Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B

Percentage Accurate: 76.9% → 89.9%

Time: 12.4s

Alternatives: 17

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 76.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.9% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \sqrt[3]{a - t}\\ t_2 := y \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+77}:\\ \;\;\;\;\mathsf{fma}\left(-1, \mathsf{fma}\left(a, \frac{y}{t}, \frac{a}{t} \cdot \left(y \cdot \frac{a - z}{t}\right)\right), x\right) + t\_2\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+93}:\\ \;\;\;\;\left(y + x\right) + \frac{y}{t\_1} \cdot \frac{t - z}{{t\_1}^{2}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t\_2 - a \cdot \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (cbrt (- a t))) (t_2 (* y (/ z t))))
   (if (<= t -2.9e+77)
     (+ (fma -1.0 (fma a (/ y t) (* (/ a t) (* y (/ (- a z) t)))) x) t_2)
     (if (<= t 5.5e+93)
       (+ (+ y x) (* (/ y t_1) (/ (- t z) (pow t_1 2.0))))
       (+ x (- t_2 (* a (/ y t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = cbrt((a - t));
	double t_2 = y * (z / t);
	double tmp;
	if (t <= -2.9e+77) {
		tmp = fma(-1.0, fma(a, (y / t), ((a / t) * (y * ((a - z) / t)))), x) + t_2;
	} else if (t <= 5.5e+93) {
		tmp = (y + x) + ((y / t_1) * ((t - z) / pow(t_1, 2.0)));
	} else {
		tmp = x + (t_2 - (a * (y / t)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = cbrt(Float64(a - t))
	t_2 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (t <= -2.9e+77)
		tmp = Float64(fma(-1.0, fma(a, Float64(y / t), Float64(Float64(a / t) * Float64(y * Float64(Float64(a - z) / t)))), x) + t_2);
	elseif (t <= 5.5e+93)
		tmp = Float64(Float64(y + x) + Float64(Float64(y / t_1) * Float64(Float64(t - z) / (t_1 ^ 2.0))));
	else
		tmp = Float64(x + Float64(t_2 - Float64(a * Float64(y / t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[Power[N[(a - t), $MachinePrecision], 1/3], $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.9e+77], N[(N[(-1.0 * N[(a * N[(y / t), $MachinePrecision] + N[(N[(a / t), $MachinePrecision] * N[(y * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[t, 5.5e+93], N[(N[(y + x), $MachinePrecision] + N[(N[(y / t$95$1), $MachinePrecision] * N[(N[(t - z), $MachinePrecision] / N[Power[t$95$1, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$2 - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.9000000000000002e77

   1. Initial program 47.2%

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

      1. add-cube-cbrt 47.4%

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

      2. times-frac 62.2%

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

      3. pow2 62.2%

         \[\leadsto \left(x + y\right) - \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 62.2%

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y}{\sqrt[3]{a - t}}} \]
   5. Step-by-step derivation

      1. clear-num 62.2%

         \[\leadsto \left(x + y\right) - \color{blue}{\frac{1}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t}}} \cdot \frac{y}{\sqrt[3]{a - t}} \]

      2. frac-times 62.2%

         \[\leadsto \left(x + y\right) - \color{blue}{\frac{1 \cdot y}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t} \cdot \sqrt[3]{a - t}}} \]

      3. *-un-lft-identity 62.2%

         \[\leadsto \left(x + y\right) - \frac{\color{blue}{y}}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t} \cdot \sqrt[3]{a - t}} \]

   6. Applied egg-rr 62.2%

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{y}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t} \cdot \sqrt[3]{a - t}}} \]
   7. Step-by-step derivation

      1. associate-*l/ 62.2%

         \[\leadsto \left(x + y\right) - \frac{y}{\color{blue}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2} \cdot \sqrt[3]{a - t}}{z - t}}} \]

      2. unpow2 62.2%

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

      3. rem-3cbrt-lft 61.9%

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

   8. Simplified 61.9%

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

   9. Taylor expanded in t around inf 63.9%

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

   11. Simplified 87.8%

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

   if -2.9000000000000002e77 < t < 5.5000000000000003e93

   1. Initial program 93.3%

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

      1. add-cube-cbrt 93.0%

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

      2. times-frac 94.6%

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

      3. pow2 94.6%

         \[\leadsto \left(x + y\right) - \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 94.6%

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y}{\sqrt[3]{a - t}}} \]

   if 5.5000000000000003e93 < t

   1. Initial program 63.1%

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

      1. sub-neg 63.1%

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

      2. +-commutative 63.1%

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

      3. distribute-frac-neg 63.1%

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

      4. distribute-rgt-neg-out 63.1%

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

      5. associate-/l* 67.2%

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

      6. fma-define 67.5%

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

      7. distribute-frac-neg 67.5%

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

      8. distribute-neg-frac2 67.5%

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

      9. sub-neg 67.5%

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

      10. distribute-neg-in 67.5%

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

      11. remove-double-neg 67.5%

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

      12. +-commutative 67.5%

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

      13. sub-neg 67.5%

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

   3. Simplified 67.5%

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

   5. Taylor expanded in t around inf 80.3%

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

      1. associate--l+ 80.3%

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

      2. associate-+r+ 86.8%

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

      3. distribute-rgt1-in 86.8%

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

      4. metadata-eval 86.8%

         \[\leadsto x + \left(\left(\color{blue}{0} \cdot y + \frac{y \cdot z}{t}\right) - \frac{a \cdot y}{t}\right) \]

      5. mul0-lft 86.8%

         \[\leadsto x + \left(\left(\color{blue}{0} + \frac{y \cdot z}{t}\right) - \frac{a \cdot y}{t}\right) \]

      6. associate-/l* 88.6%

         \[\leadsto x + \left(\left(0 + \color{blue}{y \cdot \frac{z}{t}}\right) - \frac{a \cdot y}{t}\right) \]

      7. associate-/l* 98.1%

         \[\leadsto x + \left(\left(0 + y \cdot \frac{z}{t}\right) - \color{blue}{a \cdot \frac{y}{t}}\right) \]

   7. Simplified 98.1%

      \[\leadsto \color{blue}{x + \left(\left(0 + y \cdot \frac{z}{t}\right) - a \cdot \frac{y}{t}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+77}:\\ \;\;\;\;\mathsf{fma}\left(-1, \mathsf{fma}\left(a, \frac{y}{t}, \frac{a}{t} \cdot \left(y \cdot \frac{a - z}{t}\right)\right), x\right) + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+93}:\\ \;\;\;\;\left(y + x\right) + \frac{y}{\sqrt[3]{a - t}} \cdot \frac{t - z}{{\left(\sqrt[3]{a - t}\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{z}{t} - a \cdot \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -6.9 \cdot 10^{+77}:\\ \;\;\;\;\mathsf{fma}\left(-1, \mathsf{fma}\left(a, \frac{y}{t}, \frac{a}{t} \cdot \left(y \cdot \frac{a - z}{t}\right)\right), x\right) + t\_1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+89}:\\ \;\;\;\;\left(y + x\right) - \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t\_1 - a \cdot \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z t))))
   (if (<= t -6.9e+77)
     (+ (fma -1.0 (fma a (/ y t) (* (/ a t) (* y (/ (- a z) t)))) x) t_1)
     (if (<= t 9e+89)
       (- (+ y x) (/ y (/ (- a t) (- z t))))
       (+ x (- t_1 (* a (/ y t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / t);
	double tmp;
	if (t <= -6.9e+77) {
		tmp = fma(-1.0, fma(a, (y / t), ((a / t) * (y * ((a - z) / t)))), x) + t_1;
	} else if (t <= 9e+89) {
		tmp = (y + x) - (y / ((a - t) / (z - t)));
	} else {
		tmp = x + (t_1 - (a * (y / t)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (t <= -6.9e+77)
		tmp = Float64(fma(-1.0, fma(a, Float64(y / t), Float64(Float64(a / t) * Float64(y * Float64(Float64(a - z) / t)))), x) + t_1);
	elseif (t <= 9e+89)
		tmp = Float64(Float64(y + x) - Float64(y / Float64(Float64(a - t) / Float64(z - t))));
	else
		tmp = Float64(x + Float64(t_1 - Float64(a * Float64(y / t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.9e+77], N[(N[(-1.0 * N[(a * N[(y / t), $MachinePrecision] + N[(N[(a / t), $MachinePrecision] * N[(y * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, 9e+89], N[(N[(y + x), $MachinePrecision] - N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$1 - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.89999999999999959e77

