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

Percentage Accurate: 75.0% → 91.9%

Time: 14.7s

Alternatives: 18

Speedup: 0.8×

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: 75.0% 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: 91.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t} + \left(a + 1\right)\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t_1}\\ t_3 := \frac{y}{t \cdot \frac{\mathsf{fma}\left(y, \frac{b}{t}, a + 1\right)}{z}}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq -4 \cdot 10^{-253}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot t_1} + \frac{x}{t_1}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{-279}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+296}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + t \cdot \left(\frac{\frac{x}{y}}{b} + \frac{-1 - a}{\frac{y \cdot \left(b \cdot b\right)}{z}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ (* y b) t) (+ a 1.0)))
        (t_2 (/ (+ x (/ (* y z) t)) t_1))
        (t_3 (/ y (* t (/ (fma y (/ b t) (+ a 1.0)) z)))))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 -4e-253)
       (+ (/ (* y z) (* t t_1)) (/ x t_1))
       (if (<= t_2 5e-279)
         (/ (+ x (/ y (/ t z))) (+ (+ a 1.0) (* y (/ b t))))
         (if (<= t_2 2e+296)
           t_2
           (if (<= t_2 INFINITY)
             t_3
             (+
              (/ z b)
              (*
               t
               (+ (/ (/ x y) b) (/ (- -1.0 a) (/ (* y (* b b)) z))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * b) / t) + (a + 1.0);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double t_3 = y / (t * (fma(y, (b / t), (a + 1.0)) / z));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= -4e-253) {
		tmp = ((y * z) / (t * t_1)) + (x / t_1);
	} else if (t_2 <= 5e-279) {
		tmp = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)));
	} else if (t_2 <= 2e+296) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = (z / b) + (t * (((x / y) / b) + ((-1.0 - a) / ((y * (b * b)) / z))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0))
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / t_1)
	t_3 = Float64(y / Float64(t * Float64(fma(y, Float64(b / t), Float64(a + 1.0)) / z)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= -4e-253)
		tmp = Float64(Float64(Float64(y * z) / Float64(t * t_1)) + Float64(x / t_1));
	elseif (t_2 <= 5e-279)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	elseif (t_2 <= 2e+296)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(Float64(z / b) + Float64(t * Float64(Float64(Float64(x / y) / b) + Float64(Float64(-1.0 - a) / Float64(Float64(y * Float64(b * b)) / z)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $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[(y / N[(t * N[(N[(y * N[(b / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, -4e-253], N[(N[(N[(y * z), $MachinePrecision] / N[(t * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e-279], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+296], t$95$2, If[LessEqual[t$95$2, Infinity], t$95$3, N[(N[(z / b), $MachinePrecision] + N[(t * N[(N[(N[(x / y), $MachinePrecision] / b), $MachinePrecision] + N[(N[(-1.0 - a), $MachinePrecision] / N[(N[(y * N[(b * b), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -inf.0 or 1.99999999999999996e296 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 31.0%

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

      1. *-commutative 31.0%

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

      2. associate-*l/ 51.4%

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

      3. *-commutative 51.4%

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

      4. associate-*l/ 51.3%

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

   3. Simplified 51.3%

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

   4. Taylor expanded in x around 0 55.0%

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

      1. times-frac 75.6%

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

      2. associate-+r+ 75.6%

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

      3. associate-*r/ 72.0%

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

      4. +-commutative 72.0%

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

      5. fma-udef 72.0%

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

   6. Simplified 72.0%

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

      1. *-commutative 72.0%

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

      2. clear-num 72.1%

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

      3. frac-times 89.2%

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

      4. *-un-lft-identity 89.2%

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

      5. fma-udef 89.2%

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

      6. *-commutative 89.2%

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

      7. associate-*l/ 92.8%

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

      8. *-commutative 92.8%

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

      9. associate-+r+ 92.8%

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

      10. *-commutative 92.8%

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

      11. associate-*l/ 89.2%

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

      12. *-commutative 89.2%

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

      13. fma-def 89.2%

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

   8. Applied egg-rr 89.2%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -4.0000000000000003e-253

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-/l* 98.4%

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

      3. associate-*l/ 98.4%

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

      4. *-commutative 98.4%

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

      5. cancel-sign-sub 98.4%

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

      6. *-commutative 98.4%

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

      7. associate-*l/ 98.4%

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

      8. associate-+r- 98.4%

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

      9. associate-*l/ 98.4%

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

      10. *-commutative 98.4%

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

      11. cancel-sign-sub 98.4%

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

      12. *-commutative 98.4%

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

      13. associate-/r/ 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in x around 0 99.7%

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

   if -4.0000000000000003e-253 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 4.99999999999999969e-279

   1. Initial program 63.3%

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

      1. *-commutative 63.3%

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

      2. associate-*l/ 65.2%

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

      3. *-commutative 65.2%

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

      4. associate-*l/ 82.6%

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

   3. Simplified 82.6%

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

   4. Taylor expanded in z around 0 80.7%

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

      1. associate-/l* 82.6%

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

   6. Simplified 82.6%

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

   if 4.99999999999999969e-279 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 1.99999999999999996e296

   1. Initial program 99.9%

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

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

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

      2. associate-*l/ 0.6%

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

      3. *-commutative 0.6%

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

      4. associate-*l/ 14.8%

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

   3. Simplified 14.8%

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

   4. Taylor expanded in t around 0 59.7%

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

      1. *-commutative 59.7%

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

      2. associate-/r* 63.1%

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

      3. associate-/l* 89.5%

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

      4. unpow2 89.5%

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

   6. Simplified 89.5%

      \[\leadsto \color{blue}{\frac{z}{b} + t \cdot \left(\frac{\frac{x}{y}}{b} - \frac{1 + a}{\frac{y \cdot \left(b \cdot b\right)}{z}}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{y}{t \cdot \frac{\mathsf{fma}\left(y, \frac{b}{t}, a + 1\right)}{z}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -4 \cdot 10^{-253}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(\frac{y \cdot b}{t} + \left(a + 1\right)\right)} + \frac{x}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 5 \cdot 10^{-279}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 2 \cdot 10^{+296}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;\frac{y}{t \cdot \frac{\mathsf{fma}\left(y, \frac{b}{t}, a + 1\right)}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + t \cdot \left(\frac{\frac{x}{y}}{b} + \frac{-1 - a}{\frac{y \cdot \left(b \cdot b\right)}{z}}\right)\\ \end{array} \]

