Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.2% → 95.1%

Time: 25.2s

Alternatives: 21

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: 95.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ t_2 := \frac{z}{t - x}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-280}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\left(t - \frac{y}{t_2}\right) + \frac{a}{t_2}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))) (t_2 (/ z (- t x))))
   (if (<= t_1 -1e-280)
     (fma (/ (- y z) (- a z)) (- t x) x)
     (if (<= t_1 0.0)
       (+ (- t (/ y t_2)) (/ a t_2))
       (+ x (/ (- t x) (/ (- a z) (- y z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double t_2 = z / (t - x);
	double tmp;
	if (t_1 <= -1e-280) {
		tmp = fma(((y - z) / (a - z)), (t - x), x);
	} else if (t_1 <= 0.0) {
		tmp = (t - (y / t_2)) + (a / t_2);
	} else {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	t_2 = Float64(z / Float64(t - x))
	tmp = 0.0
	if (t_1 <= -1e-280)
		tmp = fma(Float64(Float64(y - z) / Float64(a - z)), Float64(t - x), x);
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(t - Float64(y / t_2)) + Float64(a / t_2));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-280], N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(t - N[(y / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(a / t$95$2), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.9999999999999996e-281

   1. Initial program 91.8%

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

      1. +-commutative 91.8%

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

      2. remove-double-neg 91.8%

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

      3. unsub-neg 91.8%

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

      4. associate-*r/ 76.4%

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

      5. associate-/l* 91.5%

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

      6. associate-/r/ 95.8%

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

      7. fma-neg 95.8%

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

      8. remove-double-neg 95.8%

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

   3. Simplified 95.8%

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

   if -9.9999999999999996e-281 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.6%

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

   2. Taylor expanded in y around 0 2.7%

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

      1. div-sub 2.7%

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

      2. associate-*r/ 2.7%

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

      3. mul-1-neg 2.7%

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

      4. distribute-lft-neg-out 2.7%

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

      5. associate-*r/ 3.6%

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

      6. *-commutative 3.6%

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

      7. distribute-lft-out 3.6%

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

      8. sub-neg 3.6%

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

      9. associate-/r/ 3.6%

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

   4. Simplified 3.6%

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

   5. Taylor expanded in z around inf 82.2%

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

      1. sub-neg 82.2%

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

      2. +-commutative 82.2%

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

      3. mul-1-neg 82.2%

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

      4. unsub-neg 82.2%

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

      5. associate-/l* 89.0%

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

      6. mul-1-neg 89.0%

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

      7. remove-double-neg 89.0%

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

      8. associate-/l* 99.7%

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

   7. Simplified 99.7%

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

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

   1. Initial program 91.6%

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

   2. Taylor expanded in y around 0 77.2%

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

      1. div-sub 77.2%

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

      2. associate-*r/ 77.2%

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

      3. mul-1-neg 77.2%

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

      4. distribute-lft-neg-out 77.2%

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

      5. associate-*r/ 90.5%

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

      6. *-commutative 90.5%

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

      7. distribute-lft-out 91.6%

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

      8. sub-neg 91.6%

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

      9. associate-/r/ 97.5%

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

   4. Simplified 97.5%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-280}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;\left(t - \frac{y}{\frac{z}{t - x}}\right) + \frac{a}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 2: 88.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-208}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-150}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+294}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -1e-208)
     t_1
     (if (<= t_1 2e-150)
       (- t (/ (* (- t x) (- y a)) z))
       (if (<= t_1 2e+294) t_1 (+ x (/ (* (- y z) (- t x)) (- a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -1e-208) {
		tmp = t_1;
	} else if (t_1 <= 2e-150) {
		tmp = t - (((t - x) * (y - a)) / z);
	} else if (t_1 <= 2e+294) {
		tmp = t_1;
	} else {
		tmp = x + (((y - z) * (t - x)) / (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) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_1 <= (-1d-208)) then
        tmp = t_1
    else if (t_1 <= 2d-150) then
        tmp = t - (((t - x) * (y - a)) / z)
    else if (t_1 <= 2d+294) then
        tmp = t_1
    else
        tmp = x + (((y - z) * (t - x)) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -1e-208) {
		tmp = t_1;
	} else if (t_1 <= 2e-150) {
		tmp = t - (((t - x) * (y - a)) / z);
	} else if (t_1 <= 2e+294) {
		tmp = t_1;
	} else {
		tmp = x + (((y - z) * (t - x)) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_1 <= -1e-208:
		tmp = t_1
	elif t_1 <= 2e-150:
		tmp = t - (((t - x) * (y - a)) / z)
	elif t_1 <= 2e+294:
		tmp = t_1
	else:
		tmp = x + (((y - z) * (t - x)) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -1e-208)
		tmp = t_1;
	elseif (t_1 <= 2e-150)
		tmp = Float64(t - Float64(Float64(Float64(t - x) * Float64(y - a)) / z));
	elseif (t_1 <= 2e+294)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_1 <= -1e-208)
		tmp = t_1;
	elseif (t_1 <= 2e-150)
		tmp = t - (((t - x) * (y - a)) / z);
	elseif (t_1 <= 2e+294)
		tmp = t_1;
	else
		tmp = x + (((y - z) * (t - x)) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-208], t$95$1, If[LessEqual[t$95$1, 2e-150], N[(t - N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+294], t$95$1, N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.0000000000000001e-208 or 2.00000000000000001e-150 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 2.00000000000000013e294