   1. Initial program 47.2%

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

      1. add-cube-cbrt 47.4%

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

      2. times-frac 62.2%

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

      3. pow2 62.2%

         \[\leadsto \left(x + y\right) - \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 62.2%

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y}{\sqrt[3]{a - t}}} \]
   5. Step-by-step derivation

      1. clear-num 62.2%

         \[\leadsto \left(x + y\right) - \color{blue}{\frac{1}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t}}} \cdot \frac{y}{\sqrt[3]{a - t}} \]

      2. frac-times 62.2%

         \[\leadsto \left(x + y\right) - \color{blue}{\frac{1 \cdot y}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t} \cdot \sqrt[3]{a - t}}} \]

      3. *-un-lft-identity 62.2%

         \[\leadsto \left(x + y\right) - \frac{\color{blue}{y}}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t} \cdot \sqrt[3]{a - t}} \]

   6. Applied egg-rr 62.2%

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{y}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t} \cdot \sqrt[3]{a - t}}} \]
   7. Step-by-step derivation

      1. associate-*l/ 62.2%

         \[\leadsto \left(x + y\right) - \frac{y}{\color{blue}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2} \cdot \sqrt[3]{a - t}}{z - t}}} \]

      2. unpow2 62.2%

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

      3. rem-3cbrt-lft 61.9%

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

   8. Simplified 61.9%

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

   9. Taylor expanded in t around inf 63.9%

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

   11. Simplified 87.8%

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

   if -6.89999999999999959e77 < t < 9e89

   1. Initial program 93.3%

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

      1. add-cube-cbrt 93.0%

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

      2. times-frac 94.6%

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

      3. pow2 94.6%

         \[\leadsto \left(x + y\right) - \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 94.6%

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y}{\sqrt[3]{a - t}}} \]
   5. Step-by-step derivation

      1. clear-num 94.6%

         \[\leadsto \left(x + y\right) - \color{blue}{\frac{1}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t}}} \cdot \frac{y}{\sqrt[3]{a - t}} \]

      2. frac-times 93.6%

         \[\leadsto \left(x + y\right) - \color{blue}{\frac{1 \cdot y}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t} \cdot \sqrt[3]{a - t}}} \]

      3. *-un-lft-identity 93.6%

         \[\leadsto \left(x + y\right) - \frac{\color{blue}{y}}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t} \cdot \sqrt[3]{a - t}} \]

   6. Applied egg-rr 93.6%

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{y}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t} \cdot \sqrt[3]{a - t}}} \]
   7. Step-by-step derivation

      1. associate-*l/ 93.6%

         \[\leadsto \left(x + y\right) - \frac{y}{\color{blue}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2} \cdot \sqrt[3]{a - t}}{z - t}}} \]

      2. unpow2 93.6%

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

      3. rem-3cbrt-lft 93.9%

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

   8. Simplified 93.9%

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

   if 9e89 < t

   1. Initial program 63.1%

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

      1. sub-neg 63.1%

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

      2. +-commutative 63.1%

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

      3. distribute-frac-neg 63.1%

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

      4. distribute-rgt-neg-out 63.1%

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

      5. associate-/l* 67.2%

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

      6. fma-define 67.5%

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

      7. distribute-frac-neg 67.5%

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

      8. distribute-neg-frac2 67.5%

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

      9. sub-neg 67.5%

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

      10. distribute-neg-in 67.5%

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

      11. remove-double-neg 67.5%

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

      12. +-commutative 67.5%

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

      13. sub-neg 67.5%

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

   3. Simplified 67.5%

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

   5. Taylor expanded in t around inf 80.3%

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

      1. associate--l+ 80.3%

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

      2. associate-+r+ 86.8%

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

      3. distribute-rgt1-in 86.8%

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

      4. metadata-eval 86.8%

         \[\leadsto x + \left(\left(\color{blue}{0} \cdot y + \frac{y \cdot z}{t}\right) - \frac{a \cdot y}{t}\right) \]

      5. mul0-lft 86.8%

         \[\leadsto x + \left(\left(\color{blue}{0} + \frac{y \cdot z}{t}\right) - \frac{a \cdot y}{t}\right) \]

      6. associate-/l* 88.6%

         \[\leadsto x + \left(\left(0 + \color{blue}{y \cdot \frac{z}{t}}\right) - \frac{a \cdot y}{t}\right) \]

      7. associate-/l* 98.1%

         \[\leadsto x + \left(\left(0 + y \cdot \frac{z}{t}\right) - \color{blue}{a \cdot \frac{y}{t}}\right) \]

   7. Simplified 98.1%

      \[\leadsto \color{blue}{x + \left(\left(0 + y \cdot \frac{z}{t}\right) - a \cdot \frac{y}{t}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.9 \cdot 10^{+77}:\\ \;\;\;\;\mathsf{fma}\left(-1, \mathsf{fma}\left(a, \frac{y}{t}, \frac{a}{t} \cdot \left(y \cdot \frac{a - z}{t}\right)\right), x\right) + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+89}:\\ \;\;\;\;\left(y + x\right) - \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{z}{t} - a \cdot \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 63.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t - a}\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -850000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.55 \lor \neg \left(z \leq 3.2 \cdot 10^{+183} \lor \neg \left(z \leq 2 \cdot 10^{+231}\right) \land z \leq 1.3 \cdot 10^{+252}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- t a)))))
   (if (<= z -3.4e+118)
     t_1
     (if (<= z -850000000.0)
       x
       (if (or (<= z -3.55)
               (not
                (or (<= z 3.2e+183)
                    (and (not (<= z 2e+231)) (<= z 1.3e+252)))))
         t_1
         (+ y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (t - a));
	double tmp;
	if (z <= -3.4e+118) {
		tmp = t_1;
	} else if (z <= -850000000.0) {
		tmp = x;
	} else if ((z <= -3.55) || !((z <= 3.2e+183) || (!(z <= 2e+231) && (z <= 1.3e+252)))) {
		tmp = t_1;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z / (t - a))
    if (z <= (-3.4d+118)) then
        tmp = t_1
    else if (z <= (-850000000.0d0)) then
        tmp = x
    else if ((z <= (-3.55d0)) .or. (.not. (z <= 3.2d+183) .or. (.not. (z <= 2d+231)) .and. (z <= 1.3d+252))) then
        tmp = t_1
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (t - a));
	double tmp;
	if (z <= -3.4e+118) {
		tmp = t_1;
	} else if (z <= -850000000.0) {
		tmp = x;
	} else if ((z <= -3.55) || !((z <= 3.2e+183) || (!(z <= 2e+231) && (z <= 1.3e+252)))) {
		tmp = t_1;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / (t - a))
	tmp = 0
	if z <= -3.4e+118:
		tmp = t_1
	elif z <= -850000000.0:
		tmp = x
	elif (z <= -3.55) or not ((z <= 3.2e+183) or (not (z <= 2e+231) and (z <= 1.3e+252))):
		tmp = t_1
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(t - a)))
	tmp = 0.0
	if (z <= -3.4e+118)
		tmp = t_1;
	elseif (z <= -850000000.0)
		tmp = x;
	elseif ((z <= -3.55) || !((z <= 3.2e+183) || (!(z <= 2e+231) && (z <= 1.3e+252))))
		tmp = t_1;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / (t - a));
	tmp = 0.0;
	if (z <= -3.4e+118)
		tmp = t_1;
	elseif (z <= -850000000.0)
		tmp = x;
	elseif ((z <= -3.55) || ~(((z <= 3.2e+183) || (~((z <= 2e+231)) && (z <= 1.3e+252)))))
		tmp = t_1;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e+118], t$95$1, If[LessEqual[z, -850000000.0], x, If[Or[LessEqual[z, -3.55], N[Not[Or[LessEqual[z, 3.2e+183], And[N[Not[LessEqual[z, 2e+231]], $MachinePrecision], LessEqual[z, 1.3e+252]]]], $MachinePrecision]], t$95$1, N[(y + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.39999999999999986e118 or -8.5e8 < z < -3.5499999999999998 or 3.2000000000000002e183 < z < 2.0000000000000001e231 or 1.30000000000000009e252 < z

   1. Initial program 82.8%

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

      1. sub-neg 82.8%

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

      2. +-commutative 82.8%

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

      3. distribute-frac-neg 82.8%

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

      4. distribute-rgt-neg-out 82.8%

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

      5. associate-/l* 88.7%

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

      6. fma-define 88.9%

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

      7. distribute-frac-neg 88.9%

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

      8. distribute-neg-frac2 88.9%

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

      9. sub-neg 88.9%

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

      10. distribute-neg-in 88.9%

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

      11. remove-double-neg 88.9%

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

      12. +-commutative 88.9%

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

      13. sub-neg 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in z around inf 70.6%

