Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3

Percentage Accurate: 68.4% → 88.1%

Time: 26.1s

Alternatives: 27

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.1% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+131}:\\ \;\;\;\;t + \frac{y - a}{{\left(\sqrt[3]{z}\right)}^{2}} \cdot \frac{x - t}{\sqrt[3]{z}}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+223}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-1, t \cdot \frac{y - z}{z}, x \cdot \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5e+131)
   (+ t (* (/ (- y a) (pow (cbrt z) 2.0)) (/ (- x t) (cbrt z))))
   (if (<= z 3.4e+223)
     (fma (- t x) (/ (- y z) (- a z)) x)
     (fma -1.0 (* t (/ (- y z) z)) (* x (/ y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5e+131) {
		tmp = t + (((y - a) / pow(cbrt(z), 2.0)) * ((x - t) / cbrt(z)));
	} else if (z <= 3.4e+223) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else {
		tmp = fma(-1.0, (t * ((y - z) / z)), (x * (y / z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5e+131)
		tmp = Float64(t + Float64(Float64(Float64(y - a) / (cbrt(z) ^ 2.0)) * Float64(Float64(x - t) / cbrt(z))));
	elseif (z <= 3.4e+223)
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	else
		tmp = fma(-1.0, Float64(t * Float64(Float64(y - z) / z)), Float64(x * Float64(y / z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5e+131], N[(t + N[(N[(N[(y - a), $MachinePrecision] / N[Power[N[Power[z, 1/3], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[Power[z, 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e+223], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(-1.0 * N[(t * N[(N[(y - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.99999999999999995e131

   1. Initial program 26.4%

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

      1. associate-/l* 48.6%

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

   3. Simplified 48.6%

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

   5. Taylor expanded in z around inf 73.1%

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

      1. associate--l+ 73.1%

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

      2. associate-*r/ 73.1%

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

      3. associate-*r/ 73.1%

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

      4. mul-1-neg 73.1%

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

      5. div-sub 73.1%

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

      6. mul-1-neg 73.1%

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

      7. distribute-lft-out-- 73.1%

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

      8. associate-*r/ 73.1%

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

      9. mul-1-neg 73.1%

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

      10. unsub-neg 73.1%

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

      11. distribute-rgt-out-- 73.1%

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

   7. Simplified 73.1%

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

      1. *-commutative 73.1%

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

      2. add-cube-cbrt 72.5%

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

      3. times-frac 92.1%

         \[\leadsto t - \color{blue}{\frac{y - a}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{t - x}{\sqrt[3]{z}}} \]

      4. pow2 92.1%

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

   9. Applied egg-rr 92.1%

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

   if -4.99999999999999995e131 < z < 3.3999999999999998e223

   1. Initial program 78.7%

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

      1. +-commutative 78.7%

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

      2. *-commutative 78.7%

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

      3. associate-/l* 91.4%

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

      4. fma-define 91.5%

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

   3. Simplified 91.5%

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

   if 3.3999999999999998e223 < z

   1. Initial program 27.2%

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

      1. associate-/l* 26.8%

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

   3. Simplified 26.8%

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

      1. clear-num 27.0%

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

      2. un-div-inv 27.0%

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

   6. Applied egg-rr 27.0%

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

   7. Taylor expanded in a around 0 22.4%

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

      1. neg-mul-1 22.4%

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

      2. distribute-neg-frac2 22.4%

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

   9. Simplified 22.4%

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

   10. Taylor expanded in x around 0 56.0%

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

       1. fma-define 56.0%

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

       2. associate-/l* 87.7%

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

       3. associate-/l* 92.1%

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

   12. Simplified 92.1%

       \[\leadsto \color{blue}{\mathsf{fma}\left(-1, t \cdot \frac{y - z}{z}, x \cdot \frac{y}{z}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+131}:\\ \;\;\;\;t + \frac{y - a}{{\left(\sqrt[3]{z}\right)}^{2}} \cdot \frac{x - t}{\sqrt[3]{z}}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+223}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-1, t \cdot \frac{y - z}{z}, x \cdot \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - y}{z}\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+139}:\\ \;\;\;\;\mathsf{fma}\left(1, t, \left(t - x\right) \cdot t\_1\right) + \mathsf{fma}\left(t\_1, t - x, \left(y - a\right) \cdot \frac{t - x}{z}\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+222}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-1, t \cdot \frac{y - z}{z}, x \cdot \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- a y) z)))
   (if (<= z -2.3e+139)
     (+
      (fma 1.0 t (* (- t x) t_1))
      (fma t_1 (- t x) (* (- y a) (/ (- t x) z))))
     (if (<= z 5.5e+222)
       (fma (- t x) (/ (- y z) (- a z)) x)
       (fma -1.0 (* t (/ (- y z) z)) (* x (/ y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a - y) / z;
	double tmp;
	if (z <= -2.3e+139) {
		tmp = fma(1.0, t, ((t - x) * t_1)) + fma(t_1, (t - x), ((y - a) * ((t - x) / z)));
	} else if (z <= 5.5e+222) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else {
		tmp = fma(-1.0, (t * ((y - z) / z)), (x * (y / z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a - y) / z)
	tmp = 0.0
	if (z <= -2.3e+139)
		tmp = Float64(fma(1.0, t, Float64(Float64(t - x) * t_1)) + fma(t_1, Float64(t - x), Float64(Float64(y - a) * Float64(Float64(t - x) / z))));
	elseif (z <= 5.5e+222)
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	else
		tmp = fma(-1.0, Float64(t * Float64(Float64(y - z) / z)), Float64(x * Float64(y / z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -2.3e+139], N[(N[(1.0 * t + N[(N[(t - x), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(t - x), $MachinePrecision] + N[(N[(y - a), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e+222], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(-1.0 * N[(t * N[(N[(y - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3e139

   1. Initial program 24.9%

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

      1. associate-/l* 48.3%

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

   3. Simplified 48.3%

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

   5. Taylor expanded in z around inf 71.6%

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

      1. associate--l+ 71.6%

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

      2. associate-*r/ 71.6%

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

      3. associate-*r/ 71.6%

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

      4. mul-1-neg 71.6%

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

      5. div-sub 71.6%

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

      6. mul-1-neg 71.6%

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

      7. distribute-lft-out-- 71.6%

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

      8. associate-*r/ 71.6%

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

      9. mul-1-neg 71.6%

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

      10. unsub-neg 71.6%

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

      11. distribute-rgt-out-- 71.6%

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

   7. Simplified 71.6%

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

      1. *-un-lft-identity 71.6%

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

      2. associate-/l* 89.9%

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

      3. prod-diff 87.2%

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

   9. Applied egg-rr 87.2%

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

       1. distribute-rgt-neg-in 87.2%

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

       2. distribute-neg-frac2 87.2%

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

       3. associate-*l/ 65.4%

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

       4. associate-*r/ 84.4%

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

   11. Simplified 84.4%

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

   if -2.3e139 < z < 5.4999999999999999e222

   1. Initial program 78.5%

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

      1. +-commutative 78.5%

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

      2. *-commutative 78.5%

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

      3. associate-/l* 91.0%

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

      4. fma-define 91.1%

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

   3. Simplified 91.1%

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

   if 5.4999999999999999e222 < z

   1. Initial program 27.2%

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

      1. associate-/l* 26.8%

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

   3. Simplified 26.8%

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

      1. clear-num 27.0%

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

      2. un-div-inv 27.0%

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

   6. Applied egg-rr 27.0%

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

   7. Taylor expanded in a around 0 22.4%

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

      1. neg-mul-1 22.4%

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

      2. distribute-neg-frac2 22.4%

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

   9. Simplified 22.4%

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

   10. Taylor expanded in x around 0 56.0%

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

       1. fma-define 56.0%

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

       2. associate-/l* 87.7%

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

       3. associate-/l* 92.1%

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

   12. Simplified 92.1%

       \[\leadsto \color{blue}{\mathsf{fma}\left(-1, t \cdot \frac{y - z}{z}, x \cdot \frac{y}{z}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+139}:\\ \;\;\;\;\mathsf{fma}\left(1, t, \left(t - x\right) \cdot \frac{a - y}{z}\right) + \mathsf{fma}\left(\frac{a - y}{z}, t - x, \left(y - a\right) \cdot \frac{t - x}{z}\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+222}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-1, t \cdot \frac{y - z}{z}, x \cdot \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-306} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- t x) (- y z)) (- z a)))))
   (if (or (<= t_1 -5e-306) (not (<= t_1 0.0)))
     (fma (- t x) (/ (- y z) (- a z)) x)
     (+ t (/ (* (- y a) x) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((t - x) * (y - z)) / (z - a));
	double tmp;
	if ((t_1 <= -5e-306) || !(t_1 <= 0.0)) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else {
		tmp = t + (((y - a) * x) / z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(t - x) * Float64(y - z)) / Float64(z - a)))
	tmp = 0.0
	if ((t_1 <= -5e-306) || !(t_1 <= 0.0))
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	else
		tmp = Float64(t + Float64(Float64(Float64(y - a) * x) / z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(t - x), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-306], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(t + N[(N[(N[(y - a), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.99999999999999998e-306 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 72.4%

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

      1. +-commutative 72.4%

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

      2. *-commutative 72.4%

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

      3. associate-/l* 88.8%

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

      4. fma-define 88.9%

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

   3. Simplified 88.9%

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

   if -4.99999999999999998e-306 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.1%

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

      1. associate-/l* 3.8%

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

   3. Simplified 3.8%

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

   5. Taylor expanded in z around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. associate-*r/ 99.9%

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

      4. mul-1-neg 99.9%

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

      5. div-sub 99.9%

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

      6. mul-1-neg 99.9%

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

      7. distribute-lft-out-- 99.9%

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

      8. associate-*r/ 99.9%

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

      9. mul-1-neg 99.9%

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

      10. unsub-neg 99.9%

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

      11. distribute-rgt-out-- 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in t around 0 99.9%

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

      1. associate-*r/ 99.9%

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

      2. associate-*r* 99.9%

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

      3. neg-mul-1 99.9%

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

   10. Simplified 99.9%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z - a} \leq -5 \cdot 10^{-306} \lor \neg \left(x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z - a} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+134}:\\ \;\;\;\;t - \frac{x \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+223}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-1, t \cdot \frac{y - z}{z}, x \cdot \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.8e+134)
   (- t (/ (* x (- a y)) z))
   (if (<= z 1.45e+223)
     (fma (- t x) (/ (- y z) (- a z)) x)
     (fma -1.0 (* t (/ (- y z) z)) (* x (/ y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e+134) {
		tmp = t - ((x * (a - y)) / z);
	} else if (z <= 1.45e+223) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else {
		tmp = fma(-1.0, (t * ((y - z) / z)), (x * (y / z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.8e+134)
		tmp = Float64(t - Float64(Float64(x * Float64(a - y)) / z));
	elseif (z <= 1.45e+223)
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	else
		tmp = fma(-1.0, Float64(t * Float64(Float64(y - z) / z)), Float64(x * Float64(y / z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.8e+134], N[(t - N[(N[(x * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+223], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(-1.0 * N[(t * N[(N[(y - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.79999999999999994e134