   1. Initial program 95.7%

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

   if -1.0000000000000001e-208 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 2.00000000000000001e-150

   1. Initial program 12.3%

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

   2. Taylor expanded in z around -inf 75.9%

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

      1. +-commutative 75.9%

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

      2. mul-1-neg 75.9%

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

      3. unsub-neg 75.9%

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

      4. distribute-rgt-out-- 75.9%

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

   4. Simplified 75.9%

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

   if 2.00000000000000013e294 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 75.0%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-208}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 2 \cdot 10^{-150}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 2 \cdot 10^{+294}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \end{array} \]

Alternative 3: 95.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ t_2 := \frac{z}{t - x}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-280} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(t - \frac{y}{t_2}\right) + \frac{a}{t_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))) (t_2 (/ z (- t x))))
   (if (or (<= t_1 -1e-280) (not (<= t_1 0.0)))
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (+ (- t (/ y t_2)) (/ a t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double t_2 = z / (t - x);
	double tmp;
	if ((t_1 <= -1e-280) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = (t - (y / t_2)) + (a / 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 - x) / (a - z)))
    t_2 = z / (t - x)
    if ((t_1 <= (-1d-280)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = (t - (y / t_2)) + (a / 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 - x) / (a - z)));
	double t_2 = z / (t - x);
	double tmp;
	if ((t_1 <= -1e-280) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = (t - (y / t_2)) + (a / t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	t_2 = z / (t - x)
	tmp = 0
	if (t_1 <= -1e-280) or not (t_1 <= 0.0):
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = (t - (y / t_2)) + (a / t_2)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	t_2 = Float64(z / Float64(t - x))
	tmp = 0.0
	if ((t_1 <= -1e-280) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(Float64(t - Float64(y / t_2)) + Float64(a / t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	t_2 = z / (t - x);
	tmp = 0.0;
	if ((t_1 <= -1e-280) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = (t - (y / t_2)) + (a / 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[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-280], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - N[(y / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(a / t$95$2), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.9999999999999996e-281 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.7%

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

   2. Taylor expanded in y around 0 77.7%

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

      1. div-sub 78.2%

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

      2. associate-*r/ 78.2%

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

      3. mul-1-neg 78.2%

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

      4. distribute-lft-neg-out 78.2%

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

      5. associate-*r/ 89.4%

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

      6. *-commutative 89.4%

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

      7. distribute-lft-out 91.7%

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

      8. sub-neg 91.7%

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

      9. associate-/r/ 96.4%

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

   4. Simplified 96.4%

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

   if -9.9999999999999996e-281 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.6%

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

   2. Taylor expanded in y around 0 2.7%

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

      1. div-sub 2.7%

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

      2. associate-*r/ 2.7%

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

      3. mul-1-neg 2.7%

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

      4. distribute-lft-neg-out 2.7%

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

      5. associate-*r/ 3.6%

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

      6. *-commutative 3.6%

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

      7. distribute-lft-out 3.6%

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

      8. sub-neg 3.6%

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

      9. associate-/r/ 3.6%

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

   4. Simplified 3.6%

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

   5. Taylor expanded in z around inf 82.2%

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

      1. sub-neg 82.2%

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

      2. +-commutative 82.2%

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

      3. mul-1-neg 82.2%

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

      4. unsub-neg 82.2%

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

      5. associate-/l* 89.0%

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

      6. mul-1-neg 89.0%

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

      7. remove-double-neg 89.0%

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

      8. associate-/l* 99.7%

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

   7. Simplified 99.7%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-280} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(t - \frac{y}{\frac{z}{t - x}}\right) + \frac{a}{\frac{z}{t - x}}\\ \end{array} \]

