Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.2% → 92.7%

Time: 16.6s

Alternatives: 20

Speedup: 0.3×

Specification

Math

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

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(y - z) * Float64(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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 80.2% accurate, 1.0× speedup

Math

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

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(y - z) * Float64(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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 92.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ t_2 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -4 \cdot 10^{-263}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{-285}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \mathbf{elif}\;t_2 \leq 10^{+305}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y z) (- x t)) (- a z))))
        (t_2 (+ x (* (- z y) (/ (- x t) (- a z))))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -4e-263)
       t_2
       (if (<= t_2 5e-285)
         (- t (/ (- t x) (/ z (- y a))))
         (if (<= t_2 1e+305) (fma (- y z) (/ (- t x) (- a z)) x) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - z) * (x - t)) / (a - z));
	double t_2 = x + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -4e-263) {
		tmp = t_2;
	} else if (t_2 <= 5e-285) {
		tmp = t - ((t - x) / (z / (y - a)));
	} else if (t_2 <= 1e+305) {
		tmp = fma((y - z), ((t - x) / (a - z)), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - z) * Float64(x - t)) / Float64(a - z)))
	t_2 = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -4e-263)
		tmp = t_2;
	elseif (t_2 <= 5e-285)
		tmp = Float64(t - Float64(Float64(t - x) / Float64(z / Float64(y - a))));
	elseif (t_2 <= 1e+305)
		tmp = fma(Float64(y - z), Float64(Float64(t - x) / Float64(a - z)), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(y - z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -4e-263], t$95$2, If[LessEqual[t$95$2, 5e-285], N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+305], N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -inf.0 or 9.9999999999999994e304 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 74.4%

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

      1. associate-*r/ 100.0%

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

   3. Simplified 100.0%

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

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4e-263

   1. Initial program 92.4%

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

   if -4e-263 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 5.00000000000000018e-285

   1. Initial program 3.3%

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

   2. Taylor expanded in z around inf 74.6%

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

      1. associate--l+ 74.6%

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

      2. associate-*r/ 74.6%

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

      3. associate-*r/ 74.6%

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

      4. div-sub 74.6%

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

      5. distribute-lft-out-- 74.6%

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

      6. associate-*r/ 74.6%

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

      7. mul-1-neg 74.6%

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

      8. unsub-neg 74.6%

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

      9. distribute-rgt-out-- 75.2%

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

      10. associate-/l* 96.4%

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

   4. Simplified 96.4%

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

   if 5.00000000000000018e-285 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 9.9999999999999994e304

   1. Initial program 97.5%

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

      1. +-commutative 97.5%

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

      2. fma-def 97.5%

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

   3. Simplified 97.5%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -\infty:\\ \;\;\;\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{elif}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -4 \cdot 10^{-263}:\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{elif}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 5 \cdot 10^{-285}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \mathbf{elif}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 10^{+305}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \end{array} \]

Alternative 2: 94.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-263} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z y) (/ (- x t) (- a z))))))
   (if (or (<= t_1 -4e-263) (not (<= t_1 0.0)))
     (fma (/ (- y z) (- a z)) (- t x) x)
     (- t (/ (- t x) (/ z (- y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if ((t_1 <= -4e-263) || !(t_1 <= 0.0)) {
		tmp = fma(((y - z) / (a - z)), (t - x), x);
	} else {
		tmp = t - ((t - x) / (z / (y - a)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -4e-263) || !(t_1 <= 0.0))
		tmp = fma(Float64(Float64(y - z) / Float64(a - z)), Float64(t - x), x);
	else
		tmp = Float64(t - Float64(Float64(t - x) / Float64(z / Float64(y - a))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e-263], 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[(t - N[(N[(t - x), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4e-263 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.6%

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

      1. +-commutative 90.6%

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

      2. remove-double-neg 90.6%

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

      3. unsub-neg 90.6%

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

      4. associate-*r/ 79.9%

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

      5. associate-/l* 91.4%

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

      6. associate-/r/ 95.5%

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

      7. fma-neg 95.5%

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

      8. remove-double-neg 95.5%

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

   3. Simplified 95.5%

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

   if -4e-263 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.0%

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

   2. Taylor expanded in z around inf 72.6%

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

      1. associate--l+ 72.6%

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

      2. associate-*r/ 72.6%

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

      3. associate-*r/ 72.6%

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

      4. div-sub 72.6%

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

      5. distribute-lft-out-- 72.6%

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

      6. associate-*r/ 72.6%

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

      7. mul-1-neg 72.6%

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

      8. unsub-neg 72.6%

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

      9. distribute-rgt-out-- 73.3%

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

      10. associate-/l* 96.1%

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

   4. Simplified 96.1%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -4 \cdot 10^{-263} \lor \neg \left(x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 3: 92.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ t_2 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -4 \cdot 10^{-263}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{-285}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \mathbf{elif}\;t_2 \leq 10^{+305}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y z) (- x t)) (- a z))))
        (t_2 (+ x (* (- z y) (/ (- x t) (- a z))))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -4e-263)
       t_2
       (if (<= t_2 5e-285)
         (- t (/ (- t x) (/ z (- y a))))
         (if (<= t_2 1e+305) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - z) * (x - t)) / (a - z));
	double t_2 = x + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -4e-263) {
		tmp = t_2;
	} else if (t_2 <= 5e-285) {
		tmp = t - ((t - x) / (z / (y - a)));
	} else if (t_2 <= 1e+305) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - z) * (x - t)) / (a - z));
	double t_2 = x + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -4e-263) {
		tmp = t_2;
	} else if (t_2 <= 5e-285) {
		tmp = t - ((t - x) / (z / (y - a)));
	} else if (t_2 <= 1e+305) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((y - z) * (x - t)) / (a - z))
	t_2 = x + ((z - y) * ((x - t) / (a - z)))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -4e-263:
		tmp = t_2
	elif t_2 <= 5e-285:
		tmp = t - ((t - x) / (z / (y - a)))
	elif t_2 <= 1e+305:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - z) * Float64(x - t)) / Float64(a - z)))
	t_2 = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -4e-263)
		tmp = t_2;
	elseif (t_2 <= 5e-285)
		tmp = Float64(t - Float64(Float64(t - x) / Float64(z / Float64(y - a))));
	elseif (t_2 <= 1e+305)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((y - z) * (x - t)) / (a - z));
	t_2 = x + ((z - y) * ((x - t) / (a - z)));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -4e-263)
		tmp = t_2;
	elseif (t_2 <= 5e-285)
		tmp = t - ((t - x) / (z / (y - a)));
	elseif (t_2 <= 1e+305)
		tmp = t_2;
	else
		tmp = t_1;
	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[(x - t), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -4e-263], t$95$2, If[LessEqual[t$95$2, 5e-285], N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+305], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -inf.0 or 9.9999999999999994e304 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 74.4%