   1. Initial program 26.4%

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

      1. associate-/l* 48.6%

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

   3. Simplified 48.6%

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

   5. Taylor expanded in z around inf 73.1%

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

      1. associate--l+ 73.1%

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

      2. associate-*r/ 73.1%

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

      3. associate-*r/ 73.1%

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

      4. mul-1-neg 73.1%

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

      5. div-sub 73.1%

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

      6. mul-1-neg 73.1%

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

      7. distribute-lft-out-- 73.1%

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

      8. associate-*r/ 73.1%

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

      9. mul-1-neg 73.1%

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

      10. unsub-neg 73.1%

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

      11. distribute-rgt-out-- 73.1%

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

   7. Simplified 73.1%

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

   8. Taylor expanded in t around 0 80.5%

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

      1. associate-*r/ 80.5%

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

      2. associate-*r* 80.5%

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

      3. neg-mul-1 80.5%

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

   10. Simplified 80.5%

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

   if -1.79999999999999994e134 < z < 1.4500000000000001e223

   1. Initial program 78.7%

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

      1. +-commutative 78.7%

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

      2. *-commutative 78.7%

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

      3. associate-/l* 91.4%

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

      4. fma-define 91.5%

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

   3. Simplified 91.5%

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

   if 1.4500000000000001e223 < z

   1. Initial program 27.2%

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

      1. associate-/l* 26.8%

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

   3. Simplified 26.8%

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

      1. clear-num 27.0%

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

      2. un-div-inv 27.0%

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

   6. Applied egg-rr 27.0%

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

   7. Taylor expanded in a around 0 22.4%

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

      1. neg-mul-1 22.4%

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

      2. distribute-neg-frac2 22.4%

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

   9. Simplified 22.4%

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

   10. Taylor expanded in x around 0 56.0%

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

       1. fma-define 56.0%

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

       2. associate-/l* 87.7%

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

       3. associate-/l* 92.1%

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

   12. Simplified 92.1%

       \[\leadsto \color{blue}{\mathsf{fma}\left(-1, t \cdot \frac{y - z}{z}, x \cdot \frac{y}{z}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+134}:\\ \;\;\;\;t - \frac{x \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+223}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-1, t \cdot \frac{y - z}{z}, x \cdot \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-306}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot x}{z}\\ \mathbf{elif}\;t\_1 \leq 10^{+261}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - \left(y - z\right) \cdot \left(\left(x - t\right) \cdot \frac{1}{a - z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- t x) (- y z)) (- z a)))))
   (if (<= t_1 (- INFINITY))
     (+ t (* y (/ (- x t) z)))
     (if (<= t_1 -5e-306)
       t_1
       (if (<= t_1 0.0)
         (+ t (/ (* (- y a) x) z))
         (if (<= t_1 1e+261)
           t_1
           (- x (* (- y z) (* (- x t) (/ 1.0 (- a z)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((t - x) * (y - z)) / (z - a));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t + (y * ((x - t) / z));
	} else if (t_1 <= -5e-306) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t + (((y - a) * x) / z);
	} else if (t_1 <= 1e+261) {
		tmp = t_1;
	} else {
		tmp = x - ((y - z) * ((x - t) * (1.0 / (a - z))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((t - x) * (y - z)) / (z - a));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t + (y * ((x - t) / z));
	} else if (t_1 <= -5e-306) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t + (((y - a) * x) / z);
	} else if (t_1 <= 1e+261) {
		tmp = t_1;
	} else {
		tmp = x - ((y - z) * ((x - t) * (1.0 / (a - z))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((t - x) * (y - z)) / (z - a))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t + (y * ((x - t) / z))
	elif t_1 <= -5e-306:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = t + (((y - a) * x) / z)
	elif t_1 <= 1e+261:
		tmp = t_1
	else:
		tmp = x - ((y - z) * ((x - t) * (1.0 / (a - z))))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(t - x) * Float64(y - z)) / Float64(z - a)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	elseif (t_1 <= -5e-306)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(y - a) * x) / z));
	elseif (t_1 <= 1e+261)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(Float64(y - z) * Float64(Float64(x - t) * Float64(1.0 / Float64(a - z)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((t - x) * (y - z)) / (z - a));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t + (y * ((x - t) / z));
	elseif (t_1 <= -5e-306)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = t + (((y - a) * x) / z);
	elseif (t_1 <= 1e+261)
		tmp = t_1;
	else
		tmp = x - ((y - z) * ((x - t) * (1.0 / (a - z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(t - x), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-306], t$95$1, If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(N[(y - a), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+261], t$95$1, N[(x - N[(N[(y - z), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] * N[(1.0 / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 31.7%

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

      1. associate-/l* 69.7%

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

   3. Simplified 69.7%

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

   5. Taylor expanded in z around inf 51.0%

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

      1. associate--l+ 51.0%

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

      2. associate-*r/ 51.0%

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

      3. associate-*r/ 51.0%

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

      4. mul-1-neg 51.0%

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

      5. div-sub 51.0%

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

      6. mul-1-neg 51.0%

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

      7. distribute-lft-out-- 51.0%

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

      8. associate-*r/ 51.0%

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

      9. mul-1-neg 51.0%

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

      10. unsub-neg 51.0%

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

      11. distribute-rgt-out-- 53.2%

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

   7. Simplified 53.2%

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

   8. Taylor expanded in y around inf 53.3%

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

      1. associate-/l* 70.5%

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

   10. Simplified 70.5%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.99999999999999998e-306 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 9.9999999999999993e260

   1. Initial program 98.2%

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

   if -4.99999999999999998e-306 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.1%

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

      1. associate-/l* 3.8%

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

   3. Simplified 3.8%

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

   5. Taylor expanded in z around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. associate-*r/ 99.9%

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

      4. mul-1-neg 99.9%

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

      5. div-sub 99.9%

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

      6. mul-1-neg 99.9%

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

      7. distribute-lft-out-- 99.9%

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

      8. associate-*r/ 99.9%

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

      9. mul-1-neg 99.9%

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

      10. unsub-neg 99.9%

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

      11. distribute-rgt-out-- 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in t around 0 99.9%

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

      1. associate-*r/ 99.9%

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

      2. associate-*r* 99.9%

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

      3. neg-mul-1 99.9%

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

   10. Simplified 99.9%

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

   if 9.9999999999999993e260 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 34.9%

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

      1. associate-/l* 80.0%

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

   3. Simplified 80.0%

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

      1. clear-num 80.0%

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

      2. associate-/r/ 80.2%

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

   6. Applied egg-rr 80.2%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z - a} \leq -\infty:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z - a} \leq -5 \cdot 10^{-306}:\\ \;\;\;\;x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z - a}\\ \mathbf{elif}\;x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z - a} \leq 0:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot x}{z}\\ \mathbf{elif}\;x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z - a} \leq 10^{+261}:\\ \;\;\;\;x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x - \left(y - z\right) \cdot \left(\left(x - t\right) \cdot \frac{1}{a - z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-306}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot x}{z}\\ \mathbf{elif}\;t\_1 \leq 10^{+261}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- t x) (- y z)) (- z a)))))
   (if (<= t_1 (- INFINITY))
     (+ t (* y (/ (- x t) z)))
     (if (<= t_1 -5e-306)
       t_1
       (if (<= t_1 0.0)
         (+ t (/ (* (- y a) x) z))
         (if (<= t_1 1e+261) t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((t - x) * (y - z)) / (z - a));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t + (y * ((x - t) / z));
	} else if (t_1 <= -5e-306) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t + (((y - a) * x) / z);
	} else if (t_1 <= 1e+261) {
		tmp = t_1;
	} else {
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((t - x) * (y - z)) / (z - a));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t + (y * ((x - t) / z));
	} else if (t_1 <= -5e-306) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t + (((y - a) * x) / z);
	} else if (t_1 <= 1e+261) {
		tmp = t_1;
	} else {
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((t - x) * (y - z)) / (z - a))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t + (y * ((x - t) / z))
	elif t_1 <= -5e-306:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = t + (((y - a) * x) / z)
	elif t_1 <= 1e+261:
		tmp = t_1
	else:
		tmp = x + ((y - z) * ((t - x) / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(t - x) * Float64(y - z)) / Float64(z - a)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	elseif (t_1 <= -5e-306)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(y - a) * x) / z));
	elseif (t_1 <= 1e+261)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((t - x) * (y - z)) / (z - a));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t + (y * ((x - t) / z));
	elseif (t_1 <= -5e-306)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = t + (((y - a) * x) / z);
	elseif (t_1 <= 1e+261)
		tmp = t_1;
	else
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(t - x), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-306], t$95$1, If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(N[(y - a), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+261], t$95$1, N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 31.7%

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

      1. associate-/l* 69.7%

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

   3. Simplified 69.7%

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

   5. Taylor expanded in z around inf 51.0%

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

      1. associate--l+ 51.0%

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

      2. associate-*r/ 51.0%

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

      3. associate-*r/ 51.0%

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

      4. mul-1-neg 51.0%

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

      5. div-sub 51.0%

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

      6. mul-1-neg 51.0%

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

      7. distribute-lft-out-- 51.0%

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

      8. associate-*r/ 51.0%

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

      9. mul-1-neg 51.0%

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

      10. unsub-neg 51.0%

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

      11. distribute-rgt-out-- 53.2%

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

   7. Simplified 53.2%

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

   8. Taylor expanded in y around inf 53.3%

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

      1. associate-/l* 70.5%

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

   10. Simplified 70.5%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.99999999999999998e-306 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 9.9999999999999993e260

   1. Initial program 98.2%

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

   if -4.99999999999999998e-306 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.1%

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

      1. associate-/l* 3.8%

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

   3. Simplified 3.8%

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

   5. Taylor expanded in z around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. associate-*r/ 99.9%

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

      4. mul-1-neg 99.9%

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

      5. div-sub 99.9%

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

      6. mul-1-neg 99.9%

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

      7. distribute-lft-out-- 99.9%

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

      8. associate-*r/ 99.9%

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

      9. mul-1-neg 99.9%

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

      10. unsub-neg 99.9%

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

      11. distribute-rgt-out-- 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in t around 0 99.9%

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

      1. associate-*r/ 99.9%

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

      2. associate-*r* 99.9%

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

      3. neg-mul-1 99.9%

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

   10. Simplified 99.9%

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

   if 9.9999999999999993e260 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 34.9%

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

      1. associate-/l* 80.0%

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

   3. Simplified 80.0%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z - a} \leq -\infty:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z - a} \leq -5 \cdot 10^{-306}:\\ \;\;\;\;x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z - a}\\ \mathbf{elif}\;x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z - a} \leq 0:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot x}{z}\\ \mathbf{elif}\;x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z - a} \leq 10^{+261}:\\ \;\;\;\;x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-306}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot x}{z}\\ \mathbf{elif}\;t\_1 \leq 10^{+261}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- t x) (- y z)) (- z a)))))
   (if (<= t_1 (- INFINITY))
     (+ t (* y (/ (- x t) z)))
     (if (<= t_1 -5e-306)
       t_1
       (if (<= t_1 0.0)
         (+ t (/ (* (- y a) x) z))
         (if (<= t_1 1e+261) t_1 (+ x (/ (- y z) (/ (- a z) (- t x))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((t - x) * (y - z)) / (z - a));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t + (y * ((x - t) / z));
	} else if (t_1 <= -5e-306) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t + (((y - a) * x) / z);
	} else if (t_1 <= 1e+261) {
		tmp = t_1;
	} else {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((t - x) * (y - z)) / (z - a));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t + (y * ((x - t) / z));
	} else if (t_1 <= -5e-306) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t + (((y - a) * x) / z);
	} else if (t_1 <= 1e+261) {
		tmp = t_1;
	} else {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((t - x) * (y - z)) / (z - a))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t + (y * ((x - t) / z))
	elif t_1 <= -5e-306:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = t + (((y - a) * x) / z)
	elif t_1 <= 1e+261:
		tmp = t_1
	else:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(t - x) * Float64(y - z)) / Float64(z - a)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	elseif (t_1 <= -5e-306)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(y - a) * x) / z));
	elseif (t_1 <= 1e+261)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((t - x) * (y - z)) / (z - a));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t + (y * ((x - t) / z));
	elseif (t_1 <= -5e-306)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = t + (((y - a) * x) / z);
	elseif (t_1 <= 1e+261)
		tmp = t_1;
	else
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(t - x), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-306], t$95$1, If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(N[(y - a), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+261], t$95$1, N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 31.7%

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

      1. associate-/l* 69.7%

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

   3. Simplified 69.7%

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

   5. Taylor expanded in z around inf 51.0%

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

      1. associate--l+ 51.0%

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

      2. associate-*r/ 51.0%

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

      3. associate-*r/ 51.0%

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

      4. mul-1-neg 51.0%

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

      5. div-sub 51.0%

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

      6. mul-1-neg 51.0%

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

      7. distribute-lft-out-- 51.0%

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

      8. associate-*r/ 51.0%

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

      9. mul-1-neg 51.0%

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

      10. unsub-neg 51.0%

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

      11. distribute-rgt-out-- 53.2%

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

   7. Simplified 53.2%

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

   8. Taylor expanded in y around inf 53.3%

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

      1. associate-/l* 70.5%

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

   10. Simplified 70.5%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.99999999999999998e-306 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 9.9999999999999993e260

   1. Initial program 98.2%

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

   if -4.99999999999999998e-306 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.1%

