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

Percentage Accurate: 75.5% → 93.3%

Time: 15.4s

Alternatives: 14

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: 75.5% 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: 93.3% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_2 := 1 + \mathsf{fma}\left(y, \frac{b}{t}, a\right)\\ t_3 := \mathsf{fma}\left(\frac{y}{t}, \frac{z}{t\_2}, \frac{x}{t\_2}\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-309}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+206}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))
        (t_2 (+ 1.0 (fma y (/ b t) a)))
        (t_3 (fma (/ y t) (/ z t_2) (/ x t_2))))
   (if (<= t_1 (- INFINITY))
     t_3
     (if (<= t_1 -2e-309)
       t_1
       (if (<= t_1 0.0)
         (/ (+ z (* t (/ x y))) b)
         (if (<= t_1 2e+206) t_1 (if (<= t_1 INFINITY) t_3 (/ z b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double t_2 = 1.0 + fma(y, (b / t), a);
	double t_3 = fma((y / t), (z / t_2), (x / t_2));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_1 <= -2e-309) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (z + (t * (x / y))) / b;
	} else if (t_1 <= 2e+206) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	t_2 = Float64(1.0 + fma(y, Float64(b / t), a))
	t_3 = fma(Float64(y / t), Float64(z / t_2), Float64(x / t_2))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_1 <= -2e-309)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(z + Float64(t * Float64(x / y))) / b);
	elseif (t_1 <= 2e+206)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = 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]}, Block[{t$95$2 = N[(1.0 + N[(y * N[(b / t), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y / t), $MachinePrecision] * N[(z / t$95$2), $MachinePrecision] + N[(x / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$3, If[LessEqual[t$95$1, -2e-309], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(z + N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t$95$1, 2e+206], t$95$1, If[LessEqual[t$95$1, Infinity], t$95$3, N[(z / b), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 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 or 2.0000000000000001e206 < (/.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 52.3%

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

      1. associate-/l* 79.2%

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

      2. associate-/l* 79.1%

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

   3. Simplified 79.1%

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

   5. Taylor expanded in x around 0 60.3%

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

      1. +-commutative 60.3%

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

      2. times-frac 97.8%

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

      3. fma-define 97.8%

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

      4. +-commutative 97.8%

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

      5. associate-*l/ 95.7%

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

      6. *-commutative 95.7%

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

      7. fma-define 95.7%

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

      8. +-commutative 95.7%

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

      9. associate-*l/ 95.8%

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

      10. *-commutative 95.8%

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

      11. fma-define 95.8%

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

   7. Simplified 95.8%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.9999999999999988e-309 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.0000000000000001e206

   1. Initial program 99.5%

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

   if -1.9999999999999988e-309 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -0.0