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

      1. associate-*r/ 100.0%

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

   3. Simplified 100.0%

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

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4e-263 or 5.00000000000000018e-285 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 9.9999999999999994e304

   1. Initial program 94.9%

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

   if -4e-263 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 5.00000000000000018e-285

   1. Initial program 3.3%

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

   2. Taylor expanded in z around inf 74.6%

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

      1. associate--l+ 74.6%

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

      2. associate-*r/ 74.6%

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

      3. associate-*r/ 74.6%

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

      4. div-sub 74.6%

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

      5. distribute-lft-out-- 74.6%

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

      6. associate-*r/ 74.6%

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

      7. mul-1-neg 74.6%

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

      8. unsub-neg 74.6%

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

      9. distribute-rgt-out-- 75.2%

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

      10. associate-/l* 96.4%

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

   4. Simplified 96.4%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -\infty:\\ \;\;\;\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{elif}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -4 \cdot 10^{-263}:\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{elif}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 5 \cdot 10^{-285}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \mathbf{elif}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 10^{+305}:\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \end{array} \]

Alternative 4: 91.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-263} \lor \neg \left(t_1 \leq 5 \cdot 10^{-285}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z y) (/ (- x t) (- a z))))))
   (if (or (<= t_1 -4e-263) (not (<= t_1 5e-285)))
     t_1
     (- t (/ (- t x) (/ z (- y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if ((t_1 <= -4e-263) || !(t_1 <= 5e-285)) {
		tmp = t_1;
	} else {
		tmp = t - ((t - x) / (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 + ((z - y) * ((x - t) / (a - z)))
    if ((t_1 <= (-4d-263)) .or. (.not. (t_1 <= 5d-285))) then
        tmp = t_1
    else
        tmp = t - ((t - x) / (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 + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if ((t_1 <= -4e-263) || !(t_1 <= 5e-285)) {
		tmp = t_1;
	} else {
		tmp = t - ((t - x) / (z / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - y) * ((x - t) / (a - z)))
	tmp = 0
	if (t_1 <= -4e-263) or not (t_1 <= 5e-285):
		tmp = t_1
	else:
		tmp = t - ((t - x) / (z / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -4e-263) || !(t_1 <= 5e-285))
		tmp = t_1;
	else
		tmp = Float64(t - Float64(Float64(t - x) / Float64(z / Float64(y - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - y) * ((x - t) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -4e-263) || ~((t_1 <= 5e-285)))
		tmp = t_1;
	else
		tmp = t - ((t - x) / (z / (y - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e-263], N[Not[LessEqual[t$95$1, 5e-285]], $MachinePrecision]], t$95$1, N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4e-263 or 5.00000000000000018e-285 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.3%

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

   if -4e-263 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 5.00000000000000018e-285

   1. Initial program 3.3%

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

   2. Taylor expanded in z around inf 74.6%

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

      1. associate--l+ 74.6%

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

      2. associate-*r/ 74.6%

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

      3. associate-*r/ 74.6%

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

      4. div-sub 74.6%

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

      5. distribute-lft-out-- 74.6%

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

      6. associate-*r/ 74.6%

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

      7. mul-1-neg 74.6%

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

      8. unsub-neg 74.6%

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

      9. distribute-rgt-out-- 75.2%

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

      10. associate-/l* 96.4%

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

   4. Simplified 96.4%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -4 \cdot 10^{-263} \lor \neg \left(x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 5 \cdot 10^{-285}\right):\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 5: 58.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{-11}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-153}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-251}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.75 \cdot 10^{-283}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{a}{z}\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= t -4.5e-11)
     t_2
     (if (<= t -5.8e-92)
       t_1
       (if (<= t -1.35e-153)
         (* y (/ (- t x) (- a z)))
         (if (<= t -8.2e-251)
           t_1
           (if (<= t -2.75e-283)
             (* x (- (/ y z) (/ a z)))
             (if (<= t 1.6e-60) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -4.5e-11) {
		tmp = t_2;
	} else if (t <= -5.8e-92) {
		tmp = t_1;
	} else if (t <= -1.35e-153) {
		tmp = y * ((t - x) / (a - z));
	} else if (t <= -8.2e-251) {
		tmp = t_1;
	} else if (t <= -2.75e-283) {
		tmp = x * ((y / z) - (a / z));
	} else if (t <= 1.6e-60) {
		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 * (1.0d0 - (y / a))
    t_2 = t * ((y - z) / (a - z))
    if (t <= (-4.5d-11)) then
        tmp = t_2
    else if (t <= (-5.8d-92)) then
        tmp = t_1
    else if (t <= (-1.35d-153)) then
        tmp = y * ((t - x) / (a - z))
    else if (t <= (-8.2d-251)) then
        tmp = t_1
    else if (t <= (-2.75d-283)) then
        tmp = x * ((y / z) - (a / z))
    else if (t <= 1.6d-60) 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 * (1.0 - (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -4.5e-11) {
		tmp = t_2;
	} else if (t <= -5.8e-92) {
		tmp = t_1;
	} else if (t <= -1.35e-153) {
		tmp = y * ((t - x) / (a - z));
	} else if (t <= -8.2e-251) {
		tmp = t_1;
	} else if (t <= -2.75e-283) {
		tmp = x * ((y / z) - (a / z));
	} else if (t <= 1.6e-60) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -4.5e-11:
		tmp = t_2
	elif t <= -5.8e-92:
		tmp = t_1
	elif t <= -1.35e-153:
		tmp = y * ((t - x) / (a - z))
	elif t <= -8.2e-251:
		tmp = t_1
	elif t <= -2.75e-283:
		tmp = x * ((y / z) - (a / z))
	elif t <= 1.6e-60:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (t <= -4.5e-11)
		tmp = t_2;
	elseif (t <= -5.8e-92)
		tmp = t_1;
	elseif (t <= -1.35e-153)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (t <= -8.2e-251)
		tmp = t_1;
	elseif (t <= -2.75e-283)
		tmp = Float64(x * Float64(Float64(y / z) - Float64(a / z)));
	elseif (t <= 1.6e-60)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -4.5e-11)
		tmp = t_2;
	elseif (t <= -5.8e-92)
		tmp = t_1;
	elseif (t <= -1.35e-153)
		tmp = y * ((t - x) / (a - z));
	elseif (t <= -8.2e-251)
		tmp = t_1;
	elseif (t <= -2.75e-283)
		tmp = x * ((y / z) - (a / z));
	elseif (t <= 1.6e-60)
		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[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.5e-11], t$95$2, If[LessEqual[t, -5.8e-92], t$95$1, If[LessEqual[t, -1.35e-153], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8.2e-251], t$95$1, If[LessEqual[t, -2.75e-283], N[(x * N[(N[(y / z), $MachinePrecision] - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e-60], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.5e-11 or 1.6000000000000001e-60 < t