Alternative 4: 88.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-208} \lor \neg \left(t_1 \leq 2 \cdot 10^{-150}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -1e-208) (not (<= t_1 2e-150)))
     t_1
     (- t (/ (* (- t x) (- y a)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-208) || !(t_1 <= 2e-150)) {
		tmp = t_1;
	} else {
		tmp = t - (((t - x) * (y - a)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-1d-208)) .or. (.not. (t_1 <= 2d-150))) then
        tmp = t_1
    else
        tmp = t - (((t - x) * (y - a)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-208) || !(t_1 <= 2e-150)) {
		tmp = t_1;
	} else {
		tmp = t - (((t - x) * (y - a)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -1e-208) or not (t_1 <= 2e-150):
		tmp = t_1
	else:
		tmp = t - (((t - x) * (y - a)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -1e-208) || !(t_1 <= 2e-150))
		tmp = t_1;
	else
		tmp = Float64(t - Float64(Float64(Float64(t - x) * Float64(y - a)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -1e-208) || ~((t_1 <= 2e-150)))
		tmp = t_1;
	else
		tmp = t - (((t - x) * (y - a)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-208], N[Not[LessEqual[t$95$1, 2e-150]], $MachinePrecision]], t$95$1, N[(t - N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.0000000000000001e-208 or 2.00000000000000001e-150 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 93.9%

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

   if -1.0000000000000001e-208 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 2.00000000000000001e-150

   1. Initial program 12.3%

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

   2. Taylor expanded in z around -inf 75.9%

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

      1. +-commutative 75.9%

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

      2. mul-1-neg 75.9%

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

      3. unsub-neg 75.9%

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

      4. distribute-rgt-out-- 75.9%

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

   4. Simplified 75.9%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-208} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 2 \cdot 10^{-150}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \end{array} \]

Alternative 5: 93.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-280} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -1e-280) (not (<= t_1 0.0)))
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (- t (/ (* (- t x) (- y a)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-280) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t - (((t - x) * (y - a)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-1d-280)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = t - (((t - x) * (y - a)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-280) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t - (((t - x) * (y - a)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -1e-280) or not (t_1 <= 0.0):
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = t - (((t - x) * (y - a)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -1e-280) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(t - Float64(Float64(Float64(t - x) * Float64(y - a)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -1e-280) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = t - (((t - x) * (y - a)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-280], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.9999999999999996e-281 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.7%

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

   2. Taylor expanded in y around 0 77.7%

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

      1. div-sub 78.2%

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

      2. associate-*r/ 78.2%

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

      3. mul-1-neg 78.2%

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

      4. distribute-lft-neg-out 78.2%

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

      5. associate-*r/ 89.4%

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

      6. *-commutative 89.4%

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

      7. distribute-lft-out 91.7%

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

      8. sub-neg 91.7%

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

      9. associate-/r/ 96.4%

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

   4. Simplified 96.4%

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

   if -9.9999999999999996e-281 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.6%

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

   2. Taylor expanded in z around -inf 82.3%

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

      1. +-commutative 82.3%

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

      2. mul-1-neg 82.3%

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

      3. unsub-neg 82.3%

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

      4. distribute-rgt-out-- 82.3%

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

   4. Simplified 82.3%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-280} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \end{array} \]

