;
	} else if (t < 3.036967103737246e-130) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))))
	tmp = 0
	if t < -1.3659085366310088e-271:
		tmp = t_1
	elif t < 3.036967103737246e-130:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 * Float64(Float64(x + Float64(Float64(y / t) * z)) * Float64(1.0 / Float64(Float64(a + 1.0) + Float64(Float64(y / t) * b)))))
	tmp = 0.0
	if (t < -1.3659085366310088e-271)
		tmp = t_1;
	elseif (t < 3.036967103737246e-130)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))));
	tmp = 0.0;
	if (t < -1.3659085366310088e-271)
		tmp = t_1;
	elseif (t < 3.036967103737246e-130)
		tmp = z / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.0 * N[(N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.3659085366310088e-271], t$95$1, If[Less[t, 3.036967103737246e-130], N[(z / b), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024182 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -1707385670788761/12500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* 1 (* (+ x (* (/ y t) z)) (/ 1 (+ (+ a 1) (* (/ y t) b))))) (if (< t 1518483551868623/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ z b) (* 1 (* (+ x (* (/ y t) z)) (/ 1 (+ (+ a 1) (* (/ y t) b))))))))

  (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))