   1. Initial program 85.7%

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

   2. Taylor expanded in x around 0 47.1%

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

      1. associate-*r/ 68.7%

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

   4. Simplified 68.7%

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

   if -4.5e-11 < t < -5.79999999999999969e-92 or -1.35000000000000005e-153 < t < -8.1999999999999997e-251 or -2.74999999999999976e-283 < t < 1.6000000000000001e-60

   1. Initial program 79.2%

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

   2. Taylor expanded in z around 0 71.0%

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

   3. Taylor expanded in x around inf 71.2%

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

      1. mul-1-neg 71.2%

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

      2. unsub-neg 71.2%

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

   5. Simplified 71.2%

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

   if -5.79999999999999969e-92 < t < -1.35000000000000005e-153

   1. Initial program 90.1%

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

   2. Taylor expanded in y around inf 80.4%

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

      1. div-sub 80.4%

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

   4. Simplified 80.4%

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

   if -8.1999999999999997e-251 < t < -2.74999999999999976e-283

   1. Initial program 17.7%

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

      1. +-commutative 17.7%

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

      2. remove-double-neg 17.7%

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

      3. unsub-neg 17.7%

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

      4. associate-*r/ 18.7%

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

      5. associate-/l* 17.3%

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

      6. associate-/r/ 18.7%

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

      7. fma-neg 18.7%

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

      8. remove-double-neg 18.7%

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

   3. Simplified 18.7%

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

   4. Taylor expanded in z around -inf 86.0%

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

   5. Taylor expanded in x around inf 73.3%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-11}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-92}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-153}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-251}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq -2.75 \cdot 10^{-283}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{a}{z}\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 6: 77.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t}{a - z}\\ t_2 := t - \frac{t - x}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+146}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-210}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+127}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ t (- a z)))))
        (t_2 (- t (/ (- t x) (/ z (- y a))))))
   (if (<= z -4.2e+146)
     t_2
     (if (<= z -5.4e-210)
       t_1
       (if (<= z 2.45e-60)
         (+ x (/ (- t x) (/ a (- y z))))
         (if (<= z 3.7e+127) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (t / (a - z)));
	double t_2 = t - ((t - x) / (z / (y - a)));
	double tmp;
	if (z <= -4.2e+146) {
		tmp = t_2;
	} else if (z <= -5.4e-210) {
		tmp = t_1;
	} else if (z <= 2.45e-60) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else if (z <= 3.7e+127) {
		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 + ((y - z) * (t / (a - z)))
    t_2 = t - ((t - x) / (z / (y - a)))
    if (z <= (-4.2d+146)) then
        tmp = t_2
    else if (z <= (-5.4d-210)) then
        tmp = t_1
    else if (z <= 2.45d-60) then
        tmp = x + ((t - x) / (a / (y - z)))
    else if (z <= 3.7d+127) 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 + ((y - z) * (t / (a - z)));
	double t_2 = t - ((t - x) / (z / (y - a)));
	double tmp;
	if (z <= -4.2e+146) {
		tmp = t_2;
	} else if (z <= -5.4e-210) {
		tmp = t_1;
	} else if (z <= 2.45e-60) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else if (z <= 3.7e+127) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * (t / (a - z)))
	t_2 = t - ((t - x) / (z / (y - a)))
	tmp = 0
	if z <= -4.2e+146:
		tmp = t_2
	elif z <= -5.4e-210:
		tmp = t_1
	elif z <= 2.45e-60:
		tmp = x + ((t - x) / (a / (y - z)))
	elif z <= 3.7e+127:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))))
	t_2 = Float64(t - Float64(Float64(t - x) / Float64(z / Float64(y - a))))
	tmp = 0.0
	if (z <= -4.2e+146)
		tmp = t_2;
	elseif (z <= -5.4e-210)
		tmp = t_1;
	elseif (z <= 2.45e-60)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	elseif (z <= 3.7e+127)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * (t / (a - z)));
	t_2 = t - ((t - x) / (z / (y - a)));
	tmp = 0.0;
	if (z <= -4.2e+146)
		tmp = t_2;
	elseif (z <= -5.4e-210)
		tmp = t_1;
	elseif (z <= 2.45e-60)
		tmp = x + ((t - x) / (a / (y - z)));
	elseif (z <= 3.7e+127)
		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[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e+146], t$95$2, If[LessEqual[z, -5.4e-210], t$95$1, If[LessEqual[z, 2.45e-60], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e+127], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.2000000000000001e146 or 3.6999999999999998e127 < z

   1. Initial program 57.7%

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

   2. Taylor expanded in z around inf 60.4%

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

      1. associate--l+ 60.4%

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

      2. associate-*r/ 60.4%

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

      3. associate-*r/ 60.4%

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

      4. div-sub 60.4%

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

      5. distribute-lft-out-- 60.4%

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

      6. associate-*r/ 60.4%

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

      7. mul-1-neg 60.4%

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

      8. unsub-neg 60.4%

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

      9. distribute-rgt-out-- 60.7%

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

      10. associate-/l* 87.0%

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

   4. Simplified 87.0%

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

   if -4.2000000000000001e146 < z < -5.39999999999999983e-210 or 2.44999999999999994e-60 < z < 3.6999999999999998e127