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

      1. associate-/l* 3.8%

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

   3. Simplified 3.8%

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

   5. Taylor expanded in z around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. associate-*r/ 99.9%

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

      4. mul-1-neg 99.9%

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

      5. div-sub 99.9%

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

      6. mul-1-neg 99.9%

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

      7. distribute-lft-out-- 99.9%

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

      8. associate-*r/ 99.9%

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

      9. mul-1-neg 99.9%

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

      10. unsub-neg 99.9%

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

      11. distribute-rgt-out-- 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in t around 0 99.9%

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

      1. associate-*r/ 99.9%

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

      2. associate-*r* 99.9%

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

      3. neg-mul-1 99.9%

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

   10. Simplified 99.9%

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

   if 9.9999999999999993e260 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 34.9%

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

      1. associate-/l* 80.0%

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

   3. Simplified 80.0%

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

      1. clear-num 80.0%

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

      2. un-div-inv 80.1%

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

   6. Applied egg-rr 80.1%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z - a} \leq -\infty:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z - a} \leq -5 \cdot 10^{-306}:\\ \;\;\;\;x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z - a}\\ \mathbf{elif}\;x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z - a} \leq 0:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot x}{z}\\ \mathbf{elif}\;x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z - a} \leq 10^{+261}:\\ \;\;\;\;x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 90.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-306} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{-1}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- t x) (- y z)) (- z a)))))
   (if (or (<= t_1 -5e-306) (not (<= t_1 0.0)))
     (- x (* (- t x) (/ -1.0 (/ (- a z) (- y z)))))
     (+ t (/ (* (- y a) x) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((t - x) * (y - z)) / (z - a));
	double tmp;
	if ((t_1 <= -5e-306) || !(t_1 <= 0.0)) {
		tmp = x - ((t - x) * (-1.0 / ((a - z) / (y - z))));
	} else {
		tmp = t + (((y - a) * x) / 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) :: t_1
    real(8) :: tmp
    t_1 = x - (((t - x) * (y - z)) / (z - a))
    if ((t_1 <= (-5d-306)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x - ((t - x) * ((-1.0d0) / ((a - z) / (y - z))))
    else
        tmp = t + (((y - a) * x) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((t - x) * (y - z)) / (z - a));
	double tmp;
	if ((t_1 <= -5e-306) || !(t_1 <= 0.0)) {
		tmp = x - ((t - x) * (-1.0 / ((a - z) / (y - z))));
	} else {
		tmp = t + (((y - a) * x) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((t - x) * (y - z)) / (z - a))
	tmp = 0
	if (t_1 <= -5e-306) or not (t_1 <= 0.0):
		tmp = x - ((t - x) * (-1.0 / ((a - z) / (y - z))))
	else:
		tmp = t + (((y - a) * x) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(t - x) * Float64(y - z)) / Float64(z - a)))
	tmp = 0.0
	if ((t_1 <= -5e-306) || !(t_1 <= 0.0))
		tmp = Float64(x - Float64(Float64(t - x) * Float64(-1.0 / Float64(Float64(a - z) / Float64(y - z)))));
	else
		tmp = Float64(t + Float64(Float64(Float64(y - a) * x) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((t - x) * (y - z)) / (z - a));
	tmp = 0.0;
	if ((t_1 <= -5e-306) || ~((t_1 <= 0.0)))
		tmp = x - ((t - x) * (-1.0 / ((a - z) / (y - z))));
	else
		tmp = t + (((y - a) * x) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(t - x), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-306], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x - N[(N[(t - x), $MachinePrecision] * N[(-1.0 / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(y - a), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.99999999999999998e-306 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 72.4%

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

      1. associate-/l* 82.3%

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

   3. Simplified 82.3%

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

      1. associate-*r/ 72.4%

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

      2. clear-num 72.4%

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

      3. associate-/r* 88.8%

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

   6. Applied egg-rr 88.8%

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

      1. associate-/r/ 88.8%

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

   8. Simplified 88.8%

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

   if -4.99999999999999998e-306 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.1%

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

      1. associate-/l* 3.8%

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

   3. Simplified 3.8%

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

   5. Taylor expanded in z around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. associate-*r/ 99.9%

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

      4. mul-1-neg 99.9%

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

      5. div-sub 99.9%

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

      6. mul-1-neg 99.9%

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

      7. distribute-lft-out-- 99.9%

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

      8. associate-*r/ 99.9%

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

      9. mul-1-neg 99.9%

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

      10. unsub-neg 99.9%

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

      11. distribute-rgt-out-- 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in t around 0 99.9%

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

      1. associate-*r/ 99.9%

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

      2. associate-*r* 99.9%

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

      3. neg-mul-1 99.9%

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

   10. Simplified 99.9%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z - a} \leq -5 \cdot 10^{-306} \lor \neg \left(x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z - a} \leq 0\right):\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{-1}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 37.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;a \leq -1.6 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.15 \cdot 10^{-185}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-133}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+15}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+175}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- a z)))))
   (if (<= a -1.6e+28)
     x
     (if (<= a -2.15e-185)
       t
       (if (<= a 2.25e-209)
         (* x (/ y z))
         (if (<= a 1.65e-133)
           t
           (if (<= a 4.5e-42)
             t_1
             (if (<= a 4e+15) t (if (<= a 8e+175) t_1 x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (a <= -1.6e+28) {
		tmp = x;
	} else if (a <= -2.15e-185) {
		tmp = t;
	} else if (a <= 2.25e-209) {
		tmp = x * (y / z);
	} else if (a <= 1.65e-133) {
		tmp = t;
	} else if (a <= 4.5e-42) {
		tmp = t_1;
	} else if (a <= 4e+15) {
		tmp = t;
	} else if (a <= 8e+175) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t * (y / (a - z))
    if (a <= (-1.6d+28)) then
        tmp = x
    else if (a <= (-2.15d-185)) then
        tmp = t
    else if (a <= 2.25d-209) then
        tmp = x * (y / z)
    else if (a <= 1.65d-133) then
        tmp = t
    else if (a <= 4.5d-42) then
        tmp = t_1
    else if (a <= 4d+15) then
        tmp = t
    else if (a <= 8d+175) then
        tmp = t_1
    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 t_1 = t * (y / (a - z));
	double tmp;
	if (a <= -1.6e+28) {
		tmp = x;
	} else if (a <= -2.15e-185) {
		tmp = t;
	} else if (a <= 2.25e-209) {
		tmp = x * (y / z);
	} else if (a <= 1.65e-133) {
		tmp = t;
	} else if (a <= 4.5e-42) {
		tmp = t_1;
	} else if (a <= 4e+15) {
		tmp = t;
	} else if (a <= 8e+175) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / (a - z))
	tmp = 0
	if a <= -1.6e+28:
		tmp = x
	elif a <= -2.15e-185:
		tmp = t
	elif a <= 2.25e-209:
		tmp = x * (y / z)
	elif a <= 1.65e-133:
		tmp = t
	elif a <= 4.5e-42:
		tmp = t_1
	elif a <= 4e+15:
		tmp = t
	elif a <= 8e+175:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (a <= -1.6e+28)
		tmp = x;
	elseif (a <= -2.15e-185)
		tmp = t;
	elseif (a <= 2.25e-209)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 1.65e-133)
		tmp = t;
	elseif (a <= 4.5e-42)
		tmp = t_1;
	elseif (a <= 4e+15)
		tmp = t;
	elseif (a <= 8e+175)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / (a - z));
	tmp = 0.0;
	if (a <= -1.6e+28)
		tmp = x;
	elseif (a <= -2.15e-185)
		tmp = t;
	elseif (a <= 2.25e-209)
		tmp = x * (y / z);
	elseif (a <= 1.65e-133)
		tmp = t;
	elseif (a <= 4.5e-42)
		tmp = t_1;
	elseif (a <= 4e+15)
		tmp = t;
	elseif (a <= 8e+175)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.6e+28], x, If[LessEqual[a, -2.15e-185], t, If[LessEqual[a, 2.25e-209], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.65e-133], t, If[LessEqual[a, 4.5e-42], t$95$1, If[LessEqual[a, 4e+15], t, If[LessEqual[a, 8e+175], t$95$1, x]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.6e28 or 7.9999999999999995e175 < a

   1. Initial program 73.9%

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

      1. associate-/l* 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in a around inf 52.6%

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

   if -1.6e28 < a < -2.15e-185 or 2.2499999999999999e-209 < a < 1.65000000000000005e-133 or 4.5e-42 < a < 4e15

   1. Initial program 52.8%

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

      1. associate-/l* 57.5%

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

   3. Simplified 57.5%

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

   5. Taylor expanded in z around inf 48.9%

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

   if -2.15e-185 < a < 2.2499999999999999e-209

   1. Initial program 59.1%

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

      1. associate-/l* 65.3%

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

   3. Simplified 65.3%

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

      1. clear-num 65.2%

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

      2. un-div-inv 65.4%

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

   6. Applied egg-rr 65.4%

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

   7. Taylor expanded in a around 0 61.8%

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

      1. neg-mul-1 61.8%

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

      2. distribute-neg-frac2 61.8%

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

   9. Simplified 61.8%

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

   10. Taylor expanded in x around inf 50.7%

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

       1. associate-/l* 54.5%

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

   12. Simplified 54.5%

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

   if 1.65000000000000005e-133 < a < 4.5e-42 or 4e15 < a < 7.9999999999999995e175

   1. Initial program 76.1%

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

      1. associate-/l* 81.0%

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

   3. Simplified 81.0%

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

   5. Taylor expanded in x around 0 47.3%

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

   6. Taylor expanded in y around inf 39.0%

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

      1. associate-/l* 39.1%

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

   8. Simplified 39.1%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.15 \cdot 10^{-185}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-133}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-42}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+15}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+175}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 36.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ \mathbf{if}\;a \leq -1.6 \cdot 10^{+29}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.25 \cdot 10^{-187}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-209}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-133}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 120000000:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+175}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ y z))))
   (if (<= a -1.6e+29)
     x
     (if (<= a -2.25e-187)
       t
       (if (<= a 9.5e-209)
         t_1
         (if (<= a 5.3e-133)
           t
           (if (<= a 6.4e-43)
             t_1
             (if (<= a 120000000.0)
               t
               (if (<= a 8e+175) (* t (/ y a)) x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (a <= -1.6e+29) {
		tmp = x;
	} else if (a <= -2.25e-187) {
		tmp = t;
	} else if (a <= 9.5e-209) {
		tmp = t_1;
	} else if (a <= 5.3e-133) {
		tmp = t;
	} else if (a <= 6.4e-43) {
		tmp = t_1;
	} else if (a <= 120000000.0) {
		tmp = t;
	} else if (a <= 8e+175) {
		tmp = t * (y / a);
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (y / z)
    if (a <= (-1.6d+29)) then
        tmp = x
    else if (a <= (-2.25d-187)) then
        tmp = t
    else if (a <= 9.5d-209) then
        tmp = t_1
    else if (a <= 5.3d-133) then
        tmp = t
    else if (a <= 6.4d-43) then
        tmp = t_1
    else if (a <= 120000000.0d0) then
        tmp = t
    else if (a <= 8d+175) then
        tmp = t * (y / a)
    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 t_1 = x * (y / z);
	double tmp;
	if (a <= -1.6e+29) {
		tmp = x;
	} else if (a <= -2.25e-187) {
		tmp = t;
	} else if (a <= 9.5e-209) {
		tmp = t_1;
	} else if (a <= 5.3e-133) {
		tmp = t;
	} else if (a <= 6.4e-43) {
		tmp = t_1;
	} else if (a <= 120000000.0) {
		tmp = t;
	} else if (a <= 8e+175) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (y / z)
	tmp = 0
	if a <= -1.6e+29:
		tmp = x
	elif a <= -2.25e-187:
		tmp = t
	elif a <= 9.5e-209:
		tmp = t_1
	elif a <= 5.3e-133:
		tmp = t
	elif a <= 6.4e-43:
		tmp = t_1
	elif a <= 120000000.0:
		tmp = t
	elif a <= 8e+175:
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (a <= -1.6e+29)
		tmp = x;
	elseif (a <= -2.25e-187)
		tmp = t;
	elseif (a <= 9.5e-209)
		tmp = t_1;
	elseif (a <= 5.3e-133)
		tmp = t;
	elseif (a <= 6.4e-43)
		tmp = t_1;
	elseif (a <= 120000000.0)
		tmp = t;
	elseif (a <= 8e+175)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y / z);
	tmp = 0.0;
	if (a <= -1.6e+29)
		tmp = x;
	elseif (a <= -2.25e-187)
		tmp = t;
	elseif (a <= 9.5e-209)
		tmp = t_1;
	elseif (a <= 5.3e-133)
		tmp = t;
	elseif (a <= 6.4e-43)
		tmp = t_1;
	elseif (a <= 120000000.0)
		tmp = t;
	elseif (a <= 8e+175)
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.6e+29], x, If[LessEqual[a, -2.25e-187], t, If[LessEqual[a, 9.5e-209], t$95$1, If[LessEqual[a, 5.3e-133], t, If[LessEqual[a, 6.4e-43], t$95$1, If[LessEqual[a, 120000000.0], t, If[LessEqual[a, 8e+175], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.59999999999999993e29 or 7.9999999999999995e175 < a