Alternative 2: 89.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t} + \left(a + 1\right)\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{t_1}\\ \mathbf{elif}\;t_2 \leq -4 \cdot 10^{-253}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{-279}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + t \cdot \left(\frac{\frac{x}{y}}{b} + \frac{-1 - a}{\frac{y \cdot \left(b \cdot b\right)}{z}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ (* y b) t) (+ a 1.0))) (t_2 (/ (+ x (/ (* y z) t)) t_1)))
   (if (<= t_2 (- INFINITY))
     (* (/ y t) (/ z t_1))
     (if (<= t_2 -4e-253)
       t_2
       (if (<= t_2 5e-279)
         (/ (+ x (/ y (/ t z))) (+ (+ a 1.0) (* y (/ b t))))
         (if (<= t_2 INFINITY)
           t_2
           (+
            (/ z b)
            (* t (+ (/ (/ x y) b) (/ (- -1.0 a) (/ (* y (* b b)) z)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * b) / t) + (a + 1.0);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (y / t) * (z / t_1);
	} else if (t_2 <= -4e-253) {
		tmp = t_2;
	} else if (t_2 <= 5e-279) {
		tmp = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)));
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = (z / b) + (t * (((x / y) / b) + ((-1.0 - a) / ((y * (b * b)) / z))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * b) / t) + (a + 1.0);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = (y / t) * (z / t_1);
	} else if (t_2 <= -4e-253) {
		tmp = t_2;
	} else if (t_2 <= 5e-279) {
		tmp = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)));
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = (z / b) + (t * (((x / y) / b) + ((-1.0 - a) / ((y * (b * b)) / z))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y * b) / t) + (a + 1.0)
	t_2 = (x + ((y * z) / t)) / t_1
	tmp = 0
	if t_2 <= -math.inf:
		tmp = (y / t) * (z / t_1)
	elif t_2 <= -4e-253:
		tmp = t_2
	elif t_2 <= 5e-279:
		tmp = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)))
	elif t_2 <= math.inf:
		tmp = t_2
	else:
		tmp = (z / b) + (t * (((x / y) / b) + ((-1.0 - a) / ((y * (b * b)) / z))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0))
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(y / t) * Float64(z / t_1));
	elseif (t_2 <= -4e-253)
		tmp = t_2;
	elseif (t_2 <= 5e-279)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	elseif (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(Float64(z / b) + Float64(t * Float64(Float64(Float64(x / y) / b) + Float64(Float64(-1.0 - a) / Float64(Float64(y * Float64(b * b)) / z)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y * b) / t) + (a + 1.0);
	t_2 = (x + ((y * z) / t)) / t_1;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = (y / t) * (z / t_1);
	elseif (t_2 <= -4e-253)
		tmp = t_2;
	elseif (t_2 <= 5e-279)
		tmp = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)));
	elseif (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = (z / b) + (t * (((x / y) / b) + ((-1.0 - a) / ((y * (b * b)) / z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(y / t), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -4e-253], t$95$2, If[LessEqual[t$95$2, 5e-279], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$2, N[(N[(z / b), $MachinePrecision] + N[(t * N[(N[(N[(x / y), $MachinePrecision] / b), $MachinePrecision] + N[(N[(-1.0 - a), $MachinePrecision] / N[(N[(y * N[(b * b), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -inf.0

   1. Initial program 24.1%

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

      1. *-commutative 24.1%

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

      2. associate-*l/ 47.4%

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

      3. *-commutative 47.4%

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

      4. associate-*l/ 47.2%

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

   3. Simplified 47.2%

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

   4. Taylor expanded in x around 0 58.9%

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

      1. times-frac 76.6%

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

      2. associate-+r+ 76.6%

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

      3. associate-*r/ 70.6%

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

      4. +-commutative 70.6%

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

      5. fma-udef 70.6%

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

   6. Simplified 70.6%

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

   7. Taylor expanded in z around inf 76.6%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -4.0000000000000003e-253 or 4.99999999999999969e-279 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 95.8%

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

   if -4.0000000000000003e-253 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 4.99999999999999969e-279

   1. Initial program 63.3%

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

      1. *-commutative 63.3%

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

      2. associate-*l/ 65.2%

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

      3. *-commutative 65.2%

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

      4. associate-*l/ 82.6%

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

   3. Simplified 82.6%

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

   4. Taylor expanded in z around 0 80.7%

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

      1. associate-/l* 82.6%

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

   6. Simplified 82.6%

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

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

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

      2. associate-*l/ 0.6%

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

      3. *-commutative 0.6%

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

      4. associate-*l/ 14.8%

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

   3. Simplified 14.8%

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

   4. Taylor expanded in t around 0 59.7%

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

      1. *-commutative 59.7%

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

      2. associate-/r* 63.1%

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

      3. associate-/l* 89.5%

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

      4. unpow2 89.5%

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

   6. Simplified 89.5%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -4 \cdot 10^{-253}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 5 \cdot 10^{-279}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + t \cdot \left(\frac{\frac{x}{y}}{b} + \frac{-1 - a}{\frac{y \cdot \left(b \cdot b\right)}{z}}\right)\\ \end{array} \]

Alternative 3: 89.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t} + \left(a + 1\right)\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{t_1}\\ \mathbf{elif}\;t_2 \leq -4 \cdot 10^{-253}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{-279}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ (* y b) t) (+ a 1.0))) (t_2 (/ (+ x (/ (* y z) t)) t_1)))
   (if (<= t_2 (- INFINITY))
     (* (/ y t) (/ z t_1))
     (if (<= t_2 -4e-253)
       t_2
       (if (<= t_2 5e-279)
         (/ (+ x (/ y (/ t z))) (+ (+ a 1.0) (* y (/ b t))))
         (if (<= t_2 INFINITY) t_2 (/ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * b) / t) + (a + 1.0);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (y / t) * (z / t_1);
	} else if (t_2 <= -4e-253) {
		tmp = t_2;
	} else if (t_2 <= 5e-279) {
		tmp = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)));
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = 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 = ((y * b) / t) + (a + 1.0);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = (y / t) * (z / t_1);
	} else if (t_2 <= -4e-253) {
		tmp = t_2;
	} else if (t_2 <= 5e-279) {
		tmp = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)));
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y * b) / t) + (a + 1.0)
	t_2 = (x + ((y * z) / t)) / t_1
	tmp = 0
	if t_2 <= -math.inf:
		tmp = (y / t) * (z / t_1)
	elif t_2 <= -4e-253:
		tmp = t_2
	elif t_2 <= 5e-279:
		tmp = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)))
	elif t_2 <= math.inf:
		tmp = t_2
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0))
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(y / t) * Float64(z / t_1));
	elseif (t_2 <= -4e-253)
		tmp = t_2;
	elseif (t_2 <= 5e-279)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	elseif (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y * b) / t) + (a + 1.0);
	t_2 = (x + ((y * z) / t)) / t_1;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = (y / t) * (z / t_1);
	elseif (t_2 <= -4e-253)
		tmp = t_2;
	elseif (t_2 <= 5e-279)
		tmp = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)));
	elseif (t_2 <= Inf)
		tmp = 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[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(y / t), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -4e-253], t$95$2, If[LessEqual[t$95$2, 5e-279], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$2, N[(z / b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -inf.0

   1. Initial program 24.1%

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

      1. *-commutative 24.1%

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

      2. associate-*l/ 47.4%

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

      3. *-commutative 47.4%

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

      4. associate-*l/ 47.2%

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

   3. Simplified 47.2%

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

   4. Taylor expanded in x around 0 58.9%

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

      1. times-frac 76.6%

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

      2. associate-+r+ 76.6%

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

      3. associate-*r/ 70.6%

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

      4. +-commutative 70.6%

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

      5. fma-udef 70.6%

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

   6. Simplified 70.6%

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

   7. Taylor expanded in z around inf 76.6%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -4.0000000000000003e-253 or 4.99999999999999969e-279 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 95.8%

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

   if -4.0000000000000003e-253 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 4.99999999999999969e-279