   1. Initial program 90.6%

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

   2. Taylor expanded in t around inf 80.5%

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

   if -5.39999999999999983e-210 < z < 2.44999999999999994e-60

   1. Initial program 88.5%

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

   2. Taylor expanded in a around inf 75.6%

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

      1. associate-/l* 84.9%

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

   4. Simplified 84.9%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+146}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-210}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+127}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 7: 77.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{t - x}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -4 \cdot 10^{+146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-210}:\\ \;\;\;\;x + \left(y - z\right) \cdot \left(t \cdot \frac{1}{a - z}\right)\\ \mathbf{elif}\;z \leq 10^{-57}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+129}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ (- t x) (/ z (- y a))))))
   (if (<= z -4e+146)
     t_1
     (if (<= z -8.8e-210)
       (+ x (* (- y z) (* t (/ 1.0 (- a z)))))
       (if (<= z 1e-57)
         (+ x (/ (- t x) (/ a (- y z))))
         (if (<= z 1.45e+129) (+ x (* (- y z) (/ t (- a z)))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((t - x) / (z / (y - a)));
	double tmp;
	if (z <= -4e+146) {
		tmp = t_1;
	} else if (z <= -8.8e-210) {
		tmp = x + ((y - z) * (t * (1.0 / (a - z))));
	} else if (z <= 1e-57) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else if (z <= 1.45e+129) {
		tmp = x + ((y - z) * (t / (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 = t - ((t - x) / (z / (y - a)))
    if (z <= (-4d+146)) then
        tmp = t_1
    else if (z <= (-8.8d-210)) then
        tmp = x + ((y - z) * (t * (1.0d0 / (a - z))))
    else if (z <= 1d-57) then
        tmp = x + ((t - x) / (a / (y - z)))
    else if (z <= 1.45d+129) then
        tmp = x + ((y - z) * (t / (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 = t - ((t - x) / (z / (y - a)));
	double tmp;
	if (z <= -4e+146) {
		tmp = t_1;
	} else if (z <= -8.8e-210) {
		tmp = x + ((y - z) * (t * (1.0 / (a - z))));
	} else if (z <= 1e-57) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else if (z <= 1.45e+129) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((t - x) / (z / (y - a)))
	tmp = 0
	if z <= -4e+146:
		tmp = t_1
	elif z <= -8.8e-210:
		tmp = x + ((y - z) * (t * (1.0 / (a - z))))
	elif z <= 1e-57:
		tmp = x + ((t - x) / (a / (y - z)))
	elif z <= 1.45e+129:
		tmp = x + ((y - z) * (t / (a - z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(t - x) / Float64(z / Float64(y - a))))
	tmp = 0.0
	if (z <= -4e+146)
		tmp = t_1;
	elseif (z <= -8.8e-210)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t * Float64(1.0 / Float64(a - z)))));
	elseif (z <= 1e-57)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	elseif (z <= 1.45e+129)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((t - x) / (z / (y - a)));
	tmp = 0.0;
	if (z <= -4e+146)
		tmp = t_1;
	elseif (z <= -8.8e-210)
		tmp = x + ((y - z) * (t * (1.0 / (a - z))));
	elseif (z <= 1e-57)
		tmp = x + ((t - x) / (a / (y - z)));
	elseif (z <= 1.45e+129)
		tmp = x + ((y - z) * (t / (a - z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4e+146], t$95$1, If[LessEqual[z, -8.8e-210], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t * N[(1.0 / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e-57], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+129], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.99999999999999973e146 or 1.45000000000000001e129 < z

   1. Initial program 57.7%

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

   2. Taylor expanded in z around inf 60.4%

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

      1. associate--l+ 60.4%

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

      2. associate-*r/ 60.4%

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

      3. associate-*r/ 60.4%

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

      4. div-sub 60.4%

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

      5. distribute-lft-out-- 60.4%

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

      6. associate-*r/ 60.4%

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

      7. mul-1-neg 60.4%

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

      8. unsub-neg 60.4%

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

      9. distribute-rgt-out-- 60.7%

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

      10. associate-/l* 87.0%

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

   4. Simplified 87.0%

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

   if -3.99999999999999973e146 < z < -8.79999999999999958e-210

   1. Initial program 93.0%

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

   2. Taylor expanded in t around inf 83.8%

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

      1. div-inv 83.8%

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

   4. Applied egg-rr 83.8%

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

   if -8.79999999999999958e-210 < z < 9.99999999999999955e-58

   1. Initial program 88.5%

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

   2. Taylor expanded in a around inf 75.6%

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

      1. associate-/l* 84.9%

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

   4. Simplified 84.9%

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

   if 9.99999999999999955e-58 < z < 1.45000000000000001e129

   1. Initial program 85.2%

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

   2. Taylor expanded in t around inf 73.4%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+146}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-210}:\\ \;\;\;\;x + \left(y - z\right) \cdot \left(t \cdot \frac{1}{a - z}\right)\\ \mathbf{elif}\;z \leq 10^{-57}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+129}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 8: 59.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -3.2 \cdot 10^{-12}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.28 \cdot 10^{-250}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-283}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= t -3.2e-12)
     t_2
     (if (<= t -1.28e-250)
       t_1
       (if (<= t -1.45e-283) (* x (/ (- y a) z)) (if (<= t 4e-63) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -3.2e-12) {
		tmp = t_2;
	} else if (t <= -1.28e-250) {
		tmp = t_1;
	} else if (t <= -1.45e-283) {
		tmp = x * ((y - a) / z);
	} else if (t <= 4e-63) {
		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 * (1.0d0 - (y / a))
    t_2 = t * ((y - z) / (a - z))
    if (t <= (-3.2d-12)) then
        tmp = t_2
    else if (t <= (-1.28d-250)) then
        tmp = t_1
    else if (t <= (-1.45d-283)) then
        tmp = x * ((y - a) / z)
    else if (t <= 4d-63) 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 * (1.0 - (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -3.2e-12) {
		tmp = t_2;
	} else if (t <= -1.28e-250) {
		tmp = t_1;
	} else if (t <= -1.45e-283) {
		tmp = x * ((y - a) / z);
	} else if (t <= 4e-63) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -3.2e-12:
		tmp = t_2
	elif t <= -1.28e-250:
		tmp = t_1
	elif t <= -1.45e-283:
		tmp = x * ((y - a) / z)
	elif t <= 4e-63:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (t <= -3.2e-12)
		tmp = t_2;
	elseif (t <= -1.28e-250)
		tmp = t_1;
	elseif (t <= -1.45e-283)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (t <= 4e-63)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -3.2e-12)
		tmp = t_2;
	elseif (t <= -1.28e-250)
		tmp = t_1;
	elseif (t <= -1.45e-283)
		tmp = x * ((y - a) / z);
	elseif (t <= 4e-63)
		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[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.2e-12], t$95$2, If[LessEqual[t, -1.28e-250], t$95$1, If[LessEqual[t, -1.45e-283], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e-63], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.2000000000000001e-12 or 4.00000000000000027e-63 < t

