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

Percentage Accurate: 67.8% → 90.6%

Time: 23.1s

Alternatives: 19

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: 67.8% 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: 90.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-293} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - a}{z}, x - t, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (or (<= t_1 -5e-293) (not (<= t_1 0.0)))
     (fma (/ (- y z) (- a z)) (- t x) x)
     (fma (/ (- y a) z) (- x t) t))))

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 ((t_1 <= -5e-293) || !(t_1 <= 0.0)) {
		tmp = fma(((y - z) / (a - z)), (t - x), x);
	} else {
		tmp = fma(((y - a) / z), (x - t), t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -5e-293) || !(t_1 <= 0.0))
		tmp = fma(Float64(Float64(y - z) / Float64(a - z)), Float64(t - x), x);
	else
		tmp = fma(Float64(Float64(y - a) / z), Float64(x - t), t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-293], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * N[(x - t), $MachinePrecision] + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -5.0000000000000003e-293 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 72.6%

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

      1. +-commutative 72.6%

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

      2. associate-*l/ 90.6%

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

      3. fma-def 90.6%

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

   3. Simplified 90.6%

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

   if -5.0000000000000003e-293 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 3.9%

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

      1. associate-*l/ 3.9%

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

   3. Simplified 3.9%

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

   4. Taylor expanded in z around inf 99.4%

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

      1. associate--l+ 99.4%

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

      2. associate-*r/ 99.4%

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

      3. associate-*r/ 99.4%

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

      4. div-sub 99.4%

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

      5. distribute-lft-out-- 99.4%

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

      6. associate-*r/ 99.4%

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

      7. distribute-rgt-out-- 99.4%

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

      8. mul-1-neg 99.4%

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

      9. unsub-neg 99.4%

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

      10. associate-/l* 99.4%

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

   6. Simplified 99.4%

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

   7. Taylor expanded in t around -inf 99.4%

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

      1. neg-mul-1 99.4%

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

      2. unsub-neg 99.4%

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

      3. distribute-lft-out-- 99.4%

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

      4. *-rgt-identity 99.4%

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

      5. associate-*r/ 99.7%

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

      6. associate-+l- 99.7%

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

      7. distribute-rgt-out-- 99.7%

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

      8. associate-*l/ 99.4%

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

      9. associate-*r/ 99.8%

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

      10. *-commutative 99.8%

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

      11. cancel-sign-sub-inv 99.8%

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

      12. +-commutative 99.8%

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

      13. *-commutative 99.8%

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

      14. distribute-rgt-neg-in 99.8%

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

      15. associate-*r/ 99.4%

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

      16. associate-*l/ 99.7%

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

      17. distribute-rgt-neg-in 99.7%

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

      18. fma-def 99.8%

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

   9. Simplified 99.8%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -5 \cdot 10^{-293} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - a}{z}, x - t, t\right)\\ \end{array} \]

Alternative 2: 90.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-293} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - a}{z}, x - t, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (or (<= t_1 -5e-293) (not (<= t_1 0.0)))
     (+ x (* (- t x) (/ (- y z) (- a z))))
     (fma (/ (- y a) z) (- x t) t))))

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 ((t_1 <= -5e-293) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = fma(((y - a) / z), (x - t), t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -5e-293) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / Float64(a - z))));
	else
		tmp = fma(Float64(Float64(y - a) / z), Float64(x - t), t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-293], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * N[(x - t), $MachinePrecision] + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -5.0000000000000003e-293 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 72.6%

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

      1. associate-*l/ 90.6%

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

   3. Simplified 90.6%

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

   if -5.0000000000000003e-293 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 3.9%

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

      1. associate-*l/ 3.9%

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

   3. Simplified 3.9%

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

   4. Taylor expanded in z around inf 99.4%

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

      1. associate--l+ 99.4%

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

      2. associate-*r/ 99.4%

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

      3. associate-*r/ 99.4%

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

      4. div-sub 99.4%

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

      5. distribute-lft-out-- 99.4%

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

      6. associate-*r/ 99.4%

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

      7. distribute-rgt-out-- 99.4%

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

      8. mul-1-neg 99.4%

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

      9. unsub-neg 99.4%

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

      10. associate-/l* 99.4%

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

   6. Simplified 99.4%

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

   7. Taylor expanded in t around -inf 99.4%

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

      1. neg-mul-1 99.4%

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

      2. unsub-neg 99.4%

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

      3. distribute-lft-out-- 99.4%

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

      4. *-rgt-identity 99.4%

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

      5. associate-*r/ 99.7%

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

      6. associate-+l- 99.7%

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

      7. distribute-rgt-out-- 99.7%

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

      8. associate-*l/ 99.4%

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

      9. associate-*r/ 99.8%

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

      10. *-commutative 99.8%

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

      11. cancel-sign-sub-inv 99.8%

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

      12. +-commutative 99.8%

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

      13. *-commutative 99.8%

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

      14. distribute-rgt-neg-in 99.8%

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

      15. associate-*r/ 99.4%

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

      16. associate-*l/ 99.7%

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

      17. distribute-rgt-neg-in 99.7%

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

      18. fma-def 99.8%

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

   9. Simplified 99.8%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -5 \cdot 10^{-293} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - a}{z}, x - t, t\right)\\ \end{array} \]

Alternative 3: 90.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-293} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (or (<= t_1 -5e-293) (not (<= t_1 0.0)))
     (+ x (* (- t x) (/ (- y z) (- a z))))
     (+ t (/ (- x t) (/ z (- y a)))))))

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 ((t_1 <= -5e-293) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = t + ((x - t) / (z / (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) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - z) * (t - x)) / (a - z))
    if ((t_1 <= (-5d-293)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) * ((y - z) / (a - z)))
    else
        tmp = t + ((x - t) / (z / (y - a)))
    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 ((t_1 <= -5e-293) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if (t_1 <= -5e-293) or not (t_1 <= 0.0):
		tmp = x + ((t - x) * ((y - z) / (a - z)))
	else:
		tmp = t + ((x - t) / (z / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -5e-293) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / Float64(a - z))));
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	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 ((t_1 <= -5e-293) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	else
		tmp = t + ((x - t) / (z / (y - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-293], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -5.0000000000000003e-293 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 72.6%

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

      1. associate-*l/ 90.6%

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

   3. Simplified 90.6%

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

   if -5.0000000000000003e-293 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 3.9%