   1. Initial program 63.3%

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

      1. *-commutative 63.3%

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

      2. associate-*l/ 65.2%

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

      3. *-commutative 65.2%

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

      4. associate-*l/ 82.6%

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

   3. Simplified 82.6%

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

   4. Taylor expanded in z around 0 80.7%

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

      1. associate-/l* 82.6%

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

   6. Simplified 82.6%

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

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

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

      2. associate-*l/ 0.6%

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

      3. *-commutative 0.6%

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

      4. associate-*l/ 14.8%

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

   3. Simplified 14.8%

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

   4. Taylor expanded in t around 0 89.5%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -4 \cdot 10^{-253}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 5 \cdot 10^{-279}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 4: 88.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t} + \left(a + 1\right)\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t_1}\\ \mathbf{if}\;t_2 \leq -4 \cdot 10^{-253}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot t_1} + \frac{x}{t_1}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{-279}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + t \cdot \left(\frac{\frac{x}{y}}{b} + \frac{-1 - a}{\frac{y \cdot \left(b \cdot b\right)}{z}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ (* y b) t) (+ a 1.0))) (t_2 (/ (+ x (/ (* y z) t)) t_1)))
   (if (<= t_2 -4e-253)
     (+ (/ (* y z) (* t t_1)) (/ x t_1))
     (if (<= t_2 5e-279)
       (/ (+ x (/ y (/ t z))) (+ (+ a 1.0) (* y (/ b t))))
       (if (<= t_2 INFINITY)
         t_2
         (+
          (/ z b)
          (* t (+ (/ (/ x y) b) (/ (- -1.0 a) (/ (* y (* b b)) z))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * b) / t) + (a + 1.0);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double tmp;
	if (t_2 <= -4e-253) {
		tmp = ((y * z) / (t * t_1)) + (x / t_1);
	} else if (t_2 <= 5e-279) {
		tmp = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)));
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = (z / b) + (t * (((x / y) / b) + ((-1.0 - a) / ((y * (b * b)) / z))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * b) / t) + (a + 1.0);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double tmp;
	if (t_2 <= -4e-253) {
		tmp = ((y * z) / (t * t_1)) + (x / t_1);
	} else if (t_2 <= 5e-279) {
		tmp = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)));
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = (z / b) + (t * (((x / y) / b) + ((-1.0 - a) / ((y * (b * b)) / z))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y * b) / t) + (a + 1.0)
	t_2 = (x + ((y * z) / t)) / t_1
	tmp = 0
	if t_2 <= -4e-253:
		tmp = ((y * z) / (t * t_1)) + (x / t_1)
	elif t_2 <= 5e-279:
		tmp = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)))
	elif t_2 <= math.inf:
		tmp = t_2
	else:
		tmp = (z / b) + (t * (((x / y) / b) + ((-1.0 - a) / ((y * (b * b)) / z))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0))
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / t_1)
	tmp = 0.0
	if (t_2 <= -4e-253)
		tmp = Float64(Float64(Float64(y * z) / Float64(t * t_1)) + Float64(x / t_1));
	elseif (t_2 <= 5e-279)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	elseif (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(Float64(z / b) + Float64(t * Float64(Float64(Float64(x / y) / b) + Float64(Float64(-1.0 - a) / Float64(Float64(y * Float64(b * b)) / z)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y * b) / t) + (a + 1.0);
	t_2 = (x + ((y * z) / t)) / t_1;
	tmp = 0.0;
	if (t_2 <= -4e-253)
		tmp = ((y * z) / (t * t_1)) + (x / t_1);
	elseif (t_2 <= 5e-279)
		tmp = (x + (y / (t / z))) / ((a + 1.0) + (y * (b / t)));
	elseif (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = (z / b) + (t * (((x / y) / b) + ((-1.0 - a) / ((y * (b * b)) / z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -4e-253], N[(N[(N[(y * z), $MachinePrecision] / N[(t * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e-279], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$2, N[(N[(z / b), $MachinePrecision] + N[(t * N[(N[(N[(x / y), $MachinePrecision] / b), $MachinePrecision] + N[(N[(-1.0 - a), $MachinePrecision] / N[(N[(y * N[(b * b), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -4.0000000000000003e-253

   1. Initial program 86.6%

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

      1. *-commutative 86.6%

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

      2. associate-/l* 89.6%

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

      3. associate-*l/ 86.2%

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

      4. *-commutative 86.2%

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

      5. cancel-sign-sub 86.2%

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

      6. *-commutative 86.2%

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

      7. associate-*l/ 89.6%

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

      8. associate-+r- 89.6%

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

      9. associate-*l/ 86.2%

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

      10. *-commutative 86.2%

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

      11. cancel-sign-sub 86.2%

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

      12. *-commutative 86.2%

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

      13. associate-/r/ 85.5%

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

   3. Simplified 85.5%

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

   4. Taylor expanded in x around 0 92.7%

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

   if -4.0000000000000003e-253 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 4.99999999999999969e-279

   1. Initial program 63.3%

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

      1. *-commutative 63.3%

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

      2. associate-*l/ 65.2%

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

      3. *-commutative 65.2%

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

      4. associate-*l/ 82.6%

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

   3. Simplified 82.6%

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

   4. Taylor expanded in z around 0 80.7%

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

      1. associate-/l* 82.6%

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

   6. Simplified 82.6%

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

   if 4.99999999999999969e-279 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 92.4%

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

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

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

      2. associate-*l/ 0.6%

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

      3. *-commutative 0.6%

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

      4. associate-*l/ 14.8%

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

   3. Simplified 14.8%

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

   4. Taylor expanded in t around 0 59.7%

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

      1. *-commutative 59.7%

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

      2. associate-/r* 63.1%

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

      3. associate-/l* 89.5%

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

      4. unpow2 89.5%

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

   6. Simplified 89.5%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -4 \cdot 10^{-253}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(\frac{y \cdot b}{t} + \left(a + 1\right)\right)} + \frac{x}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 5 \cdot 10^{-279}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq \infty:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + t \cdot \left(\frac{\frac{x}{y}}{b} + \frac{-1 - a}{\frac{y \cdot \left(b \cdot b\right)}{z}}\right)\\ \end{array} \]

Alternative 5: 59.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{if}\;t \leq -1.55 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -90000:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{-139}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-187}:\\ \;\;\;\;\frac{x}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-103}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a (+ 1.0 (/ y (/ t b)))))))
   (if (<= t -1.55e+103)
     t_1
     (if (<= t -90000.0)
       (* (/ y t) (/ z (+ a 1.0)))
       (if (<= t -1.7e-34)
         t_1
         (if (<= t -4.7e-139)
           (/ z b)
           (if (<= t -1.05e-187)
             (/ x (+ (/ (* y b) t) (+ a 1.0)))
             (if (<= t 5.8e-103) (/ z b) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + (1.0 + (y / (t / b))));
	double tmp;
	if (t <= -1.55e+103) {
		tmp = t_1;
	} else if (t <= -90000.0) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (t <= -1.7e-34) {
		tmp = t_1;
	} else if (t <= -4.7e-139) {
		tmp = z / b;
	} else if (t <= -1.05e-187) {
		tmp = x / (((y * b) / t) + (a + 1.0));
	} else if (t <= 5.8e-103) {
		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 = x / (a + (1.0d0 + (y / (t / b))))
    if (t <= (-1.55d+103)) then
        tmp = t_1
    else if (t <= (-90000.0d0)) then
        tmp = (y / t) * (z / (a + 1.0d0))
    else if (t <= (-1.7d-34)) then
        tmp = t_1
    else if (t <= (-4.7d-139)) then
        tmp = z / b
    else if (t <= (-1.05d-187)) then
        tmp = x / (((y * b) / t) + (a + 1.0d0))
    else if (t <= 5.8d-103) 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 = x / (a + (1.0 + (y / (t / b))));
	double tmp;
	if (t <= -1.55e+103) {
		tmp = t_1;
	} else if (t <= -90000.0) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (t <= -1.7e-34) {
		tmp = t_1;
	} else if (t <= -4.7e-139) {
		tmp = z / b;
	} else if (t <= -1.05e-187) {
		tmp = x / (((y * b) / t) + (a + 1.0));
	} else if (t <= 5.8e-103) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + (1.0 + (y / (t / b))))
	tmp = 0
	if t <= -1.55e+103:
		tmp = t_1
	elif t <= -90000.0:
		tmp = (y / t) * (z / (a + 1.0))
	elif t <= -1.7e-34:
		tmp = t_1
	elif t <= -4.7e-139:
		tmp = z / b
	elif t <= -1.05e-187:
		tmp = x / (((y * b) / t) + (a + 1.0))
	elif t <= 5.8e-103:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + Float64(1.0 + Float64(y / Float64(t / b)))))
	tmp = 0.0
	if (t <= -1.55e+103)
		tmp = t_1;
	elseif (t <= -90000.0)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	elseif (t <= -1.7e-34)
		tmp = t_1;
	elseif (t <= -4.7e-139)
		tmp = Float64(z / b);
	elseif (t <= -1.05e-187)
		tmp = Float64(x / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)));
	elseif (t <= 5.8e-103)
		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 = x / (a + (1.0 + (y / (t / b))));
	tmp = 0.0;
	if (t <= -1.55e+103)
		tmp = t_1;
	elseif (t <= -90000.0)
		tmp = (y / t) * (z / (a + 1.0));
	elseif (t <= -1.7e-34)
		tmp = t_1;
	elseif (t <= -4.7e-139)
		tmp = z / b;
	elseif (t <= -1.05e-187)
		tmp = x / (((y * b) / t) + (a + 1.0));
	elseif (t <= 5.8e-103)
		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[(x / N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.55e+103], t$95$1, If[LessEqual[t, -90000.0], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.7e-34], t$95$1, If[LessEqual[t, -4.7e-139], N[(z / b), $MachinePrecision], If[LessEqual[t, -1.05e-187], N[(x / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e-103], N[(z / b), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.5500000000000001e103 or -9e4 < t < -1.7e-34 or 5.7999999999999997e-103 < t