   1. Initial program 73.9%

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

      1. associate-/l* 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in a around inf 52.6%

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

   if -1.59999999999999993e29 < a < -2.2499999999999999e-187 or 9.50000000000000028e-209 < a < 5.29999999999999983e-133 or 6.3999999999999997e-43 < a < 1.2e8

   1. Initial program 53.5%

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

      1. associate-/l* 56.6%

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

   3. Simplified 56.6%

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

   5. Taylor expanded in z around inf 48.2%

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

   if -2.2499999999999999e-187 < a < 9.50000000000000028e-209 or 5.29999999999999983e-133 < a < 6.3999999999999997e-43

   1. Initial program 62.5%

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

      1. associate-/l* 65.3%

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

   3. Simplified 65.3%

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

      1. clear-num 65.3%

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

      2. un-div-inv 65.3%

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

   6. Applied egg-rr 65.3%

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

   7. Taylor expanded in a around 0 53.4%

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

      1. neg-mul-1 53.4%

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

      2. distribute-neg-frac2 53.4%

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

   9. Simplified 53.4%

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

   10. Taylor expanded in x around inf 43.5%

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

       1. associate-/l* 49.1%

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

   12. Simplified 49.1%

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

   if 1.2e8 < a < 7.9999999999999995e175

   1. Initial program 78.6%

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

      1. associate-/l* 91.7%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in x around 0 45.0%

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

   6. Taylor expanded in z around 0 33.4%

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

      1. associate-/l* 33.4%

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

   8. Simplified 33.4%

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

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+29}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.25 \cdot 10^{-187}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-133}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 120000000:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+175}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ t_2 := x - x \cdot \frac{y}{a}\\ t_3 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;x \leq -3 \cdot 10^{+105}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-44}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+71}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z))))
        (t_2 (- x (* x (/ y a))))
        (t_3 (* t (/ (- y z) (- a z)))))
   (if (<= x -3e+105)
     t_2
     (if (<= x -1.95e-50)
       t_1
       (if (<= x 4.5e-44)
         t_3
         (if (<= x 1.05e+56) t_1 (if (<= x 1.6e+71) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double t_2 = x - (x * (y / a));
	double t_3 = t * ((y - z) / (a - z));
	double tmp;
	if (x <= -3e+105) {
		tmp = t_2;
	} else if (x <= -1.95e-50) {
		tmp = t_1;
	} else if (x <= 4.5e-44) {
		tmp = t_3;
	} else if (x <= 1.05e+56) {
		tmp = t_1;
	} else if (x <= 1.6e+71) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * ((t - x) / (a - z))
    t_2 = x - (x * (y / a))
    t_3 = t * ((y - z) / (a - z))
    if (x <= (-3d+105)) then
        tmp = t_2
    else if (x <= (-1.95d-50)) then
        tmp = t_1
    else if (x <= 4.5d-44) then
        tmp = t_3
    else if (x <= 1.05d+56) then
        tmp = t_1
    else if (x <= 1.6d+71) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double t_2 = x - (x * (y / a));
	double t_3 = t * ((y - z) / (a - z));
	double tmp;
	if (x <= -3e+105) {
		tmp = t_2;
	} else if (x <= -1.95e-50) {
		tmp = t_1;
	} else if (x <= 4.5e-44) {
		tmp = t_3;
	} else if (x <= 1.05e+56) {
		tmp = t_1;
	} else if (x <= 1.6e+71) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	t_2 = x - (x * (y / a))
	t_3 = t * ((y - z) / (a - z))
	tmp = 0
	if x <= -3e+105:
		tmp = t_2
	elif x <= -1.95e-50:
		tmp = t_1
	elif x <= 4.5e-44:
		tmp = t_3
	elif x <= 1.05e+56:
		tmp = t_1
	elif x <= 1.6e+71:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	t_2 = Float64(x - Float64(x * Float64(y / a)))
	t_3 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (x <= -3e+105)
		tmp = t_2;
	elseif (x <= -1.95e-50)
		tmp = t_1;
	elseif (x <= 4.5e-44)
		tmp = t_3;
	elseif (x <= 1.05e+56)
		tmp = t_1;
	elseif (x <= 1.6e+71)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / (a - z));
	t_2 = x - (x * (y / a));
	t_3 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (x <= -3e+105)
		tmp = t_2;
	elseif (x <= -1.95e-50)
		tmp = t_1;
	elseif (x <= 4.5e-44)
		tmp = t_3;
	elseif (x <= 1.05e+56)
		tmp = t_1;
	elseif (x <= 1.6e+71)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3e+105], t$95$2, If[LessEqual[x, -1.95e-50], t$95$1, If[LessEqual[x, 4.5e-44], t$95$3, If[LessEqual[x, 1.05e+56], t$95$1, If[LessEqual[x, 1.6e+71], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.0000000000000001e105 or 1.60000000000000012e71 < x

   1. Initial program 50.3%

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

      1. associate-/l* 65.8%

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

   3. Simplified 65.8%

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

   5. Taylor expanded in z around 0 46.3%

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

   6. Taylor expanded in t around 0 48.3%

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

      1. associate-*r* 48.3%

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

      2. neg-mul-1 48.3%

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

   8. Simplified 48.3%

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

   9. Taylor expanded in y around 0 48.3%

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

       1. mul-1-neg 48.3%

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

       2. associate-*r/ 56.2%

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

       3. sub-neg 56.2%

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

   11. Simplified 56.2%

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

   if -3.0000000000000001e105 < x < -1.9500000000000001e-50 or 4.4999999999999999e-44 < x < 1.05000000000000009e56

   1. Initial program 71.4%

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

      1. associate-/l* 83.7%

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

   3. Simplified 83.7%

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

   5. Taylor expanded in y around inf 59.3%

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

      1. div-sub 59.3%

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

   7. Simplified 59.3%

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

   if -1.9500000000000001e-50 < x < 4.4999999999999999e-44 or 1.05000000000000009e56 < x < 1.60000000000000012e71

   1. Initial program 78.7%

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

      1. associate-/l* 80.2%

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

   3. Simplified 80.2%

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

   5. Taylor expanded in x around 0 65.9%

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

      1. associate-/l* 77.4%

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

   7. Simplified 77.4%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+105}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-50}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-44}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+56}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+71}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 82.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+134}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot x}{z}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 10^{-276}:\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+223}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= z -1.35e+134)
     (+ t (/ (* (- y a) x) z))
     (if (<= z -1.55e-174)
       t_1
       (if (<= z 1e-276)
         (+ x (* (- x t) (/ (- z y) a)))
         (if (<= z 2.25e+223) t_1 (+ t (/ (* y (- x t)) z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (z <= -1.35e+134) {
		tmp = t + (((y - a) * x) / z);
	} else if (z <= -1.55e-174) {
		tmp = t_1;
	} else if (z <= 1e-276) {
		tmp = x + ((x - t) * ((z - y) / a));
	} else if (z <= 2.25e+223) {
		tmp = t_1;
	} else {
		tmp = t + ((y * (x - t)) / 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) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if (z <= (-1.35d+134)) then
        tmp = t + (((y - a) * x) / z)
    else if (z <= (-1.55d-174)) then
        tmp = t_1
    else if (z <= 1d-276) then
        tmp = x + ((x - t) * ((z - y) / a))
    else if (z <= 2.25d+223) then
        tmp = t_1
    else
        tmp = t + ((y * (x - t)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (z <= -1.35e+134) {
		tmp = t + (((y - a) * x) / z);
	} else if (z <= -1.55e-174) {
		tmp = t_1;
	} else if (z <= 1e-276) {
		tmp = x + ((x - t) * ((z - y) / a));
	} else if (z <= 2.25e+223) {
		tmp = t_1;
	} else {
		tmp = t + ((y * (x - t)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if z <= -1.35e+134:
		tmp = t + (((y - a) * x) / z)
	elif z <= -1.55e-174:
		tmp = t_1
	elif z <= 1e-276:
		tmp = x + ((x - t) * ((z - y) / a))
	elif z <= 2.25e+223:
		tmp = t_1
	else:
		tmp = t + ((y * (x - t)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (z <= -1.35e+134)
		tmp = Float64(t + Float64(Float64(Float64(y - a) * x) / z));
	elseif (z <= -1.55e-174)
		tmp = t_1;
	elseif (z <= 1e-276)
		tmp = Float64(x + Float64(Float64(x - t) * Float64(Float64(z - y) / a)));
	elseif (z <= 2.25e+223)
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (z <= -1.35e+134)
		tmp = t + (((y - a) * x) / z);
	elseif (z <= -1.55e-174)
		tmp = t_1;
	elseif (z <= 1e-276)
		tmp = x + ((x - t) * ((z - y) / a));
	elseif (z <= 2.25e+223)
		tmp = t_1;
	else
		tmp = t + ((y * (x - t)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+134], N[(t + N[(N[(N[(y - a), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.55e-174], t$95$1, If[LessEqual[z, 1e-276], N[(x + N[(N[(x - t), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.25e+223], t$95$1, N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.35e134