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

      1. associate-/l* 76.1%

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

   7. Simplified 76.1%

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

   if -3.39999999999999986e118 < z < -8.5e8

   1. Initial program 76.9%

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

   3. Taylor expanded in x around inf 60.3%

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

   if -3.5499999999999998 < z < 3.2000000000000002e183 or 2.0000000000000001e231 < z < 1.30000000000000009e252

   1. Initial program 77.7%

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

   3. Taylor expanded in a around inf 69.2%

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

      1. +-commutative 69.2%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 69.2%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+118}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;z \leq -850000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.55 \lor \neg \left(z \leq 3.2 \cdot 10^{+183} \lor \neg \left(z \leq 2 \cdot 10^{+231}\right) \land z \leq 1.3 \cdot 10^{+252}\right):\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+130}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{+70}:\\ \;\;\;\;y - y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-14} \lor \neg \left(a \leq 2.2 \cdot 10^{+53}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.5e+130)
   (+ y x)
   (if (<= a -2.65e+70)
     (- y (* y (/ z a)))
     (if (or (<= a -8e-14) (not (<= a 2.2e+53)))
       (+ y x)
       (- x (/ (* y (- a z)) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.5e+130) {
		tmp = y + x;
	} else if (a <= -2.65e+70) {
		tmp = y - (y * (z / a));
	} else if ((a <= -8e-14) || !(a <= 2.2e+53)) {
		tmp = y + x;
	} else {
		tmp = x - ((y * (a - z)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-6.5d+130)) then
        tmp = y + x
    else if (a <= (-2.65d+70)) then
        tmp = y - (y * (z / a))
    else if ((a <= (-8d-14)) .or. (.not. (a <= 2.2d+53))) then
        tmp = y + x
    else
        tmp = x - ((y * (a - z)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.5e+130) {
		tmp = y + x;
	} else if (a <= -2.65e+70) {
		tmp = y - (y * (z / a));
	} else if ((a <= -8e-14) || !(a <= 2.2e+53)) {
		tmp = y + x;
	} else {
		tmp = x - ((y * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.5e+130:
		tmp = y + x
	elif a <= -2.65e+70:
		tmp = y - (y * (z / a))
	elif (a <= -8e-14) or not (a <= 2.2e+53):
		tmp = y + x
	else:
		tmp = x - ((y * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.5e+130)
		tmp = Float64(y + x);
	elseif (a <= -2.65e+70)
		tmp = Float64(y - Float64(y * Float64(z / a)));
	elseif ((a <= -8e-14) || !(a <= 2.2e+53))
		tmp = Float64(y + x);
	else
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.5e+130)
		tmp = y + x;
	elseif (a <= -2.65e+70)
		tmp = y - (y * (z / a));
	elseif ((a <= -8e-14) || ~((a <= 2.2e+53)))
		tmp = y + x;
	else
		tmp = x - ((y * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.5e+130], N[(y + x), $MachinePrecision], If[LessEqual[a, -2.65e+70], N[(y - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -8e-14], N[Not[LessEqual[a, 2.2e+53]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.5e130 or -2.65e70 < a < -7.99999999999999999e-14 or 2.19999999999999999e53 < a

   1. Initial program 82.0%

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

   3. Taylor expanded in a around inf 78.2%

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

      1. +-commutative 78.2%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 78.2%

      \[\leadsto \color{blue}{y + x} \]

   if -6.5e130 < a < -2.65e70

   1. Initial program 75.4%

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

      1. add-cube-cbrt 75.2%

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

      2. times-frac 81.8%

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

      3. pow2 81.8%

         \[\leadsto \left(x + y\right) - \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 81.8%

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y}{\sqrt[3]{a - t}}} \]
   5. Step-by-step derivation

      1. clear-num 81.8%

         \[\leadsto \left(x + y\right) - \color{blue}{\frac{1}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t}}} \cdot \frac{y}{\sqrt[3]{a - t}} \]

      2. frac-times 81.0%

         \[\leadsto \left(x + y\right) - \color{blue}{\frac{1 \cdot y}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t} \cdot \sqrt[3]{a - t}}} \]

      3. *-un-lft-identity 81.0%

         \[\leadsto \left(x + y\right) - \frac{\color{blue}{y}}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t} \cdot \sqrt[3]{a - t}} \]

   6. Applied egg-rr 81.0%

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{y}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t} \cdot \sqrt[3]{a - t}}} \]
   7. Step-by-step derivation

      1. associate-*l/ 81.8%

         \[\leadsto \left(x + y\right) - \frac{y}{\color{blue}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2} \cdot \sqrt[3]{a - t}}{z - t}}} \]

      2. unpow2 81.8%

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

      3. rem-3cbrt-lft 81.5%

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

   8. Simplified 81.5%

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

   9. Taylor expanded in t around 0 82.3%

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

   10. Taylor expanded in x around 0 58.4%

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

       1. associate-*r/ 64.3%

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

   12. Simplified 64.3%

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

   if -7.99999999999999999e-14 < a < 2.19999999999999999e53

   1. Initial program 77.4%

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

   3. Taylor expanded in t around inf 79.9%

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

      1. associate--l+ 79.9%

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

      2. distribute-lft-out-- 79.9%

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

      3. div-sub 80.0%

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

      4. mul-1-neg 80.0%

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

      5. unsub-neg 80.0%

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

      6. *-commutative 80.0%

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

      7. distribute-lft-out-- 80.0%

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

   5. Simplified 80.0%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+130}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{+70}:\\ \;\;\;\;y - y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-14} \lor \neg \left(a \leq 2.2 \cdot 10^{+53}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+130}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{+70}:\\ \;\;\;\;y - y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-14} \lor \neg \left(a \leq 5.5 \cdot 10^{+52}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.5e+130)
   (+ y x)
   (if (<= a -2.7e+70)
     (- y (* y (/ z a)))
     (if (or (<= a -8e-14) (not (<= a 5.5e+52)))
       (+ y x)
       (+ x (/ (* y z) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.5e+130) {
		tmp = y + x;
	} else if (a <= -2.7e+70) {
		tmp = y - (y * (z / a));
	} else if ((a <= -8e-14) || !(a <= 5.5e+52)) {
		tmp = y + x;
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-6.5d+130)) then
        tmp = y + x
    else if (a <= (-2.7d+70)) then
        tmp = y - (y * (z / a))
    else if ((a <= (-8d-14)) .or. (.not. (a <= 5.5d+52))) then
        tmp = y + x
    else
        tmp = x + ((y * z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.5e+130) {
		tmp = y + x;
	} else if (a <= -2.7e+70) {
		tmp = y - (y * (z / a));
	} else if ((a <= -8e-14) || !(a <= 5.5e+52)) {
		tmp = y + x;
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.5e+130:
		tmp = y + x
	elif a <= -2.7e+70:
		tmp = y - (y * (z / a))
	elif (a <= -8e-14) or not (a <= 5.5e+52):
		tmp = y + x
	else:
		tmp = x + ((y * z) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.5e+130)
		tmp = Float64(y + x);
	elseif (a <= -2.7e+70)
		tmp = Float64(y - Float64(y * Float64(z / a)));
	elseif ((a <= -8e-14) || !(a <= 5.5e+52))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(Float64(y * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.5e+130)
		tmp = y + x;
	elseif (a <= -2.7e+70)
		tmp = y - (y * (z / a));
	elseif ((a <= -8e-14) || ~((a <= 5.5e+52)))
		tmp = y + x;
	else
		tmp = x + ((y * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.5e+130], N[(y + x), $MachinePrecision], If[LessEqual[a, -2.7e+70], N[(y - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -8e-14], N[Not[LessEqual[a, 5.5e+52]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.5e130 or -2.7e70 < a < -7.99999999999999999e-14 or 5.49999999999999996e52 < a

   1. Initial program 82.0%

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

   3. Taylor expanded in a around inf 78.2%

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

      1. +-commutative 78.2%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 78.2%

      \[\leadsto \color{blue}{y + x} \]

   if -6.5e130 < a < -2.7e70

   1. Initial program 75.4%

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

      1. add-cube-cbrt 75.2%

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

      2. times-frac 81.8%

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

      3. pow2 81.8%

         \[\leadsto \left(x + y\right) - \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 81.8%

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y}{\sqrt[3]{a - t}}} \]
   5. Step-by-step derivation

      1. clear-num 81.8%

         \[\leadsto \left(x + y\right) - \color{blue}{\frac{1}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t}}} \cdot \frac{y}{\sqrt[3]{a - t}} \]