   1. Initial program 83.1%

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

      1. *-commutative 83.1%

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

      2. associate-/l* 85.2%

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

      3. associate-*l/ 93.8%

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

      4. *-commutative 93.8%

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

      5. cancel-sign-sub 93.8%

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

      6. *-commutative 93.8%

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

      7. associate-*l/ 85.2%

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

      8. associate-+r- 85.2%

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

      9. associate-*l/ 93.8%

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

      10. *-commutative 93.8%

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

      11. cancel-sign-sub 93.8%

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

      12. *-commutative 93.8%

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

      13. associate-/r/ 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in x around inf 73.8%

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

   if -1.5500000000000001e103 < t < -9e4

   1. Initial program 72.8%

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

      1. *-commutative 72.8%

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

      2. associate-*l/ 83.1%

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

      3. *-commutative 83.1%

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

      4. associate-*l/ 83.1%

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

   3. Simplified 83.1%

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

   4. Taylor expanded in x around 0 55.5%

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

      1. times-frac 76.8%

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

      2. associate-+r+ 76.8%

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

      3. associate-*r/ 76.8%

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

      4. +-commutative 76.8%

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

      5. fma-udef 76.8%

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

   6. Simplified 76.8%

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

   7. Taylor expanded in y around 0 71.0%

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

   if -1.7e-34 < t < -4.70000000000000027e-139 or -1.04999999999999996e-187 < t < 5.7999999999999997e-103

   1. Initial program 60.0%

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

      1. *-commutative 60.0%

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

      2. associate-*l/ 49.6%

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

      3. *-commutative 49.6%

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

      4. associate-*l/ 44.8%

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

   3. Simplified 44.8%

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

   4. Taylor expanded in t around 0 62.4%

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

   if -4.70000000000000027e-139 < t < -1.04999999999999996e-187

   1. Initial program 84.0%

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

      1. *-commutative 84.0%

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

      2. associate-/l* 76.2%

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

      3. associate-*l/ 75.9%

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

      4. *-commutative 75.9%

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

      5. cancel-sign-sub 75.9%

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

      6. *-commutative 75.9%

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

      7. associate-*l/ 76.2%

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

      8. associate-+r- 76.2%

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

      9. associate-*l/ 75.9%

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

      10. *-commutative 75.9%

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

      11. cancel-sign-sub 75.9%

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

      12. *-commutative 75.9%

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

      13. associate-/r/ 68.1%

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

   3. Simplified 68.1%

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

   4. Taylor expanded in x around inf 60.0%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+103}:\\ \;\;\;\;\frac{x}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;t \leq -90000:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-34}:\\ \;\;\;\;\frac{x}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{-139}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-187}:\\ \;\;\;\;\frac{x}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-103}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \end{array} \]

Alternative 6: 80.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-183} \lor \neg \left(t \leq 2.9 \cdot 10^{-110}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -8e-183) (not (<= t 2.9e-110)))
   (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t))))
   (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -8e-183) || !(t <= 2.9e-110)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} 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 <= (-8d-183)) .or. (.not. (t <= 2.9d-110))) then
        tmp = (x + (y * (z / t))) / ((a + 1.0d0) + (y * (b / t)))
    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 <= -8e-183) || !(t <= 2.9e-110)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -8e-183) or not (t <= 2.9e-110):
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -8e-183) || !(t <= 2.9e-110))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	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 <= -8e-183) || ~((t <= 2.9e-110)))
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -8e-183], N[Not[LessEqual[t, 2.9e-110]], $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[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.00000000000000004e-183 or 2.9000000000000002e-110 < t

   1. Initial program 80.3%

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

      1. *-commutative 80.3%

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

      2. associate-*l/ 81.3%

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

      3. *-commutative 81.3%

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

      4. associate-*l/ 86.8%

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

   3. Simplified 86.8%

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

   if -8.00000000000000004e-183 < t < 2.9000000000000002e-110

   1. Initial program 59.3%

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

      1. *-commutative 59.3%

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

      2. associate-*l/ 47.5%

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

      3. *-commutative 47.5%

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

      4. associate-*l/ 41.3%

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

   3. Simplified 41.3%

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

   4. Taylor expanded in t around 0 64.8%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-183} \lor \neg \left(t \leq 2.9 \cdot 10^{-110}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 7: 80.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-183}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-178}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.2e-183)
   (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t))))
   (if (<= t 1.9e-178)
     (/ z b)
     (/ (+ x (/ z (/ t y))) (+ a (+ 1.0 (/ y (/ t b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.2e-183) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else if (t <= 1.9e-178) {
		tmp = z / b;
	} else {
		tmp = (x + (z / (t / y))) / (a + (1.0 + (y / (t / 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 <= (-4.2d-183)) then
        tmp = (x + (y * (z / t))) / ((a + 1.0d0) + (y * (b / t)))
    else if (t <= 1.9d-178) then
        tmp = z / b
    else
        tmp = (x + (z / (t / y))) / (a + (1.0d0 + (y / (t / 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 <= -4.2e-183) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else if (t <= 1.9e-178) {
		tmp = z / b;
	} else {
		tmp = (x + (z / (t / y))) / (a + (1.0 + (y / (t / b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4.2e-183:
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	elif t <= 1.9e-178:
		tmp = z / b
	else:
		tmp = (x + (z / (t / y))) / (a + (1.0 + (y / (t / b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.2e-183)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	elseif (t <= 1.9e-178)
		tmp = Float64(z / b);
	else
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) / Float64(a + Float64(1.0 + Float64(y / Float64(t / b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4.2e-183)
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	elseif (t <= 1.9e-178)
		tmp = z / b;
	else
		tmp = (x + (z / (t / y))) / (a + (1.0 + (y / (t / b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.2e-183], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e-178], N[(z / b), $MachinePrecision], N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.2000000000000004e-183