   1. Initial program 26.4%

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

      1. associate-/l* 48.6%

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

   3. Simplified 48.6%

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

   5. Taylor expanded in z around inf 73.1%

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

      1. associate--l+ 73.1%

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

      2. associate-*r/ 73.1%

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

      3. associate-*r/ 73.1%

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

      4. mul-1-neg 73.1%

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

      5. div-sub 73.1%

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

      6. mul-1-neg 73.1%

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

      7. distribute-lft-out-- 73.1%

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

      8. associate-*r/ 73.1%

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

      9. mul-1-neg 73.1%

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

      10. unsub-neg 73.1%

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

      11. distribute-rgt-out-- 73.1%

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

   7. Simplified 73.1%

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

   8. Taylor expanded in t around 0 80.5%

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

      1. associate-*r/ 80.5%

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

      2. associate-*r* 80.5%

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

      3. neg-mul-1 80.5%

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

   10. Simplified 80.5%

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

   if -1.35e134 < z < -1.5499999999999999e-174 or 1e-276 < z < 2.25e223

   1. Initial program 74.7%

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

      1. associate-/l* 87.0%

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

   3. Simplified 87.0%

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

   if -1.5499999999999999e-174 < z < 1e-276

   1. Initial program 95.1%

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

      1. associate-/l* 82.7%

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

   3. Simplified 82.7%

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

   5. Taylor expanded in a around inf 92.5%

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

      1. associate-/l* 95.0%

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

   7. Simplified 95.0%

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

   if 2.25e223 < z

   1. Initial program 27.2%

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

      1. associate-/l* 26.8%

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

   3. Simplified 26.8%

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

   5. Taylor expanded in z around inf 78.7%

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

      1. associate--l+ 78.7%

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

      2. associate-*r/ 78.7%

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

      3. associate-*r/ 78.7%

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

      4. mul-1-neg 78.7%

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

      5. div-sub 78.7%

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

      6. mul-1-neg 78.7%

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

      7. distribute-lft-out-- 78.7%

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

      8. associate-*r/ 78.7%

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

      9. mul-1-neg 78.7%

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

      10. unsub-neg 78.7%

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

      11. distribute-rgt-out-- 78.7%

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

   7. Simplified 78.7%

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

   8. Taylor expanded in y around inf 87.7%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+134}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot x}{z}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-174}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 10^{-276}:\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+223}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 82.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+133}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot x}{z}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-175}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-227}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{1}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+223}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= z -3.1e+133)
     (+ t (/ (* (- y a) x) z))
     (if (<= z -1.95e-175)
       t_1
       (if (<= z 1.35e-227)
         (+ x (* (- t x) (/ 1.0 (/ (- a z) y))))
         (if (<= z 1.7e+223) t_1 (+ t (/ (* y (- x t)) z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (z <= -3.1e+133) {
		tmp = t + (((y - a) * x) / z);
	} else if (z <= -1.95e-175) {
		tmp = t_1;
	} else if (z <= 1.35e-227) {
		tmp = x + ((t - x) * (1.0 / ((a - z) / y)));
	} else if (z <= 1.7e+223) {
		tmp = t_1;
	} else {
		tmp = t + ((y * (x - t)) / 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) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if (z <= (-3.1d+133)) then
        tmp = t + (((y - a) * x) / z)
    else if (z <= (-1.95d-175)) then
        tmp = t_1
    else if (z <= 1.35d-227) then
        tmp = x + ((t - x) * (1.0d0 / ((a - z) / y)))
    else if (z <= 1.7d+223) then
        tmp = t_1
    else
        tmp = t + ((y * (x - t)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (z <= -3.1e+133) {
		tmp = t + (((y - a) * x) / z);
	} else if (z <= -1.95e-175) {
		tmp = t_1;
	} else if (z <= 1.35e-227) {
		tmp = x + ((t - x) * (1.0 / ((a - z) / y)));
	} else if (z <= 1.7e+223) {
		tmp = t_1;
	} else {
		tmp = t + ((y * (x - t)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if z <= -3.1e+133:
		tmp = t + (((y - a) * x) / z)
	elif z <= -1.95e-175:
		tmp = t_1
	elif z <= 1.35e-227:
		tmp = x + ((t - x) * (1.0 / ((a - z) / y)))
	elif z <= 1.7e+223:
		tmp = t_1
	else:
		tmp = t + ((y * (x - t)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (z <= -3.1e+133)
		tmp = Float64(t + Float64(Float64(Float64(y - a) * x) / z));
	elseif (z <= -1.95e-175)
		tmp = t_1;
	elseif (z <= 1.35e-227)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(1.0 / Float64(Float64(a - z) / y))));
	elseif (z <= 1.7e+223)
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (z <= -3.1e+133)
		tmp = t + (((y - a) * x) / z);
	elseif (z <= -1.95e-175)
		tmp = t_1;
	elseif (z <= 1.35e-227)
		tmp = x + ((t - x) * (1.0 / ((a - z) / y)));
	elseif (z <= 1.7e+223)
		tmp = t_1;
	else
		tmp = t + ((y * (x - t)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e+133], N[(t + N[(N[(N[(y - a), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.95e-175], t$95$1, If[LessEqual[z, 1.35e-227], N[(x + N[(N[(t - x), $MachinePrecision] * N[(1.0 / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+223], t$95$1, N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.1e133

   1. Initial program 26.4%

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

      1. associate-/l* 48.6%

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

   3. Simplified 48.6%

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

   5. Taylor expanded in z around inf 73.1%

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

      1. associate--l+ 73.1%

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

      2. associate-*r/ 73.1%

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

      3. associate-*r/ 73.1%

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

      4. mul-1-neg 73.1%

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

      5. div-sub 73.1%

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

      6. mul-1-neg 73.1%

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

      7. distribute-lft-out-- 73.1%

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

      8. associate-*r/ 73.1%

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

      9. mul-1-neg 73.1%

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

      10. unsub-neg 73.1%

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

      11. distribute-rgt-out-- 73.1%

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

   7. Simplified 73.1%

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

   8. Taylor expanded in t around 0 80.5%

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

      1. associate-*r/ 80.5%

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

      2. associate-*r* 80.5%

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

      3. neg-mul-1 80.5%

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

   10. Simplified 80.5%

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

   if -3.1e133 < z < -1.94999999999999999e-175 or 1.35e-227 < z < 1.6999999999999999e223

   1. Initial program 73.1%

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

      1. associate-/l* 86.5%

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

   3. Simplified 86.5%

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

   if -1.94999999999999999e-175 < z < 1.35e-227

   1. Initial program 94.4%

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

      1. associate-/l* 85.2%

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

   3. Simplified 85.2%

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

      1. associate-*r/ 94.4%

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

      2. clear-num 94.4%

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

      3. associate-/r* 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. associate-/r/ 99.8%

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

   8. Simplified 99.8%

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

   9. Taylor expanded in y around inf 97.6%

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

   if 1.6999999999999999e223 < z

   1. Initial program 27.2%

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

      1. associate-/l* 26.8%

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

   3. Simplified 26.8%

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

   5. Taylor expanded in z around inf 78.7%

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

      1. associate--l+ 78.7%

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

      2. associate-*r/ 78.7%

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

      3. associate-*r/ 78.7%

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

      4. mul-1-neg 78.7%

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

      5. div-sub 78.7%

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

      6. mul-1-neg 78.7%

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

      7. distribute-lft-out-- 78.7%

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

      8. associate-*r/ 78.7%

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

      9. mul-1-neg 78.7%

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

      10. unsub-neg 78.7%

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

      11. distribute-rgt-out-- 78.7%

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

   7. Simplified 78.7%

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

   8. Taylor expanded in y around inf 87.7%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+133}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot x}{z}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-175}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-227}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{1}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+223}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 82.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+131}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot x}{z}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-175}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 10^{-228}:\\ \;\;\;\;x + \frac{-1}{\frac{\frac{a - z}{y}}{x - t}}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+223}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= z -1.45e+131)
     (+ t (/ (* (- y a) x) z))
     (if (<= z -3.6e-175)
       t_1
       (if (<= z 1e-228)
         (+ x (/ -1.0 (/ (/ (- a z) y) (- x t))))
         (if (<= z 2.6e+223) t_1 (+ t (/ (* y (- x t)) z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (z <= -1.45e+131) {
		tmp = t + (((y - a) * x) / z);
	} else if (z <= -3.6e-175) {
		tmp = t_1;
	} else if (z <= 1e-228) {
		tmp = x + (-1.0 / (((a - z) / y) / (x - t)));
	} else if (z <= 2.6e+223) {
		tmp = t_1;
	} else {
		tmp = t + ((y * (x - t)) / 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) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if (z <= (-1.45d+131)) then
        tmp = t + (((y - a) * x) / z)
    else if (z <= (-3.6d-175)) then
        tmp = t_1
    else if (z <= 1d-228) then
        tmp = x + ((-1.0d0) / (((a - z) / y) / (x - t)))
    else if (z <= 2.6d+223) then
        tmp = t_1
    else
        tmp = t + ((y * (x - t)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (z <= -1.45e+131) {
		tmp = t + (((y - a) * x) / z);
	} else if (z <= -3.6e-175) {
		tmp = t_1;
	} else if (z <= 1e-228) {
		tmp = x + (-1.0 / (((a - z) / y) / (x - t)));
	} else if (z <= 2.6e+223) {
		tmp = t_1;
	} else {
		tmp = t + ((y * (x - t)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if z <= -1.45e+131:
		tmp = t + (((y - a) * x) / z)
	elif z <= -3.6e-175:
		tmp = t_1
	elif z <= 1e-228:
		tmp = x + (-1.0 / (((a - z) / y) / (x - t)))
	elif z <= 2.6e+223:
		tmp = t_1
	else:
		tmp = t + ((y * (x - t)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (z <= -1.45e+131)
		tmp = Float64(t + Float64(Float64(Float64(y - a) * x) / z));
	elseif (z <= -3.6e-175)
		tmp = t_1;
	elseif (z <= 1e-228)
		tmp = Float64(x + Float64(-1.0 / Float64(Float64(Float64(a - z) / y) / Float64(x - t))));
	elseif (z <= 2.6e+223)
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (z <= -1.45e+131)
		tmp = t + (((y - a) * x) / z);
	elseif (z <= -3.6e-175)
		tmp = t_1;
	elseif (z <= 1e-228)
		tmp = x + (-1.0 / (((a - z) / y) / (x - t)));
	elseif (z <= 2.6e+223)
		tmp = t_1;
	else
		tmp = t + ((y * (x - t)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.45e+131], N[(t + N[(N[(N[(y - a), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.6e-175], t$95$1, If[LessEqual[z, 1e-228], N[(x + N[(-1.0 / N[(N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision] / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+223], t$95$1, N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.45000000000000005e131

   1. Initial program 26.4%

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

      1. associate-/l* 48.6%

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

   3. Simplified 48.6%

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

   5. Taylor expanded in z around inf 73.1%

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

      1. associate--l+ 73.1%

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

      2. associate-*r/ 73.1%

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

      3. associate-*r/ 73.1%

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

      4. mul-1-neg 73.1%

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

      5. div-sub 73.1%

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

      6. mul-1-neg 73.1%

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

      7. distribute-lft-out-- 73.1%

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

      8. associate-*r/ 73.1%

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

      9. mul-1-neg 73.1%

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

      10. unsub-neg 73.1%

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

      11. distribute-rgt-out-- 73.1%

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

   7. Simplified 73.1%

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

   8. Taylor expanded in t around 0 80.5%

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

      1. associate-*r/ 80.5%

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

      2. associate-*r* 80.5%

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

      3. neg-mul-1 80.5%

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

   10. Simplified 80.5%

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

   if -1.45000000000000005e131 < z < -3.6e-175 or 1.00000000000000003e-228 < z < 2.6000000000000002e223

   1. Initial program 73.1%

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

      1. associate-/l* 86.5%

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

   3. Simplified 86.5%

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

   if -3.6e-175 < z < 1.00000000000000003e-228

   1. Initial program 94.4%

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

      1. associate-/l* 85.2%

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

   3. Simplified 85.2%

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

      1. associate-*r/ 94.4%

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

      2. clear-num 94.4%

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

      3. associate-/r* 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around inf 97.7%

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

   if 2.6000000000000002e223 < z

   1. Initial program 27.2%

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

      1. associate-/l* 26.8%

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

   3. Simplified 26.8%

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

   5. Taylor expanded in z around inf 78.7%

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

      1. associate--l+ 78.7%

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

      2. associate-*r/ 78.7%

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

      3. associate-*r/ 78.7%

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

      4. mul-1-neg 78.7%

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

      5. div-sub 78.7%

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

      6. mul-1-neg 78.7%

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

      7. distribute-lft-out-- 78.7%

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

      8. associate-*r/ 78.7%

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

      9. mul-1-neg 78.7%

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

      10. unsub-neg 78.7%

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

      11. distribute-rgt-out-- 78.7%

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

   7. Simplified 78.7%

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

   8. Taylor expanded in y around inf 87.7%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+131}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot x}{z}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-175}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 10^{-228}:\\ \;\;\;\;x + \frac{-1}{\frac{\frac{a - z}{y}}{x - t}}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+223}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 41.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.1 \cdot 10^{-184}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-209}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-133}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+54}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.7e+24)
   x
   (if (<= a -5.1e-184)
     t
     (if (<= a 9.2e-209)
       (* y (/ (- x t) z))
       (if (<= a 1.3e-133) t (if (<= a 2.2e+54) (* t (/ y (- a z))) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.7e+24) {
		tmp = x;
	} else if (a <= -5.1e-184) {
		tmp = t;
	} else if (a <= 9.2e-209) {
		tmp = y * ((x - t) / z);
	} else if (a <= 1.3e-133) {
		tmp = t;
	} else if (a <= 2.2e+54) {
		tmp = t * (y / (a - z));
	} 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 (a <= (-2.7d+24)) then
        tmp = x
    else if (a <= (-5.1d-184)) then
        tmp = t
    else if (a <= 9.2d-209) then
        tmp = y * ((x - t) / z)
    else if (a <= 1.3d-133) then
        tmp = t
    else if (a <= 2.2d+54) then
        tmp = t * (y / (a - z))
    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 (a <= -2.7e+24) {
		tmp = x;
	} else if (a <= -5.1e-184) {
		tmp = t;
	} else if (a <= 9.2e-209) {
		tmp = y * ((x - t) / z);
	} else if (a <= 1.3e-133) {
		tmp = t;
	} else if (a <= 2.2e+54) {
		tmp = t * (y / (a - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.7e+24:
		tmp = x
	elif a <= -5.1e-184:
		tmp = t
	elif a <= 9.2e-209:
		tmp = y * ((x - t) / z)
	elif a <= 1.3e-133:
		tmp = t
	elif a <= 2.2e+54:
		tmp = t * (y / (a - z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.7e+24)
		tmp = x;
	elseif (a <= -5.1e-184)
		tmp = t;
	elseif (a <= 9.2e-209)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	elseif (a <= 1.3e-133)
		tmp = t;
	elseif (a <= 2.2e+54)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.7e+24)
		tmp = x;
	elseif (a <= -5.1e-184)
		tmp = t;
	elseif (a <= 9.2e-209)
		tmp = y * ((x - t) / z);
	elseif (a <= 1.3e-133)
		tmp = t;
	elseif (a <= 2.2e+54)
		tmp = t * (y / (a - z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.7e+24], x, If[LessEqual[a, -5.1e-184], t, If[LessEqual[a, 9.2e-209], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.3e-133], t, If[LessEqual[a, 2.2e+54], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.7e24 or 2.1999999999999999e54 < a