      2. frac-times 81.0%

         \[\leadsto \left(x + y\right) - \color{blue}{\frac{1 \cdot y}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t} \cdot \sqrt[3]{a - t}}} \]

      3. *-un-lft-identity 81.0%

         \[\leadsto \left(x + y\right) - \frac{\color{blue}{y}}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t} \cdot \sqrt[3]{a - t}} \]

   6. Applied egg-rr 81.0%

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{y}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t} \cdot \sqrt[3]{a - t}}} \]
   7. Step-by-step derivation

      1. associate-*l/ 81.8%

         \[\leadsto \left(x + y\right) - \frac{y}{\color{blue}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2} \cdot \sqrt[3]{a - t}}{z - t}}} \]

      2. unpow2 81.8%

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

      3. rem-3cbrt-lft 81.5%

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

   8. Simplified 81.5%

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

   9. Taylor expanded in t around 0 82.3%

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

   10. Taylor expanded in x around 0 58.4%

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

       1. associate-*r/ 64.3%

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

   12. Simplified 64.3%

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

   if -7.99999999999999999e-14 < a < 5.49999999999999996e52

   1. Initial program 77.4%

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

      1. sub-neg 77.4%

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

      2. +-commutative 77.4%

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

      3. distribute-frac-neg 77.4%

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

      4. distribute-rgt-neg-out 77.4%

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

      5. associate-/l* 78.2%

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

      6. fma-define 78.4%

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

      7. distribute-frac-neg 78.4%

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

      8. distribute-neg-frac2 78.4%

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

      9. sub-neg 78.4%

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

      10. distribute-neg-in 78.4%

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

      11. remove-double-neg 78.4%

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

      12. +-commutative 78.4%

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

      13. sub-neg 78.4%

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

   3. Simplified 78.4%

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

   5. Taylor expanded in t around inf 72.7%

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

      1. associate--l+ 72.7%

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

      2. associate-+r+ 79.9%

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

      3. distribute-rgt1-in 79.9%

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

      4. metadata-eval 79.9%

         \[\leadsto x + \left(\left(\color{blue}{0} \cdot y + \frac{y \cdot z}{t}\right) - \frac{a \cdot y}{t}\right) \]

      5. mul0-lft 79.9%

         \[\leadsto x + \left(\left(\color{blue}{0} + \frac{y \cdot z}{t}\right) - \frac{a \cdot y}{t}\right) \]

      6. associate-/l* 78.5%

         \[\leadsto x + \left(\left(0 + \color{blue}{y \cdot \frac{z}{t}}\right) - \frac{a \cdot y}{t}\right) \]

      7. associate-/l* 77.2%

         \[\leadsto x + \left(\left(0 + y \cdot \frac{z}{t}\right) - \color{blue}{a \cdot \frac{y}{t}}\right) \]

   7. Simplified 77.2%

      \[\leadsto \color{blue}{x + \left(\left(0 + y \cdot \frac{z}{t}\right) - a \cdot \frac{y}{t}\right)} \]

   8. Taylor expanded in a around 0 76.0%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+130}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{+70}:\\ \;\;\;\;y - y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-14} \lor \neg \left(a \leq 5.5 \cdot 10^{+52}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+217}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+185} \lor \neg \left(z \leq 6 \cdot 10^{+229}\right) \land z \leq 7.8 \cdot 10^{+251}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.9e+217)
   (/ (* y z) t)
   (if (or (<= z 3.5e+185) (and (not (<= z 6e+229)) (<= z 7.8e+251)))
     (+ y x)
     (* y (/ z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.9e+217) {
		tmp = (y * z) / t;
	} else if ((z <= 3.5e+185) || (!(z <= 6e+229) && (z <= 7.8e+251))) {
		tmp = y + x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.9d+217)) then
        tmp = (y * z) / t
    else if ((z <= 3.5d+185) .or. (.not. (z <= 6d+229)) .and. (z <= 7.8d+251)) then
        tmp = y + x
    else
        tmp = y * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.9e+217) {
		tmp = (y * z) / t;
	} else if ((z <= 3.5e+185) || (!(z <= 6e+229) && (z <= 7.8e+251))) {
		tmp = y + x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.9e+217:
		tmp = (y * z) / t
	elif (z <= 3.5e+185) or (not (z <= 6e+229) and (z <= 7.8e+251)):
		tmp = y + x
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.9e+217)
		tmp = Float64(Float64(y * z) / t);
	elseif ((z <= 3.5e+185) || (!(z <= 6e+229) && (z <= 7.8e+251)))
		tmp = Float64(y + x);
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.9e+217)
		tmp = (y * z) / t;
	elseif ((z <= 3.5e+185) || (~((z <= 6e+229)) && (z <= 7.8e+251)))
		tmp = y + x;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.9e+217], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[Or[LessEqual[z, 3.5e+185], And[N[Not[LessEqual[z, 6e+229]], $MachinePrecision], LessEqual[z, 7.8e+251]]], N[(y + x), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.90000000000000001e217

   1. Initial program 95.0%

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

      1. sub-neg 95.0%

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

      2. +-commutative 95.0%

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

      3. distribute-frac-neg 95.0%

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

      4. distribute-rgt-neg-out 95.0%

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

      5. associate-/l* 90.3%

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

      6. fma-define 90.3%

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

      7. distribute-frac-neg 90.3%

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

      8. distribute-neg-frac2 90.3%

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

      9. sub-neg 90.3%

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

      10. distribute-neg-in 90.3%

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

      11. remove-double-neg 90.3%

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

      12. +-commutative 90.3%

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

      13. sub-neg 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in z around inf 85.0%

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

   6. Taylor expanded in t around inf 69.4%

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

   if -1.90000000000000001e217 < z < 3.50000000000000023e185 or 5.99999999999999995e229 < z < 7.79999999999999951e251

   1. Initial program 77.3%

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

   3. Taylor expanded in a around inf 63.7%

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

      1. +-commutative 63.7%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 63.7%

      \[\leadsto \color{blue}{y + x} \]

   if 3.50000000000000023e185 < z < 5.99999999999999995e229 or 7.79999999999999951e251 < z

   1. Initial program 80.8%

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

      1. sub-neg 80.8%

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

      2. +-commutative 80.8%

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

      3. distribute-frac-neg 80.8%

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

      4. distribute-rgt-neg-out 80.8%

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

      5. associate-/l* 89.6%

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

      6. fma-define 89.6%

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

      7. distribute-frac-neg 89.6%

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

      8. distribute-neg-frac2 89.6%

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

      9. sub-neg 89.6%

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

      10. distribute-neg-in 89.6%

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

      11. remove-double-neg 89.6%

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

      12. +-commutative 89.6%

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

      13. sub-neg 89.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in z around inf 77.3%

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

   6. Taylor expanded in t around inf 49.7%

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

      1. associate-*r/ 53.0%

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

   8. Simplified 53.0%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+217}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+185} \lor \neg \left(z \leq 6 \cdot 10^{+229}\right) \land z \leq 7.8 \cdot 10^{+251}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 90.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+78} \lor \neg \left(t \leq 2.5 \cdot 10^{+94}\right):\\ \;\;\;\;x + \left(y \cdot \frac{z}{t} - a \cdot \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \frac{y}{\frac{a - t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.1e+78) (not (<= t 2.5e+94)))
   (+ x (- (* y (/ z t)) (* a (/ y t))))
   (- (+ y x) (/ y (/ (- a t) (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.1e+78) || !(t <= 2.5e+94)) {
		tmp = x + ((y * (z / t)) - (a * (y / t)));
	} else {
		tmp = (y + x) - (y / ((a - t) / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.1d+78)) .or. (.not. (t <= 2.5d+94))) then
        tmp = x + ((y * (z / t)) - (a * (y / t)))
    else
        tmp = (y + x) - (y / ((a - t) / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.1e+78) || !(t <= 2.5e+94)) {
		tmp = x + ((y * (z / t)) - (a * (y / t)));
	} else {
		tmp = (y + x) - (y / ((a - t) / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.1e+78) or not (t <= 2.5e+94):
		tmp = x + ((y * (z / t)) - (a * (y / t)))
	else:
		tmp = (y + x) - (y / ((a - t) / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.1e+78) || !(t <= 2.5e+94))
		tmp = Float64(x + Float64(Float64(y * Float64(z / t)) - Float64(a * Float64(y / t))));
	else
		tmp = Float64(Float64(y + x) - Float64(y / Float64(Float64(a - t) / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.1e+78) || ~((t <= 2.5e+94)))
		tmp = x + ((y * (z / t)) - (a * (y / t)));
	else
		tmp = (y + x) - (y / ((a - t) / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.1e+78], N[Not[LessEqual[t, 2.5e+94]], $MachinePrecision]], N[(x + N[(N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision] - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y + x), $MachinePrecision] - N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.10000000000000007e78 or 2.50000000000000005e94 < t