   1. Initial program 42.4%

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

      1. associate-/l* 42.3%

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

      2. associate-/l* 65.1%

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

   3. Simplified 65.1%

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

   5. Taylor expanded in x around 0 42.4%

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

      1. +-commutative 42.4%

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

      2. times-frac 26.1%

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

      3. fma-define 26.1%

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

      4. +-commutative 26.1%

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

      5. associate-*l/ 31.1%

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

      6. *-commutative 31.1%

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

      7. fma-define 31.1%

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

      8. +-commutative 31.1%

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

      9. associate-*l/ 48.8%

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

      10. *-commutative 48.8%

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

      11. fma-define 48.8%

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

   7. Simplified 48.8%

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

   8. Taylor expanded in b around inf 69.1%

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

      1. associate-/l* 76.8%

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

   10. Simplified 76.8%

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

   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. associate-/l* 0.6%

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

      2. associate-/l* 11.2%

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

   3. Simplified 11.2%

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

   5. Taylor expanded in y around inf 96.3%

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

Alternative 2: 93.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_2 := 1 + \left(a + y \cdot \frac{b}{t}\right)\\ t_3 := z \cdot \left(\frac{\frac{x}{z}}{t\_2} + \frac{y}{t \cdot t\_2}\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-309}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+279}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))
        (t_2 (+ 1.0 (+ a (* y (/ b t)))))
        (t_3 (* z (+ (/ (/ x z) t_2) (/ y (* t t_2))))))
   (if (<= t_1 (- INFINITY))
     t_3
     (if (<= t_1 -2e-309)
       t_1
       (if (<= t_1 0.0)
         (/ (+ z (* t (/ x y))) b)
         (if (<= t_1 5e+279) t_1 (if (<= t_1 INFINITY) t_3 (/ z b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double t_2 = 1.0 + (a + (y * (b / t)));
	double t_3 = z * (((x / z) / t_2) + (y / (t * t_2)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_1 <= -2e-309) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (z + (t * (x / y))) / b;
	} else if (t_1 <= 5e+279) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_3;
	} 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 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double t_2 = 1.0 + (a + (y * (b / t)));
	double t_3 = z * (((x / z) / t_2) + (y / (t * t_2)));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else if (t_1 <= -2e-309) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (z + (t * (x / y))) / b;
	} else if (t_1 <= 5e+279) {
		tmp = t_1;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))
	t_2 = 1.0 + (a + (y * (b / t)))
	t_3 = z * (((x / z) / t_2) + (y / (t * t_2)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_3
	elif t_1 <= -2e-309:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = (z + (t * (x / y))) / b
	elif t_1 <= 5e+279:
		tmp = t_1
	elif t_1 <= math.inf:
		tmp = t_3
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	t_2 = Float64(1.0 + Float64(a + Float64(y * Float64(b / t))))
	t_3 = Float64(z * Float64(Float64(Float64(x / z) / t_2) + Float64(y / Float64(t * t_2))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_1 <= -2e-309)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(z + Float64(t * Float64(x / y))) / b);
	elseif (t_1 <= 5e+279)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	t_2 = 1.0 + (a + (y * (b / t)));
	t_3 = z * (((x / z) / t_2) + (y / (t * t_2)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_3;
	elseif (t_1 <= -2e-309)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = (z + (t * (x / y))) / b;
	elseif (t_1 <= 5e+279)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_3;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = 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]}, Block[{t$95$2 = N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(N[(x / z), $MachinePrecision] / t$95$2), $MachinePrecision] + N[(y / N[(t * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$3, If[LessEqual[t$95$1, -2e-309], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(z + N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t$95$1, 5e+279], t$95$1, If[LessEqual[t$95$1, Infinity], t$95$3, N[(z / b), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 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 or 5.0000000000000002e279 < (/.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 43.8%

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

      1. associate-/l* 75.5%

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

      2. associate-/l* 75.4%

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

   3. Simplified 75.4%

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

   5. Taylor expanded in z around inf 91.8%

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

      1. associate-/r* 94.8%

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

      2. associate-*l/ 94.8%

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

      3. *-commutative 94.8%

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

      4. associate-*l/ 92.2%

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

      5. *-commutative 92.2%

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

   7. Simplified 92.2%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.9999999999999988e-309 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 5.0000000000000002e279

   1. Initial program 99.5%

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

   if -1.9999999999999988e-309 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -0.0