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

      1. associate-*l/ 3.9%

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

   3. Simplified 3.9%

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

   4. Taylor expanded in z around inf 99.4%

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

      1. associate--l+ 99.4%

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

      2. associate-*r/ 99.4%

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

      3. associate-*r/ 99.4%

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

      4. div-sub 99.4%

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

      5. distribute-lft-out-- 99.4%

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

      6. associate-*r/ 99.4%

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

      7. distribute-rgt-out-- 99.4%

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

      8. mul-1-neg 99.4%

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

      9. unsub-neg 99.4%

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

      10. associate-/l* 99.4%

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

   6. Simplified 99.4%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -5 \cdot 10^{-293} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 4: 71.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+94}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+14}:\\ \;\;\;\;x + z \cdot \frac{x - t}{a - z}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-75}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a - z} + 1\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+61}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ t (/ (- x t) (/ z (- y a))))))
   (if (<= z -1.35e+94)
     t_2
     (if (<= z -4.1e+41)
       (+ x (/ y (/ a (- t x))))
       (if (<= z -2e+36)
         (* x (/ (- y a) z))
         (if (<= z -1.1e+14)
           (+ x (* z (/ (- x t) (- a z))))
           (if (<= z -2.1e-24)
             t_1
             (if (<= z -2.9e-75)
               (* x (+ (/ (- z y) (- a z)) 1.0))
               (if (<= z -4.5e-95)
                 t_1
                 (if (<= z 1.8e+61) (+ x (* (- t x) (/ y a))) 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 = t + ((x - t) / (z / (y - a)));
	double tmp;
	if (z <= -1.35e+94) {
		tmp = t_2;
	} else if (z <= -4.1e+41) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= -2e+36) {
		tmp = x * ((y - a) / z);
	} else if (z <= -1.1e+14) {
		tmp = x + (z * ((x - t) / (a - z)));
	} else if (z <= -2.1e-24) {
		tmp = t_1;
	} else if (z <= -2.9e-75) {
		tmp = x * (((z - y) / (a - z)) + 1.0);
	} else if (z <= -4.5e-95) {
		tmp = t_1;
	} else if (z <= 1.8e+61) {
		tmp = x + ((t - x) * (y / a));
	} 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 = t + ((x - t) / (z / (y - a)))
    if (z <= (-1.35d+94)) then
        tmp = t_2
    else if (z <= (-4.1d+41)) then
        tmp = x + (y / (a / (t - x)))
    else if (z <= (-2d+36)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-1.1d+14)) then
        tmp = x + (z * ((x - t) / (a - z)))
    else if (z <= (-2.1d-24)) then
        tmp = t_1
    else if (z <= (-2.9d-75)) then
        tmp = x * (((z - y) / (a - z)) + 1.0d0)
    else if (z <= (-4.5d-95)) then
        tmp = t_1
    else if (z <= 1.8d+61) then
        tmp = x + ((t - x) * (y / a))
    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 = t + ((x - t) / (z / (y - a)));
	double tmp;
	if (z <= -1.35e+94) {
		tmp = t_2;
	} else if (z <= -4.1e+41) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= -2e+36) {
		tmp = x * ((y - a) / z);
	} else if (z <= -1.1e+14) {
		tmp = x + (z * ((x - t) / (a - z)));
	} else if (z <= -2.1e-24) {
		tmp = t_1;
	} else if (z <= -2.9e-75) {
		tmp = x * (((z - y) / (a - z)) + 1.0);
	} else if (z <= -4.5e-95) {
		tmp = t_1;
	} else if (z <= 1.8e+61) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = t + ((x - t) / (z / (y - a)))
	tmp = 0
	if z <= -1.35e+94:
		tmp = t_2
	elif z <= -4.1e+41:
		tmp = x + (y / (a / (t - x)))
	elif z <= -2e+36:
		tmp = x * ((y - a) / z)
	elif z <= -1.1e+14:
		tmp = x + (z * ((x - t) / (a - z)))
	elif z <= -2.1e-24:
		tmp = t_1
	elif z <= -2.9e-75:
		tmp = x * (((z - y) / (a - z)) + 1.0)
	elif z <= -4.5e-95:
		tmp = t_1
	elif z <= 1.8e+61:
		tmp = x + ((t - x) * (y / a))
	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(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))))
	tmp = 0.0
	if (z <= -1.35e+94)
		tmp = t_2;
	elseif (z <= -4.1e+41)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif (z <= -2e+36)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -1.1e+14)
		tmp = Float64(x + Float64(z * Float64(Float64(x - t) / Float64(a - z))));
	elseif (z <= -2.1e-24)
		tmp = t_1;
	elseif (z <= -2.9e-75)
		tmp = Float64(x * Float64(Float64(Float64(z - y) / Float64(a - z)) + 1.0));
	elseif (z <= -4.5e-95)
		tmp = t_1;
	elseif (z <= 1.8e+61)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	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 = t + ((x - t) / (z / (y - a)));
	tmp = 0.0;
	if (z <= -1.35e+94)
		tmp = t_2;
	elseif (z <= -4.1e+41)
		tmp = x + (y / (a / (t - x)));
	elseif (z <= -2e+36)
		tmp = x * ((y - a) / z);
	elseif (z <= -1.1e+14)
		tmp = x + (z * ((x - t) / (a - z)));
	elseif (z <= -2.1e-24)
		tmp = t_1;
	elseif (z <= -2.9e-75)
		tmp = x * (((z - y) / (a - z)) + 1.0);
	elseif (z <= -4.5e-95)
		tmp = t_1;
	elseif (z <= 1.8e+61)
		tmp = x + ((t - x) * (y / a));
	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[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+94], t$95$2, If[LessEqual[z, -4.1e+41], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2e+36], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.1e+14], N[(x + N[(z * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.1e-24], t$95$1, If[LessEqual[z, -2.9e-75], N[(x * N[(N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.5e-95], t$95$1, If[LessEqual[z, 1.8e+61], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -1.3500000000000001e94 or 1.80000000000000005e61 < z

   1. Initial program 44.3%

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

      1. associate-*l/ 71.9%

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

   3. Simplified 71.9%

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

   4. Taylor expanded in z around inf 64.0%

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

      1. associate--l+ 64.0%

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

      2. associate-*r/ 64.0%

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

      3. associate-*r/ 64.0%

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

      4. div-sub 64.0%

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

      5. distribute-lft-out-- 64.0%

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

      6. associate-*r/ 64.0%

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

      7. distribute-rgt-out-- 64.1%

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

      8. mul-1-neg 64.1%

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

      9. unsub-neg 64.1%

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

      10. associate-/l* 84.1%

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

   6. Simplified 84.1%

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

   if -1.3500000000000001e94 < z < -4.1000000000000004e41

   1. Initial program 58.0%

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

      1. associate-*l/ 89.0%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in z around 0 63.2%

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

      1. associate-/l* 80.8%

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

   6. Simplified 80.8%

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

   if -4.1000000000000004e41 < z < -2.00000000000000008e36

   1. Initial program 2.8%

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

      1. associate-*l/ 2.8%

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

   3. Simplified 2.8%

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

   4. Taylor expanded in z around inf 99.2%

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

      1. associate--l+ 99.2%

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

      2. associate-*r/ 99.2%

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

      3. associate-*r/ 99.2%

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

      4. div-sub 99.2%

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

      5. distribute-lft-out-- 99.2%

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

      6. associate-*r/ 99.2%

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

      7. distribute-rgt-out-- 99.2%

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

      8. mul-1-neg 99.2%

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

      9. unsub-neg 99.2%

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

      10. associate-/l* 99.6%

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

   6. Simplified 99.6%

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

   7. Taylor expanded in t around 0 99.2%

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

      1. associate-*r/ 100.0%

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

   9. Simplified 100.0%

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

   if -2.00000000000000008e36 < z < -1.1e14

   1. Initial program 80.6%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 80.6%

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

      1. mul-1-neg 80.6%

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

      2. associate-*r/ 100.0%

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

      3. unsub-neg 100.0%

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

   6. Simplified 100.0%

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

   if -1.1e14 < z < -2.0999999999999999e-24 or -2.9000000000000002e-75 < z < -4.5e-95

   1. Initial program 89.2%

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

      1. associate-*l/ 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in x around 0 78.5%

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

      1. associate-*r/ 89.0%

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

   6. Simplified 89.0%

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

   if -2.0999999999999999e-24 < z < -2.9000000000000002e-75

   1. Initial program 90.6%

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

      1. associate-*l/ 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in x around inf 80.1%

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

      1. mul-1-neg 80.1%

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

      2. unsub-neg 80.1%

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

   6. Simplified 80.1%

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

   if -4.5e-95 < z < 1.80000000000000005e61

   1. Initial program 87.1%

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

      1. associate-*l/ 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in z around 0 79.5%

      \[\leadsto x + \color{blue}{\frac{y}{a}} \cdot \left(t - x\right) \]
3. Recombined 7 regimes into one program.

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+94}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+14}:\\ \;\;\;\;x + z \cdot \frac{x - t}{a - z}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-24}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-75}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a - z} + 1\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-95}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+61}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 5: 71.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{t - x}\\ t_2 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+94}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{y}{t_1}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -37000000000000:\\ \;\;\;\;x - \frac{z}{t_1}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-9}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-63}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+61}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ a (- t x))) (t_2 (+ t (/ (- x t) (/ z (- y a))))))
   (if (<= z -1.35e+94)
     t_2
     (if (<= z -5.5e+41)
       (+ x (/ y t_1))
       (if (<= z -2e+36)
         (* x (/ (- y a) z))
         (if (<= z -37000000000000.0)
           (- x (/ z t_1))
           (if (<= z -1.55e-9)
             t_2
             (if (<= z -6.6e-63)
               (* y (/ (- t x) (- a z)))
               (if (<= z 8.5e+61) (+ x (* (- t x) (/ y a))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (t - x);
	double t_2 = t + ((x - t) / (z / (y - a)));
	double tmp;
	if (z <= -1.35e+94) {
		tmp = t_2;
	} else if (z <= -5.5e+41) {
		tmp = x + (y / t_1);
	} else if (z <= -2e+36) {
		tmp = x * ((y - a) / z);
	} else if (z <= -37000000000000.0) {
		tmp = x - (z / t_1);
	} else if (z <= -1.55e-9) {
		tmp = t_2;
	} else if (z <= -6.6e-63) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 8.5e+61) {
		tmp = x + ((t - x) * (y / a));
	} 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 = a / (t - x)
    t_2 = t + ((x - t) / (z / (y - a)))
    if (z <= (-1.35d+94)) then
        tmp = t_2
    else if (z <= (-5.5d+41)) then
        tmp = x + (y / t_1)
    else if (z <= (-2d+36)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-37000000000000.0d0)) then
        tmp = x - (z / t_1)
    else if (z <= (-1.55d-9)) then
        tmp = t_2
    else if (z <= (-6.6d-63)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 8.5d+61) then
        tmp = x + ((t - x) * (y / a))
    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 = a / (t - x);
	double t_2 = t + ((x - t) / (z / (y - a)));
	double tmp;
	if (z <= -1.35e+94) {
		tmp = t_2;
	} else if (z <= -5.5e+41) {
		tmp = x + (y / t_1);
	} else if (z <= -2e+36) {
		tmp = x * ((y - a) / z);
	} else if (z <= -37000000000000.0) {
		tmp = x - (z / t_1);
	} else if (z <= -1.55e-9) {
		tmp = t_2;
	} else if (z <= -6.6e-63) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 8.5e+61) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = a / (t - x)
	t_2 = t + ((x - t) / (z / (y - a)))
	tmp = 0
	if z <= -1.35e+94:
		tmp = t_2
	elif z <= -5.5e+41:
		tmp = x + (y / t_1)
	elif z <= -2e+36:
		tmp = x * ((y - a) / z)
	elif z <= -37000000000000.0:
		tmp = x - (z / t_1)
	elif z <= -1.55e-9:
		tmp = t_2
	elif z <= -6.6e-63:
		tmp = y * ((t - x) / (a - z))
	elif z <= 8.5e+61:
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(a / Float64(t - x))
	t_2 = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))))
	tmp = 0.0
	if (z <= -1.35e+94)
		tmp = t_2;
	elseif (z <= -5.5e+41)
		tmp = Float64(x + Float64(y / t_1));
	elseif (z <= -2e+36)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -37000000000000.0)
		tmp = Float64(x - Float64(z / t_1));
	elseif (z <= -1.55e-9)
		tmp = t_2;
	elseif (z <= -6.6e-63)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 8.5e+61)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = a / (t - x);
	t_2 = t + ((x - t) / (z / (y - a)));
	tmp = 0.0;
	if (z <= -1.35e+94)
		tmp = t_2;
	elseif (z <= -5.5e+41)
		tmp = x + (y / t_1);
	elseif (z <= -2e+36)
		tmp = x * ((y - a) / z);
	elseif (z <= -37000000000000.0)
		tmp = x - (z / t_1);
	elseif (z <= -1.55e-9)
		tmp = t_2;
	elseif (z <= -6.6e-63)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 8.5e+61)
		tmp = x + ((t - x) * (y / a));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+94], t$95$2, If[LessEqual[z, -5.5e+41], N[(x + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2e+36], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -37000000000000.0], N[(x - N[(z / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.55e-9], t$95$2, If[LessEqual[z, -6.6e-63], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e+61], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.3500000000000001e94 or -3.7e13 < z < -1.55000000000000002e-9 or 8.50000000000000035e61 < z