   1. Initial program 85.7%

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

   2. Taylor expanded in x around 0 47.1%

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

      1. associate-*r/ 68.7%

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

   4. Simplified 68.7%

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

   if -3.2000000000000001e-12 < t < -1.27999999999999993e-250 or -1.44999999999999994e-283 < t < 4.00000000000000027e-63

   1. Initial program 81.3%

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

   2. Taylor expanded in z around 0 66.5%

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

   3. Taylor expanded in x around inf 66.5%

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

      1. mul-1-neg 66.5%

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

      2. unsub-neg 66.5%

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

   5. Simplified 66.5%

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

   if -1.27999999999999993e-250 < t < -1.44999999999999994e-283

   1. Initial program 17.7%

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

      1. +-commutative 17.7%

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

      2. remove-double-neg 17.7%

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

      3. unsub-neg 17.7%

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

      4. associate-*r/ 18.7%

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

      5. associate-/l* 17.3%

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

      6. associate-/r/ 18.7%

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

      7. fma-neg 18.7%

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

      8. remove-double-neg 18.7%

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

   3. Simplified 18.7%

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

   4. Taylor expanded in z around -inf 86.0%

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

   5. Taylor expanded in x around inf 73.3%

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

      1. div-sub 73.1%

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

   7. Simplified 73.1%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-12}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -1.28 \cdot 10^{-250}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-283}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-63}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 9: 59.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -2 \cdot 10^{-15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-248}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-283}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{a}{z}\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= t -2e-15)
     t_2
     (if (<= t -3.8e-248)
       t_1
       (if (<= t -5.2e-283)
         (* x (- (/ y z) (/ a z)))
         (if (<= t 6e-64) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -2e-15) {
		tmp = t_2;
	} else if (t <= -3.8e-248) {
		tmp = t_1;
	} else if (t <= -5.2e-283) {
		tmp = x * ((y / z) - (a / z));
	} else if (t <= 6e-64) {
		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 * (1.0d0 - (y / a))
    t_2 = t * ((y - z) / (a - z))
    if (t <= (-2d-15)) then
        tmp = t_2
    else if (t <= (-3.8d-248)) then
        tmp = t_1
    else if (t <= (-5.2d-283)) then
        tmp = x * ((y / z) - (a / z))
    else if (t <= 6d-64) 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 * (1.0 - (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -2e-15) {
		tmp = t_2;
	} else if (t <= -3.8e-248) {
		tmp = t_1;
	} else if (t <= -5.2e-283) {
		tmp = x * ((y / z) - (a / z));
	} else if (t <= 6e-64) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -2e-15:
		tmp = t_2
	elif t <= -3.8e-248:
		tmp = t_1
	elif t <= -5.2e-283:
		tmp = x * ((y / z) - (a / z))
	elif t <= 6e-64:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (t <= -2e-15)
		tmp = t_2;
	elseif (t <= -3.8e-248)
		tmp = t_1;
	elseif (t <= -5.2e-283)
		tmp = Float64(x * Float64(Float64(y / z) - Float64(a / z)));
	elseif (t <= 6e-64)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -2e-15)
		tmp = t_2;
	elseif (t <= -3.8e-248)
		tmp = t_1;
	elseif (t <= -5.2e-283)
		tmp = x * ((y / z) - (a / z));
	elseif (t <= 6e-64)
		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[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e-15], t$95$2, If[LessEqual[t, -3.8e-248], t$95$1, If[LessEqual[t, -5.2e-283], N[(x * N[(N[(y / z), $MachinePrecision] - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e-64], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.0000000000000002e-15 or 6.0000000000000001e-64 < t

   1. Initial program 85.7%

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

   2. Taylor expanded in x around 0 47.1%

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

      1. associate-*r/ 68.7%

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

   4. Simplified 68.7%

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

   if -2.0000000000000002e-15 < t < -3.7999999999999999e-248 or -5.2000000000000002e-283 < t < 6.0000000000000001e-64