   1. Initial program 42.4%

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

      1. associate-/l* 42.3%

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

      2. associate-/l* 65.1%

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

   3. Simplified 65.1%

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

   5. Taylor expanded in x around 0 42.4%

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

      1. +-commutative 42.4%

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

      2. times-frac 26.1%

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

      3. fma-define 26.1%

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

      4. +-commutative 26.1%

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

      5. associate-*l/ 31.1%

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

      6. *-commutative 31.1%

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

      7. fma-define 31.1%

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

      8. +-commutative 31.1%

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

      9. associate-*l/ 48.8%

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

      10. *-commutative 48.8%

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

      11. fma-define 48.8%

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

   7. Simplified 48.8%

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

   8. Taylor expanded in b around inf 69.1%

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

      1. associate-/l* 76.8%

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

   10. Simplified 76.8%

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

   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. associate-/l* 0.6%

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

      2. associate-/l* 11.2%

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

   3. Simplified 11.2%

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

   5. Taylor expanded in y around inf 96.3%

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

Alternative 3: 89.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_2 := \left(a + 1\right) + y \cdot \frac{b}{t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{t\_2}\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-309}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+206}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))
        (t_2 (+ (+ a 1.0) (* y (/ b t)))))
   (if (<= t_1 (- INFINITY))
     (/ (+ x (/ y (/ t z))) t_2)
     (if (<= t_1 -2e-309)
       t_1
       (if (<= t_1 0.0)
         (/ (+ z (* t (/ x y))) b)
         (if (<= t_1 2e+206)
           t_1
           (if (<= t_1 INFINITY) (/ (+ x (* y (/ z t))) t_2) (/ z b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double t_2 = (a + 1.0) + (y * (b / t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x + (y / (t / z))) / t_2;
	} else if (t_1 <= -2e-309) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (z + (t * (x / y))) / b;
	} else if (t_1 <= 2e+206) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (x + (y * (z / t))) / t_2;
	} 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 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double t_2 = (a + 1.0) + (y * (b / t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x + (y / (t / z))) / t_2;
	} else if (t_1 <= -2e-309) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (z + (t * (x / y))) / b;
	} else if (t_1 <= 2e+206) {
		tmp = t_1;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (x + (y * (z / t))) / t_2;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))
	t_2 = (a + 1.0) + (y * (b / t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x + (y / (t / z))) / t_2
	elif t_1 <= -2e-309:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = (z + (t * (x / y))) / b
	elif t_1 <= 2e+206:
		tmp = t_1
	elif t_1 <= math.inf:
		tmp = (x + (y * (z / t))) / t_2
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	t_2 = Float64(Float64(a + 1.0) + Float64(y * Float64(b / t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / t_2);
	elseif (t_1 <= -2e-309)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(z + Float64(t * Float64(x / y))) / b);
	elseif (t_1 <= 2e+206)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / t_2);
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	t_2 = (a + 1.0) + (y * (b / t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x + (y / (t / z))) / t_2;
	elseif (t_1 <= -2e-309)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = (z + (t * (x / y))) / b;
	elseif (t_1 <= 2e+206)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = (x + (y * (z / t))) / t_2;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = 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]}, Block[{t$95$2 = N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[t$95$1, -2e-309], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(z + N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t$95$1, 2e+206], t$95$1, If[LessEqual[t$95$1, Infinity], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 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 42.3%

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

      1. associate-/l* 74.4%

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

      2. associate-/l* 74.4%

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

   3. Simplified 74.4%

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

      1. clear-num 74.4%

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

      2. un-div-inv 74.6%

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

   6. Applied egg-rr 74.6%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -1.9999999999999988e-309 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2.0000000000000001e206

   1. Initial program 99.5%

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

   if -1.9999999999999988e-309 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -0.0

   1. Initial program 42.4%

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

      1. associate-/l* 42.3%

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

      2. associate-/l* 65.1%

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

   3. Simplified 65.1%

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

   5. Taylor expanded in x around 0 42.4%

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

      1. +-commutative 42.4%

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

      2. times-frac 26.1%

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

      3. fma-define 26.1%

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

      4. +-commutative 26.1%

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

      5. associate-*l/ 31.1%

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

      6. *-commutative 31.1%

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

      7. fma-define 31.1%

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

      8. +-commutative 31.1%

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

      9. associate-*l/ 48.8%

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

      10. *-commutative 48.8%

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

      11. fma-define 48.8%

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

   7. Simplified 48.8%

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

   8. Taylor expanded in b around inf 69.1%

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

      1. associate-/l* 76.8%

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

   10. Simplified 76.8%

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

   if 2.0000000000000001e206 < (/.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 57.1%

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

      1. associate-/l* 81.6%

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

      2. associate-/l* 81.4%

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

   3. Simplified 81.4%

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

   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. associate-/l* 0.6%

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

      2. associate-/l* 11.2%

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

   3. Simplified 11.2%

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

   5. Taylor expanded in y around inf 96.3%

      \[\leadsto \color{blue}{\frac{z}{b}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 4: 88.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + 1\right) + \frac{y \cdot b}{t}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t\_1}\\ t_3 := \frac{x + z \cdot \left(y \cdot \frac{1}{t}\right)}{t\_1}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-309}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ a 1.0) (/ (* y b) t)))
        (t_2 (/ (+ x (/ (* y z) t)) t_1))
        (t_3 (/ (+ x (* z (* y (/ 1.0 t)))) t_1)))
   (if (<= t_2 -2e-309)
     t_3
     (if (<= t_2 0.0)
       (/ (+ z (* t (/ x y))) b)
       (if (<= t_2 INFINITY) t_3 (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + 1.0) + ((y * b) / t);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double t_3 = (x + (z * (y * (1.0 / t)))) / t_1;
	double tmp;
	if (t_2 <= -2e-309) {
		tmp = t_3;
	} else if (t_2 <= 0.0) {
		tmp = (z + (t * (x / y))) / b;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_3;
	} 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 = (a + 1.0) + ((y * b) / t);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double t_3 = (x + (z * (y * (1.0 / t)))) / t_1;
	double tmp;
	if (t_2 <= -2e-309) {
		tmp = t_3;
	} else if (t_2 <= 0.0) {
		tmp = (z + (t * (x / y))) / b;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + 1.0) + ((y * b) / t)
	t_2 = (x + ((y * z) / t)) / t_1
	t_3 = (x + (z * (y * (1.0 / t)))) / t_1
	tmp = 0
	if t_2 <= -2e-309:
		tmp = t_3
	elif t_2 <= 0.0:
		tmp = (z + (t * (x / y))) / b
	elif t_2 <= math.inf:
		tmp = t_3
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t))
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / t_1)
	t_3 = Float64(Float64(x + Float64(z * Float64(y * Float64(1.0 / t)))) / t_1)
	tmp = 0.0
	if (t_2 <= -2e-309)
		tmp = t_3;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(z + Float64(t * Float64(x / y))) / b);
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + 1.0) + ((y * b) / t);
	t_2 = (x + ((y * z) / t)) / t_1;
	t_3 = (x + (z * (y * (1.0 / t)))) / t_1;
	tmp = 0.0;
	if (t_2 <= -2e-309)
		tmp = t_3;
	elseif (t_2 <= 0.0)
		tmp = (z + (t * (x / y))) / b;
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(z * N[(y * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-309], t$95$3, If[LessEqual[t$95$2, 0.0], N[(N[(z + N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$3, 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))) < -1.9999999999999988e-309 or -0.0 < (/.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 88.1%