   1. Initial program 55.4%

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

      1. sub-neg 55.4%

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

      2. +-commutative 55.4%

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

      3. distribute-frac-neg 55.4%

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

      4. distribute-rgt-neg-out 55.4%

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

      5. associate-/l* 63.7%

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

      6. fma-define 63.9%

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

      7. distribute-frac-neg 63.9%

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

      8. distribute-neg-frac2 63.9%

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

      9. sub-neg 63.9%

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

      10. distribute-neg-in 63.9%

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

      11. remove-double-neg 63.9%

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

      12. +-commutative 63.9%

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

      13. sub-neg 63.9%

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

   3. Simplified 63.9%

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

   5. Taylor expanded in t around inf 73.0%

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

      1. associate--l+ 73.0%

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

      2. associate-+r+ 80.3%

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

      3. distribute-rgt1-in 80.3%

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

      4. metadata-eval 80.3%

         \[\leadsto x + \left(\left(\color{blue}{0} \cdot y + \frac{y \cdot z}{t}\right) - \frac{a \cdot y}{t}\right) \]

      5. mul0-lft 80.3%

         \[\leadsto x + \left(\left(\color{blue}{0} + \frac{y \cdot z}{t}\right) - \frac{a \cdot y}{t}\right) \]

      6. associate-/l* 84.8%

         \[\leadsto x + \left(\left(0 + \color{blue}{y \cdot \frac{z}{t}}\right) - \frac{a \cdot y}{t}\right) \]

      7. associate-/l* 92.9%

         \[\leadsto x + \left(\left(0 + y \cdot \frac{z}{t}\right) - \color{blue}{a \cdot \frac{y}{t}}\right) \]

   7. Simplified 92.9%

      \[\leadsto \color{blue}{x + \left(\left(0 + y \cdot \frac{z}{t}\right) - a \cdot \frac{y}{t}\right)} \]

   if -1.10000000000000007e78 < t < 2.50000000000000005e94

   1. Initial program 93.3%

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

      1. add-cube-cbrt 93.0%

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

      2. times-frac 94.6%

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

      3. pow2 94.6%

         \[\leadsto \left(x + y\right) - \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 94.6%

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y}{\sqrt[3]{a - t}}} \]
   5. Step-by-step derivation

      1. clear-num 94.6%

         \[\leadsto \left(x + y\right) - \color{blue}{\frac{1}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t}}} \cdot \frac{y}{\sqrt[3]{a - t}} \]

      2. frac-times 93.6%

         \[\leadsto \left(x + y\right) - \color{blue}{\frac{1 \cdot y}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t} \cdot \sqrt[3]{a - t}}} \]

      3. *-un-lft-identity 93.6%

         \[\leadsto \left(x + y\right) - \frac{\color{blue}{y}}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t} \cdot \sqrt[3]{a - t}} \]

   6. Applied egg-rr 93.6%

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{y}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t} \cdot \sqrt[3]{a - t}}} \]
   7. Step-by-step derivation

      1. associate-*l/ 93.6%

         \[\leadsto \left(x + y\right) - \frac{y}{\color{blue}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2} \cdot \sqrt[3]{a - t}}{z - t}}} \]

      2. unpow2 93.6%

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

      3. rem-3cbrt-lft 93.9%

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

   8. Simplified 93.9%

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+78} \lor \neg \left(t \leq 2.5 \cdot 10^{+94}\right):\\ \;\;\;\;x + \left(y \cdot \frac{z}{t} - a \cdot \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \frac{y}{\frac{a - t}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+77}:\\ \;\;\;\;y \cdot \left(\left(\frac{z}{t} + \frac{x}{y}\right) - \frac{a}{t}\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+129}:\\ \;\;\;\;\left(y + x\right) - \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9.2e+77)
   (* y (- (+ (/ z t) (/ x y)) (/ a t)))
   (if (<= t 3.2e+129)
     (- (+ y x) (* (- z t) (/ y (- a t))))
     (- x (* a (/ y t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.2e+77) {
		tmp = y * (((z / t) + (x / y)) - (a / t));
	} else if (t <= 3.2e+129) {
		tmp = (y + x) - ((z - t) * (y / (a - t)));
	} else {
		tmp = x - (a * (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-9.2d+77)) then
        tmp = y * (((z / t) + (x / y)) - (a / t))
    else if (t <= 3.2d+129) then
        tmp = (y + x) - ((z - t) * (y / (a - t)))
    else
        tmp = x - (a * (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.2e+77) {
		tmp = y * (((z / t) + (x / y)) - (a / t));
	} else if (t <= 3.2e+129) {
		tmp = (y + x) - ((z - t) * (y / (a - t)));
	} else {
		tmp = x - (a * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9.2e+77:
		tmp = y * (((z / t) + (x / y)) - (a / t))
	elif t <= 3.2e+129:
		tmp = (y + x) - ((z - t) * (y / (a - t)))
	else:
		tmp = x - (a * (y / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9.2e+77)
		tmp = Float64(y * Float64(Float64(Float64(z / t) + Float64(x / y)) - Float64(a / t)));
	elseif (t <= 3.2e+129)
		tmp = Float64(Float64(y + x) - Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x - Float64(a * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9.2e+77)
		tmp = y * (((z / t) + (x / y)) - (a / t));
	elseif (t <= 3.2e+129)
		tmp = (y + x) - ((z - t) * (y / (a - t)));
	else
		tmp = x - (a * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9.2e+77], N[(y * N[(N[(N[(z / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision] - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e+129], N[(N[(y + x), $MachinePrecision] - N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.19999999999999979e77

   1. Initial program 47.2%

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

   3. Taylor expanded in t around inf 73.4%

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

      1. associate--l+ 73.4%

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

      2. distribute-lft-out-- 73.4%

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

      3. div-sub 73.4%

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

      4. mul-1-neg 73.4%

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

      5. unsub-neg 73.4%

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

      6. *-commutative 73.4%

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

      7. distribute-lft-out-- 73.4%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in y around inf 79.8%

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

   if -9.19999999999999979e77 < t < 3.2000000000000002e129

   1. Initial program 90.9%

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

      1. associate-/l* 92.0%

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

      2. *-commutative 92.0%

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

   4. Applied egg-rr 92.0%

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

   if 3.2000000000000002e129 < t

   1. Initial program 64.2%

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

   3. Taylor expanded in t around inf 89.9%

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

      1. associate--l+ 89.9%

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

      2. distribute-lft-out-- 89.9%

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

      3. div-sub 89.9%

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

      4. mul-1-neg 89.9%

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

      5. unsub-neg 89.9%

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

      6. *-commutative 89.9%

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

      7. distribute-lft-out-- 89.9%

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

   5. Simplified 89.9%

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

   6. Taylor expanded in a around inf 84.1%

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

      1. associate-/l* 94.1%

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

   8. Simplified 94.1%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+77}:\\ \;\;\;\;y \cdot \left(\left(\frac{z}{t} + \frac{x}{y}\right) - \frac{a}{t}\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+129}:\\ \;\;\;\;\left(y + x\right) - \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+223}:\\ \;\;\;\;y \cdot \left(\left(\frac{z}{t} + \frac{x}{y}\right) - \frac{a}{t}\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+129}:\\ \;\;\;\;\left(y + x\right) - \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.4e+223)
   (* y (- (+ (/ z t) (/ x y)) (/ a t)))
   (if (<= t 4.2e+129)
     (- (+ y x) (/ y (/ (- a t) (- z t))))
     (- x (* a (/ y t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.4e+223) {
		tmp = y * (((z / t) + (x / y)) - (a / t));
	} else if (t <= 4.2e+129) {
		tmp = (y + x) - (y / ((a - t) / (z - t)));
	} else {
		tmp = x - (a * (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-4.4d+223)) then
        tmp = y * (((z / t) + (x / y)) - (a / t))
    else if (t <= 4.2d+129) then
        tmp = (y + x) - (y / ((a - t) / (z - t)))
    else
        tmp = x - (a * (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.4e+223) {
		tmp = y * (((z / t) + (x / y)) - (a / t));
	} else if (t <= 4.2e+129) {
		tmp = (y + x) - (y / ((a - t) / (z - t)));
	} else {
		tmp = x - (a * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.4e+223:
		tmp = y * (((z / t) + (x / y)) - (a / t))
	elif t <= 4.2e+129:
		tmp = (y + x) - (y / ((a - t) / (z - t)))
	else:
		tmp = x - (a * (y / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.4e+223)
		tmp = Float64(y * Float64(Float64(Float64(z / t) + Float64(x / y)) - Float64(a / t)));
	elseif (t <= 4.2e+129)
		tmp = Float64(Float64(y + x) - Float64(y / Float64(Float64(a - t) / Float64(z - t))));
	else
		tmp = Float64(x - Float64(a * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.4e+223)
		tmp = y * (((z / t) + (x / y)) - (a / t));
	elseif (t <= 4.2e+129)
		tmp = (y + x) - (y / ((a - t) / (z - t)));
	else
		tmp = x - (a * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.4e+223], N[(y * N[(N[(N[(z / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision] - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e+129], N[(N[(y + x), $MachinePrecision] - N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.3999999999999999e223