   1. Initial program 45.9%

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

      1. associate-*l/ 72.3%

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

   3. Simplified 72.3%

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

   4. Taylor expanded in z around inf 64.7%

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

      1. associate--l+ 64.7%

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

      2. associate-*r/ 64.7%

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

      3. associate-*r/ 64.7%

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

      4. div-sub 64.7%

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

      5. distribute-lft-out-- 64.7%

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

      6. associate-*r/ 64.7%

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

      7. distribute-rgt-out-- 64.9%

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

      8. mul-1-neg 64.9%

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

      9. unsub-neg 64.9%

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

      10. associate-/l* 83.9%

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

   6. Simplified 83.9%

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

   if -1.3500000000000001e94 < z < -5.5000000000000003e41

   1. Initial program 58.0%

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

      1. associate-*l/ 89.0%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in z around 0 63.2%

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

      1. associate-/l* 80.8%

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

   6. Simplified 80.8%

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

   if -5.5000000000000003e41 < z < -2.00000000000000008e36

   1. Initial program 2.8%

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

      1. associate-*l/ 2.8%

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

   3. Simplified 2.8%

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

   4. Taylor expanded in z around inf 99.2%

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

      1. associate--l+ 99.2%

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

      2. associate-*r/ 99.2%

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

      3. associate-*r/ 99.2%

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

      4. div-sub 99.2%

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

      5. distribute-lft-out-- 99.2%

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

      6. associate-*r/ 99.2%

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

      7. distribute-rgt-out-- 99.2%

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

      8. mul-1-neg 99.2%

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

      9. unsub-neg 99.2%

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

      10. associate-/l* 99.6%

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

   6. Simplified 99.6%

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

   7. Taylor expanded in t around 0 99.2%

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

      1. associate-*r/ 100.0%

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

   9. Simplified 100.0%

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

   if -2.00000000000000008e36 < z < -3.7e13

   1. Initial program 80.6%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 80.6%

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

      1. mul-1-neg 80.6%

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

      2. associate-*r/ 100.0%

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

      3. unsub-neg 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in a around inf 80.6%

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

      1. mul-1-neg 80.6%

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

      2. unsub-neg 80.6%

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

      3. associate-/l* 99.7%

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

   9. Simplified 99.7%

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

   if -1.55000000000000002e-9 < z < -6.59999999999999987e-63

   1. Initial program 86.5%

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

      1. associate-*l/ 86.4%

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

   3. Simplified 86.4%

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

   4. Taylor expanded in y around inf 85.9%

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

      1. div-sub 85.9%

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

   6. Simplified 85.9%

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

   if -6.59999999999999987e-63 < z < 8.50000000000000035e61

   1. Initial program 87.9%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in z around 0 79.1%

      \[\leadsto x + \color{blue}{\frac{y}{a}} \cdot \left(t - x\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+94}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -37000000000000:\\ \;\;\;\;x - \frac{z}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-9}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-63}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+61}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 6: 68.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{t - x}\\ t_2 := t + y \cdot \frac{x - t}{z}\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+94}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{y}{t_1}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+14}:\\ \;\;\;\;x - \frac{z}{t_1}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-10}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-63}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+64}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ a (- t x))) (t_2 (+ t (* y (/ (- x t) z)))))
   (if (<= z -1.65e+94)
     t_2
     (if (<= z -3.4e+41)
       (+ x (/ y t_1))
       (if (<= z -2e+36)
         (* x (/ (- y a) z))
         (if (<= z -1.05e+14)
           (- x (/ z t_1))
           (if (<= z -6.2e-10)
             (* t (/ (- y z) (- a z)))
             (if (<= z -3.4e-63)
               (* y (/ (- t x) (- a z)))
               (if (<= z 6.6e+64) (+ x (* (- t x) (/ y a))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (t - x);
	double t_2 = t + (y * ((x - t) / z));
	double tmp;
	if (z <= -1.65e+94) {
		tmp = t_2;
	} else if (z <= -3.4e+41) {
		tmp = x + (y / t_1);
	} else if (z <= -2e+36) {
		tmp = x * ((y - a) / z);
	} else if (z <= -1.05e+14) {
		tmp = x - (z / t_1);
	} else if (z <= -6.2e-10) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= -3.4e-63) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 6.6e+64) {
		tmp = x + ((t - x) * (y / a));
	} 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 = a / (t - x)
    t_2 = t + (y * ((x - t) / z))
    if (z <= (-1.65d+94)) then
        tmp = t_2
    else if (z <= (-3.4d+41)) then
        tmp = x + (y / t_1)
    else if (z <= (-2d+36)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-1.05d+14)) then
        tmp = x - (z / t_1)
    else if (z <= (-6.2d-10)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= (-3.4d-63)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 6.6d+64) then
        tmp = x + ((t - x) * (y / a))
    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 = a / (t - x);
	double t_2 = t + (y * ((x - t) / z));
	double tmp;
	if (z <= -1.65e+94) {
		tmp = t_2;
	} else if (z <= -3.4e+41) {
		tmp = x + (y / t_1);
	} else if (z <= -2e+36) {
		tmp = x * ((y - a) / z);
	} else if (z <= -1.05e+14) {
		tmp = x - (z / t_1);
	} else if (z <= -6.2e-10) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= -3.4e-63) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 6.6e+64) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = a / (t - x)
	t_2 = t + (y * ((x - t) / z))
	tmp = 0
	if z <= -1.65e+94:
		tmp = t_2
	elif z <= -3.4e+41:
		tmp = x + (y / t_1)
	elif z <= -2e+36:
		tmp = x * ((y - a) / z)
	elif z <= -1.05e+14:
		tmp = x - (z / t_1)
	elif z <= -6.2e-10:
		tmp = t * ((y - z) / (a - z))
	elif z <= -3.4e-63:
		tmp = y * ((t - x) / (a - z))
	elif z <= 6.6e+64:
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(a / Float64(t - x))
	t_2 = Float64(t + Float64(y * Float64(Float64(x - t) / z)))
	tmp = 0.0
	if (z <= -1.65e+94)
		tmp = t_2;
	elseif (z <= -3.4e+41)
		tmp = Float64(x + Float64(y / t_1));
	elseif (z <= -2e+36)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -1.05e+14)
		tmp = Float64(x - Float64(z / t_1));
	elseif (z <= -6.2e-10)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= -3.4e-63)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 6.6e+64)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = a / (t - x);
	t_2 = t + (y * ((x - t) / z));
	tmp = 0.0;
	if (z <= -1.65e+94)
		tmp = t_2;
	elseif (z <= -3.4e+41)
		tmp = x + (y / t_1);
	elseif (z <= -2e+36)
		tmp = x * ((y - a) / z);
	elseif (z <= -1.05e+14)
		tmp = x - (z / t_1);
	elseif (z <= -6.2e-10)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= -3.4e-63)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 6.6e+64)
		tmp = x + ((t - x) * (y / a));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.65e+94], t$95$2, If[LessEqual[z, -3.4e+41], N[(x + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2e+36], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.05e+14], N[(x - N[(z / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.2e-10], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.4e-63], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e+64], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -1.65e94 or 6.59999999999999976e64 < z

   1. Initial program 44.3%

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

      1. associate-*l/ 71.9%

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

   3. Simplified 71.9%

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

   4. Taylor expanded in z around inf 64.0%

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

      1. associate--l+ 64.0%

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

      2. associate-*r/ 64.0%

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

      3. associate-*r/ 64.0%

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

      4. div-sub 64.0%

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

      5. distribute-lft-out-- 64.0%

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

      6. associate-*r/ 64.0%

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

      7. distribute-rgt-out-- 64.1%

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

      8. mul-1-neg 64.1%

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

      9. unsub-neg 64.1%

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

      10. associate-/l* 84.1%

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

   6. Simplified 84.1%

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

   7. Taylor expanded in y around inf 60.3%

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

      1. associate-*r/ 71.2%

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

   9. Simplified 71.2%

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

   if -1.65e94 < z < -3.39999999999999998e41

   1. Initial program 58.0%

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

      1. associate-*l/ 89.0%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in z around 0 63.2%