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

      1. associate-*r/ 89.6%

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

      2. *-commutative 89.6%

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

      3. div-inv 89.5%

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

      4. associate-*l* 92.8%

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

   4. Applied egg-rr 92.8%

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

   if -1.9999999999999988e-309 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -0.0

   1. Initial program 42.4%

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

      1. associate-/l* 42.3%

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

      2. associate-/l* 65.1%

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

   3. Simplified 65.1%

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

   5. Taylor expanded in x around 0 42.4%

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

      1. +-commutative 42.4%

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

      2. times-frac 26.1%

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

      3. fma-define 26.1%

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

      4. +-commutative 26.1%

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

      5. associate-*l/ 31.1%

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

      6. *-commutative 31.1%

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

      7. fma-define 31.1%

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

      8. +-commutative 31.1%

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

      9. associate-*l/ 48.8%

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

      10. *-commutative 48.8%

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

      11. fma-define 48.8%

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

   7. Simplified 48.8%

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

   8. Taylor expanded in b around inf 69.1%

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

      1. associate-/l* 76.8%

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

   10. Simplified 76.8%

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

   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. associate-/l* 0.6%

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

      2. associate-/l* 11.2%

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

   3. Simplified 11.2%

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

   5. Taylor expanded in y around inf 96.3%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -2 \cdot 10^{-309}:\\ \;\;\;\;\frac{x + z \cdot \left(y \cdot \frac{1}{t}\right)}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;\frac{x + z \cdot \left(y \cdot \frac{1}{t}\right)}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{-27} \lor \neg \left(t \leq 1.25 \cdot 10^{-60}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.75e-27) (not (<= t 1.25e-60)))
   (/ (+ 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 <= -1.75e-27) || !(t <= 1.25e-60)) {
		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 <= (-1.75d-27)) .or. (.not. (t <= 1.25d-60))) 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 <= -1.75e-27) || !(t <= 1.25e-60)) {
		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 <= -1.75e-27) or not (t <= 1.25e-60):
		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 <= -1.75e-27) || !(t <= 1.25e-60))
		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 <= -1.75e-27) || ~((t <= 1.25e-60)))
		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, -1.75e-27], N[Not[LessEqual[t, 1.25e-60]], $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 < -1.7500000000000001e-27 or 1.25e-60 < t