   1. Initial program 81.3%

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

   2. Taylor expanded in z around 0 66.5%

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

   3. Taylor expanded in x around inf 66.5%

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

      1. mul-1-neg 66.5%

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

      2. unsub-neg 66.5%

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

   5. Simplified 66.5%

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

   if -3.7999999999999999e-248 < t < -5.2000000000000002e-283

   1. Initial program 17.7%

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

      1. +-commutative 17.7%

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

      2. remove-double-neg 17.7%

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

      3. unsub-neg 17.7%

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

      4. associate-*r/ 18.7%

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

      5. associate-/l* 17.3%

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

      6. associate-/r/ 18.7%

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

      7. fma-neg 18.7%

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

      8. remove-double-neg 18.7%

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

   3. Simplified 18.7%

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

   4. Taylor expanded in z around -inf 86.0%

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

   5. Taylor expanded in x around inf 73.3%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-248}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-283}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{a}{z}\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-64}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 10: 73.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{if}\;a \leq -10000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-131}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-33}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ t (- a z))))))
   (if (<= a -10000.0)
     t_1
     (if (<= a -3.1e-131)
       (+ x (/ (* y (- t x)) a))
       (if (<= a 1.25e-33) (+ t (/ (- x t) (/ z y))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (t / (a - z)));
	double tmp;
	if (a <= -10000.0) {
		tmp = t_1;
	} else if (a <= -3.1e-131) {
		tmp = x + ((y * (t - x)) / a);
	} else if (a <= 1.25e-33) {
		tmp = t + ((x - t) / (z / y));
	} 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 + ((y - z) * (t / (a - z)))
    if (a <= (-10000.0d0)) then
        tmp = t_1
    else if (a <= (-3.1d-131)) then
        tmp = x + ((y * (t - x)) / a)
    else if (a <= 1.25d-33) then
        tmp = t + ((x - t) / (z / y))
    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 + ((y - z) * (t / (a - z)));
	double tmp;
	if (a <= -10000.0) {
		tmp = t_1;
	} else if (a <= -3.1e-131) {
		tmp = x + ((y * (t - x)) / a);
	} else if (a <= 1.25e-33) {
		tmp = t + ((x - t) / (z / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * (t / (a - z)))
	tmp = 0
	if a <= -10000.0:
		tmp = t_1
	elif a <= -3.1e-131:
		tmp = x + ((y * (t - x)) / a)
	elif a <= 1.25e-33:
		tmp = t + ((x - t) / (z / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))))
	tmp = 0.0
	if (a <= -10000.0)
		tmp = t_1;
	elseif (a <= -3.1e-131)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / a));
	elseif (a <= 1.25e-33)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * (t / (a - z)));
	tmp = 0.0;
	if (a <= -10000.0)
		tmp = t_1;
	elseif (a <= -3.1e-131)
		tmp = x + ((y * (t - x)) / a);
	elseif (a <= 1.25e-33)
		tmp = t + ((x - t) / (z / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -10000.0], t$95$1, If[LessEqual[a, -3.1e-131], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.25e-33], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1e4 or 1.25000000000000007e-33 < a

   1. Initial program 90.5%

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

   2. Taylor expanded in t around inf 78.4%

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

   if -1e4 < a < -3.10000000000000021e-131

   1. Initial program 79.6%

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

   2. Taylor expanded in z around 0 66.4%

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

   if -3.10000000000000021e-131 < a < 1.25000000000000007e-33

   1. Initial program 69.4%

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

   2. Taylor expanded in z around inf 73.3%

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

      1. associate--l+ 73.3%

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

      2. associate-*r/ 73.3%

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

      3. associate-*r/ 73.3%

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

      4. div-sub 73.4%

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

      5. distribute-lft-out-- 73.4%

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

      6. associate-*r/ 73.4%

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

      7. mul-1-neg 73.4%

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

      8. unsub-neg 73.4%

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

      9. distribute-rgt-out-- 73.4%

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

      10. associate-/l* 80.7%

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

   4. Simplified 80.7%

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

   5. Taylor expanded in y around inf 78.6%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -10000:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-131}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-33}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array} \]

Alternative 11: 48.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -3.9 \cdot 10^{+136}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-220}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -3.9e+136)
     t
     (if (<= z -1.3e-192)
       t_1
       (if (<= z -4.9e-220) (* (- t x) (/ y a)) (if (<= z 3.2e+95) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -3.9e+136) {
		tmp = t;
	} else if (z <= -1.3e-192) {
		tmp = t_1;
	} else if (z <= -4.9e-220) {
		tmp = (t - x) * (y / a);
	} else if (z <= 3.2e+95) {
		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 * (1.0d0 - (y / a))
    if (z <= (-3.9d+136)) then
        tmp = t
    else if (z <= (-1.3d-192)) then
        tmp = t_1
    else if (z <= (-4.9d-220)) then
        tmp = (t - x) * (y / a)
    else if (z <= 3.2d+95) 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 * (1.0 - (y / a));
	double tmp;
	if (z <= -3.9e+136) {
		tmp = t;
	} else if (z <= -1.3e-192) {
		tmp = t_1;
	} else if (z <= -4.9e-220) {
		tmp = (t - x) * (y / a);
	} else if (z <= 3.2e+95) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -3.9e+136:
		tmp = t
	elif z <= -1.3e-192:
		tmp = t_1
	elif z <= -4.9e-220:
		tmp = (t - x) * (y / a)
	elif z <= 3.2e+95:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -3.9e+136)
		tmp = t;
	elseif (z <= -1.3e-192)
		tmp = t_1;
	elseif (z <= -4.9e-220)
		tmp = Float64(Float64(t - x) * Float64(y / a));
	elseif (z <= 3.2e+95)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -3.9e+136)
		tmp = t;
	elseif (z <= -1.3e-192)
		tmp = t_1;
	elseif (z <= -4.9e-220)
		tmp = (t - x) * (y / a);
	elseif (z <= 3.2e+95)
		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[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.9e+136], t, If[LessEqual[z, -1.3e-192], t$95$1, If[LessEqual[z, -4.9e-220], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+95], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.90000000000000019e136 or 3.2000000000000001e95 < z

   1. Initial program 60.0%

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

   2. Taylor expanded in z around inf 48.9%

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

   if -3.90000000000000019e136 < z < -1.3000000000000001e-192 or -4.9000000000000002e-220 < z < 3.2000000000000001e95

   1. Initial program 89.7%

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

   2. Taylor expanded in z around 0 65.8%

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

   3. Taylor expanded in x around inf 58.4%

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

      1. mul-1-neg 58.4%

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

      2. unsub-neg 58.4%

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

   5. Simplified 58.4%

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

   if -1.3000000000000001e-192 < z < -4.9000000000000002e-220

   1. Initial program 91.3%

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

   2. Taylor expanded in z around 0 57.2%

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

   3. Taylor expanded in y around inf 65.7%

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

      1. div-sub 65.7%

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

      2. associate-*r/ 57.2%

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

      3. associate-/l* 65.7%

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

      4. associate-/r/ 65.7%

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

   5. Simplified 65.7%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+136}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-192}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-220}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12: 72.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{-131} \lor \neg \left(a \leq 7.1 \cdot 10^{-34}\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.9e-131) (not (<= a 7.1e-34)))
   (+ x (/ (- t x) (/ a (- y z))))
   (+ t (/ (- x t) (/ z y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.9e-131) || !(a <= 7.1e-34)) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else {
		tmp = t + ((x - t) / (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.9d-131)) .or. (.not. (a <= 7.1d-34))) then
        tmp = x + ((t - x) / (a / (y - z)))
    else
        tmp = t + ((x - t) / (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.9e-131) || !(a <= 7.1e-34)) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else {
		tmp = t + ((x - t) / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.9e-131) or not (a <= 7.1e-34):
		tmp = x + ((t - x) / (a / (y - z)))
	else:
		tmp = t + ((x - t) / (z / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.9e-131) || !(a <= 7.1e-34))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.9e-131) || ~((a <= 7.1e-34)))
		tmp = x + ((t - x) / (a / (y - z)));
	else
		tmp = t + ((x - t) / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.9e-131], N[Not[LessEqual[a, 7.1e-34]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.9000000000000002e-131 or 7.10000000000000036e-34 < a