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

      1. associate-/l* 80.8%

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

   6. Simplified 80.8%

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

   if -3.39999999999999998e41 < z < -2.00000000000000008e36

   1. Initial program 2.8%

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

      1. associate-*l/ 2.8%

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

   3. Simplified 2.8%

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

   4. Taylor expanded in z around inf 99.2%

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

      1. associate--l+ 99.2%

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

      2. associate-*r/ 99.2%

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

      3. associate-*r/ 99.2%

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

      4. div-sub 99.2%

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

      5. distribute-lft-out-- 99.2%

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

      6. associate-*r/ 99.2%

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

      7. distribute-rgt-out-- 99.2%

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

      8. mul-1-neg 99.2%

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

      9. unsub-neg 99.2%

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

      10. associate-/l* 99.6%

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

   6. Simplified 99.6%

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

   7. Taylor expanded in t around 0 99.2%

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

      1. associate-*r/ 100.0%

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

   9. Simplified 100.0%

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

   if -2.00000000000000008e36 < z < -1.05e14

   1. Initial program 80.6%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 80.6%

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

      1. mul-1-neg 80.6%

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

      2. associate-*r/ 100.0%

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

      3. unsub-neg 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in a around inf 80.6%

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

      1. mul-1-neg 80.6%

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

      2. unsub-neg 80.6%

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

      3. associate-/l* 99.7%

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

   9. Simplified 99.7%

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

   if -1.05e14 < z < -6.2000000000000003e-10

   1. Initial program 80.5%

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

      1. associate-*l/ 80.5%

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

   3. Simplified 80.5%

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

   4. Taylor expanded in x around 0 80.3%

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

      1. associate-*r/ 80.3%

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

   6. Simplified 80.3%

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

   if -6.2000000000000003e-10 < z < -3.39999999999999998e-63

   1. Initial program 86.5%

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

      1. associate-*l/ 86.4%

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

   3. Simplified 86.4%

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

   4. Taylor expanded in y around inf 85.9%

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

      1. div-sub 85.9%

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

   6. Simplified 85.9%

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

   if -3.39999999999999998e-63 < z < 6.59999999999999976e64

   1. Initial program 87.9%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in z around 0 79.1%

      \[\leadsto x + \color{blue}{\frac{y}{a}} \cdot \left(t - x\right) \]
3. Recombined 7 regimes into one program.

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+94}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+14}:\\ \;\;\;\;x - \frac{z}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-10}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-63}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+64}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \]

Alternative 7: 59.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -3 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-155}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-309}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-228}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+119}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))))
   (if (<= a -3e+41)
     t_1
     (if (<= a -2.2e-155)
       (* y (/ (- t x) (- a z)))
       (if (<= a -7e-309)
         (/ (- t) (/ z (- y z)))
         (if (<= a 1.05e-228)
           (/ (- y) (/ z (- t x)))
           (if (<= a 2.2e+119) (* t (/ (- y z) (- a z))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double tmp;
	if (a <= -3e+41) {
		tmp = t_1;
	} else if (a <= -2.2e-155) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= -7e-309) {
		tmp = -t / (z / (y - z));
	} else if (a <= 1.05e-228) {
		tmp = -y / (z / (t - x));
	} else if (a <= 2.2e+119) {
		tmp = t * ((y - z) / (a - z));
	} 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 = x + (t * (y / a))
    if (a <= (-3d+41)) then
        tmp = t_1
    else if (a <= (-2.2d-155)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= (-7d-309)) then
        tmp = -t / (z / (y - z))
    else if (a <= 1.05d-228) then
        tmp = -y / (z / (t - x))
    else if (a <= 2.2d+119) then
        tmp = t * ((y - z) / (a - z))
    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 = x + (t * (y / a));
	double tmp;
	if (a <= -3e+41) {
		tmp = t_1;
	} else if (a <= -2.2e-155) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= -7e-309) {
		tmp = -t / (z / (y - z));
	} else if (a <= 1.05e-228) {
		tmp = -y / (z / (t - x));
	} else if (a <= 2.2e+119) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	tmp = 0
	if a <= -3e+41:
		tmp = t_1
	elif a <= -2.2e-155:
		tmp = y * ((t - x) / (a - z))
	elif a <= -7e-309:
		tmp = -t / (z / (y - z))
	elif a <= 1.05e-228:
		tmp = -y / (z / (t - x))
	elif a <= 2.2e+119:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (a <= -3e+41)
		tmp = t_1;
	elseif (a <= -2.2e-155)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= -7e-309)
		tmp = Float64(Float64(-t) / Float64(z / Float64(y - z)));
	elseif (a <= 1.05e-228)
		tmp = Float64(Float64(-y) / Float64(z / Float64(t - x)));
	elseif (a <= 2.2e+119)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	tmp = 0.0;
	if (a <= -3e+41)
		tmp = t_1;
	elseif (a <= -2.2e-155)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= -7e-309)
		tmp = -t / (z / (y - z));
	elseif (a <= 1.05e-228)
		tmp = -y / (z / (t - x));
	elseif (a <= 2.2e+119)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3e+41], t$95$1, If[LessEqual[a, -2.2e-155], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7e-309], N[((-t) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e-228], N[((-y) / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.2e+119], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.9999999999999998e41 or 2.2000000000000001e119 < a

   1. Initial program 71.5%

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

      1. associate-*l/ 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in z around 0 71.3%

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

   5. Taylor expanded in t around inf 62.5%

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

      1. associate-*r/ 66.4%

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

   7. Simplified 66.4%

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

   if -2.9999999999999998e41 < a < -2.1999999999999999e-155

   1. Initial program 62.2%

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

      1. associate-*l/ 67.6%

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

   3. Simplified 67.6%

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

   4. Taylor expanded in y around inf 50.3%

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

      1. div-sub 50.3%

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

   6. Simplified 50.3%

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

   if -2.1999999999999999e-155 < a < -6.9999999999999984e-309

   1. Initial program 65.7%

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

      1. associate-*l/ 79.3%

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

   3. Simplified 79.3%

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

   4. Taylor expanded in x around 0 60.8%

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

   5. Taylor expanded in a around 0 64.7%

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

      1. mul-1-neg 64.7%

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

      2. associate-/l* 74.8%

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

      3. distribute-neg-frac 74.8%

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

   7. Simplified 74.8%

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

   if -6.9999999999999984e-309 < a < 1.04999999999999995e-228

   1. Initial program 78.4%

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

      1. associate-*l/ 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in y around -inf 77.8%

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

      1. associate-*l/ 84.8%

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

   6. Simplified 84.8%

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

   7. Taylor expanded in a around 0 77.8%

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

      1. mul-1-neg 77.8%

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

      2. associate-/l* 84.9%

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

      3. distribute-neg-frac 84.9%

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

   9. Simplified 84.9%

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

   if 1.04999999999999995e-228 < a < 2.2000000000000001e119

   1. Initial program 61.9%

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

      1. associate-*l/ 82.9%

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

   3. Simplified 82.9%

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

   4. Taylor expanded in x around 0 43.5%

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

      1. associate-*r/ 60.8%

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

   6. Simplified 60.8%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{+41}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-155}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-309}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-228}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+119}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 8: 59.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -1.15 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-149}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-306}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-228}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+115}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))))
   (if (<= a -1.15e+39)
     t_1
     (if (<= a -2.1e-149)
       (* (- t x) (/ y (- a z)))
       (if (<= a 2.7e-306)
         (/ (- t) (/ z (- y z)))
         (if (<= a 1.85e-228)
           (/ (- y) (/ z (- t x)))
           (if (<= a 3.4e+115) (* t (/ (- y z) (- a z))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double tmp;
	if (a <= -1.15e+39) {
		tmp = t_1;
	} else if (a <= -2.1e-149) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 2.7e-306) {
		tmp = -t / (z / (y - z));
	} else if (a <= 1.85e-228) {
		tmp = -y / (z / (t - x));
	} else if (a <= 3.4e+115) {
		tmp = t * ((y - z) / (a - z));
	} 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 = x + (t * (y / a))
    if (a <= (-1.15d+39)) then
        tmp = t_1
    else if (a <= (-2.1d-149)) then
        tmp = (t - x) * (y / (a - z))
    else if (a <= 2.7d-306) then
        tmp = -t / (z / (y - z))
    else if (a <= 1.85d-228) then
        tmp = -y / (z / (t - x))
    else if (a <= 3.4d+115) then
        tmp = t * ((y - z) / (a - z))
    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 = x + (t * (y / a));
	double tmp;
	if (a <= -1.15e+39) {
		tmp = t_1;
	} else if (a <= -2.1e-149) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 2.7e-306) {
		tmp = -t / (z / (y - z));
	} else if (a <= 1.85e-228) {
		tmp = -y / (z / (t - x));
	} else if (a <= 3.4e+115) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	tmp = 0
	if a <= -1.15e+39:
		tmp = t_1
	elif a <= -2.1e-149:
		tmp = (t - x) * (y / (a - z))
	elif a <= 2.7e-306:
		tmp = -t / (z / (y - z))
	elif a <= 1.85e-228:
		tmp = -y / (z / (t - x))
	elif a <= 3.4e+115:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (a <= -1.15e+39)
		tmp = t_1;
	elseif (a <= -2.1e-149)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (a <= 2.7e-306)
		tmp = Float64(Float64(-t) / Float64(z / Float64(y - z)));
	elseif (a <= 1.85e-228)
		tmp = Float64(Float64(-y) / Float64(z / Float64(t - x)));
	elseif (a <= 3.4e+115)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	tmp = 0.0;
	if (a <= -1.15e+39)
		tmp = t_1;
	elseif (a <= -2.1e-149)
		tmp = (t - x) * (y / (a - z));
	elseif (a <= 2.7e-306)
		tmp = -t / (z / (y - z));
	elseif (a <= 1.85e-228)
		tmp = -y / (z / (t - x));
	elseif (a <= 3.4e+115)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.15e+39], t$95$1, If[LessEqual[a, -2.1e-149], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e-306], N[((-t) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.85e-228], N[((-y) / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.4e+115], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.15000000000000006e39 or 3.4000000000000001e115 < a