   1. Initial program 73.6%

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

      1. associate-/l* 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in a around inf 47.5%

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

   if -2.7e24 < a < -5.0999999999999998e-184 or 9.1999999999999999e-209 < a < 1.3e-133

   1. Initial program 57.3%

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

      1. associate-/l* 59.4%

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

   3. Simplified 59.4%

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

   5. Taylor expanded in z around inf 47.5%

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

   if -5.0999999999999998e-184 < a < 9.1999999999999999e-209

   1. Initial program 59.1%

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

      1. associate-/l* 65.3%

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

   3. Simplified 65.3%

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

      1. clear-num 65.2%

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

      2. un-div-inv 65.4%

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

   6. Applied egg-rr 65.4%

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

   7. Taylor expanded in a around 0 61.8%

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

      1. neg-mul-1 61.8%

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

      2. distribute-neg-frac2 61.8%

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

   9. Simplified 61.8%

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

   10. Taylor expanded in y around inf 58.2%

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

       1. div-sub 58.3%

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

   12. Simplified 58.3%

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

   if 1.3e-133 < a < 2.1999999999999999e54

   1. Initial program 66.6%

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

      1. associate-/l* 68.8%

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

   3. Simplified 68.8%

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

   5. Taylor expanded in x around 0 46.7%

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

   6. Taylor expanded in y around inf 33.2%

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

      1. associate-/l* 33.2%

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

   8. Simplified 33.2%

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

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.1 \cdot 10^{-184}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-209}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-133}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+54}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 59.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+67} \lor \neg \left(x \leq -7 \cdot 10^{-34} \lor \neg \left(x \leq -1.3 \cdot 10^{-55}\right) \land x \leq 1.5 \cdot 10^{+19}\right):\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.3e+67)
         (not (or (<= x -7e-34) (and (not (<= x -1.3e-55)) (<= x 1.5e+19)))))
   (- x (* x (/ y a)))
   (* t (/ (- y z) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.3e+67) || !((x <= -7e-34) || (!(x <= -1.3e-55) && (x <= 1.5e+19)))) {
		tmp = x - (x * (y / a));
	} else {
		tmp = t * ((y - z) / (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 ((x <= (-1.3d+67)) .or. (.not. (x <= (-7d-34)) .or. (.not. (x <= (-1.3d-55))) .and. (x <= 1.5d+19))) then
        tmp = x - (x * (y / a))
    else
        tmp = t * ((y - z) / (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 ((x <= -1.3e+67) || !((x <= -7e-34) || (!(x <= -1.3e-55) && (x <= 1.5e+19)))) {
		tmp = x - (x * (y / a));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1.3e+67) or not ((x <= -7e-34) or (not (x <= -1.3e-55) and (x <= 1.5e+19))):
		tmp = x - (x * (y / a))
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.3e+67) || !((x <= -7e-34) || (!(x <= -1.3e-55) && (x <= 1.5e+19))))
		tmp = Float64(x - Float64(x * Float64(y / a)));
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -1.3e+67) || ~(((x <= -7e-34) || (~((x <= -1.3e-55)) && (x <= 1.5e+19)))))
		tmp = x - (x * (y / a));
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.3e+67], N[Not[Or[LessEqual[x, -7e-34], And[N[Not[LessEqual[x, -1.3e-55]], $MachinePrecision], LessEqual[x, 1.5e+19]]]], $MachinePrecision]], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3e67 or -7e-34 < x < -1.2999999999999999e-55 or 1.5e19 < x

   1. Initial program 56.0%

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

      1. associate-/l* 70.1%

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

   3. Simplified 70.1%

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

   5. Taylor expanded in z around 0 47.5%

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

   6. Taylor expanded in t around 0 48.6%

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

      1. associate-*r* 48.6%

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

      2. neg-mul-1 48.6%

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

   8. Simplified 48.6%

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

   9. Taylor expanded in y around 0 48.6%

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

       1. mul-1-neg 48.6%

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

       2. associate-*r/ 55.4%

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

       3. sub-neg 55.4%

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

   11. Simplified 55.4%

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

   if -1.3e67 < x < -7e-34 or -1.2999999999999999e-55 < x < 1.5e19

   1. Initial program 76.7%

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

      1. associate-/l* 80.8%

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

   3. Simplified 80.8%

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

   5. Taylor expanded in x around 0 59.6%

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

      1. associate-/l* 71.1%

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

   7. Simplified 71.1%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+67} \lor \neg \left(x \leq -7 \cdot 10^{-34} \lor \neg \left(x \leq -1.3 \cdot 10^{-55}\right) \land x \leq 1.5 \cdot 10^{+19}\right):\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 63.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + y \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -1.85 \cdot 10^{+17}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-192}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-222}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 29000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (* y (/ (- t x) a)))))
   (if (<= a -1.85e+17)
     t_2
     (if (<= a -4e-192)
       t_1
       (if (<= a -2.4e-222)
         (* y (/ x z))
         (if (<= a 29000000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -1.85e+17) {
		tmp = t_2;
	} else if (a <= -4e-192) {
		tmp = t_1;
	} else if (a <= -2.4e-222) {
		tmp = y * (x / z);
	} else if (a <= 29000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x + (y * ((t - x) / a))
    if (a <= (-1.85d+17)) then
        tmp = t_2
    else if (a <= (-4d-192)) then
        tmp = t_1
    else if (a <= (-2.4d-222)) then
        tmp = y * (x / z)
    else if (a <= 29000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -1.85e+17) {
		tmp = t_2;
	} else if (a <= -4e-192) {
		tmp = t_1;
	} else if (a <= -2.4e-222) {
		tmp = y * (x / z);
	} else if (a <= 29000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x + (y * ((t - x) / a))
	tmp = 0
	if a <= -1.85e+17:
		tmp = t_2
	elif a <= -4e-192:
		tmp = t_1
	elif a <= -2.4e-222:
		tmp = y * (x / z)
	elif a <= 29000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x + Float64(y * Float64(Float64(t - x) / a)))
	tmp = 0.0
	if (a <= -1.85e+17)
		tmp = t_2;
	elseif (a <= -4e-192)
		tmp = t_1;
	elseif (a <= -2.4e-222)
		tmp = Float64(y * Float64(x / z));
	elseif (a <= 29000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x + (y * ((t - x) / a));
	tmp = 0.0;
	if (a <= -1.85e+17)
		tmp = t_2;
	elseif (a <= -4e-192)
		tmp = t_1;
	elseif (a <= -2.4e-222)
		tmp = y * (x / z);
	elseif (a <= 29000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.85e+17], t$95$2, If[LessEqual[a, -4e-192], t$95$1, If[LessEqual[a, -2.4e-222], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 29000000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.85e17 or 2.9e10 < a

   1. Initial program 75.6%

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

      1. associate-/l* 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in z around 0 67.1%

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

      1. associate-/l* 74.0%

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

   7. Simplified 74.0%

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

   if -1.85e17 < a < -4.0000000000000004e-192 or -2.39999999999999993e-222 < a < 2.9e10

   1. Initial program 58.7%

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

      1. associate-/l* 60.5%

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

   3. Simplified 60.5%

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

   5. Taylor expanded in x around 0 46.0%

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

      1. associate-/l* 59.6%

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

   7. Simplified 59.6%

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

   if -4.0000000000000004e-192 < a < -2.39999999999999993e-222

   1. Initial program 36.9%

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

      1. associate-/l* 56.7%

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

   3. Simplified 56.7%

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

      1. clear-num 56.5%

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

      2. un-div-inv 56.5%

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

   6. Applied egg-rr 56.5%

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

   7. Taylor expanded in a around 0 56.5%

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

      1. neg-mul-1 56.5%

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

      2. distribute-neg-frac2 56.5%

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

   9. Simplified 56.5%

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

   10. Taylor expanded in y around inf 77.9%

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

       1. div-sub 77.9%

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

   12. Simplified 77.9%

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

   13. Taylor expanded in x around inf 78.0%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{+17}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-192}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-222}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 29000000000:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 63.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -13800000000:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq -1.76 \cdot 10^{-16}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+21}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -2.8e+86)
     t_1
     (if (<= z -13800000000.0)
       (* y (/ (- t x) (- a z)))
       (if (<= z -1.76e-16)
         (* t (/ z (- z a)))
         (if (<= z 3.8e+21) (+ x (/ (* y (- t x)) a)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -2.8e+86) {
		tmp = t_1;
	} else if (z <= -13800000000.0) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= -1.76e-16) {
		tmp = t * (z / (z - a));
	} else if (z <= 3.8e+21) {
		tmp = x + ((y * (t - x)) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (z <= (-2.8d+86)) then
        tmp = t_1
    else if (z <= (-13800000000.0d0)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= (-1.76d-16)) then
        tmp = t * (z / (z - a))
    else if (z <= 3.8d+21) then
        tmp = x + ((y * (t - x)) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -2.8e+86) {
		tmp = t_1;
	} else if (z <= -13800000000.0) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= -1.76e-16) {
		tmp = t * (z / (z - a));
	} else if (z <= 3.8e+21) {
		tmp = x + ((y * (t - x)) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -2.8e+86:
		tmp = t_1
	elif z <= -13800000000.0:
		tmp = y * ((t - x) / (a - z))
	elif z <= -1.76e-16:
		tmp = t * (z / (z - a))
	elif z <= 3.8e+21:
		tmp = x + ((y * (t - x)) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -2.8e+86)
		tmp = t_1;
	elseif (z <= -13800000000.0)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= -1.76e-16)
		tmp = Float64(t * Float64(z / Float64(z - a)));
	elseif (z <= 3.8e+21)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -2.8e+86)
		tmp = t_1;
	elseif (z <= -13800000000.0)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= -1.76e-16)
		tmp = t * (z / (z - a));
	elseif (z <= 3.8e+21)
		tmp = x + ((y * (t - x)) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e+86], t$95$1, If[LessEqual[z, -13800000000.0], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.76e-16], N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+21], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.80000000000000004e86 or 3.8e21 < z