   1. Initial program 29.6%

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

   3. Taylor expanded in t around inf 70.9%

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

      1. associate--l+ 70.9%

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

      2. distribute-lft-out-- 70.9%

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

      3. div-sub 70.9%

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

      4. mul-1-neg 70.9%

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

      5. unsub-neg 70.9%

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

      6. *-commutative 70.9%

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

      7. distribute-lft-out-- 70.9%

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

   5. Simplified 70.9%

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

   6. Taylor expanded in y around inf 84.1%

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

   if -4.3999999999999999e223 < t < 4.19999999999999993e129

   1. Initial program 87.6%

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

      1. add-cube-cbrt 87.4%

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

      2. times-frac 90.8%

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

      3. pow2 90.8%

         \[\leadsto \left(x + y\right) - \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 90.8%

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y}{\sqrt[3]{a - t}}} \]
   5. Step-by-step derivation

      1. clear-num 90.7%

         \[\leadsto \left(x + y\right) - \color{blue}{\frac{1}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t}}} \cdot \frac{y}{\sqrt[3]{a - t}} \]

      2. frac-times 89.9%

         \[\leadsto \left(x + y\right) - \color{blue}{\frac{1 \cdot y}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t} \cdot \sqrt[3]{a - t}}} \]

      3. *-un-lft-identity 89.9%

         \[\leadsto \left(x + y\right) - \frac{\color{blue}{y}}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t} \cdot \sqrt[3]{a - t}} \]

   6. Applied egg-rr 89.9%

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{y}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t} \cdot \sqrt[3]{a - t}}} \]
   7. Step-by-step derivation

      1. associate-*l/ 89.9%

         \[\leadsto \left(x + y\right) - \frac{y}{\color{blue}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2} \cdot \sqrt[3]{a - t}}{z - t}}} \]

      2. unpow2 89.9%

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

      3. rem-3cbrt-lft 90.1%

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

   8. Simplified 90.1%

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

   if 4.19999999999999993e129 < t

   1. Initial program 64.2%

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

   3. Taylor expanded in t around inf 89.9%

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

      1. associate--l+ 89.9%

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

      2. distribute-lft-out-- 89.9%

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

      3. div-sub 89.9%

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

      4. mul-1-neg 89.9%

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

      5. unsub-neg 89.9%

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

      6. *-commutative 89.9%

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

      7. distribute-lft-out-- 89.9%

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

   5. Simplified 89.9%

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

   6. Taylor expanded in a around inf 84.1%

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

      1. associate-/l* 94.1%

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

   8. Simplified 94.1%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+223}:\\ \;\;\;\;y \cdot \left(\left(\frac{z}{t} + \frac{x}{y}\right) - \frac{a}{t}\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+129}:\\ \;\;\;\;\left(y + x\right) - \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 85.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+78}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{+125}:\\ \;\;\;\;\left(y + x\right) + y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1e+78)
   (+ x (* y (/ z t)))
   (if (<= t 5.1e+125) (+ (+ y x) (* y (/ z (- t a)))) (- x (* a (/ y t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1e+78) {
		tmp = x + (y * (z / t));
	} else if (t <= 5.1e+125) {
		tmp = (y + x) + (y * (z / (t - a)));
	} else {
		tmp = x - (a * (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1d+78)) then
        tmp = x + (y * (z / t))
    else if (t <= 5.1d+125) then
        tmp = (y + x) + (y * (z / (t - a)))
    else
        tmp = x - (a * (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1e+78) {
		tmp = x + (y * (z / t));
	} else if (t <= 5.1e+125) {
		tmp = (y + x) + (y * (z / (t - a)));
	} else {
		tmp = x - (a * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1e+78:
		tmp = x + (y * (z / t))
	elif t <= 5.1e+125:
		tmp = (y + x) + (y * (z / (t - a)))
	else:
		tmp = x - (a * (y / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1e+78)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	elseif (t <= 5.1e+125)
		tmp = Float64(Float64(y + x) + Float64(y * Float64(z / Float64(t - a))));
	else
		tmp = Float64(x - Float64(a * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1e+78)
		tmp = x + (y * (z / t));
	elseif (t <= 5.1e+125)
		tmp = (y + x) + (y * (z / (t - a)));
	else
		tmp = x - (a * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1e+78], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.1e+125], N[(N[(y + x), $MachinePrecision] + N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.00000000000000001e78

   1. Initial program 47.2%

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

   3. Taylor expanded in t around inf 73.4%

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

      1. associate--l+ 73.4%

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

      2. distribute-lft-out-- 73.4%

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

      3. div-sub 73.4%

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

      4. mul-1-neg 73.4%

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

      5. unsub-neg 73.4%

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

      6. *-commutative 73.4%

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

      7. distribute-lft-out-- 73.4%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in a around 0 65.1%

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

      1. mul-1-neg 65.1%

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

      2. distribute-frac-neg2 65.1%

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

      3. associate-/l* 75.3%

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

   8. Simplified 75.3%

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

   if -1.00000000000000001e78 < t < 5.0999999999999998e125

   1. Initial program 91.4%

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

   3. Taylor expanded in z around inf 91.2%

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

      1. associate-/l* 91.8%

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

   5. Simplified 91.8%

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

   if 5.0999999999999998e125 < t

   1. Initial program 63.6%

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

   3. Taylor expanded in t around inf 90.4%

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

      1. associate--l+ 90.4%

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

      2. distribute-lft-out-- 90.4%

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

      3. div-sub 90.4%

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

      4. mul-1-neg 90.4%

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

      5. unsub-neg 90.4%

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

      6. *-commutative 90.4%

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

      7. distribute-lft-out-- 90.4%

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

   5. Simplified 90.4%

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

   6. Taylor expanded in a around inf 82.4%

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

      1. associate-/l* 91.9%

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

   8. Simplified 91.9%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+78}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{+125}:\\ \;\;\;\;\left(y + x\right) + y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 84.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+222}:\\ \;\;\;\;y \cdot \left(\left(\frac{z}{t} + \frac{x}{y}\right) - \frac{a}{t}\right)\\ \mathbf{elif}\;t \leq 3.35 \cdot 10^{+125}:\\ \;\;\;\;\left(y + x\right) + y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.8e+222)
   (* y (- (+ (/ z t) (/ x y)) (/ a t)))
   (if (<= t 3.35e+125) (+ (+ y x) (* y (/ z (- t a)))) (- x (* a (/ y t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.8e+222) {
		tmp = y * (((z / t) + (x / y)) - (a / t));
	} else if (t <= 3.35e+125) {
		tmp = (y + x) + (y * (z / (t - a)));
	} else {
		tmp = x - (a * (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-4.8d+222)) then
        tmp = y * (((z / t) + (x / y)) - (a / t))
    else if (t <= 3.35d+125) then
        tmp = (y + x) + (y * (z / (t - a)))
    else
        tmp = x - (a * (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.8e+222) {
		tmp = y * (((z / t) + (x / y)) - (a / t));
	} else if (t <= 3.35e+125) {
		tmp = (y + x) + (y * (z / (t - a)));
	} else {
		tmp = x - (a * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.8e+222:
		tmp = y * (((z / t) + (x / y)) - (a / t))
	elif t <= 3.35e+125:
		tmp = (y + x) + (y * (z / (t - a)))
	else:
		tmp = x - (a * (y / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.8e+222)
		tmp = Float64(y * Float64(Float64(Float64(z / t) + Float64(x / y)) - Float64(a / t)));
	elseif (t <= 3.35e+125)
		tmp = Float64(Float64(y + x) + Float64(y * Float64(z / Float64(t - a))));
	else
		tmp = Float64(x - Float64(a * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.8e+222)
		tmp = y * (((z / t) + (x / y)) - (a / t));
	elseif (t <= 3.35e+125)
		tmp = (y + x) + (y * (z / (t - a)));
	else
		tmp = x - (a * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.8e+222], N[(y * N[(N[(N[(z / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision] - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.35e+125], N[(N[(y + x), $MachinePrecision] + N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.8000000000000002e222