   1. Initial program 81.8%

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

      1. *-commutative 81.8%

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

      2. associate-*l/ 83.4%

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

      3. *-commutative 83.4%

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

      4. associate-*l/ 87.1%

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

   3. Simplified 87.1%

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

   if -4.2000000000000004e-183 < t < 1.90000000000000007e-178

   1. Initial program 54.0%

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

      1. *-commutative 54.0%

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

      2. associate-*l/ 42.6%

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

      3. *-commutative 42.6%

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

      4. associate-*l/ 38.5%

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

   3. Simplified 38.5%

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

   4. Taylor expanded in t around 0 68.4%

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

   if 1.90000000000000007e-178 < t

   1. Initial program 78.6%

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

      1. *-commutative 78.6%

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

      2. associate-/l* 81.5%

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

      3. associate-*l/ 87.0%

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

      4. *-commutative 87.0%

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

      5. cancel-sign-sub 87.0%

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

      6. *-commutative 87.0%

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

      7. associate-*l/ 81.5%

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

      8. associate-+r- 81.5%

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

      9. associate-*l/ 87.0%

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

      10. *-commutative 87.0%

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

      11. cancel-sign-sub 87.0%

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

      12. *-commutative 87.0%

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

      13. associate-/r/ 85.3%

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

   3. Simplified 85.3%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-183}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-178}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \end{array} \]

Alternative 8: 60.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{if}\;t \leq -7.8 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -85000:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-37} \lor \neg \left(t \leq 1.5 \cdot 10^{-100}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a (+ 1.0 (/ y (/ t b)))))))
   (if (<= t -7.8e+102)
     t_1
     (if (<= t -85000.0)
       (* (/ y t) (/ z (+ a 1.0)))
       (if (or (<= t -2.9e-37) (not (<= t 1.5e-100))) t_1 (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + (1.0 + (y / (t / b))));
	double tmp;
	if (t <= -7.8e+102) {
		tmp = t_1;
	} else if (t <= -85000.0) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if ((t <= -2.9e-37) || !(t <= 1.5e-100)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x / (a + (1.0d0 + (y / (t / b))))
    if (t <= (-7.8d+102)) then
        tmp = t_1
    else if (t <= (-85000.0d0)) then
        tmp = (y / t) * (z / (a + 1.0d0))
    else if ((t <= (-2.9d-37)) .or. (.not. (t <= 1.5d-100))) then
        tmp = t_1
    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 t_1 = x / (a + (1.0 + (y / (t / b))));
	double tmp;
	if (t <= -7.8e+102) {
		tmp = t_1;
	} else if (t <= -85000.0) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if ((t <= -2.9e-37) || !(t <= 1.5e-100)) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + (1.0 + (y / (t / b))))
	tmp = 0
	if t <= -7.8e+102:
		tmp = t_1
	elif t <= -85000.0:
		tmp = (y / t) * (z / (a + 1.0))
	elif (t <= -2.9e-37) or not (t <= 1.5e-100):
		tmp = t_1
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + Float64(1.0 + Float64(y / Float64(t / b)))))
	tmp = 0.0
	if (t <= -7.8e+102)
		tmp = t_1;
	elseif (t <= -85000.0)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	elseif ((t <= -2.9e-37) || !(t <= 1.5e-100))
		tmp = t_1;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + (1.0 + (y / (t / b))));
	tmp = 0.0;
	if (t <= -7.8e+102)
		tmp = t_1;
	elseif (t <= -85000.0)
		tmp = (y / t) * (z / (a + 1.0));
	elseif ((t <= -2.9e-37) || ~((t <= 1.5e-100)))
		tmp = t_1;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.8e+102], t$95$1, If[LessEqual[t, -85000.0], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -2.9e-37], N[Not[LessEqual[t, 1.5e-100]], $MachinePrecision]], t$95$1, N[(z / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.7999999999999997e102 or -85000 < t < -2.90000000000000005e-37 or 1.5e-100 < t

   1. Initial program 83.1%

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

      1. *-commutative 83.1%

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

      2. associate-/l* 85.2%

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

      3. associate-*l/ 93.8%

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

      4. *-commutative 93.8%

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

      5. cancel-sign-sub 93.8%

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

      6. *-commutative 93.8%

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

      7. associate-*l/ 85.2%

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

      8. associate-+r- 85.2%

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

      9. associate-*l/ 93.8%

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

      10. *-commutative 93.8%

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

      11. cancel-sign-sub 93.8%

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

      12. *-commutative 93.8%

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

      13. associate-/r/ 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in x around inf 73.8%

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

   if -7.7999999999999997e102 < t < -85000

   1. Initial program 72.8%

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

      1. *-commutative 72.8%

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

      2. associate-*l/ 83.1%

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

      3. *-commutative 83.1%

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

      4. associate-*l/ 83.1%

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

   3. Simplified 83.1%

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

   4. Taylor expanded in x around 0 55.5%

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

      1. times-frac 76.8%

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

      2. associate-+r+ 76.8%

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

      3. associate-*r/ 76.8%

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

      4. +-commutative 76.8%

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

      5. fma-udef 76.8%

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

   6. Simplified 76.8%

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

   7. Taylor expanded in y around 0 71.0%

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

   if -2.90000000000000005e-37 < t < 1.5e-100

   1. Initial program 63.1%

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

      1. *-commutative 63.1%

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

      2. associate-*l/ 53.9%

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

      3. *-commutative 53.9%

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

      4. associate-*l/ 48.8%

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

   3. Simplified 48.8%

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

   4. Taylor expanded in t around 0 57.8%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+102}:\\ \;\;\;\;\frac{x}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;t \leq -85000:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-37} \lor \neg \left(t \leq 1.5 \cdot 10^{-100}\right):\\ \;\;\;\;\frac{x}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 9: 65.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-188} \lor \neg \left(t \leq 1.55 \cdot 10^{-94}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.2e-188) (not (<= t 1.55e-94)))
   (/ (+ x (* y (/ z t))) (+ a 1.0))
   (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.2e-188) || !(t <= 1.55e-94)) {
		tmp = (x + (y * (z / t))) / (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 <= (-1.2d-188)) .or. (.not. (t <= 1.55d-94))) then
        tmp = (x + (y * (z / t))) / (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 <= -1.2e-188) || !(t <= 1.55e-94)) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.2e-188) or not (t <= 1.55e-94):
		tmp = (x + (y * (z / t))) / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.2e-188) || !(t <= 1.55e-94))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / 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 <= -1.2e-188) || ~((t <= 1.55e-94)))
		tmp = (x + (y * (z / t))) / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.2e-188], N[Not[LessEqual[t, 1.55e-94]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.2e-188 or 1.5499999999999999e-94 < t

   1. Initial program 80.3%

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

      1. *-commutative 80.3%

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

      2. associate-*l/ 81.3%

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

      3. *-commutative 81.3%

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

      4. associate-*l/ 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in b around 0 73.0%