   1. Initial program 71.5%

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

      1. associate-*l/ 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in z around 0 71.3%

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

   5. Taylor expanded in t around inf 62.5%

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

      1. associate-*r/ 66.4%

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

   7. Simplified 66.4%

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

   if -1.15000000000000006e39 < a < -2.10000000000000011e-149

   1. Initial program 62.2%

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

      1. associate-*l/ 67.6%

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

   3. Simplified 67.6%

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

   4. Taylor expanded in y around -inf 42.5%

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

      1. associate-*l/ 50.4%

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

   6. Simplified 50.4%

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

   if -2.10000000000000011e-149 < a < 2.70000000000000009e-306

   1. Initial program 65.7%

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

      1. associate-*l/ 79.3%

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

   3. Simplified 79.3%

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

   4. Taylor expanded in x around 0 60.8%

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

   5. Taylor expanded in a around 0 64.7%

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

      1. mul-1-neg 64.7%

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

      2. associate-/l* 74.8%

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

      3. distribute-neg-frac 74.8%

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

   7. Simplified 74.8%

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

   if 2.70000000000000009e-306 < a < 1.85e-228

   1. Initial program 78.4%

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

      1. associate-*l/ 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in y around -inf 77.8%

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

      1. associate-*l/ 84.8%

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

   6. Simplified 84.8%

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

   7. Taylor expanded in a around 0 77.8%

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

      1. mul-1-neg 77.8%

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

      2. associate-/l* 84.9%

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

      3. distribute-neg-frac 84.9%

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

   9. Simplified 84.9%

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

   if 1.85e-228 < a < 3.4000000000000001e115

   1. Initial program 61.9%

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

      1. associate-*l/ 82.9%

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

   3. Simplified 82.9%

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

   4. Taylor expanded in x around 0 43.5%

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

      1. associate-*r/ 60.8%

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

   6. Simplified 60.8%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+39}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-149}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-306}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-228}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+115}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 9: 68.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot \frac{x - t}{z}\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-45}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+62}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* y (/ (- x t) z)))))
   (if (<= z -1.65e+94)
     t_1
     (if (<= z -3.4e+41)
       (+ x (/ y (/ a (- t x))))
       (if (<= z -2e+36)
         (* x (/ (- y a) z))
         (if (<= z -4.9e-45)
           (* t (/ (- y z) (- a z)))
           (if (<= z 2e+62) (+ x (* (- t x) (/ y a))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (y * ((x - t) / z));
	double tmp;
	if (z <= -1.65e+94) {
		tmp = t_1;
	} else if (z <= -3.4e+41) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= -2e+36) {
		tmp = x * ((y - a) / z);
	} else if (z <= -4.9e-45) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 2e+62) {
		tmp = x + ((t - x) * (y / 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 * ((x - t) / z))
    if (z <= (-1.65d+94)) then
        tmp = t_1
    else if (z <= (-3.4d+41)) then
        tmp = x + (y / (a / (t - x)))
    else if (z <= (-2d+36)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-4.9d-45)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= 2d+62) then
        tmp = x + ((t - x) * (y / 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 * ((x - t) / z));
	double tmp;
	if (z <= -1.65e+94) {
		tmp = t_1;
	} else if (z <= -3.4e+41) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= -2e+36) {
		tmp = x * ((y - a) / z);
	} else if (z <= -4.9e-45) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 2e+62) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (y * ((x - t) / z))
	tmp = 0
	if z <= -1.65e+94:
		tmp = t_1
	elif z <= -3.4e+41:
		tmp = x + (y / (a / (t - x)))
	elif z <= -2e+36:
		tmp = x * ((y - a) / z)
	elif z <= -4.9e-45:
		tmp = t * ((y - z) / (a - z))
	elif z <= 2e+62:
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(y * Float64(Float64(x - t) / z)))
	tmp = 0.0
	if (z <= -1.65e+94)
		tmp = t_1;
	elseif (z <= -3.4e+41)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif (z <= -2e+36)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -4.9e-45)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 2e+62)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (y * ((x - t) / z));
	tmp = 0.0;
	if (z <= -1.65e+94)
		tmp = t_1;
	elseif (z <= -3.4e+41)
		tmp = x + (y / (a / (t - x)));
	elseif (z <= -2e+36)
		tmp = x * ((y - a) / z);
	elseif (z <= -4.9e-45)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= 2e+62)
		tmp = x + ((t - x) * (y / a));
	else
		tmp = t_1;
	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]}, If[LessEqual[z, -1.65e+94], t$95$1, If[LessEqual[z, -3.4e+41], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2e+36], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.9e-45], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+62], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.65e94 or 2.00000000000000007e62 < z

   1. Initial program 44.3%

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

      1. associate-*l/ 71.9%

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

   3. Simplified 71.9%

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

   4. Taylor expanded in z around inf 64.0%

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

      1. associate--l+ 64.0%

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

      2. associate-*r/ 64.0%

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

      3. associate-*r/ 64.0%

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

      4. div-sub 64.0%

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

      5. distribute-lft-out-- 64.0%

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

      6. associate-*r/ 64.0%

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

      7. distribute-rgt-out-- 64.1%

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

      8. mul-1-neg 64.1%

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

      9. unsub-neg 64.1%

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

      10. associate-/l* 84.1%

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

   6. Simplified 84.1%

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

   7. Taylor expanded in y around inf 60.3%

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

      1. associate-*r/ 71.2%

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

   9. Simplified 71.2%

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

   if -1.65e94 < z < -3.39999999999999998e41

   1. Initial program 58.0%

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

      1. associate-*l/ 89.0%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in z around 0 63.2%

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

      1. associate-/l* 80.8%

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

   6. Simplified 80.8%

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

   if -3.39999999999999998e41 < z < -2.00000000000000008e36

   1. Initial program 2.8%

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

      1. associate-*l/ 2.8%

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

   3. Simplified 2.8%

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

   4. Taylor expanded in z around inf 99.2%

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

      1. associate--l+ 99.2%

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

      2. associate-*r/ 99.2%

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

      3. associate-*r/ 99.2%

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

      4. div-sub 99.2%

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

      5. distribute-lft-out-- 99.2%

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

      6. associate-*r/ 99.2%

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

      7. distribute-rgt-out-- 99.2%

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

      8. mul-1-neg 99.2%

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

      9. unsub-neg 99.2%

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

      10. associate-/l* 99.6%

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

   6. Simplified 99.6%

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

   7. Taylor expanded in t around 0 99.2%

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

      1. associate-*r/ 100.0%

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

   9. Simplified 100.0%

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

   if -2.00000000000000008e36 < z < -4.8999999999999998e-45

   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/ 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in x around 0 44.8%

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

      1. associate-*r/ 58.4%

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

   6. Simplified 58.4%

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

   if -4.8999999999999998e-45 < z < 2.00000000000000007e62

   1. Initial program 87.4%

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

      1. associate-*l/ 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in z around 0 78.9%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+94}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-45}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+62}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \]

Alternative 10: 38.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{+115}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -750000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-289}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.96 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- a z)))))
   (if (<= z -8.2e+115)
     t
     (if (<= z -750000000000.0)
       x
       (if (<= z -1.2e-62)
         t_1
         (if (<= z 1.05e-289)
           x
           (if (<= z 2.25e-185) t_1 (if (<= z 1.96e+65) x t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (z <= -8.2e+115) {
		tmp = t;
	} else if (z <= -750000000000.0) {
		tmp = x;
	} else if (z <= -1.2e-62) {
		tmp = t_1;
	} else if (z <= 1.05e-289) {
		tmp = x;
	} else if (z <= 2.25e-185) {
		tmp = t_1;
	} else if (z <= 1.96e+65) {
		tmp = x;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t * (y / (a - z))
    if (z <= (-8.2d+115)) then
        tmp = t
    else if (z <= (-750000000000.0d0)) then
        tmp = x
    else if (z <= (-1.2d-62)) then
        tmp = t_1
    else if (z <= 1.05d-289) then
        tmp = x
    else if (z <= 2.25d-185) then
        tmp = t_1
    else if (z <= 1.96d+65) then
        tmp = x
    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 t_1 = t * (y / (a - z));
	double tmp;
	if (z <= -8.2e+115) {
		tmp = t;
	} else if (z <= -750000000000.0) {
		tmp = x;
	} else if (z <= -1.2e-62) {
		tmp = t_1;
	} else if (z <= 1.05e-289) {
		tmp = x;
	} else if (z <= 2.25e-185) {
		tmp = t_1;
	} else if (z <= 1.96e+65) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / (a - z))
	tmp = 0
	if z <= -8.2e+115:
		tmp = t
	elif z <= -750000000000.0:
		tmp = x
	elif z <= -1.2e-62:
		tmp = t_1
	elif z <= 1.05e-289:
		tmp = x
	elif z <= 2.25e-185:
		tmp = t_1
	elif z <= 1.96e+65:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (z <= -8.2e+115)
		tmp = t;
	elseif (z <= -750000000000.0)
		tmp = x;
	elseif (z <= -1.2e-62)
		tmp = t_1;
	elseif (z <= 1.05e-289)
		tmp = x;
	elseif (z <= 2.25e-185)
		tmp = t_1;
	elseif (z <= 1.96e+65)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / (a - z));
	tmp = 0.0;
	if (z <= -8.2e+115)
		tmp = t;
	elseif (z <= -750000000000.0)
		tmp = x;
	elseif (z <= -1.2e-62)
		tmp = t_1;
	elseif (z <= 1.05e-289)
		tmp = x;
	elseif (z <= 2.25e-185)
		tmp = t_1;
	elseif (z <= 1.96e+65)
		tmp = x;
	else
		tmp = t;
	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[z, -8.2e+115], t, If[LessEqual[z, -750000000000.0], x, If[LessEqual[z, -1.2e-62], t$95$1, If[LessEqual[z, 1.05e-289], x, If[LessEqual[z, 2.25e-185], t$95$1, If[LessEqual[z, 1.96e+65], x, t]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.19999999999999925e115 or 1.9600000000000001e65 < z