   1. Initial program 88.8%

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

   2. Taylor expanded in a around inf 69.2%

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

      1. associate-/l* 80.2%

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

   4. Simplified 80.2%

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

   if -2.9000000000000002e-131 < a < 7.10000000000000036e-34

   1. Initial program 69.4%

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

   2. Taylor expanded in z around inf 73.3%

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

      1. associate--l+ 73.3%

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

      2. associate-*r/ 73.3%

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

      3. associate-*r/ 73.3%

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

      4. div-sub 73.4%

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

      5. distribute-lft-out-- 73.4%

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

      6. associate-*r/ 73.4%

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

      7. mul-1-neg 73.4%

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

      8. unsub-neg 73.4%

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

      9. distribute-rgt-out-- 73.4%

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

      10. associate-/l* 80.7%

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

   4. Simplified 80.7%

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

   5. Taylor expanded in y around inf 78.6%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{-131} \lor \neg \left(a \leq 7.1 \cdot 10^{-34}\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \end{array} \]

Alternative 13: 50.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+141}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-213}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.5e+141)
   t
   (if (<= z -1e-213)
     (+ x (* y (/ t a)))
     (if (<= z 2.05e+95) (* x (- 1.0 (/ y a))) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.5e+141) {
		tmp = t;
	} else if (z <= -1e-213) {
		tmp = x + (y * (t / a));
	} else if (z <= 2.05e+95) {
		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 <= (-1.5d+141)) then
        tmp = t
    else if (z <= (-1d-213)) then
        tmp = x + (y * (t / a))
    else if (z <= 2.05d+95) 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 <= -1.5e+141) {
		tmp = t;
	} else if (z <= -1e-213) {
		tmp = x + (y * (t / a));
	} else if (z <= 2.05e+95) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.5e+141:
		tmp = t
	elif z <= -1e-213:
		tmp = x + (y * (t / a))
	elif z <= 2.05e+95:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.5e+141)
		tmp = t;
	elseif (z <= -1e-213)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 2.05e+95)
		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 <= -1.5e+141)
		tmp = t;
	elseif (z <= -1e-213)
		tmp = x + (y * (t / a));
	elseif (z <= 2.05e+95)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.5e+141], t, If[LessEqual[z, -1e-213], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e+95], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4999999999999999e141 or 2.04999999999999993e95 < z

   1. Initial program 60.0%

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

   2. Taylor expanded in z around inf 48.9%

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

   if -1.4999999999999999e141 < z < -9.9999999999999995e-214

   1. Initial program 93.1%

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

   2. Taylor expanded in t around inf 84.0%

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

   3. Taylor expanded in z around 0 59.0%

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

      1. associate-/l* 61.4%

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

   5. Simplified 61.4%

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

      1. associate-/r/ 61.5%

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

   7. Applied egg-rr 61.5%

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

   if -9.9999999999999995e-214 < z < 2.04999999999999993e95

   1. Initial program 87.8%

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

   2. Taylor expanded in z around 0 66.6%

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

   3. Taylor expanded in x around inf 58.8%

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

      1. mul-1-neg 58.8%

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

      2. unsub-neg 58.8%

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

   5. Simplified 58.8%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+141}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-213}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 14: 51.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+136}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-302}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.1e+136)
   t
   (if (<= z -1.55e-302)
     (+ x (/ t (/ a y)))
     (if (<= z 4.5e+95) (* x (- 1.0 (/ y a))) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.1e+136) {
		tmp = t;
	} else if (z <= -1.55e-302) {
		tmp = x + (t / (a / y));
	} else if (z <= 4.5e+95) {
		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 <= (-1.1d+136)) then
        tmp = t
    else if (z <= (-1.55d-302)) then
        tmp = x + (t / (a / y))
    else if (z <= 4.5d+95) 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 <= -1.1e+136) {
		tmp = t;
	} else if (z <= -1.55e-302) {
		tmp = x + (t / (a / y));
	} else if (z <= 4.5e+95) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.1e+136:
		tmp = t
	elif z <= -1.55e-302:
		tmp = x + (t / (a / y))
	elif z <= 4.5e+95:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.1e+136)
		tmp = t;
	elseif (z <= -1.55e-302)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 4.5e+95)
		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 <= -1.1e+136)
		tmp = t;
	elseif (z <= -1.55e-302)
		tmp = x + (t / (a / y));
	elseif (z <= 4.5e+95)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.1e+136], t, If[LessEqual[z, -1.55e-302], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+95], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1e136 or 4.50000000000000017e95 < z

   1. Initial program 60.0%

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

   2. Taylor expanded in z around inf 48.9%

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

   if -1.1e136 < z < -1.54999999999999992e-302

   1. Initial program 89.7%

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

   2. Taylor expanded in t around inf 80.1%

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

   3. Taylor expanded in z around 0 62.9%

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

      1. associate-/l* 65.7%

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

   5. Simplified 65.7%

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

   if -1.54999999999999992e-302 < z < 4.50000000000000017e95

   1. Initial program 89.9%

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

   2. Taylor expanded in z around 0 61.0%

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

   3. Taylor expanded in x around inf 55.4%

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

      1. mul-1-neg 55.4%

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

      2. unsub-neg 55.4%

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

   5. Simplified 55.4%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+136}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-302}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 15: 64.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{+80} \lor \neg \left(a \leq 1.08 \cdot 10^{-8}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3e+80) (not (<= a 1.08e-8)))
   (+ x (* (- y z) (/ t a)))
   (* t (/ (- y z) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3e+80) || !(a <= 1.08e-8)) {
		tmp = x + ((y - z) * (t / a));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-3d+80)) .or. (.not. (a <= 1.08d-8))) then
        tmp = x + ((y - z) * (t / a))
    else
        tmp = t * ((y - z) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3e+80) || !(a <= 1.08e-8)) {
		tmp = x + ((y - z) * (t / a));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3e+80) or not (a <= 1.08e-8):
		tmp = x + ((y - z) * (t / a))
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3e+80) || !(a <= 1.08e-8))
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / a)));
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3e+80) || ~((a <= 1.08e-8)))
		tmp = x + ((y - z) * (t / a));
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3e+80], N[Not[LessEqual[a, 1.08e-8]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.99999999999999987e80 or 1.0800000000000001e-8 < a