   1. Initial program 37.1%

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

      1. associate-/l* 58.4%

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

   3. Simplified 58.4%

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

   5. Taylor expanded in x around 0 34.1%

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

      1. associate-/l* 54.8%

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

   7. Simplified 54.8%

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

   if -2.80000000000000004e86 < z < -1.38e10

   1. Initial program 62.9%

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

      1. associate-/l* 87.1%

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

   3. Simplified 87.1%

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

   5. Taylor expanded in y around inf 59.5%

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

      1. div-sub 59.5%

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

   7. Simplified 59.5%

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

   if -1.38e10 < z < -1.76e-16

   1. Initial program 35.2%

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

      1. associate-/l* 34.7%

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

   3. Simplified 34.7%

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

   5. Taylor expanded in x around 0 100.0%

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

   6. Taylor expanded in y around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. associate-/l* 100.0%

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

   8. Simplified 100.0%

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

   if -1.76e-16 < z < 3.8e21

   1. Initial program 92.7%

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

      1. associate-/l* 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in z around 0 79.4%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -13800000000:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq -1.76 \cdot 10^{-16}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+21}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 69.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot \frac{x - t}{z}\\ t_2 := x + y \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -1.4 \cdot 10^{-22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-89}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;a \leq 14500000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* y (/ (- x t) z)))) (t_2 (+ x (* y (/ (- t x) a)))))
   (if (<= a -1.4e-22)
     t_2
     (if (<= a 2.2e-133)
       t_1
       (if (<= a 2.2e-89)
         (/ (* y (- t x)) (- a z))
         (if (<= a 14500000000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (y * ((x - t) / z));
	double t_2 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -1.4e-22) {
		tmp = t_2;
	} else if (a <= 2.2e-133) {
		tmp = t_1;
	} else if (a <= 2.2e-89) {
		tmp = (y * (t - x)) / (a - z);
	} else if (a <= 14500000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + (y * ((x - t) / z))
    t_2 = x + (y * ((t - x) / a))
    if (a <= (-1.4d-22)) then
        tmp = t_2
    else if (a <= 2.2d-133) then
        tmp = t_1
    else if (a <= 2.2d-89) then
        tmp = (y * (t - x)) / (a - z)
    else if (a <= 14500000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (y * ((x - t) / z));
	double t_2 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -1.4e-22) {
		tmp = t_2;
	} else if (a <= 2.2e-133) {
		tmp = t_1;
	} else if (a <= 2.2e-89) {
		tmp = (y * (t - x)) / (a - z);
	} else if (a <= 14500000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (y * ((x - t) / z))
	t_2 = x + (y * ((t - x) / a))
	tmp = 0
	if a <= -1.4e-22:
		tmp = t_2
	elif a <= 2.2e-133:
		tmp = t_1
	elif a <= 2.2e-89:
		tmp = (y * (t - x)) / (a - z)
	elif a <= 14500000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(y * Float64(Float64(x - t) / z)))
	t_2 = Float64(x + Float64(y * Float64(Float64(t - x) / a)))
	tmp = 0.0
	if (a <= -1.4e-22)
		tmp = t_2;
	elseif (a <= 2.2e-133)
		tmp = t_1;
	elseif (a <= 2.2e-89)
		tmp = Float64(Float64(y * Float64(t - x)) / Float64(a - z));
	elseif (a <= 14500000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (y * ((x - t) / z));
	t_2 = x + (y * ((t - x) / a));
	tmp = 0.0;
	if (a <= -1.4e-22)
		tmp = t_2;
	elseif (a <= 2.2e-133)
		tmp = t_1;
	elseif (a <= 2.2e-89)
		tmp = (y * (t - x)) / (a - z);
	elseif (a <= 14500000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.4e-22], t$95$2, If[LessEqual[a, 2.2e-133], t$95$1, If[LessEqual[a, 2.2e-89], N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 14500000000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.39999999999999997e-22 or 1.45e13 < a

   1. Initial program 76.2%

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

      1. associate-/l* 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in z around 0 66.7%

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

      1. associate-/l* 73.2%

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

   7. Simplified 73.2%

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

   if -1.39999999999999997e-22 < a < 2.2000000000000001e-133 or 2.20000000000000012e-89 < a < 1.45e13

   1. Initial program 53.5%

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

      1. associate-/l* 59.7%

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

   3. Simplified 59.7%

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

   5. Taylor expanded in z around inf 75.8%

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

      1. associate--l+ 75.8%

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

      2. associate-*r/ 75.8%

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

      3. associate-*r/ 75.8%

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

      4. mul-1-neg 75.8%

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

      5. div-sub 75.8%

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

      6. mul-1-neg 75.8%

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

      7. distribute-lft-out-- 75.8%

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

      8. associate-*r/ 75.8%

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

      9. mul-1-neg 75.8%

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

      10. unsub-neg 75.8%

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

      11. distribute-rgt-out-- 75.8%

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

   7. Simplified 75.8%

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

   8. Taylor expanded in y around inf 71.3%

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

      1. associate-/l* 76.4%

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

   10. Simplified 76.4%

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

   if 2.2000000000000001e-133 < a < 2.20000000000000012e-89

   1. Initial program 78.2%

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

      1. associate-/l* 57.0%

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

   3. Simplified 57.0%

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

   5. Taylor expanded in y around -inf 70.3%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{-22}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-133}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-89}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;a \leq 14500000000000:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 64.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+130}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot x}{z}\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{+23}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 46:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.8e+130)
   (+ t (/ (* (- y a) x) z))
   (if (<= z -2.05e+23)
     (* y (/ (- t x) (- a z)))
     (if (<= z 46.0) (+ x (/ (* y (- t x)) a)) (+ t (* y (/ (- x t) z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e+130) {
		tmp = t + (((y - a) * x) / z);
	} else if (z <= -2.05e+23) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 46.0) {
		tmp = x + ((y * (t - x)) / a);
	} else {
		tmp = t + (y * ((x - t) / 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 (z <= (-1.8d+130)) then
        tmp = t + (((y - a) * x) / z)
    else if (z <= (-2.05d+23)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 46.0d0) then
        tmp = x + ((y * (t - x)) / a)
    else
        tmp = t + (y * ((x - t) / 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 (z <= -1.8e+130) {
		tmp = t + (((y - a) * x) / z);
	} else if (z <= -2.05e+23) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 46.0) {
		tmp = x + ((y * (t - x)) / a);
	} else {
		tmp = t + (y * ((x - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.8e+130:
		tmp = t + (((y - a) * x) / z)
	elif z <= -2.05e+23:
		tmp = y * ((t - x) / (a - z))
	elif z <= 46.0:
		tmp = x + ((y * (t - x)) / a)
	else:
		tmp = t + (y * ((x - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.8e+130)
		tmp = Float64(t + Float64(Float64(Float64(y - a) * x) / z));
	elseif (z <= -2.05e+23)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 46.0)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / a));
	else
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.8e+130)
		tmp = t + (((y - a) * x) / z);
	elseif (z <= -2.05e+23)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 46.0)
		tmp = x + ((y * (t - x)) / a);
	else
		tmp = t + (y * ((x - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.8e+130], N[(t + N[(N[(N[(y - a), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.05e+23], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 46.0], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.8000000000000001e130

   1. Initial program 26.4%

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

      1. associate-/l* 48.6%

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

   3. Simplified 48.6%

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

   5. Taylor expanded in z around inf 73.1%

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

      1. associate--l+ 73.1%

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

      2. associate-*r/ 73.1%

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

      3. associate-*r/ 73.1%

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

      4. mul-1-neg 73.1%

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

      5. div-sub 73.1%

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

      6. mul-1-neg 73.1%

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

      7. distribute-lft-out-- 73.1%

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

      8. associate-*r/ 73.1%

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

      9. mul-1-neg 73.1%

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

      10. unsub-neg 73.1%

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

      11. distribute-rgt-out-- 73.1%

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

   7. Simplified 73.1%

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

   8. Taylor expanded in t around 0 80.5%

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

      1. associate-*r/ 80.5%

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

      2. associate-*r* 80.5%

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

      3. neg-mul-1 80.5%

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

   10. Simplified 80.5%

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

   if -1.8000000000000001e130 < z < -2.04999999999999998e23

   1. Initial program 56.5%

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

      1. associate-/l* 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in y around inf 56.8%

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

      1. div-sub 56.8%

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

   7. Simplified 56.8%

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

   if -2.04999999999999998e23 < z < 46

   1. Initial program 92.8%

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

      1. associate-/l* 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in z around 0 79.0%

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

   if 46 < z

   1. Initial program 43.0%

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

      1. associate-/l* 60.2%

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

   3. Simplified 60.2%

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

   5. Taylor expanded in z around inf 61.4%

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

      1. associate--l+ 61.4%

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

      2. associate-*r/ 61.4%

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

      3. associate-*r/ 61.4%

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

      4. mul-1-neg 61.4%

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

      5. div-sub 61.4%

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

      6. mul-1-neg 61.4%

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

      7. distribute-lft-out-- 61.4%

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

      8. associate-*r/ 61.4%

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

      9. mul-1-neg 61.4%

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

      10. unsub-neg 61.4%

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

      11. distribute-rgt-out-- 61.4%

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

   7. Simplified 61.4%

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

   8. Taylor expanded in y around inf 60.1%

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

      1. associate-/l* 64.0%

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

   10. Simplified 64.0%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+130}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot x}{z}\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{+23}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 46:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 70.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+117}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot x}{z}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+43}:\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.05e+117)
   (+ t (/ (* (- y a) x) z))
   (if (<= z 4.3e+43)
     (+ x (* (- x t) (/ (- z y) a)))
     (+ t (* y (/ (- x t) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.05e+117) {
		tmp = t + (((y - a) * x) / z);
	} else if (z <= 4.3e+43) {
		tmp = x + ((x - t) * ((z - y) / a));
	} else {
		tmp = t + (y * ((x - t) / 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 (z <= (-2.05d+117)) then
        tmp = t + (((y - a) * x) / z)
    else if (z <= 4.3d+43) then
        tmp = x + ((x - t) * ((z - y) / a))
    else
        tmp = t + (y * ((x - t) / 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 (z <= -2.05e+117) {
		tmp = t + (((y - a) * x) / z);
	} else if (z <= 4.3e+43) {
		tmp = x + ((x - t) * ((z - y) / a));
	} else {
		tmp = t + (y * ((x - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.05e+117:
		tmp = t + (((y - a) * x) / z)
	elif z <= 4.3e+43:
		tmp = x + ((x - t) * ((z - y) / a))
	else:
		tmp = t + (y * ((x - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.05e+117)
		tmp = Float64(t + Float64(Float64(Float64(y - a) * x) / z));
	elseif (z <= 4.3e+43)
		tmp = Float64(x + Float64(Float64(x - t) * Float64(Float64(z - y) / a)));
	else
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.05e+117)
		tmp = t + (((y - a) * x) / z);
	elseif (z <= 4.3e+43)
		tmp = x + ((x - t) * ((z - y) / a));
	else
		tmp = t + (y * ((x - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.05e+117], N[(t + N[(N[(N[(y - a), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.3e+43], N[(x + N[(N[(x - t), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.05e117

   1. Initial program 25.9%

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

      1. associate-/l* 49.8%

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

   3. Simplified 49.8%

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

   5. Taylor expanded in z around inf 71.4%

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

      1. associate--l+ 71.4%

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

      2. associate-*r/ 71.4%

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

      3. associate-*r/ 71.4%

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

      4. mul-1-neg 71.4%

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

      5. div-sub 71.4%

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

      6. mul-1-neg 71.4%

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

      7. distribute-lft-out-- 71.4%

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

      8. associate-*r/ 71.4%

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

      9. mul-1-neg 71.4%

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

      10. unsub-neg 71.4%

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

      11. distribute-rgt-out-- 71.4%

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

   7. Simplified 71.4%

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

   8. Taylor expanded in t around 0 78.6%

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

      1. associate-*r/ 78.6%

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

      2. associate-*r* 78.6%

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

      3. neg-mul-1 78.6%

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

   10. Simplified 78.6%

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

   if -2.05e117 < z < 4.3e43

   1. Initial program 86.1%

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

      1. associate-/l* 88.3%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in a around inf 71.8%