   1. Initial program 41.3%

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

      1. associate-*l/ 69.8%

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

   3. Simplified 69.8%

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

   4. Taylor expanded in z around inf 51.0%

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

   if -8.19999999999999925e115 < z < -7.5e11 or -1.19999999999999992e-62 < z < 1.0499999999999999e-289 or 2.2500000000000001e-185 < z < 1.9600000000000001e65

   1. Initial program 82.0%

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

      1. associate-*l/ 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in a around inf 44.7%

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

   if -7.5e11 < z < -1.19999999999999992e-62 or 1.0499999999999999e-289 < z < 2.2500000000000001e-185

   1. Initial program 90.0%

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

      1. associate-*l/ 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in y around -inf 58.6%

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

      1. associate-*l/ 61.9%

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

   6. Simplified 61.9%

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

   7. Taylor expanded in t around inf 42.3%

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

      1. associate-*r/ 55.2%

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

   9. Simplified 55.2%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+115}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -750000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-62}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-289}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-185}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.96 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 11: 63.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+127}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+62}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+91}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+114}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a}{\frac{-z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5e+127)
   (+ t (/ a (/ z (- t x))))
   (if (<= z 2.5e+62)
     (+ x (* (- t x) (/ y a)))
     (if (<= z 4.5e+91)
       (* t (/ (- y z) (- a z)))
       (if (<= z 4.5e+114)
         (* y (/ (- t x) (- a z)))
         (+ t (/ a (/ (- z) x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5e+127) {
		tmp = t + (a / (z / (t - x)));
	} else if (z <= 2.5e+62) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 4.5e+91) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 4.5e+114) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = t + (a / (-z / 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 (z <= (-5d+127)) then
        tmp = t + (a / (z / (t - x)))
    else if (z <= 2.5d+62) then
        tmp = x + ((t - x) * (y / a))
    else if (z <= 4.5d+91) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= 4.5d+114) then
        tmp = y * ((t - x) / (a - z))
    else
        tmp = t + (a / (-z / 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 (z <= -5e+127) {
		tmp = t + (a / (z / (t - x)));
	} else if (z <= 2.5e+62) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 4.5e+91) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 4.5e+114) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = t + (a / (-z / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5e+127:
		tmp = t + (a / (z / (t - x)))
	elif z <= 2.5e+62:
		tmp = x + ((t - x) * (y / a))
	elif z <= 4.5e+91:
		tmp = t * ((y - z) / (a - z))
	elif z <= 4.5e+114:
		tmp = y * ((t - x) / (a - z))
	else:
		tmp = t + (a / (-z / x))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5e+127)
		tmp = Float64(t + Float64(a / Float64(z / Float64(t - x))));
	elseif (z <= 2.5e+62)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (z <= 4.5e+91)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 4.5e+114)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	else
		tmp = Float64(t + Float64(a / Float64(Float64(-z) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5e+127)
		tmp = t + (a / (z / (t - x)));
	elseif (z <= 2.5e+62)
		tmp = x + ((t - x) * (y / a));
	elseif (z <= 4.5e+91)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= 4.5e+114)
		tmp = y * ((t - x) / (a - z));
	else
		tmp = t + (a / (-z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5e+127], N[(t + N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+62], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+91], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+114], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(a / N[((-z) / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.0000000000000004e127

   1. Initial program 30.3%

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

      1. associate-*l/ 67.1%

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

   3. Simplified 67.1%

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

   4. Taylor expanded in z around inf 60.9%

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

      1. associate--l+ 60.9%

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

      2. associate-*r/ 60.9%

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

      3. associate-*r/ 60.9%

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

      4. div-sub 60.9%

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

      5. distribute-lft-out-- 60.9%

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

      6. associate-*r/ 60.9%

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

      7. distribute-rgt-out-- 61.4%

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

      8. mul-1-neg 61.4%

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

      9. unsub-neg 61.4%

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

      10. associate-/l* 90.5%

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

   6. Simplified 90.5%

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

   7. Taylor expanded in y around 0 54.6%

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

      1. sub-neg 54.6%

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

      2. mul-1-neg 54.6%

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

      3. remove-double-neg 54.6%

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

      4. associate-/l* 66.3%

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

   9. Simplified 66.3%

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

   if -5.0000000000000004e127 < z < 2.50000000000000014e62

   1. Initial program 83.5%

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

      1. associate-*l/ 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in z around 0 73.3%

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

   if 2.50000000000000014e62 < z < 4.5e91

   1. Initial program 64.2%

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

      1. associate-*l/ 75.7%

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

   3. Simplified 75.7%

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

   4. Taylor expanded in x around 0 64.5%

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

      1. associate-*r/ 76.4%

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

   6. Simplified 76.4%

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

   if 4.5e91 < z < 4.5000000000000001e114

   1. Initial program 44.1%

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

      1. associate-*l/ 80.6%

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

   3. Simplified 80.6%

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

   4. Taylor expanded in y around inf 91.6%

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

      1. div-sub 91.6%

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

   6. Simplified 91.6%

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

   if 4.5000000000000001e114 < z

   1. Initial program 46.3%

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

      1. associate-*l/ 69.5%

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

   3. Simplified 69.5%

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

   4. Taylor expanded in z around inf 67.3%

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

      1. associate--l+ 67.3%

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

      2. associate-*r/ 67.3%

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

      3. associate-*r/ 67.3%

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

      4. div-sub 67.3%

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

      5. distribute-lft-out-- 67.3%

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

      6. associate-*r/ 67.3%

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

      7. distribute-rgt-out-- 67.3%

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

      8. mul-1-neg 67.3%

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

      9. unsub-neg 67.3%

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

      10. associate-/l* 85.9%

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

   6. Simplified 85.9%

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

   7. Taylor expanded in y around 0 57.7%

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

      1. sub-neg 57.7%

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

      2. mul-1-neg 57.7%

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

      3. remove-double-neg 57.7%

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

      4. associate-/l* 69.6%

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

   9. Simplified 69.6%

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

   10. Taylor expanded in t around 0 69.6%

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

       1. associate-*r/ 69.6%

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

       2. neg-mul-1 69.6%

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

   12. Simplified 69.6%

       \[\leadsto t + \frac{a}{\color{blue}{\frac{-z}{x}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+127}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+62}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+91}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+114}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a}{\frac{-z}{x}}\\ \end{array} \]

Alternative 12: 54.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ t_2 := t + \frac{a}{\frac{-z}{x}}\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{+125}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-141}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-291}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))) (t_2 (+ t (/ a (/ (- z) x)))))
   (if (<= z -5.6e+125)
     t_2
     (if (<= z -1.15e-141)
       t_1
       (if (<= z 4.5e-291)
         (* x (- 1.0 (/ y a)))
         (if (<= z 5.8e+114) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double t_2 = t + (a / (-z / x));
	double tmp;
	if (z <= -5.6e+125) {
		tmp = t_2;
	} else if (z <= -1.15e-141) {
		tmp = t_1;
	} else if (z <= 4.5e-291) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 5.8e+114) {
		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 = x + (t * (y / a))
    t_2 = t + (a / (-z / x))
    if (z <= (-5.6d+125)) then
        tmp = t_2
    else if (z <= (-1.15d-141)) then
        tmp = t_1
    else if (z <= 4.5d-291) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 5.8d+114) 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 = x + (t * (y / a));
	double t_2 = t + (a / (-z / x));
	double tmp;
	if (z <= -5.6e+125) {
		tmp = t_2;
	} else if (z <= -1.15e-141) {
		tmp = t_1;
	} else if (z <= 4.5e-291) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 5.8e+114) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	t_2 = t + (a / (-z / x))
	tmp = 0
	if z <= -5.6e+125:
		tmp = t_2
	elif z <= -1.15e-141:
		tmp = t_1
	elif z <= 4.5e-291:
		tmp = x * (1.0 - (y / a))
	elif z <= 5.8e+114:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	t_2 = Float64(t + Float64(a / Float64(Float64(-z) / x)))
	tmp = 0.0
	if (z <= -5.6e+125)
		tmp = t_2;
	elseif (z <= -1.15e-141)
		tmp = t_1;
	elseif (z <= 4.5e-291)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 5.8e+114)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	t_2 = t + (a / (-z / x));
	tmp = 0.0;
	if (z <= -5.6e+125)
		tmp = t_2;
	elseif (z <= -1.15e-141)
		tmp = t_1;
	elseif (z <= 4.5e-291)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 5.8e+114)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(a / N[((-z) / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.6e+125], t$95$2, If[LessEqual[z, -1.15e-141], t$95$1, If[LessEqual[z, 4.5e-291], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e+114], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.6000000000000002e125 or 5.8000000000000001e114 < z