   1. Initial program 89.1%

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

   2. Taylor expanded in t around inf 78.5%

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

   3. Taylor expanded in a around inf 76.0%

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

   if -2.99999999999999987e80 < a < 1.0800000000000001e-8

   1. Initial program 75.5%

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

   2. Taylor expanded in x around 0 45.3%

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

      1. associate-*r/ 60.8%

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

   4. Simplified 60.8%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{+80} \lor \neg \left(a \leq 1.08 \cdot 10^{-8}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 16: 62.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{-83} \lor \neg \left(a \leq 2 \cdot 10^{-54}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.15e-83) (not (<= a 2e-54)))
   (+ x (/ y (/ a (- t x))))
   (* t (/ (- y z) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.15e-83) || !(a <= 2e-54)) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.15d-83)) .or. (.not. (a <= 2d-54))) then
        tmp = x + (y / (a / (t - x)))
    else
        tmp = t * ((y - z) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.15e-83) || !(a <= 2e-54)) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.15e-83) or not (a <= 2e-54):
		tmp = x + (y / (a / (t - x)))
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.15e-83) || !(a <= 2e-54))
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.15e-83) || ~((a <= 2e-54)))
		tmp = x + (y / (a / (t - x)));
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.15e-83], N[Not[LessEqual[a, 2e-54]], $MachinePrecision]], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.14999999999999995e-83 or 2.0000000000000001e-54 < a

   1. Initial program 89.5%

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

   2. Taylor expanded in z around 0 64.8%

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

      1. associate-/l* 73.0%

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

   4. Simplified 73.0%

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

   if -1.14999999999999995e-83 < a < 2.0000000000000001e-54

   1. Initial program 69.1%

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

   2. Taylor expanded in x around 0 50.3%

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

      1. associate-*r/ 64.3%

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

   4. Simplified 64.3%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{-83} \lor \neg \left(a \leq 2 \cdot 10^{-54}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 17: 68.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-131} \lor \neg \left(a \leq 7.7 \cdot 10^{-34}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.1e-131) (not (<= a 7.7e-34)))
   (+ x (/ y (/ a (- t x))))
   (+ t (/ (- x t) (/ z y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.1e-131) || !(a <= 7.7e-34)) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t + ((x - t) / (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-3.1d-131)) .or. (.not. (a <= 7.7d-34))) then
        tmp = x + (y / (a / (t - x)))
    else
        tmp = t + ((x - t) / (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.1e-131) || !(a <= 7.7e-34)) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t + ((x - t) / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.1e-131) or not (a <= 7.7e-34):
		tmp = x + (y / (a / (t - x)))
	else:
		tmp = t + ((x - t) / (z / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.1e-131) || !(a <= 7.7e-34))
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.1e-131) || ~((a <= 7.7e-34)))
		tmp = x + (y / (a / (t - x)));
	else
		tmp = t + ((x - t) / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.1e-131], N[Not[LessEqual[a, 7.7e-34]], $MachinePrecision]], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.10000000000000021e-131 or 7.7e-34 < a

   1. Initial program 88.8%

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

   2. Taylor expanded in z around 0 64.6%

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

      1. associate-/l* 72.5%

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

   4. Simplified 72.5%

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

   if -3.10000000000000021e-131 < a < 7.7e-34

   1. Initial program 69.4%

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

   2. Taylor expanded in z around inf 73.3%

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

      1. associate--l+ 73.3%

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

      2. associate-*r/ 73.3%

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

      3. associate-*r/ 73.3%

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

      4. div-sub 73.4%

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

      5. distribute-lft-out-- 73.4%

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

      6. associate-*r/ 73.4%

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

      7. mul-1-neg 73.4%

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

      8. unsub-neg 73.4%

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

      9. distribute-rgt-out-- 73.4%

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

      10. associate-/l* 80.7%

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

   4. Simplified 80.7%

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

   5. Taylor expanded in y around inf 78.6%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-131} \lor \neg \left(a \leq 7.7 \cdot 10^{-34}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \end{array} \]

Alternative 18: 49.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+138}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+97}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.2e+138) t (if (<= z 1.7e+97) (* x (- 1.0 (/ y a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e+138) {
		tmp = t;
	} else if (z <= 1.7e+97) {
		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 <= (-3.2d+138)) then
        tmp = t
    else if (z <= 1.7d+97) 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 <= -3.2e+138) {
		tmp = t;
	} else if (z <= 1.7e+97) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.2e+138:
		tmp = t
	elif z <= 1.7e+97:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.2e+138)
		tmp = t;
	elseif (z <= 1.7e+97)
		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 <= -3.2e+138)
		tmp = t;
	elseif (z <= 1.7e+97)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.2e+138], t, If[LessEqual[z, 1.7e+97], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2000000000000001e138 or 1.70000000000000005e97 < z

   1. Initial program 60.0%

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

   2. Taylor expanded in z around inf 48.9%

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

   if -3.2000000000000001e138 < z < 1.70000000000000005e97

   1. Initial program 89.8%

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

   2. Taylor expanded in z around 0 65.3%

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

   3. Taylor expanded in x around inf 56.7%

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

      1. mul-1-neg 56.7%

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

      2. unsub-neg 56.7%

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

   5. Simplified 56.7%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{a}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+138}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+97}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 19: 39.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+58}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+96}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.6e+58) t (if (<= z 2.2e+96) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.6e+58) {
		tmp = t;
	} else if (z <= 2.2e+96) {
		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 <= (-2.6d+58)) then
        tmp = t
    else if (z <= 2.2d+96) 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 <= -2.6e+58) {
		tmp = t;
	} else if (z <= 2.2e+96) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.6e+58:
		tmp = t
	elif z <= 2.2e+96:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.6e+58)
		tmp = t;
	elseif (z <= 2.2e+96)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.6e+58)
		tmp = t;
	elseif (z <= 2.2e+96)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.6e+58], t, If[LessEqual[z, 2.2e+96], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -2.59999999999999988e58 or 2.1999999999999999e96 < z

   1. Initial program 64.5%

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

   2. Taylor expanded in z around inf 45.8%

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

   if -2.59999999999999988e58 < z < 2.1999999999999999e96

   1. Initial program 90.1%

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

   2. Taylor expanded in a around inf 40.0%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+58}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+96}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 20: 26.0% 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 82.0%

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

2. Taylor expanded in z around inf 19.8%

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

3. Final simplification 19.8%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023293 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))