   1. Initial program 79.3%

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

      1. associate-/l* 87.9%

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

      2. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

   if -1.7500000000000001e-27 < t < 1.25e-60

   1. Initial program 63.2%

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

      1. associate-/l* 55.1%

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

      2. associate-/l* 47.8%

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

   3. Simplified 47.8%

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

   5. Taylor expanded in x around 0 66.8%

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

      1. +-commutative 66.8%

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

      2. times-frac 59.7%

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

      3. fma-define 59.8%

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

      4. +-commutative 59.8%

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

      5. associate-*l/ 52.3%

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

      6. *-commutative 52.3%

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

      7. fma-define 52.3%

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

      8. +-commutative 52.3%

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

      9. associate-*l/ 47.7%

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

      10. *-commutative 47.7%

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

      11. fma-define 47.7%

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

   7. Simplified 47.7%

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

   8. Taylor expanded in b around inf 72.1%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{-27} \lor \neg \left(t \leq 1.25 \cdot 10^{-60}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -1.75 \cdot 10^{-27}:\\ \;\;\;\;\frac{t\_1}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-60}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z t)))))
   (if (<= t -1.75e-27)
     (/ t_1 (+ (+ a 1.0) (/ y (/ t b))))
     (if (<= t 2.1e-60)
       (/ (+ z (/ (* x t) y)) b)
       (/ t_1 (+ (+ a 1.0) (* y (/ b t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * (z / t));
	double tmp;
	if (t <= -1.75e-27) {
		tmp = t_1 / ((a + 1.0) + (y / (t / b)));
	} else if (t <= 2.1e-60) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = t_1 / ((a + 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) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / t))
    if (t <= (-1.75d-27)) then
        tmp = t_1 / ((a + 1.0d0) + (y / (t / b)))
    else if (t <= 2.1d-60) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = t_1 / ((a + 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 t_1 = x + (y * (z / t));
	double tmp;
	if (t <= -1.75e-27) {
		tmp = t_1 / ((a + 1.0) + (y / (t / b)));
	} else if (t <= 2.1e-60) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = t_1 / ((a + 1.0) + (y * (b / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * (z / t))
	tmp = 0
	if t <= -1.75e-27:
		tmp = t_1 / ((a + 1.0) + (y / (t / b)))
	elif t <= 2.1e-60:
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = t_1 / ((a + 1.0) + (y * (b / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * Float64(z / t)))
	tmp = 0.0
	if (t <= -1.75e-27)
		tmp = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(y / Float64(t / b))));
	elseif (t <= 2.1e-60)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * (z / t));
	tmp = 0.0;
	if (t <= -1.75e-27)
		tmp = t_1 / ((a + 1.0) + (y / (t / b)));
	elseif (t <= 2.1e-60)
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = t_1 / ((a + 1.0) + (y * (b / t)));
	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]}, If[LessEqual[t, -1.75e-27], N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.1e-60], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.7500000000000001e-27

   1. Initial program 76.0%

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

      1. associate-/l* 85.3%

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

      2. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in y around 0 85.3%

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

      1. associate-*r/ 98.4%

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

      2. *-commutative 98.4%

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

      3. associate-/r/ 97.8%

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

   7. Simplified 97.8%

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

   if -1.7500000000000001e-27 < t < 2.09999999999999991e-60

   1. Initial program 63.2%

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

      1. associate-/l* 55.1%

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

      2. associate-/l* 47.8%

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

   3. Simplified 47.8%

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

   5. Taylor expanded in x around 0 66.8%

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

      1. +-commutative 66.8%

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

      2. times-frac 59.7%

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

      3. fma-define 59.8%

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

      4. +-commutative 59.8%

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

      5. associate-*l/ 52.3%

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

      6. *-commutative 52.3%

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

      7. fma-define 52.3%

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

      8. +-commutative 52.3%

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

      9. associate-*l/ 47.7%

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

      10. *-commutative 47.7%

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

      11. fma-define 47.7%

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

   7. Simplified 47.7%

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

   8. Taylor expanded in b around inf 72.1%

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

   if 2.09999999999999991e-60 < t

   1. Initial program 82.8%

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

      1. associate-/l* 90.8%

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

      2. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{-27}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-60}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -720000 \lor \neg \left(t \leq 3 \cdot 10^{-22}\right):\\ \;\;\;\;\frac{x}{a + 1} + \frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -720000.0) (not (<= t 3e-22)))
   (+ (/ x (+ a 1.0)) (* (/ y t) (/ z (+ a 1.0))))
   (/ (+ z (/ (* x t) y)) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -720000.0) || !(t <= 3e-22)) {
		tmp = (x / (a + 1.0)) + ((y / t) * (z / (a + 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) :: tmp
    if ((t <= (-720000.0d0)) .or. (.not. (t <= 3d-22))) then
        tmp = (x / (a + 1.0d0)) + ((y / t) * (z / (a + 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 tmp;
	if ((t <= -720000.0) || !(t <= 3e-22)) {
		tmp = (x / (a + 1.0)) + ((y / t) * (z / (a + 1.0)));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -720000.0) or not (t <= 3e-22):
		tmp = (x / (a + 1.0)) + ((y / t) * (z / (a + 1.0)))
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -720000.0) || !(t <= 3e-22))
		tmp = Float64(Float64(x / Float64(a + 1.0)) + Float64(Float64(y / t) * Float64(z / Float64(a + 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)
	tmp = 0.0;
	if ((t <= -720000.0) || ~((t <= 3e-22)))
		tmp = (x / (a + 1.0)) + ((y / t) * (z / (a + 1.0)));
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -720000.0], N[Not[LessEqual[t, 3e-22]], $MachinePrecision]], N[(N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $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 < -7.2e5 or 2.9999999999999999e-22 < t