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

      1. associate-/l* 77.1%

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

   7. Simplified 77.1%

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

   if 4.3e43 < z

   1. Initial program 37.8%

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

      1. associate-/l* 56.4%

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

   3. Simplified 56.4%

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

   5. Taylor expanded in z around inf 63.2%

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

      1. associate--l+ 63.2%

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

      2. associate-*r/ 63.2%

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

      3. associate-*r/ 63.2%

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

      4. mul-1-neg 63.2%

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

      5. div-sub 63.2%

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

      6. mul-1-neg 63.2%

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

      7. distribute-lft-out-- 63.2%

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

      8. associate-*r/ 63.2%

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

      9. mul-1-neg 63.2%

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

      10. unsub-neg 63.2%

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

      11. distribute-rgt-out-- 63.3%

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

   7. Simplified 63.3%

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

   8. Taylor expanded in y around inf 63.7%

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

      1. associate-/l* 68.3%

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

   10. Simplified 68.3%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+117}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot x}{z}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+43}:\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-22}:\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a}\\ \mathbf{elif}\;a \leq 60:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.8e-22)
   (+ x (* (- x t) (/ (- z y) a)))
   (if (<= a 60.0)
     (+ t (/ (* (- y a) (- x t)) z))
     (+ x (/ (- y z) (/ a (- t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.8e-22) {
		tmp = x + ((x - t) * ((z - y) / a));
	} else if (a <= 60.0) {
		tmp = t + (((y - a) * (x - t)) / z);
	} else {
		tmp = x + ((y - z) / (a / (t - 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 (a <= (-1.8d-22)) then
        tmp = x + ((x - t) * ((z - y) / a))
    else if (a <= 60.0d0) then
        tmp = t + (((y - a) * (x - t)) / z)
    else
        tmp = x + ((y - z) / (a / (t - 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 (a <= -1.8e-22) {
		tmp = x + ((x - t) * ((z - y) / a));
	} else if (a <= 60.0) {
		tmp = t + (((y - a) * (x - t)) / z);
	} else {
		tmp = x + ((y - z) / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.8e-22:
		tmp = x + ((x - t) * ((z - y) / a))
	elif a <= 60.0:
		tmp = t + (((y - a) * (x - t)) / z)
	else:
		tmp = x + ((y - z) / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.8e-22)
		tmp = Float64(x + Float64(Float64(x - t) * Float64(Float64(z - y) / a)));
	elseif (a <= 60.0)
		tmp = Float64(t + Float64(Float64(Float64(y - a) * Float64(x - t)) / z));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.8e-22)
		tmp = x + ((x - t) * ((z - y) / a));
	elseif (a <= 60.0)
		tmp = t + (((y - a) * (x - t)) / z);
	else
		tmp = x + ((y - z) / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.8e-22], N[(x + N[(N[(x - t), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 60.0], N[(t + N[(N[(N[(y - a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.7999999999999999e-22

   1. Initial program 76.9%

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

      1. associate-/l* 84.8%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in a around inf 68.7%

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

      1. associate-/l* 78.0%

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

   7. Simplified 78.0%

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

   if -1.7999999999999999e-22 < a < 60

   1. Initial program 55.4%

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

      1. associate-/l* 59.5%

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

   3. Simplified 59.5%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 73.5%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate--l+ 73.5%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 73.5%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 73.5%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. mul-1-neg 73.5%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \frac{\color{blue}{-a \cdot \left(t - x\right)}}{z}\right) \]

      5. div-sub 73.5%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - \left(-a \cdot \left(t - x\right)\right)}{z}} \]

      6. mul-1-neg 73.5%

         \[\leadsto t + \frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - \color{blue}{-1 \cdot \left(a \cdot \left(t - x\right)\right)}}{z} \]

      7. distribute-lft-out-- 73.5%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      8. associate-*r/ 73.5%

         \[\leadsto t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      9. mul-1-neg 73.5%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      10. unsub-neg 73.5%

          \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      11. distribute-rgt-out-- 73.5%

          \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

   7. Simplified 73.5%

      \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

   if 60 < a

   1. Initial program 75.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 94.4%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 94.4%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 94.4%

         \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\frac{1}{\frac{a - z}{t - x}}} \]

      2. un-div-inv 94.5%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   6. Applied egg-rr 94.5%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   7. Taylor expanded in a around inf 82.2%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a}{t - x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-22}:\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a}\\ \mathbf{elif}\;a \leq 60:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 69.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.06 \cdot 10^{-22} \lor \neg \left(a \leq 5.5 \cdot 10^{+15}\right):\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.06e-22) (not (<= a 5.5e+15)))
   (+ x (* y (/ (- t x) a)))
   (+ t (* y (/ (- x t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.06e-22) || !(a <= 5.5e+15)) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t + (y * ((x - t) / 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 <= (-1.06d-22)) .or. (.not. (a <= 5.5d+15))) then
        tmp = x + (y * ((t - x) / a))
    else
        tmp = t + (y * ((x - t) / 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 <= -1.06e-22) || !(a <= 5.5e+15)) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t + (y * ((x - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.06e-22) or not (a <= 5.5e+15):
		tmp = x + (y * ((t - x) / a))
	else:
		tmp = t + (y * ((x - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.06e-22) || !(a <= 5.5e+15))
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	else
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.06e-22) || ~((a <= 5.5e+15)))
		tmp = x + (y * ((t - x) / a));
	else
		tmp = t + (y * ((x - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.06e-22], N[Not[LessEqual[a, 5.5e+15]], $MachinePrecision]], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.06000000000000008e-22 or 5.5e15 < a

   1. Initial program 76.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 89.5%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 89.5%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 66.7%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 73.2%

         \[\leadsto x + \color{blue}{y \cdot \frac{t - x}{a}} \]

   7. Simplified 73.2%

      \[\leadsto \color{blue}{x + y \cdot \frac{t - x}{a}} \]

   if -1.06000000000000008e-22 < a < 5.5e15

   1. Initial program 55.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 59.5%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 59.5%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 73.5%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate--l+ 73.5%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 73.5%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 73.5%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. mul-1-neg 73.5%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \frac{\color{blue}{-a \cdot \left(t - x\right)}}{z}\right) \]

      5. div-sub 73.5%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - \left(-a \cdot \left(t - x\right)\right)}{z}} \]

      6. mul-1-neg 73.5%

         \[\leadsto t + \frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - \color{blue}{-1 \cdot \left(a \cdot \left(t - x\right)\right)}}{z} \]

      7. distribute-lft-out-- 73.5%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      8. associate-*r/ 73.5%

         \[\leadsto t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      9. mul-1-neg 73.5%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      10. unsub-neg 73.5%

          \[\leadsto \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      11. distribute-rgt-out-- 73.5%

          \[\leadsto t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]

   7. Simplified 73.5%

      \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

   8. Taylor expanded in y around inf 68.5%

      \[\leadsto t - \color{blue}{\frac{y \cdot \left(t - x\right)}{z}} \]
   9. Step-by-step derivation

      1. associate-/l* 72.4%

         \[\leadsto t - \color{blue}{y \cdot \frac{t - x}{z}} \]

   10. Simplified 72.4%

       \[\leadsto t - \color{blue}{y \cdot \frac{t - x}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.06 \cdot 10^{-22} \lor \neg \left(a \leq 5.5 \cdot 10^{+15}\right):\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 55.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+91} \lor \neg \left(z \leq 4.1 \cdot 10^{+44}\right):\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.4e+91) (not (<= z 4.1e+44)))
   (* t (/ z (- z a)))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.4e+91) || !(z <= 4.1e+44)) {
		tmp = t * (z / (z - a));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-5.4d+91)) .or. (.not. (z <= 4.1d+44))) then
        tmp = t * (z / (z - a))
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.4e+91) || !(z <= 4.1e+44)) {
		tmp = t * (z / (z - a));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.4e+91) or not (z <= 4.1e+44):
		tmp = t * (z / (z - a))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.4e+91) || !(z <= 4.1e+44))
		tmp = Float64(t * Float64(z / Float64(z - a)));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.4e+91) || ~((z <= 4.1e+44)))
		tmp = t * (z / (z - a));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.4e+91], N[Not[LessEqual[z, 4.1e+44]], $MachinePrecision]], N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4e91 or 4.09999999999999965e44 < z

   1. Initial program 33.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 55.0%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 55.0%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 33.7%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]

   6. Taylor expanded in y around 0 28.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot z}{a - z}} \]
   7. Step-by-step derivation

      1. mul-1-neg 28.7%

         \[\leadsto \color{blue}{-\frac{t \cdot z}{a - z}} \]

      2. associate-/l* 50.0%

         \[\leadsto -\color{blue}{t \cdot \frac{z}{a - z}} \]

   8. Simplified 50.0%

      \[\leadsto \color{blue}{-t \cdot \frac{z}{a - z}} \]

   if -5.4e91 < z < 4.09999999999999965e44

   1. Initial program 86.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 88.1%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 88.1%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 69.2%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]

   6. Taylor expanded in t around inf 57.4%

      \[\leadsto x + \color{blue}{\frac{t \cdot y}{a}} \]
   7. Step-by-step derivation

      1. associate-/l* 59.6%

         \[\leadsto x + \color{blue}{t \cdot \frac{y}{a}} \]

   8. Simplified 59.6%

      \[\leadsto x + \color{blue}{t \cdot \frac{y}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+91} \lor \neg \left(z \leq 4.1 \cdot 10^{+44}\right):\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 53.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+89}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+75}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.3e+89) t (if (<= z 3.1e+75) (+ x (* t (/ y a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.3e+89) {
		tmp = t;
	} else if (z <= 3.1e+75) {
		tmp = x + (t * (y / a));
	} else {
		tmp = 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 <= (-4.3d+89)) then
        tmp = t
    else if (z <= 3.1d+75) then
        tmp = x + (t * (y / a))
    else
        tmp = 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 <= -4.3e+89) {
		tmp = t;
	} else if (z <= 3.1e+75) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.3e+89:
		tmp = t
	elif z <= 3.1e+75:
		tmp = x + (t * (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.3e+89)
		tmp = t;
	elseif (z <= 3.1e+75)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.3e+89)
		tmp = t;
	elseif (z <= 3.1e+75)
		tmp = x + (t * (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.3e+89], t, If[LessEqual[z, 3.1e+75], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -4.3000000000000002e89 or 3.1000000000000001e75 < z

   1. Initial program 31.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 52.5%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 52.5%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 48.9%

      \[\leadsto \color{blue}{t} \]

   if -4.3000000000000002e89 < z < 3.1000000000000001e75

   1. Initial program 85.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 87.8%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 87.8%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 66.0%

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(t - x\right)}{a}} \]

   6. Taylor expanded in t around inf 55.4%

      \[\leadsto x + \color{blue}{\frac{t \cdot y}{a}} \]
   7. Step-by-step derivation

      1. associate-/l* 57.5%

         \[\leadsto x + \color{blue}{t \cdot \frac{y}{a}} \]

   8. Simplified 57.5%

      \[\leadsto x + \color{blue}{t \cdot \frac{y}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+89}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+75}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 39.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 165000000:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.9e+23) x (if (<= a 165000000.0) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.9e+23) {
		tmp = x;
	} else if (a <= 165000000.0) {
		tmp = t;
	} 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 (a <= (-1.9d+23)) then
        tmp = x
    else if (a <= 165000000.0d0) then
        tmp = t
    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 (a <= -1.9e+23) {
		tmp = x;
	} else if (a <= 165000000.0) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.9e+23:
		tmp = x
	elif a <= 165000000.0:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.9e+23)
		tmp = x;
	elseif (a <= 165000000.0)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.9e+23)
		tmp = x;
	elseif (a <= 165000000.0)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.9e+23], x, If[LessEqual[a, 165000000.0], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.89999999999999987e23 or 1.65e8 < a

   1. Initial program 75.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 90.2%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 90.2%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 45.1%

      \[\leadsto \color{blue}{x} \]

   if -1.89999999999999987e23 < a < 1.65e8

   1. Initial program 57.9%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 60.8%

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

   3. Simplified 60.8%

      \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 38.5%

      \[\leadsto \color{blue}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 165000000:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 24.7% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 t)

C

double code(double x, double y, double z, double t, double a) {
	return 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 = t
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return t;
}

Python

def code(x, y, z, t, a):
	return t

Julia

function code(x, y, z, t, a)
	return t
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = t;
end

Wolfram

code[x_, y_, z_, t_, a_] := t

Derivation

1. Initial program 66.5%

   \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
2. Step-by-step derivation

   1. associate-/l* 75.5%

      \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

3. Simplified 75.5%

   \[\leadsto \color{blue}{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \]
4. Add Preprocessing

5. Taylor expanded in z around inf 23.7%

   \[\leadsto \color{blue}{t} \]

6. Final simplification 23.7%

   \[\leadsto t \]
7. Add Preprocessing

Developer target: 84.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ y z) (- t x)))))
   (if (< z -1.2536131056095036e+188)
     t_1
     (if (< z 4.446702369113811e+64)
       (+ x (/ (- y z) (/ (- a z) (- t x))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    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 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y / z) * (t - x))
	tmp = 0
	if z < -1.2536131056095036e+188:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y / z) * Float64(t - x)))
	tmp = 0.0
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y / z) * (t - x));
	tmp = 0.0;
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y / z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.2536131056095036e+188], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024055 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :alt
  (if (< z -1.2536131056095036e+188) (- t (* (/ y z) (- t x))) (if (< z 4.446702369113811e+64) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x)))))

  (+ x (/ (* (- y z) (- t x)) (- a z))))