   1. Initial program 38.2%

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

      1. associate-*l/ 68.3%

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

   3. Simplified 68.3%

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

   4. Taylor expanded in z around inf 64.1%

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

      1. associate--l+ 64.1%

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

      2. associate-*r/ 64.1%

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

      3. associate-*r/ 64.1%

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

      4. div-sub 64.1%

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

      5. distribute-lft-out-- 64.1%

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

      6. associate-*r/ 64.1%

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

      7. distribute-rgt-out-- 64.3%

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

      8. mul-1-neg 64.3%

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

      9. unsub-neg 64.3%

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

      10. associate-/l* 88.2%

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

   6. Simplified 88.2%

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

   7. Taylor expanded in y around 0 56.1%

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

      1. sub-neg 56.1%

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

      2. mul-1-neg 56.1%

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

      3. remove-double-neg 56.1%

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

      4. associate-/l* 67.9%

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

   9. Simplified 67.9%

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

   10. Taylor expanded in t around 0 67.5%

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

       1. associate-*r/ 67.5%

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

       2. neg-mul-1 67.5%

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

   12. Simplified 67.5%

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

   if -5.6000000000000002e125 < z < -1.14999999999999997e-141 or 4.49999999999999974e-291 < z < 5.8000000000000001e114

   1. Initial program 78.5%

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

      1. associate-*l/ 90.0%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in z around 0 65.0%

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

   5. Taylor expanded in t around inf 53.4%

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

      1. associate-*r/ 57.1%

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

   7. Simplified 57.1%

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

   if -1.14999999999999997e-141 < z < 4.49999999999999974e-291

   1. Initial program 95.0%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 93.6%

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

   5. Taylor expanded in x around inf 82.7%

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

      1. mul-1-neg 82.7%

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

      2. unsub-neg 82.7%

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

   7. Simplified 82.7%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+125}:\\ \;\;\;\;t + \frac{a}{\frac{-z}{x}}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-141}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-291}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+114}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{a}{\frac{-z}{x}}\\ \end{array} \]

Alternative 13: 52.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+130}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-291}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+115}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))))
   (if (<= z -3.8e+130)
     t
     (if (<= z -3.8e-140)
       t_1
       (if (<= z 9e-291) (* x (- 1.0 (/ y a))) (if (<= z 1.75e+115) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double tmp;
	if (z <= -3.8e+130) {
		tmp = t;
	} else if (z <= -3.8e-140) {
		tmp = t_1;
	} else if (z <= 9e-291) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.75e+115) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x + (t * (y / a))
    if (z <= (-3.8d+130)) then
        tmp = t
    else if (z <= (-3.8d-140)) then
        tmp = t_1
    else if (z <= 9d-291) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 1.75d+115) then
        tmp = t_1
    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 t_1 = x + (t * (y / a));
	double tmp;
	if (z <= -3.8e+130) {
		tmp = t;
	} else if (z <= -3.8e-140) {
		tmp = t_1;
	} else if (z <= 9e-291) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.75e+115) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	tmp = 0
	if z <= -3.8e+130:
		tmp = t
	elif z <= -3.8e-140:
		tmp = t_1
	elif z <= 9e-291:
		tmp = x * (1.0 - (y / a))
	elif z <= 1.75e+115:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (z <= -3.8e+130)
		tmp = t;
	elseif (z <= -3.8e-140)
		tmp = t_1;
	elseif (z <= 9e-291)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 1.75e+115)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	tmp = 0.0;
	if (z <= -3.8e+130)
		tmp = t;
	elseif (z <= -3.8e-140)
		tmp = t_1;
	elseif (z <= 9e-291)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 1.75e+115)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e+130], t, If[LessEqual[z, -3.8e-140], t$95$1, If[LessEqual[z, 9e-291], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e+115], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.8000000000000002e130 or 1.75000000000000003e115 < z

   1. Initial program 38.2%

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

      1. associate-*l/ 68.3%

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

   3. Simplified 68.3%

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

   4. Taylor expanded in z around inf 54.4%

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

   if -3.8000000000000002e130 < z < -3.79999999999999998e-140 or 8.99999999999999948e-291 < z < 1.75000000000000003e115

   1. Initial program 78.5%

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

      1. associate-*l/ 90.0%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in z around 0 65.0%

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

   5. Taylor expanded in t around inf 53.4%

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

      1. associate-*r/ 57.1%

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

   7. Simplified 57.1%

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

   if -3.79999999999999998e-140 < z < 8.99999999999999948e-291

   1. Initial program 95.0%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 93.6%

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

   5. Taylor expanded in x around inf 82.7%

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

      1. mul-1-neg 82.7%

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

      2. unsub-neg 82.7%

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

   7. Simplified 82.7%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+130}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-140}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-291}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+115}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 14: 53.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ t_2 := \frac{t}{1 - \frac{a}{z}}\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-291}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))) (t_2 (/ t (- 1.0 (/ a z)))))
   (if (<= z -6.2e+115)
     t_2
     (if (<= z -2.7e-142)
       t_1
       (if (<= z 9e-291)
         (* x (- 1.0 (/ y a)))
         (if (<= z 9.5e+114) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double t_2 = t / (1.0 - (a / z));
	double tmp;
	if (z <= -6.2e+115) {
		tmp = t_2;
	} else if (z <= -2.7e-142) {
		tmp = t_1;
	} else if (z <= 9e-291) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 9.5e+114) {
		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 = x + (t * (y / a))
    t_2 = t / (1.0d0 - (a / z))
    if (z <= (-6.2d+115)) then
        tmp = t_2
    else if (z <= (-2.7d-142)) then
        tmp = t_1
    else if (z <= 9d-291) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 9.5d+114) 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 = x + (t * (y / a));
	double t_2 = t / (1.0 - (a / z));
	double tmp;
	if (z <= -6.2e+115) {
		tmp = t_2;
	} else if (z <= -2.7e-142) {
		tmp = t_1;
	} else if (z <= 9e-291) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 9.5e+114) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	t_2 = t / (1.0 - (a / z))
	tmp = 0
	if z <= -6.2e+115:
		tmp = t_2
	elif z <= -2.7e-142:
		tmp = t_1
	elif z <= 9e-291:
		tmp = x * (1.0 - (y / a))
	elif z <= 9.5e+114:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	t_2 = Float64(t / Float64(1.0 - Float64(a / z)))
	tmp = 0.0
	if (z <= -6.2e+115)
		tmp = t_2;
	elseif (z <= -2.7e-142)
		tmp = t_1;
	elseif (z <= 9e-291)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 9.5e+114)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	t_2 = t / (1.0 - (a / z));
	tmp = 0.0;
	if (z <= -6.2e+115)
		tmp = t_2;
	elseif (z <= -2.7e-142)
		tmp = t_1;
	elseif (z <= 9e-291)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 9.5e+114)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.2e+115], t$95$2, If[LessEqual[z, -2.7e-142], t$95$1, If[LessEqual[z, 9e-291], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+114], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.2000000000000001e115 or 9.5000000000000001e114 < z

   1. Initial program 39.6%

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

      1. associate-*l/ 69.0%

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

   3. Simplified 69.0%

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

   4. Taylor expanded in x around 0 37.5%

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

   5. Taylor expanded in y around 0 34.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot z}{a - z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 34.4%

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

      2. associate-/l* 58.0%

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

      3. distribute-neg-frac 58.0%

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

   7. Simplified 58.0%

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

      1. distribute-frac-neg 58.0%

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

      2. neg-sub0 58.0%

         \[\leadsto \color{blue}{0 - \frac{t}{\frac{a - z}{z}}} \]

      3. div-sub 58.0%

         \[\leadsto 0 - \frac{t}{\color{blue}{\frac{a}{z} - \frac{z}{z}}} \]

      4. *-inverses 58.0%

         \[\leadsto 0 - \frac{t}{\frac{a}{z} - \color{blue}{1}} \]

      5. sub-neg 58.0%

         \[\leadsto 0 - \frac{t}{\color{blue}{\frac{a}{z} + \left(-1\right)}} \]

      6. metadata-eval 58.0%

         \[\leadsto 0 - \frac{t}{\frac{a}{z} + \color{blue}{-1}} \]

   9. Applied egg-rr 58.0%

      \[\leadsto \color{blue}{0 - \frac{t}{\frac{a}{z} + -1}} \]
   10. Step-by-step derivation

       1. neg-sub0 58.0%

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

       2. neg-mul-1 58.0%

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

       3. metadata-eval 58.0%

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

       4. times-frac 58.0%

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

       5. *-commutative 58.0%

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

       6. neg-mul-1 58.0%

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

       7. *-rgt-identity 58.0%

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

       8. neg-sub0 58.0%

          \[\leadsto \frac{t}{\color{blue}{0 - \left(\frac{a}{z} + -1\right)}} \]

       9. +-commutative 58.0%

          \[\leadsto \frac{t}{0 - \color{blue}{\left(-1 + \frac{a}{z}\right)}} \]

       10. associate--r+ 58.0%

           \[\leadsto \frac{t}{\color{blue}{\left(0 - -1\right) - \frac{a}{z}}} \]