Alternative 6: 69.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \mathbf{if}\;a \leq -9.8 \cdot 10^{+23}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.85 \cdot 10^{-66}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ (* (- t x) (- y a)) z))))
   (if (<= a -9.8e+23)
     (+ x (/ (- t x) (/ a y)))
     (if (<= a 3.1e-117)
       t_1
       (if (<= a 3.85e-66)
         (* t (/ (- y z) (- a z)))
         (if (<= a 6.5e+55) t_1 (+ x (/ y (/ a (- t x))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (((t - x) * (y - a)) / z);
	double tmp;
	if (a <= -9.8e+23) {
		tmp = x + ((t - x) / (a / y));
	} else if (a <= 3.1e-117) {
		tmp = t_1;
	} else if (a <= 3.85e-66) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 6.5e+55) {
		tmp = t_1;
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - (((t - x) * (y - a)) / z)
    if (a <= (-9.8d+23)) then
        tmp = x + ((t - x) / (a / y))
    else if (a <= 3.1d-117) then
        tmp = t_1
    else if (a <= 3.85d-66) then
        tmp = t * ((y - z) / (a - z))
    else if (a <= 6.5d+55) then
        tmp = t_1
    else
        tmp = x + (y / (a / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (((t - x) * (y - a)) / z);
	double tmp;
	if (a <= -9.8e+23) {
		tmp = x + ((t - x) / (a / y));
	} else if (a <= 3.1e-117) {
		tmp = t_1;
	} else if (a <= 3.85e-66) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 6.5e+55) {
		tmp = t_1;
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (((t - x) * (y - a)) / z)
	tmp = 0
	if a <= -9.8e+23:
		tmp = x + ((t - x) / (a / y))
	elif a <= 3.1e-117:
		tmp = t_1
	elif a <= 3.85e-66:
		tmp = t * ((y - z) / (a - z))
	elif a <= 6.5e+55:
		tmp = t_1
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(Float64(t - x) * Float64(y - a)) / z))
	tmp = 0.0
	if (a <= -9.8e+23)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	elseif (a <= 3.1e-117)
		tmp = t_1;
	elseif (a <= 3.85e-66)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (a <= 6.5e+55)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (((t - x) * (y - a)) / z);
	tmp = 0.0;
	if (a <= -9.8e+23)
		tmp = x + ((t - x) / (a / y));
	elseif (a <= 3.1e-117)
		tmp = t_1;
	elseif (a <= 3.85e-66)
		tmp = t * ((y - z) / (a - z));
	elseif (a <= 6.5e+55)
		tmp = t_1;
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.8e+23], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.1e-117], t$95$1, If[LessEqual[a, 3.85e-66], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e+55], t$95$1, N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -9.8000000000000006e23

   1. Initial program 88.2%

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

   2. Taylor expanded in y around 0 74.2%

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

      1. div-sub 74.2%

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

      2. associate-*r/ 74.2%

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

      3. mul-1-neg 74.2%

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

      4. distribute-lft-neg-out 74.2%

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

      5. associate-*r/ 88.2%

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

      6. *-commutative 88.2%

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

      7. distribute-lft-out 88.2%

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

      8. sub-neg 88.2%

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

      9. associate-/r/ 95.2%

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

   4. Simplified 95.2%

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

   5. Taylor expanded in z around 0 79.7%

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

   if -9.8000000000000006e23 < a < 3.10000000000000011e-117 or 3.8500000000000001e-66 < a < 6.50000000000000027e55