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

   if -1.2e-188 < t < 1.5499999999999999e-94

   1. Initial program 59.3%

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

      1. *-commutative 59.3%

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

      2. associate-*l/ 47.5%

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

      3. *-commutative 47.5%

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

      4. associate-*l/ 42.8%

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

   3. Simplified 42.8%

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

   4. Taylor expanded in t around 0 64.8%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-188} \lor \neg \left(t \leq 1.55 \cdot 10^{-94}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 10: 56.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -78000:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-14} \lor \neg \left(t \leq 4 \cdot 10^{-88}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -4.5e+29)
     t_1
     (if (<= t -78000.0)
       (* (/ y t) (/ z a))
       (if (or (<= t -4.1e-14) (not (<= t 4e-88))) t_1 (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -4.5e+29) {
		tmp = t_1;
	} else if (t <= -78000.0) {
		tmp = (y / t) * (z / a);
	} else if ((t <= -4.1e-14) || !(t <= 4e-88)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-4.5d+29)) then
        tmp = t_1
    else if (t <= (-78000.0d0)) then
        tmp = (y / t) * (z / a)
    else if ((t <= (-4.1d-14)) .or. (.not. (t <= 4d-88))) then
        tmp = t_1
    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 t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -4.5e+29) {
		tmp = t_1;
	} else if (t <= -78000.0) {
		tmp = (y / t) * (z / a);
	} else if ((t <= -4.1e-14) || !(t <= 4e-88)) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -4.5e+29:
		tmp = t_1
	elif t <= -78000.0:
		tmp = (y / t) * (z / a)
	elif (t <= -4.1e-14) or not (t <= 4e-88):
		tmp = t_1
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -4.5e+29)
		tmp = t_1;
	elseif (t <= -78000.0)
		tmp = Float64(Float64(y / t) * Float64(z / a));
	elseif ((t <= -4.1e-14) || !(t <= 4e-88))
		tmp = t_1;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -4.5e+29)
		tmp = t_1;
	elseif (t <= -78000.0)
		tmp = (y / t) * (z / a);
	elseif ((t <= -4.1e-14) || ~((t <= 4e-88)))
		tmp = t_1;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.5e+29], t$95$1, If[LessEqual[t, -78000.0], N[(N[(y / t), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -4.1e-14], N[Not[LessEqual[t, 4e-88]], $MachinePrecision]], t$95$1, N[(z / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.5000000000000002e29 or -78000 < t < -4.1000000000000002e-14 or 3.99999999999999974e-88 < t

   1. Initial program 81.7%

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

      1. *-commutative 81.7%

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

      2. associate-*l/ 83.1%

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

      3. *-commutative 83.1%

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

      4. associate-*l/ 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in t around inf 63.5%

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

   if -4.5000000000000002e29 < t < -78000

   1. Initial program 81.7%

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

      1. *-commutative 81.7%

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

      2. associate-*l/ 90.2%

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

      3. *-commutative 90.2%

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

      4. associate-*l/ 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in x around 0 71.8%

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

      1. times-frac 89.5%

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

      2. associate-+r+ 89.5%

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

      3. associate-*r/ 89.5%

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

      4. +-commutative 89.5%

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

      5. fma-udef 89.5%

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

   6. Simplified 89.5%

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

   7. Taylor expanded in a around inf 80.9%

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

   if -4.1000000000000002e-14 < t < 3.99999999999999974e-88

   1. Initial program 64.2%

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

      1. *-commutative 64.2%

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

      2. associate-*l/ 55.3%

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

      3. *-commutative 55.3%

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

      4. associate-*l/ 50.3%

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

   3. Simplified 50.3%

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

   4. Taylor expanded in t around 0 56.2%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -78000:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-14} \lor \neg \left(t \leq 4 \cdot 10^{-88}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 11: 56.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -85000:\\ \;\;\;\;\frac{y}{\frac{t \cdot a}{z}}\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-13} \lor \neg \left(t \leq 4 \cdot 10^{-91}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -4.5e+29)
     t_1
     (if (<= t -85000.0)
       (/ y (/ (* t a) z))
       (if (or (<= t -1.15e-13) (not (<= t 4e-91))) t_1 (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -4.5e+29) {
		tmp = t_1;
	} else if (t <= -85000.0) {
		tmp = y / ((t * a) / z);
	} else if ((t <= -1.15e-13) || !(t <= 4e-91)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-4.5d+29)) then
        tmp = t_1
    else if (t <= (-85000.0d0)) then
        tmp = y / ((t * a) / z)
    else if ((t <= (-1.15d-13)) .or. (.not. (t <= 4d-91))) then
        tmp = t_1
    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 t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -4.5e+29) {
		tmp = t_1;
	} else if (t <= -85000.0) {
		tmp = y / ((t * a) / z);
	} else if ((t <= -1.15e-13) || !(t <= 4e-91)) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -4.5e+29:
		tmp = t_1
	elif t <= -85000.0:
		tmp = y / ((t * a) / z)
	elif (t <= -1.15e-13) or not (t <= 4e-91):
		tmp = t_1
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -4.5e+29)
		tmp = t_1;
	elseif (t <= -85000.0)
		tmp = Float64(y / Float64(Float64(t * a) / z));
	elseif ((t <= -1.15e-13) || !(t <= 4e-91))
		tmp = t_1;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -4.5e+29)
		tmp = t_1;
	elseif (t <= -85000.0)
		tmp = y / ((t * a) / z);
	elseif ((t <= -1.15e-13) || ~((t <= 4e-91)))
		tmp = t_1;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.5e+29], t$95$1, If[LessEqual[t, -85000.0], N[(y / N[(N[(t * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -1.15e-13], N[Not[LessEqual[t, 4e-91]], $MachinePrecision]], t$95$1, N[(z / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.5000000000000002e29 or -85000 < t < -1.1499999999999999e-13 or 4.00000000000000009e-91 < t

   1. Initial program 81.7%

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

      1. *-commutative 81.7%

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

      2. associate-*l/ 83.1%

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

      3. *-commutative 83.1%

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

      4. associate-*l/ 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in t around inf 63.5%

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

   if -4.5000000000000002e29 < t < -85000

   1. Initial program 81.7%

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

      1. *-commutative 81.7%

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

      2. associate-*l/ 90.2%

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

      3. *-commutative 90.2%

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

      4. associate-*l/ 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in b around 0 90.2%

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

   5. Taylor expanded in x around 0 71.8%

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

      1. associate-/r* 72.1%

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

      2. *-commutative 72.1%

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

      3. associate-/l* 71.2%

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

   7. Simplified 71.2%

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

   8. Taylor expanded in a around inf 71.8%

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

      1. associate-/l* 81.6%

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

      2. *-commutative 81.6%

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

   10. Simplified 81.6%

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

   if -1.1499999999999999e-13 < t < 4.00000000000000009e-91

   1. Initial program 64.2%

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

      1. *-commutative 64.2%

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

      2. associate-*l/ 55.3%

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

      3. *-commutative 55.3%

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

      4. associate-*l/ 50.3%

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

   3. Simplified 50.3%

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

   4. Taylor expanded in t around 0 56.2%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -85000:\\ \;\;\;\;\frac{y}{\frac{t \cdot a}{z}}\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-13} \lor \neg \left(t \leq 4 \cdot 10^{-91}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 12: 54.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -7.8 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -78000:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-14} \lor \neg \left(t \leq 2.4 \cdot 10^{-88}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -7.8e+102)
     t_1
     (if (<= t -78000.0)
       (* (/ y t) (/ z (+ a 1.0)))
       (if (or (<= t -2.4e-14) (not (<= t 2.4e-88))) t_1 (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -7.8e+102) {
		tmp = t_1;
	} else if (t <= -78000.0) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if ((t <= -2.4e-14) || !(t <= 2.4e-88)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x / (a + 1.0d0)
    if (t <= (-7.8d+102)) then
        tmp = t_1
    else if (t <= (-78000.0d0)) then
        tmp = (y / t) * (z / (a + 1.0d0))
    else if ((t <= (-2.4d-14)) .or. (.not. (t <= 2.4d-88))) then
        tmp = t_1
    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 t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -7.8e+102) {
		tmp = t_1;
	} else if (t <= -78000.0) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if ((t <= -2.4e-14) || !(t <= 2.4e-88)) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -7.8e+102:
		tmp = t_1
	elif t <= -78000.0:
		tmp = (y / t) * (z / (a + 1.0))
	elif (t <= -2.4e-14) or not (t <= 2.4e-88):
		tmp = t_1
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -7.8e+102)
		tmp = t_1;
	elseif (t <= -78000.0)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	elseif ((t <= -2.4e-14) || !(t <= 2.4e-88))
		tmp = t_1;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -7.8e+102)
		tmp = t_1;
	elseif (t <= -78000.0)
		tmp = (y / t) * (z / (a + 1.0));
	elseif ((t <= -2.4e-14) || ~((t <= 2.4e-88)))
		tmp = t_1;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.8e+102], t$95$1, If[LessEqual[t, -78000.0], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -2.4e-14], N[Not[LessEqual[t, 2.4e-88]], $MachinePrecision]], t$95$1, N[(z / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.7999999999999997e102 or -78000 < t < -2.4e-14 or 2.4e-88 < 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. *-commutative 82.8%