       11. metadata-eval 58.0%

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

   11. Simplified 58.0%

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

   if -6.2000000000000001e115 < z < -2.6999999999999998e-142 or 8.99999999999999948e-291 < z < 9.5000000000000001e114

   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/ 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in z around 0 65.2%

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

   5. Taylor expanded in t around inf 53.4%

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

      1. associate-*r/ 57.2%

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

   7. Simplified 57.2%

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

   if -2.6999999999999998e-142 < z < 8.99999999999999948e-291

   1. Initial program 95.0%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 93.6%

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

   5. Taylor expanded in x around inf 82.7%

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

      1. mul-1-neg 82.7%

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

      2. unsub-neg 82.7%

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

   7. Simplified 82.7%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+115}:\\ \;\;\;\;\frac{t}{1 - \frac{a}{z}}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-142}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-291}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+114}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{a}{z}}\\ \end{array} \]

Alternative 15: 58.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -2.1 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-106}:\\ \;\;\;\;y \cdot \frac{-x}{a - z}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+117}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))))
   (if (<= a -2.1e+38)
     t_1
     (if (<= a -3.8e-106)
       (* y (/ (- x) (- a z)))
       (if (<= a 2.35e+117) (* t (/ (- y z) (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double tmp;
	if (a <= -2.1e+38) {
		tmp = t_1;
	} else if (a <= -3.8e-106) {
		tmp = y * (-x / (a - z));
	} else if (a <= 2.35e+117) {
		tmp = t * ((y - z) / (a - z));
	} 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 = x + (t * (y / a))
    if (a <= (-2.1d+38)) then
        tmp = t_1
    else if (a <= (-3.8d-106)) then
        tmp = y * (-x / (a - z))
    else if (a <= 2.35d+117) then
        tmp = t * ((y - z) / (a - z))
    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 = x + (t * (y / a));
	double tmp;
	if (a <= -2.1e+38) {
		tmp = t_1;
	} else if (a <= -3.8e-106) {
		tmp = y * (-x / (a - z));
	} else if (a <= 2.35e+117) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	tmp = 0
	if a <= -2.1e+38:
		tmp = t_1
	elif a <= -3.8e-106:
		tmp = y * (-x / (a - z))
	elif a <= 2.35e+117:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (a <= -2.1e+38)
		tmp = t_1;
	elseif (a <= -3.8e-106)
		tmp = Float64(y * Float64(Float64(-x) / Float64(a - z)));
	elseif (a <= 2.35e+117)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	tmp = 0.0;
	if (a <= -2.1e+38)
		tmp = t_1;
	elseif (a <= -3.8e-106)
		tmp = y * (-x / (a - z));
	elseif (a <= 2.35e+117)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.1e+38], t$95$1, If[LessEqual[a, -3.8e-106], N[(y * N[((-x) / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.35e+117], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.1e38 or 2.35000000000000003e117 < a

   1. Initial program 71.5%

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

      1. associate-*l/ 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in z around 0 71.3%

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

   5. Taylor expanded in t around inf 62.5%

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

      1. associate-*r/ 66.4%

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

   7. Simplified 66.4%

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

   if -2.1e38 < a < -3.7999999999999999e-106

   1. Initial program 59.9%

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

      1. associate-*l/ 66.4%

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

   3. Simplified 66.4%

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

   4. Taylor expanded in y around inf 50.3%

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

      1. div-sub 50.3%

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

   6. Simplified 50.3%

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

   7. Taylor expanded in t around 0 46.8%

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

      1. neg-mul-1 46.8%

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

      2. distribute-neg-frac 46.8%

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

   9. Simplified 46.8%

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

   if -3.7999999999999999e-106 < a < 2.35000000000000003e117

   1. Initial program 65.3%

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

      1. associate-*l/ 82.4%

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

   3. Simplified 82.4%

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

   4. Taylor expanded in x around 0 47.4%

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

      1. associate-*r/ 61.6%

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

   6. Simplified 61.6%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+38}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-106}:\\ \;\;\;\;y \cdot \frac{-x}{a - z}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+117}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 16: 38.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+115}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-289}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-216}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.2e+115)
   t
   (if (<= z 2.8e-289)
     x
     (if (<= z 3.3e-216) (* t (/ y a)) (if (<= z 2.1e+65) x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.2e+115) {
		tmp = t;
	} else if (z <= 2.8e-289) {
		tmp = x;
	} else if (z <= 3.3e-216) {
		tmp = t * (y / a);
	} else if (z <= 2.1e+65) {
		tmp = x;
	} 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 <= (-8.2d+115)) then
        tmp = t
    else if (z <= 2.8d-289) then
        tmp = x
    else if (z <= 3.3d-216) then
        tmp = t * (y / a)
    else if (z <= 2.1d+65) then
        tmp = x
    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 <= -8.2e+115) {
		tmp = t;
	} else if (z <= 2.8e-289) {
		tmp = x;
	} else if (z <= 3.3e-216) {
		tmp = t * (y / a);
	} else if (z <= 2.1e+65) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.2e+115:
		tmp = t
	elif z <= 2.8e-289:
		tmp = x
	elif z <= 3.3e-216:
		tmp = t * (y / a)
	elif z <= 2.1e+65:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.2e+115)
		tmp = t;
	elseif (z <= 2.8e-289)
		tmp = x;
	elseif (z <= 3.3e-216)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 2.1e+65)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.2e+115)
		tmp = t;
	elseif (z <= 2.8e-289)
		tmp = x;
	elseif (z <= 3.3e-216)
		tmp = t * (y / a);
	elseif (z <= 2.1e+65)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.2e+115], t, If[LessEqual[z, 2.8e-289], x, If[LessEqual[z, 3.3e-216], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e+65], x, t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.19999999999999925e115 or 2.09999999999999991e65 < z

   1. Initial program 41.3%

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

      1. associate-*l/ 69.8%

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

   3. Simplified 69.8%

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

   4. Taylor expanded in z around inf 51.0%

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

   if -8.19999999999999925e115 < z < 2.79999999999999985e-289 or 3.29999999999999969e-216 < z < 2.09999999999999991e65

   1. Initial program 83.0%

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

      1. associate-*l/ 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in a around inf 41.9%

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

   if 2.79999999999999985e-289 < z < 3.29999999999999969e-216

   1. Initial program 90.2%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around -inf 70.8%

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

      1. associate-*l/ 80.5%

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

   6. Simplified 80.5%

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

   7. Taylor expanded in t around inf 61.5%

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

      1. associate-*r/ 71.2%

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

   9. Simplified 71.2%

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

   10. Taylor expanded in a around inf 71.2%

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

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+115}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-289}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-216}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 17: 48.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+115}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.2e+115) t (if (<= z 2e+65) (* x (- 1.0 (/ y a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.2e+115) {
		tmp = t;
	} else if (z <= 2e+65) {
		tmp = x * (1.0 - (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 <= (-6.2d+115)) then
        tmp = t
    else if (z <= 2d+65) then
        tmp = x * (1.0d0 - (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 <= -6.2e+115) {
		tmp = t;
	} else if (z <= 2e+65) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.2e+115:
		tmp = t
	elif z <= 2e+65:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.2e+115)
		tmp = t;
	elseif (z <= 2e+65)
		tmp = Float64(x * Float64(1.0 - 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 <= -6.2e+115)
		tmp = t;
	elseif (z <= 2e+65)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.2e+115], t, If[LessEqual[z, 2e+65], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -6.2000000000000001e115 or 2e65 < z

   1. Initial program 41.3%

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

      1. associate-*l/ 69.8%

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

   3. Simplified 69.8%

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

   4. Taylor expanded in z around inf 51.0%

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

   if -6.2000000000000001e115 < z < 2e65

   1. Initial program 83.4%

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

      1. associate-*l/ 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in z around 0 73.1%

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

   5. Taylor expanded in x around inf 56.4%

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

      1. mul-1-neg 56.4%

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

      2. unsub-neg 56.4%

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

   7. Simplified 56.4%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{a}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+115}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 18: 38.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+116}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.96 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.05e+116) t (if (<= z 1.96e+65) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.05e+116) {
		tmp = t;
	} else if (z <= 1.96e+65) {
		tmp = x;
	} 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 <= (-1.05d+116)) then
        tmp = t
    else if (z <= 1.96d+65) then
        tmp = x
    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 <= -1.05e+116) {
		tmp = t;
	} else if (z <= 1.96e+65) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.05e+116:
		tmp = t
	elif z <= 1.96e+65:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.05e+116)
		tmp = t;
	elseif (z <= 1.96e+65)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.05e+116)
		tmp = t;
	elseif (z <= 1.96e+65)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.05e+116], t, If[LessEqual[z, 1.96e+65], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0500000000000001e116 or 1.9600000000000001e65 < z

   1. Initial program 41.3%

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

      1. associate-*l/ 69.8%

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

   3. Simplified 69.8%

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

   4. Taylor expanded in z around inf 51.0%

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

   if -1.0500000000000001e116 < z < 1.9600000000000001e65

   1. Initial program 83.4%

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

      1. associate-*l/ 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in a around inf 40.7%

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

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+116}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.96 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 19: 25.3% 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 67.5%

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

   1. associate-*l/ 84.2%

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

3. Simplified 84.2%

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

4. Taylor expanded in z around inf 23.3%

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

5. Final simplification 23.3%

   \[\leadsto t \]

Developer target: 83.4% accurate, 0.8× 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 2023332 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (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))))