   1. Initial program 75.2%

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

   2. Taylor expanded in z around -inf 75.6%

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

      1. +-commutative 75.6%

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

      2. mul-1-neg 75.6%

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

      3. unsub-neg 75.6%

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

      4. distribute-rgt-out-- 75.6%

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

   4. Simplified 75.6%

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

   if 3.10000000000000011e-117 < a < 3.8500000000000001e-66

   1. Initial program 92.8%

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

   2. Taylor expanded in x around 0 70.8%

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

      1. associate-*r/ 92.4%

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

   4. Simplified 92.4%

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

   if 6.50000000000000027e55 < a

   1. Initial program 92.9%

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

   2. Taylor expanded in z around 0 68.9%

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

      1. +-commutative 68.9%

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

      2. associate-/l* 79.0%

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

   4. Simplified 79.0%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.8 \cdot 10^{+23}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-117}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq 3.85 \cdot 10^{-66}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+55}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 7: 41.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;x \leq -8.5 \cdot 10^{-116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-267}:\\ \;\;\;\;\frac{y \cdot t}{a - z}\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-282}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-162}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t}}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-14}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= x -8.5e-116)
     t_1
     (if (<= x -1.95e-267)
       (/ (* y t) (- a z))
       (if (<= x 1.9e-282)
         t
         (if (<= x 1.02e-162)
           (/ y (/ (- a z) t))
           (if (<= x 1.2e-14) t t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -8.5e-116) {
		tmp = t_1;
	} else if (x <= -1.95e-267) {
		tmp = (y * t) / (a - z);
	} else if (x <= 1.9e-282) {
		tmp = t;
	} else if (x <= 1.02e-162) {
		tmp = y / ((a - z) / t);
	} else if (x <= 1.2e-14) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (x <= (-8.5d-116)) then
        tmp = t_1
    else if (x <= (-1.95d-267)) then
        tmp = (y * t) / (a - z)
    else if (x <= 1.9d-282) then
        tmp = t
    else if (x <= 1.02d-162) then
        tmp = y / ((a - z) / t)
    else if (x <= 1.2d-14) then
        tmp = t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -8.5e-116) {
		tmp = t_1;
	} else if (x <= -1.95e-267) {
		tmp = (y * t) / (a - z);
	} else if (x <= 1.9e-282) {
		tmp = t;
	} else if (x <= 1.02e-162) {
		tmp = y / ((a - z) / t);
	} else if (x <= 1.2e-14) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if x <= -8.5e-116:
		tmp = t_1
	elif x <= -1.95e-267:
		tmp = (y * t) / (a - z)
	elif x <= 1.9e-282:
		tmp = t
	elif x <= 1.02e-162:
		tmp = y / ((a - z) / t)
	elif x <= 1.2e-14:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (x <= -8.5e-116)
		tmp = t_1;
	elseif (x <= -1.95e-267)
		tmp = Float64(Float64(y * t) / Float64(a - z));
	elseif (x <= 1.9e-282)
		tmp = t;
	elseif (x <= 1.02e-162)
		tmp = Float64(y / Float64(Float64(a - z) / t));
	elseif (x <= 1.2e-14)
		tmp = t;
	else
		tmp = t_1;
	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 (x <= -8.5e-116)
		tmp = t_1;
	elseif (x <= -1.95e-267)
		tmp = (y * t) / (a - z);
	elseif (x <= 1.9e-282)
		tmp = t;
	elseif (x <= 1.02e-162)
		tmp = y / ((a - z) / t);
	elseif (x <= 1.2e-14)
		tmp = t;
	else
		tmp = t_1;
	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[x, -8.5e-116], t$95$1, If[LessEqual[x, -1.95e-267], N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.9e-282], t, If[LessEqual[x, 1.02e-162], N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.2e-14], t, t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -8.4999999999999995e-116 or 1.2e-14 < x

   1. Initial program 81.1%

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

   2. Taylor expanded in y around 0 64.2%

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

      1. div-sub 64.8%

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

      2. associate-*r/ 64.8%

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

      3. mul-1-neg 64.8%

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

      4. distribute-lft-neg-out 64.8%

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

      5. associate-*r/ 78.5%

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

      6. *-commutative 78.5%

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

      7. distribute-lft-out 81.1%

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

      8. sub-neg 81.1%

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

      9. associate-/r/ 83.0%

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

   4. Simplified 83.0%

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

   5. Taylor expanded in z around 0 56.4%

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

   6. Taylor expanded in x around inf 52.6%

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

      1. *-commutative 52.6%

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

      2. mul-1-neg 52.6%

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

      3. unsub-neg 52.6%

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

   8. Simplified 52.6%

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

   if -8.4999999999999995e-116 < x < -1.94999999999999988e-267

   1. Initial program 85.2%

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

   2. Taylor expanded in x around 0 65.4%

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

   3. Taylor expanded in y around inf 55.0%

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

   if -1.94999999999999988e-267 < x < 1.89999999999999996e-282 or 1.01999999999999998e-162 < x < 1.2e-14

   1. Initial program 85.5%

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

   2. Taylor expanded in z around inf 46.7%

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

   if 1.89999999999999996e-282 < x < 1.01999999999999998e-162

   1. Initial program 81.2%

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

   2. Taylor expanded in x around 0 76.4%

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

   3. Taylor expanded in y around inf 47.7%

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

      1. associate-/l* 52.4%

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

   5. Simplified 52.4%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-116}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-267}:\\ \;\;\;\;\frac{y \cdot t}{a - z}\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-282}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-162}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t}}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-14}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]