   1. Initial program 29.6%

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

   3. Taylor expanded in t around inf 70.9%

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

      1. associate--l+ 70.9%

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

      2. distribute-lft-out-- 70.9%

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

      3. div-sub 70.9%

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

      4. mul-1-neg 70.9%

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

      5. unsub-neg 70.9%

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

      6. *-commutative 70.9%

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

      7. distribute-lft-out-- 70.9%

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

   5. Simplified 70.9%

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

   6. Taylor expanded in y around inf 84.1%

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

   if -4.8000000000000002e222 < t < 3.3500000000000002e125

   1. Initial program 88.0%

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

   3. Taylor expanded in z around inf 87.8%

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

      1. associate-/l* 89.9%

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

   5. Simplified 89.9%

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

   if 3.3500000000000002e125 < t

   1. Initial program 63.6%

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

   3. Taylor expanded in t around inf 90.4%

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

      1. associate--l+ 90.4%

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

      2. distribute-lft-out-- 90.4%

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

      3. div-sub 90.4%

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

      4. mul-1-neg 90.4%

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

      5. unsub-neg 90.4%

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

      6. *-commutative 90.4%

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

      7. distribute-lft-out-- 90.4%

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

   5. Simplified 90.4%

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

   6. Taylor expanded in a around inf 82.4%

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

      1. associate-/l* 91.9%

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

   8. Simplified 91.9%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+222}:\\ \;\;\;\;y \cdot \left(\left(\frac{z}{t} + \frac{x}{y}\right) - \frac{a}{t}\right)\\ \mathbf{elif}\;t \leq 3.35 \cdot 10^{+125}:\\ \;\;\;\;\left(y + x\right) + y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 81.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.7 \cdot 10^{-33} \lor \neg \left(a \leq 1820000000\right):\\ \;\;\;\;\left(y + x\right) - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.7e-33) (not (<= a 1820000000.0)))
   (- (+ y x) (/ y (/ a z)))
   (- x (/ (* y (- a z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.7e-33) || !(a <= 1820000000.0)) {
		tmp = (y + x) - (y / (a / z));
	} else {
		tmp = x - ((y * (a - z)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-5.7d-33)) .or. (.not. (a <= 1820000000.0d0))) then
        tmp = (y + x) - (y / (a / z))
    else
        tmp = x - ((y * (a - z)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.7e-33) || !(a <= 1820000000.0)) {
		tmp = (y + x) - (y / (a / z));
	} else {
		tmp = x - ((y * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5.7e-33) or not (a <= 1820000000.0):
		tmp = (y + x) - (y / (a / z))
	else:
		tmp = x - ((y * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5.7e-33) || !(a <= 1820000000.0))
		tmp = Float64(Float64(y + x) - Float64(y / Float64(a / z)));
	else
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -5.7e-33) || ~((a <= 1820000000.0)))
		tmp = (y + x) - (y / (a / z));
	else
		tmp = x - ((y * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5.7e-33], N[Not[LessEqual[a, 1820000000.0]], $MachinePrecision]], N[(N[(y + x), $MachinePrecision] - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.70000000000000025e-33 or 1.82e9 < a

   1. Initial program 80.2%

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

      1. add-cube-cbrt 80.1%

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

      2. times-frac 88.6%

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

      3. pow2 88.6%

         \[\leadsto \left(x + y\right) - \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 88.6%

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y}{\sqrt[3]{a - t}}} \]
   5. Step-by-step derivation

      1. clear-num 88.6%

         \[\leadsto \left(x + y\right) - \color{blue}{\frac{1}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t}}} \cdot \frac{y}{\sqrt[3]{a - t}} \]

      2. frac-times 88.6%

         \[\leadsto \left(x + y\right) - \color{blue}{\frac{1 \cdot y}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t} \cdot \sqrt[3]{a - t}}} \]

      3. *-un-lft-identity 88.6%

         \[\leadsto \left(x + y\right) - \frac{\color{blue}{y}}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t} \cdot \sqrt[3]{a - t}} \]

   6. Applied egg-rr 88.6%

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{y}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t} \cdot \sqrt[3]{a - t}}} \]
   7. Step-by-step derivation

      1. associate-*l/ 88.7%

         \[\leadsto \left(x + y\right) - \frac{y}{\color{blue}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2} \cdot \sqrt[3]{a - t}}{z - t}}} \]

      2. unpow2 88.7%

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

      3. rem-3cbrt-lft 88.7%

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

   8. Simplified 88.7%

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

   9. Taylor expanded in t around 0 83.8%

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

   if -5.70000000000000025e-33 < a < 1.82e9

   1. Initial program 77.7%

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

   3. Taylor expanded in t around inf 83.5%

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

      1. associate--l+ 83.5%

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

      2. distribute-lft-out-- 83.5%

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

      3. div-sub 83.5%

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

      4. mul-1-neg 83.5%

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

      5. unsub-neg 83.5%

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

      6. *-commutative 83.5%

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

      7. distribute-lft-out-- 83.5%

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

   5. Simplified 83.5%

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(a - z\right)}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.7 \cdot 10^{-33} \lor \neg \left(a \leq 1820000000\right):\\ \;\;\;\;\left(y + x\right) - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 81.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{-29}:\\ \;\;\;\;\left(y + x\right) - y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 1550000000:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.65e-29)
   (- (+ y x) (* y (/ z a)))
   (if (<= a 1550000000.0)
     (- x (/ (* y (- a z)) t))
     (- (+ y x) (/ y (/ a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.65e-29) {
		tmp = (y + x) - (y * (z / a));
	} else if (a <= 1550000000.0) {
		tmp = x - ((y * (a - z)) / t);
	} else {
		tmp = (y + x) - (y / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.65d-29)) then
        tmp = (y + x) - (y * (z / a))
    else if (a <= 1550000000.0d0) then
        tmp = x - ((y * (a - z)) / t)
    else
        tmp = (y + x) - (y / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.65e-29) {
		tmp = (y + x) - (y * (z / a));
	} else if (a <= 1550000000.0) {
		tmp = x - ((y * (a - z)) / t);
	} else {
		tmp = (y + x) - (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.65e-29:
		tmp = (y + x) - (y * (z / a))
	elif a <= 1550000000.0:
		tmp = x - ((y * (a - z)) / t)
	else:
		tmp = (y + x) - (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.65e-29)
		tmp = Float64(Float64(y + x) - Float64(y * Float64(z / a)));
	elseif (a <= 1550000000.0)
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / t));
	else
		tmp = Float64(Float64(y + x) - Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.65e-29)
		tmp = (y + x) - (y * (z / a));
	elseif (a <= 1550000000.0)
		tmp = x - ((y * (a - z)) / t);
	else
		tmp = (y + x) - (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.65e-29], N[(N[(y + x), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1550000000.0], N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(y + x), $MachinePrecision] - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.65000000000000014e-29

   1. Initial program 80.7%

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

   3. Taylor expanded in t around 0 80.7%

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

      1. +-commutative 80.7%

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

      2. associate-/l* 83.4%

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

   5. Simplified 83.4%

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

   if -1.65000000000000014e-29 < a < 1.55e9

   1. Initial program 77.7%

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

   3. Taylor expanded in t around inf 83.5%

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

      1. associate--l+ 83.5%

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

      2. distribute-lft-out-- 83.5%

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

      3. div-sub 83.5%

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

      4. mul-1-neg 83.5%

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

      5. unsub-neg 83.5%

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

      6. *-commutative 83.5%

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

      7. distribute-lft-out-- 83.5%

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

   5. Simplified 83.5%

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

   if 1.55e9 < a

   1. Initial program 79.5%

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

      1. add-cube-cbrt 79.5%

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

      2. times-frac 90.1%

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

      3. pow2 90.1%

         \[\leadsto \left(x + y\right) - \frac{z - t}{\color{blue}{{\left(\sqrt[3]{a - t}\right)}^{2}}} \cdot \frac{y}{\sqrt[3]{a - t}} \]

   4. Applied egg-rr 90.1%

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{z - t}{{\left(\sqrt[3]{a - t}\right)}^{2}} \cdot \frac{y}{\sqrt[3]{a - t}}} \]
   5. Step-by-step derivation