   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* 87.0%

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

      2. associate-/l* 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in x around 0 77.0%

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

      1. +-commutative 77.0%

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

      2. times-frac 88.2%

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

      3. fma-define 88.2%

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

      4. +-commutative 88.2%

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

      5. associate-*l/ 91.9%

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

      6. *-commutative 91.9%

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

      7. fma-define 91.9%

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

      8. +-commutative 91.9%

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

      9. associate-*l/ 97.0%

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

      10. *-commutative 97.0%

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

      11. fma-define 97.0%

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

   7. Simplified 97.0%

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

   8. Taylor expanded in b around 0 66.5%

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

      1. times-frac 75.4%

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

   10. Simplified 75.4%

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

   if -7.2e5 < t < 2.9999999999999999e-22

   1. Initial program 66.1%

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

      1. associate-/l* 58.6%

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

      2. associate-/l* 51.2%

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

   3. Simplified 51.2%

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

   5. Taylor expanded in x around 0 69.4%

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

      1. +-commutative 69.4%

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

      2. times-frac 62.9%

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

      3. fma-define 62.9%

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

      4. +-commutative 62.9%

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

      5. associate-*l/ 55.5%

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

      6. *-commutative 55.5%

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

      7. fma-define 55.5%

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

      8. +-commutative 55.5%

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

      9. associate-*l/ 51.1%

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

      10. *-commutative 51.1%

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

      11. fma-define 51.1%

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

   7. Simplified 51.1%

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

   8. Taylor expanded in b around inf 71.9%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -720000 \lor \neg \left(t \leq 3 \cdot 10^{-22}\right):\\ \;\;\;\;\frac{x}{a + 1} + \frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+46} \lor \neg \left(t \leq 5.2 \cdot 10^{-58}\right):\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -5.5e+46) (not (<= t 5.2e-58)))
   (/ x (+ 1.0 (+ a (* 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 <= -5.5e+46) || !(t <= 5.2e-58)) {
		tmp = x / (1.0 + (a + (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 <= (-5.5d+46)) .or. (.not. (t <= 5.2d-58))) then
        tmp = x / (1.0d0 + (a + (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 <= -5.5e+46) || !(t <= 5.2e-58)) {
		tmp = x / (1.0 + (a + (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 <= -5.5e+46) or not (t <= 5.2e-58):
		tmp = x / (1.0 + (a + (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 <= -5.5e+46) || !(t <= 5.2e-58))
		tmp = Float64(x / Float64(1.0 + Float64(a + 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 <= -5.5e+46) || ~((t <= 5.2e-58)))
		tmp = x / (1.0 + (a + (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, -5.5e+46], N[Not[LessEqual[t, 5.2e-58]], $MachinePrecision]], N[(x / N[(1.0 + N[(a + 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 2 regimes

2. if t < -5.4999999999999998e46 or 5.20000000000000013e-58 < t

   1. Initial program 78.3%

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

      1. associate-/l* 87.7%

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

      2. associate-/l* 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in x around inf 66.0%