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

      2. associate-*l/ 83.6%

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

      3. *-commutative 83.6%

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

      4. associate-*l/ 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in t around inf 65.1%

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

   if -7.7999999999999997e102 < t < -78000

   1. Initial program 72.8%

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

      1. *-commutative 72.8%

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

      2. associate-*l/ 83.1%

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

      3. *-commutative 83.1%

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

      4. associate-*l/ 83.1%

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

   3. Simplified 83.1%

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

   4. Taylor expanded in x around 0 55.5%

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

      1. times-frac 76.8%

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

      2. associate-+r+ 76.8%

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

      3. associate-*r/ 76.8%

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

      4. +-commutative 76.8%

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

      5. fma-udef 76.8%

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

   6. Simplified 76.8%

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

   7. Taylor expanded in y around 0 71.0%

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

   if -2.4e-14 < t < 2.4e-88

   1. Initial program 64.2%

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

      1. *-commutative 64.2%

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

      2. associate-*l/ 55.3%

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

      3. *-commutative 55.3%

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

      4. associate-*l/ 50.3%

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

   3. Simplified 50.3%

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

   4. Taylor expanded in t around 0 56.2%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+102}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -78000:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-14} \lor \neg \left(t \leq 2.4 \cdot 10^{-88}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 13: 56.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ \mathbf{if}\;a \leq -1.4:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{elif}\;a \leq 1:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t))))
   (if (<= a -1.4) (/ (+ x (* y (/ z t))) a) (if (<= a 1.0) t_1 (/ t_1 a)))))

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 (a <= -1.4) {
		tmp = (x + (y * (z / t))) / a;
	} else if (a <= 1.0) {
		tmp = t_1;
	} else {
		tmp = t_1 / a;
	}
	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 (a <= (-1.4d0)) then
        tmp = (x + (y * (z / t))) / a
    else if (a <= 1.0d0) then
        tmp = t_1
    else
        tmp = t_1 / a
    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 (a <= -1.4) {
		tmp = (x + (y * (z / t))) / a;
	} else if (a <= 1.0) {
		tmp = t_1;
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Python

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

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	tmp = 0.0
	if (a <= -1.4)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / a);
	elseif (a <= 1.0)
		tmp = t_1;
	else
		tmp = Float64(t_1 / a);
	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 (a <= -1.4)
		tmp = (x + (y * (z / t))) / a;
	elseif (a <= 1.0)
		tmp = t_1;
	else
		tmp = t_1 / a;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if a < -1.3999999999999999

   1. Initial program 76.2%

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

      1. *-commutative 76.2%

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

      2. associate-*l/ 74.7%

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

      3. *-commutative 74.7%

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

      4. associate-*l/ 77.5%

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

   3. Simplified 77.5%

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

   4. Taylor expanded in a around inf 56.1%

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

   if -1.3999999999999999 < a < 1

   1. Initial program 75.0%

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

      1. *-commutative 75.0%

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

      2. associate-*l/ 74.1%

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

      3. *-commutative 74.1%

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

      4. associate-*l/ 74.8%

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

   3. Simplified 74.8%

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

   4. Taylor expanded in b around 0 60.5%

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

   5. Taylor expanded in a around 0 57.2%

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

   if 1 < a

   1. Initial program 73.8%

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

      1. *-commutative 73.8%

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

      2. associate-*l/ 67.8%

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

      3. *-commutative 67.8%

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

      4. associate-*l/ 73.9%

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

   3. Simplified 73.9%

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

   4. Taylor expanded in a around inf 66.8%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a}\\ \mathbf{elif}\;a \leq 1:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \end{array} \]

Alternative 14: 55.8% accurate, 1.3× speedup

Math

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

FPCore

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

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 (a <= -1.0) {
		tmp = ((z / t) * (y / a)) + (x / a);
	} else if (a <= 1.0) {
		tmp = t_1;
	} else {
		tmp = t_1 / a;
	}
	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 (a <= (-1.0d0)) then
        tmp = ((z / t) * (y / a)) + (x / a)
    else if (a <= 1.0d0) then
        tmp = t_1
    else
        tmp = t_1 / a
    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 (a <= -1.0) {
		tmp = ((z / t) * (y / a)) + (x / a);
	} else if (a <= 1.0) {
		tmp = t_1;
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Python

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

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	tmp = 0.0
	if (a <= -1.0)
		tmp = Float64(Float64(Float64(z / t) * Float64(y / a)) + Float64(x / a));
	elseif (a <= 1.0)
		tmp = t_1;
	else
		tmp = Float64(t_1 / a);
	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 (a <= -1.0)
		tmp = ((z / t) * (y / a)) + (x / a);
	elseif (a <= 1.0)
		tmp = t_1;
	else
		tmp = t_1 / a;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if a < -1

   1. Initial program 76.2%

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

      1. *-commutative 76.2%

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

      2. associate-/l* 76.2%

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

      3. associate-*l/ 78.9%

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

      4. *-commutative 78.9%

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

      5. cancel-sign-sub 78.9%

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

      6. *-commutative 78.9%

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

      7. associate-*l/ 76.2%

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

      8. associate-+r- 76.2%

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

      9. associate-*l/ 78.9%

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

      10. *-commutative 78.9%

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

      11. cancel-sign-sub 78.9%

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

      12. *-commutative 78.9%

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

      13. associate-/r/ 77.5%

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

   3. Simplified 77.5%

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

   4. Taylor expanded in x around 0 79.2%

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

   5. Taylor expanded in a around inf 62.9%

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

      1. times-frac 63.0%

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

   7. Simplified 63.0%

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

   8. Taylor expanded in a around inf 56.1%

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

   if -1 < a < 1

   1. Initial program 75.0%

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

      1. *-commutative 75.0%

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

      2. associate-*l/ 74.1%

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

      3. *-commutative 74.1%

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

      4. associate-*l/ 74.8%

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

   3. Simplified 74.8%

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

   4. Taylor expanded in b around 0 60.5%

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

   5. Taylor expanded in a around 0 57.2%

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

   if 1 < a

   1. Initial program 73.8%

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

      1. *-commutative 73.8%

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

      2. associate-*l/ 67.8%

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

      3. *-commutative 67.8%

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

      4. associate-*l/ 73.9%

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

   3. Simplified 73.9%

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

   4. Taylor expanded in a around inf 66.8%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1:\\ \;\;\;\;\frac{z}{t} \cdot \frac{y}{a} + \frac{x}{a}\\ \mathbf{elif}\;a \leq 1:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \end{array} \]