      1. clear-num 90.0%

         \[\leadsto \left(x + y\right) - \color{blue}{\frac{1}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t}}} \cdot \frac{y}{\sqrt[3]{a - t}} \]

      2. frac-times 90.1%

         \[\leadsto \left(x + y\right) - \color{blue}{\frac{1 \cdot y}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t} \cdot \sqrt[3]{a - t}}} \]

      3. *-un-lft-identity 90.1%

         \[\leadsto \left(x + y\right) - \frac{\color{blue}{y}}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t} \cdot \sqrt[3]{a - t}} \]

   6. Applied egg-rr 90.1%

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{y}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2}}{z - t} \cdot \sqrt[3]{a - t}}} \]
   7. Step-by-step derivation

      1. associate-*l/ 90.1%

         \[\leadsto \left(x + y\right) - \frac{y}{\color{blue}{\frac{{\left(\sqrt[3]{a - t}\right)}^{2} \cdot \sqrt[3]{a - t}}{z - t}}} \]

      2. unpow2 90.1%

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

      3. rem-3cbrt-lft 89.9%

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

   8. Simplified 89.9%

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

   9. Taylor expanded in t around 0 84.4%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{-29}:\\ \;\;\;\;\left(y + x\right) - y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 1550000000:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 75.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-14} \lor \neg \left(a \leq 1.5 \cdot 10^{+53}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -8e-14) (not (<= a 1.5e+53))) (+ y x) (+ x (/ (* y z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8e-14) || !(a <= 1.5e+53)) {
		tmp = y + x;
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-8d-14)) .or. (.not. (a <= 1.5d+53))) then
        tmp = y + x
    else
        tmp = x + ((y * z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8e-14) || !(a <= 1.5e+53)) {
		tmp = y + x;
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -8e-14) or not (a <= 1.5e+53):
		tmp = y + x
	else:
		tmp = x + ((y * z) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -8e-14) || !(a <= 1.5e+53))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(Float64(y * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -8e-14) || ~((a <= 1.5e+53)))
		tmp = y + x;
	else
		tmp = x + ((y * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -8e-14], N[Not[LessEqual[a, 1.5e+53]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.99999999999999999e-14 or 1.49999999999999999e53 < a

   1. Initial program 81.0%

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

   3. Taylor expanded in a around inf 71.8%

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

      1. +-commutative 71.8%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 71.8%

      \[\leadsto \color{blue}{y + x} \]

   if -7.99999999999999999e-14 < a < 1.49999999999999999e53

   1. Initial program 77.4%

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

      1. sub-neg 77.4%

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

      2. +-commutative 77.4%

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

      3. distribute-frac-neg 77.4%

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

      4. distribute-rgt-neg-out 77.4%

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

      5. associate-/l* 78.2%

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

      6. fma-define 78.4%

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

      7. distribute-frac-neg 78.4%

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

      8. distribute-neg-frac2 78.4%

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

      9. sub-neg 78.4%

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

      10. distribute-neg-in 78.4%

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

      11. remove-double-neg 78.4%

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

      12. +-commutative 78.4%

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

      13. sub-neg 78.4%

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

   3. Simplified 78.4%

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

   5. Taylor expanded in t around inf 72.7%

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

      1. associate--l+ 72.7%

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

      2. associate-+r+ 79.9%

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

      3. distribute-rgt1-in 79.9%

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

      4. metadata-eval 79.9%

         \[\leadsto x + \left(\left(\color{blue}{0} \cdot y + \frac{y \cdot z}{t}\right) - \frac{a \cdot y}{t}\right) \]

      5. mul0-lft 79.9%

         \[\leadsto x + \left(\left(\color{blue}{0} + \frac{y \cdot z}{t}\right) - \frac{a \cdot y}{t}\right) \]

      6. associate-/l* 78.5%

         \[\leadsto x + \left(\left(0 + \color{blue}{y \cdot \frac{z}{t}}\right) - \frac{a \cdot y}{t}\right) \]

      7. associate-/l* 77.2%

         \[\leadsto x + \left(\left(0 + y \cdot \frac{z}{t}\right) - \color{blue}{a \cdot \frac{y}{t}}\right) \]

   7. Simplified 77.2%

      \[\leadsto \color{blue}{x + \left(\left(0 + y \cdot \frac{z}{t}\right) - a \cdot \frac{y}{t}\right)} \]

   8. Taylor expanded in a around 0 76.0%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-14} \lor \neg \left(a \leq 1.5 \cdot 10^{+53}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 59.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{-259} \lor \neg \left(a \leq 9 \cdot 10^{-99}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.7e-259) (not (<= a 9e-99))) (+ y x) (* y (/ z t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.7e-259) || !(a <= 9e-99)) {
		tmp = y + x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.7d-259)) .or. (.not. (a <= 9d-99))) then
        tmp = y + x
    else
        tmp = y * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.7e-259) || !(a <= 9e-99)) {
		tmp = y + x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.7e-259) or not (a <= 9e-99):
		tmp = y + x
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.7e-259) || !(a <= 9e-99))
		tmp = Float64(y + x);
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.7e-259) || ~((a <= 9e-99)))
		tmp = y + x;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.7e-259], N[Not[LessEqual[a, 9e-99]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.69999999999999984e-259 or 9.0000000000000006e-99 < a

   1. Initial program 80.4%

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

   3. Taylor expanded in a around inf 62.1%

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

      1. +-commutative 62.1%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 62.1%

      \[\leadsto \color{blue}{y + x} \]

   if -2.69999999999999984e-259 < a < 9.0000000000000006e-99

   1. Initial program 73.9%

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

      1. sub-neg 73.9%

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

      2. +-commutative 73.9%

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

      3. distribute-frac-neg 73.9%

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

      4. distribute-rgt-neg-out 73.9%

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

      5. associate-/l* 72.5%

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

      6. fma-define 72.9%

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

      7. distribute-frac-neg 72.9%

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

      8. distribute-neg-frac2 72.9%

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

      9. sub-neg 72.9%

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

      10. distribute-neg-in 72.9%

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

      11. remove-double-neg 72.9%

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

      12. +-commutative 72.9%

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

      13. sub-neg 72.9%

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

   3. Simplified 72.9%

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

   5. Taylor expanded in z around inf 59.3%

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

   6. Taylor expanded in t around inf 50.6%

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

      1. associate-*r/ 50.7%

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

   8. Simplified 50.7%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{-259} \lor \neg \left(a \leq 9 \cdot 10^{-99}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 59.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.3 \cdot 10^{-9}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= x 1.3e-9) (+ y x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 1.3e-9) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= 1.3d-9) then
        tmp = y + x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 1.3e-9) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= 1.3e-9:
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= 1.3e-9)
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= 1.3e-9)
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, 1.3e-9], N[(y + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if x < 1.3000000000000001e-9

   1. Initial program 77.8%

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

   3. Taylor expanded in a around inf 52.4%

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

      1. +-commutative 52.4%

         \[\leadsto \color{blue}{y + x} \]

   5. Simplified 52.4%

      \[\leadsto \color{blue}{y + x} \]

   if 1.3000000000000001e-9 < x

   1. Initial program 83.0%

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

   3. Taylor expanded in x around inf 71.4%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.3 \cdot 10^{-9}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 49.4% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 78.9%

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

3. Taylor expanded in x around inf 48.1%

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

4. Final simplification 48.1%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 88.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 < -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 < 1.4754293444577233 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (< t_2 -1.3664970889390727e-7)
     t_1
     (if (< t_2 1.4754293444577233e-239)
       (/ (- (* y (- a z)) (* x t)) (- a t))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y + x) - (((z - t) * (1.0d0 / (a - t))) * y)
    t_2 = (x + y) - (((z - t) * y) / (a - t))
    if (t_2 < (-1.3664970889390727d-7)) then
        tmp = t_1
    else if (t_2 < 1.4754293444577233d-239) then
        tmp = ((y * (a - z)) - (x * t)) / (a - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y)
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 < -1.3664970889390727e-7:
		tmp = t_1
	elif t_2 < 1.4754293444577233e-239:
		tmp = ((y * (a - z)) - (x * t)) / (a - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y + x) - Float64(Float64(Float64(z - t) * Float64(1.0 / Float64(a - t))) * y))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = Float64(Float64(Float64(y * Float64(a - z)) - Float64(x * t)) / Float64(a - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -1.3664970889390727e-7], t$95$1, If[Less[t$95$2, 1.4754293444577233e-239], N[(N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024095 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -1.3664970889390727e-7) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 1.4754293444577233e-239) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y))))

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