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

      1. associate-*l/ 71.2%

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

      2. *-commutative 71.2%

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

   7. Simplified 71.2%

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

   if -5.4999999999999998e46 < t < 5.20000000000000013e-58

   1. Initial program 65.6%

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

      1. associate-/l* 58.2%

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

      2. associate-/l* 50.9%

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

   3. Simplified 50.9%

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

   5. Taylor expanded in x around 0 68.9%

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

      1. +-commutative 68.9%

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

      2. times-frac 63.2%

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

      3. fma-define 63.2%

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

      4. +-commutative 63.2%

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

      5. associate-*l/ 55.9%

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

      6. *-commutative 55.9%

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

      7. fma-define 55.9%

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

      8. +-commutative 55.9%

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

      9. associate-*l/ 51.5%

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

      10. *-commutative 51.5%

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

      11. fma-define 51.5%

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

   7. Simplified 51.5%

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

   8. Taylor expanded in b around inf 71.0%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+46} \lor \neg \left(t \leq 5.2 \cdot 10^{-58}\right):\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+46}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-22}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.9e+46)
   (/ x (+ 1.0 (+ a (* y (/ b t)))))
   (if (<= t 2.15e-22)
     (/ (+ z (/ (* x t) y)) b)
     (/ (+ 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 (t <= -3.9e+46) {
		tmp = x / (1.0 + (a + (y * (b / t))));
	} else if (t <= 2.15e-22) {
		tmp = (z + ((x * t) / y)) / b;
	} 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 (t <= (-3.9d+46)) then
        tmp = x / (1.0d0 + (a + (y * (b / t))))
    else if (t <= 2.15d-22) then
        tmp = (z + ((x * t) / y)) / b
    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 (t <= -3.9e+46) {
		tmp = x / (1.0 + (a + (y * (b / t))));
	} else if (t <= 2.15e-22) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3.9e+46:
		tmp = x / (1.0 + (a + (y * (b / t))))
	elif t <= 2.15e-22:
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.9e+46)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(y * Float64(b / t)))));
	elseif (t <= 2.15e-22)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	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 (t <= -3.9e+46)
		tmp = x / (1.0 + (a + (y * (b / t))));
	elseif (t <= 2.15e-22)
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.9e+46], N[(x / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.15e-22], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.89999999999999995e46

   1. Initial program 73.3%

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

      1. associate-/l* 84.3%

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

      2. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 64.4%

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

      1. associate-*l/ 73.7%

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

      2. *-commutative 73.7%

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

   7. Simplified 73.7%

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

   if -3.89999999999999995e46 < t < 2.15000000000000019e-22

   1. Initial program 66.9%

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

      1. associate-/l* 59.8%

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

      2. associate-/l* 52.8%

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

   3. Simplified 52.8%

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

   5. Taylor expanded in x around 0 70.1%

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

      1. +-commutative 70.1%

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

      2. times-frac 64.6%

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

      3. fma-define 64.6%

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

      4. +-commutative 64.6%

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

      5. associate-*l/ 57.6%

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

      6. *-commutative 57.6%

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

      7. fma-define 57.6%

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

      8. +-commutative 57.6%

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

      9. associate-*l/ 53.3%

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

      10. *-commutative 53.3%

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

      11. fma-define 53.3%

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

   7. Simplified 53.3%

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

   8. Taylor expanded in b around inf 70.6%

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

   if 2.15000000000000019e-22 < t

   1. Initial program 81.5%

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

      1. associate-/l* 90.0%

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

      2. associate-/l* 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in b around 0 69.8%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+46}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-22}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.15 \cdot 10^{+46} \lor \neg \left(t \leq 250\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4.15e+46) (not (<= t 250.0)))
   (/ x (+ a 1.0))
   (/ (+ z (/ (* x t) y)) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.15e+46) || !(t <= 250.0)) {
		tmp = x / (a + 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) :: tmp
    if ((t <= (-4.15d+46)) .or. (.not. (t <= 250.0d0))) then
        tmp = x / (a + 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 tmp;
	if ((t <= -4.15e+46) || !(t <= 250.0)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -4.15e+46) or not (t <= 250.0):
		tmp = x / (a + 1.0)
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -4.15e+46) || !(t <= 250.0))
		tmp = Float64(x / Float64(a + 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)
	tmp = 0.0;
	if ((t <= -4.15e+46) || ~((t <= 250.0)))
		tmp = x / (a + 1.0);
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -4.15e+46], N[Not[LessEqual[t, 250.0]], $MachinePrecision]], N[(x / N[(a + 1.0), $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 < -4.14999999999999976e46 or 250 < t

   1. Initial program 78.0%

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

      1. associate-/l* 88.2%

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

      2. associate-/l* 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in y around 0 60.2%

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

   if -4.14999999999999976e46 < t < 250

   1. Initial program 66.9%

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

      1. associate-/l* 60.1%

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

      2. associate-/l* 53.4%

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

   3. Simplified 53.4%

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

   5. Taylor expanded in x around 0 70.0%

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

      1. +-commutative 70.0%

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

      2. times-frac 65.5%

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

      3. fma-define 65.5%

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

      4. +-commutative 65.5%

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

      5. associate-*l/ 58.7%

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

      6. *-commutative 58.7%

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

      7. fma-define 58.7%

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

      8. +-commutative 58.7%

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

      9. associate-*l/ 54.7%

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

      10. *-commutative 54.7%

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

      11. fma-define 54.7%

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

   7. Simplified 54.7%

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

   8. Taylor expanded in b around inf 69.2%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.15 \cdot 10^{+46} \lor \neg \left(t \leq 250\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.1 \cdot 10^{+47} \lor \neg \left(t \leq 1.18\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -6.1e+47) (not (<= t 1.18)))
   (/ x (+ a 1.0))
   (/ (+ z (* t (/ x y))) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -6.1e+47) || !(t <= 1.18)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = (z + (t * (x / 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 <= (-6.1d+47)) .or. (.not. (t <= 1.18d0))) then
        tmp = x / (a + 1.0d0)
    else
        tmp = (z + (t * (x / 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 <= -6.1e+47) || !(t <= 1.18)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = (z + (t * (x / y))) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -6.1e+47) or not (t <= 1.18):
		tmp = x / (a + 1.0)
	else:
		tmp = (z + (t * (x / y))) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -6.1e+47) || !(t <= 1.18))
		tmp = Float64(x / Float64(a + 1.0));
	else
		tmp = Float64(Float64(z + Float64(t * Float64(x / y))) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -6.1e+47) || ~((t <= 1.18)))
		tmp = x / (a + 1.0);
	else
		tmp = (z + (t * (x / y))) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -6.1e+47], N[Not[LessEqual[t, 1.18]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.10000000000000019e47 or 1.17999999999999994 < t