Alternative 15: 42.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-10}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 0.75:\\ \;\;\;\;x - x \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -6.5e+44)
   (/ x a)
   (if (<= a -1.8e-10) (/ z b) (if (<= a 0.75) (- x (* x a)) (/ x a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -6.5e+44) {
		tmp = x / a;
	} else if (a <= -1.8e-10) {
		tmp = z / b;
	} else if (a <= 0.75) {
		tmp = x - (x * a);
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-6.5d+44)) then
        tmp = x / a
    else if (a <= (-1.8d-10)) then
        tmp = z / b
    else if (a <= 0.75d0) then
        tmp = x - (x * a)
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -6.5e+44) {
		tmp = x / a;
	} else if (a <= -1.8e-10) {
		tmp = z / b;
	} else if (a <= 0.75) {
		tmp = x - (x * a);
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -6.5e+44:
		tmp = x / a
	elif a <= -1.8e-10:
		tmp = z / b
	elif a <= 0.75:
		tmp = x - (x * a)
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -6.5e+44)
		tmp = Float64(x / a);
	elseif (a <= -1.8e-10)
		tmp = Float64(z / b);
	elseif (a <= 0.75)
		tmp = Float64(x - Float64(x * a));
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -6.5e+44)
		tmp = x / a;
	elseif (a <= -1.8e-10)
		tmp = z / b;
	elseif (a <= 0.75)
		tmp = x - (x * a);
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -6.5e+44], N[(x / a), $MachinePrecision], If[LessEqual[a, -1.8e-10], N[(z / b), $MachinePrecision], If[LessEqual[a, 0.75], N[(x - N[(x * a), $MachinePrecision]), $MachinePrecision], N[(x / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.50000000000000018e44 or 0.75 < a

   1. Initial program 74.3%

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

      1. *-commutative 74.3%

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

      2. associate-/l* 74.3%

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

      3. associate-*l/ 79.0%

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

      4. *-commutative 79.0%

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

      5. cancel-sign-sub 79.0%

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

      6. *-commutative 79.0%

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

      7. associate-*l/ 74.3%

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

      8. associate-+r- 74.3%

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

      9. associate-*l/ 79.0%

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

      10. *-commutative 79.0%

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

      11. cancel-sign-sub 79.0%

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

      12. *-commutative 79.0%

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

      13. associate-/r/ 78.3%

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

   3. Simplified 78.3%

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

   4. Taylor expanded in x around inf 50.7%

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

   5. Taylor expanded in a around inf 47.4%

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

   if -6.50000000000000018e44 < a < -1.8e-10

   1. Initial program 74.2%

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

      1. *-commutative 74.2%

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

      2. associate-*l/ 74.2%

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

      3. *-commutative 74.2%

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

      4. associate-*l/ 80.5%

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

   3. Simplified 80.5%

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

   4. Taylor expanded in t around 0 50.2%

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

   if -1.8e-10 < a < 0.75

   1. Initial program 75.8%

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

      1. *-commutative 75.8%

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

      2. associate-*l/ 74.9%

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

      3. *-commutative 74.9%

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

      4. associate-*l/ 74.8%

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

   3. Simplified 74.8%

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

   4. Taylor expanded in t around inf 46.1%

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

   5. Taylor expanded in a around 0 46.1%

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

      1. +-commutative 46.1%

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

      2. mul-1-neg 46.1%

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

      3. unsub-neg 46.1%

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

   7. Simplified 46.1%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-10}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 0.75:\\ \;\;\;\;x - x \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 16: 56.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.75 \cdot 10^{-14} \lor \neg \left(t \leq 3.5 \cdot 10^{-94}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.75e-14) (not (<= t 3.5e-94))) (/ 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 <= -2.75e-14) || !(t <= 3.5e-94)) {
		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 <= (-2.75d-14)) .or. (.not. (t <= 3.5d-94))) 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 <= -2.75e-14) || !(t <= 3.5e-94)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.75e-14) or not (t <= 3.5e-94):
		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 <= -2.75e-14) || !(t <= 3.5e-94))
		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 <= -2.75e-14) || ~((t <= 3.5e-94)))
		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, -2.75e-14], N[Not[LessEqual[t, 3.5e-94]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.74999999999999996e-14 or 3.49999999999999998e-94 < t

   1. Initial program 81.7%

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

      1. *-commutative 81.7%

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

      2. associate-*l/ 83.5%

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

      3. *-commutative 83.5%

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

      4. associate-*l/ 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in t around inf 61.5%

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

   if -2.74999999999999996e-14 < t < 3.49999999999999998e-94

   1. Initial program 64.2%

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

      1. *-commutative 64.2%

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

      2. associate-*l/ 55.3%

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

      3. *-commutative 55.3%

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

      4. associate-*l/ 50.3%

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

   3. Simplified 50.3%

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

   4. Taylor expanded in t around 0 56.2%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.75 \cdot 10^{-14} \lor \neg \left(t \leq 3.5 \cdot 10^{-94}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 17: 43.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+46}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{+49}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -6.5e+46) (/ x a) (if (<= a 7.8e+49) (/ z b) (/ x a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -6.5e+46) {
		tmp = x / a;
	} else if (a <= 7.8e+49) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-6.5d+46)) then
        tmp = x / a
    else if (a <= 7.8d+49) then
        tmp = z / b
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -6.5e+46) {
		tmp = x / a;
	} else if (a <= 7.8e+49) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -6.5e+46:
		tmp = x / a
	elif a <= 7.8e+49:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -6.5e+46)
		tmp = Float64(x / a);
	elseif (a <= 7.8e+49)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -6.5e+46)
		tmp = x / a;
	elseif (a <= 7.8e+49)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -6.5e+46], N[(x / a), $MachinePrecision], If[LessEqual[a, 7.8e+49], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -6.50000000000000008e46 or 7.8000000000000002e49 < a

   1. Initial program 74.2%

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

      1. *-commutative 74.2%

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

      2. associate-/l* 74.2%

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

      3. associate-*l/ 78.3%

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

      4. *-commutative 78.3%

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

      5. cancel-sign-sub 78.3%

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

      6. *-commutative 78.3%

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

      7. associate-*l/ 74.2%

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

      8. associate-+r- 74.2%

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

      9. associate-*l/ 78.3%

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

      10. *-commutative 78.3%

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

      11. cancel-sign-sub 78.3%

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

      12. *-commutative 78.3%

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

      13. associate-/r/ 77.6%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in x around inf 52.4%

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

   5. Taylor expanded in a around inf 48.9%

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

   if -6.50000000000000008e46 < a < 7.8000000000000002e49

   1. Initial program 75.6%

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

      1. *-commutative 75.6%

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

      2. associate-*l/ 74.9%

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

      3. *-commutative 74.9%

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

      4. associate-*l/ 76.1%

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

   3. Simplified 76.1%

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

   4. Taylor expanded in t around 0 37.3%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+46}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{+49}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 18: 25.9% 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 75.0%

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

   1. *-commutative 75.0%

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

   2. associate-/l* 75.2%

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

   3. associate-*l/ 78.7%

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

   4. *-commutative 78.7%

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

   5. cancel-sign-sub 78.7%

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

   6. *-commutative 78.7%

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

   7. associate-*l/ 75.2%

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

   8. associate-+r- 75.2%

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

   9. associate-*l/ 78.7%

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

   10. *-commutative 78.7%

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

   11. cancel-sign-sub 78.7%

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

   12. *-commutative 78.7%

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

   13. associate-/r/ 76.3%

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

3. Simplified 76.3%

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

4. Taylor expanded in x around inf 52.9%

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

5. Taylor expanded in a around inf 25.1%

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

6. Final simplification 25.1%

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

Developer target: 79.8% accurate, 0.7× 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 2023268 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (if (< t -1.3659085366310088e-271) (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b))))) (if (< t 3.036967103737246e-130) (/ z b) (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b)))))))

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