   1. Initial program 78.0%

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

      1. associate-/l* 88.2%

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

      2. associate-/l* 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in y around 0 60.2%

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

   if -6.10000000000000019e47 < t < 1.17999999999999994

   1. Initial program 66.9%

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

      1. associate-/l* 60.1%

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

      2. associate-/l* 53.4%

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

   3. Simplified 53.4%

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

   5. Taylor expanded in x around 0 70.0%

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

      1. +-commutative 70.0%

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

      2. times-frac 65.5%

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

      3. fma-define 65.5%

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

      4. +-commutative 65.5%

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

      5. associate-*l/ 58.7%

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

      6. *-commutative 58.7%

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

      7. fma-define 58.7%

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

      8. +-commutative 58.7%

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

      9. associate-*l/ 54.7%

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

      10. *-commutative 54.7%

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

      11. fma-define 54.7%

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

   7. Simplified 54.7%

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

   8. Taylor expanded in b around inf 69.2%

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

      1. associate-/l* 67.0%

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

   10. Simplified 67.0%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.1 \cdot 10^{+47} \lor \neg \left(t \leq 1.18\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + t \cdot \frac{x}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 55.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+47} \lor \neg \left(t \leq 1.18\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -5.6e+47) (not (<= t 1.18))) (/ 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 <= -5.6e+47) || !(t <= 1.18)) {
		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 <= (-5.6d+47)) .or. (.not. (t <= 1.18d0))) 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 <= -5.6e+47) || !(t <= 1.18)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -5.6e+47) or not (t <= 1.18):
		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 <= -5.6e+47) || !(t <= 1.18))
		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 <= -5.6e+47) || ~((t <= 1.18)))
		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, -5.6e+47], N[Not[LessEqual[t, 1.18]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.59999999999999976e47 or 1.17999999999999994 < t

   1. Initial program 78.0%

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

      1. associate-/l* 88.2%

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

      2. associate-/l* 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in y around 0 60.2%

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

   if -5.59999999999999976e47 < t < 1.17999999999999994

   1. Initial program 66.9%

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

      1. associate-/l* 60.1%

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

      2. associate-/l* 53.4%

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

   3. Simplified 53.4%

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

   5. Taylor expanded in y around inf 53.4%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+47} \lor \neg \left(t \leq 1.18\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 41.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+137} \lor \neg \left(t \leq 15.5\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.7e+137) (not (<= t 15.5))) (/ x a) (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.7e+137) || !(t <= 15.5)) {
		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 <= (-2.7d+137)) .or. (.not. (t <= 15.5d0))) 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 <= -2.7e+137) || !(t <= 15.5)) {
		tmp = x / a;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.7e+137) or not (t <= 15.5):
		tmp = x / a
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.7e+137) || !(t <= 15.5))
		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 <= -2.7e+137) || ~((t <= 15.5)))
		tmp = x / a;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.7e+137], N[Not[LessEqual[t, 15.5]], $MachinePrecision]], N[(x / a), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.70000000000000017e137 or 15.5 < t

   1. Initial program 77.9%

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

      1. associate-/l* 89.0%

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

      2. associate-/l* 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in a around inf 40.3%

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

   6. Taylor expanded in x around inf 37.7%

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

   if -2.70000000000000017e137 < t < 15.5

   1. Initial program 68.3%

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

      1. associate-/l* 62.9%

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

      2. associate-/l* 58.8%

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

   3. Simplified 58.8%

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

   5. Taylor expanded in y around inf 49.5%

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

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+137} \lor \neg \left(t \leq 15.5\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 24.7% 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 72.1%

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

   1. associate-/l* 73.2%

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

   2. associate-/l* 74.1%

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

3. Simplified 74.1%

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

5. Taylor expanded in a around inf 31.3%

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

6. Taylor expanded in x around inf 21.4%

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

Developer Target 1: 79.1% 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 2024181 
(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))))