Alternative 8: 50.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-t}{\frac{z}{y - z}}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -1.5 \cdot 10^{+30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-195}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 0.0042:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t) (/ z (- y z)))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= a -1.5e+30)
     t_2
     (if (<= a -3.2e-151)
       t_1
       (if (<= a -6.8e-195) (/ (* x y) z) (if (<= a 0.0042) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -t / (z / (y - z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -1.5e+30) {
		tmp = t_2;
	} else if (a <= -3.2e-151) {
		tmp = t_1;
	} else if (a <= -6.8e-195) {
		tmp = (x * y) / z;
	} else if (a <= 0.0042) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = -t / (z / (y - z))
    t_2 = x * (1.0d0 - (y / a))
    if (a <= (-1.5d+30)) then
        tmp = t_2
    else if (a <= (-3.2d-151)) then
        tmp = t_1
    else if (a <= (-6.8d-195)) then
        tmp = (x * y) / z
    else if (a <= 0.0042d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -t / (z / (y - z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -1.5e+30) {
		tmp = t_2;
	} else if (a <= -3.2e-151) {
		tmp = t_1;
	} else if (a <= -6.8e-195) {
		tmp = (x * y) / z;
	} else if (a <= 0.0042) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -t / (z / (y - z))
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if a <= -1.5e+30:
		tmp = t_2
	elif a <= -3.2e-151:
		tmp = t_1
	elif a <= -6.8e-195:
		tmp = (x * y) / z
	elif a <= 0.0042:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-t) / Float64(z / Float64(y - z)))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (a <= -1.5e+30)
		tmp = t_2;
	elseif (a <= -3.2e-151)
		tmp = t_1;
	elseif (a <= -6.8e-195)
		tmp = Float64(Float64(x * y) / z);
	elseif (a <= 0.0042)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -t / (z / (y - z));
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (a <= -1.5e+30)
		tmp = t_2;
	elseif (a <= -3.2e-151)
		tmp = t_1;
	elseif (a <= -6.8e-195)
		tmp = (x * y) / z;
	elseif (a <= 0.0042)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-t) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.5e+30], t$95$2, If[LessEqual[a, -3.2e-151], t$95$1, If[LessEqual[a, -6.8e-195], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 0.0042], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.49999999999999989e30 or 0.00419999999999999974 < a

   1. Initial program 88.5%

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

   2. Taylor expanded in y around 0 77.0%

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

      1. div-sub 77.0%

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

      2. associate-*r/ 77.0%

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

      3. mul-1-neg 77.0%

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

      4. distribute-lft-neg-out 77.0%

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

      5. associate-*r/ 88.5%

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

      6. *-commutative 88.5%

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

      7. distribute-lft-out 88.5%

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

      8. sub-neg 88.5%

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

      9. associate-/r/ 92.1%

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

   4. Simplified 92.1%

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

   5. Taylor expanded in z around 0 76.0%

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

   6. Taylor expanded in x around inf 60.5%

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

      1. *-commutative 60.5%

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

      2. mul-1-neg 60.5%

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

      3. unsub-neg 60.5%

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

   8. Simplified 60.5%

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

   if -1.49999999999999989e30 < a < -3.20000000000000021e-151 or -6.80000000000000003e-195 < a < 0.00419999999999999974

   1. Initial program 76.8%

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

   2. Taylor expanded in x around 0 54.0%

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

   3. Taylor expanded in a around 0 46.1%

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

      1. mul-1-neg 46.1%

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

      2. associate-/l* 57.5%

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

   5. Simplified 57.5%

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

   if -3.20000000000000021e-151 < a < -6.80000000000000003e-195

   1. Initial program 81.6%

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

   2. Taylor expanded in x around inf 63.1%

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

      1. *-commutative 63.1%

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

      2. distribute-rgt-in 63.0%

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

      3. *-lft-identity 63.0%

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

      4. mul-1-neg 63.0%

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

      5. distribute-lft-neg-in 63.0%

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

      6. distribute-rgt-neg-out 63.0%

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

      7. associate-*l/ 62.9%

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

      8. distribute-rgt-neg-out 62.9%

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

      9. mul-1-neg 62.9%

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

      10. associate-*r/ 62.9%

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

      11. mul-1-neg 62.9%

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

      12. unsub-neg 62.9%

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

      13. associate-/l* 56.7%

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

   4. Simplified 56.7%

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

   5. Taylor expanded in y around inf 53.6%

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

      1. associate-*r/ 53.6%

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

      2. associate-*r* 53.6%

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

      3. mul-1-neg 53.6%

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

   7. Simplified 53.6%

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

   8. Taylor expanded in a around 0 51.8%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-151}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-195}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 0.0042:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]

Alternative 9: 50.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-t}{\frac{z}{y - z}}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -6.5 \cdot 10^{+26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-195}:\\ \;\;\;\;\frac{-y}{\frac{a - z}{x}}\\ \mathbf{elif}\;a \leq 136:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t) (/ z (- y z)))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= a -6.5e+26)
     t_2
     (if (<= a -5.4e-115)
       t_1
       (if (<= a -3e-195)
         (/ (- y) (/ (- a z) x))
         (if (<= a 136.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -t / (z / (y - z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -6.5e+26) {
		tmp = t_2;
	} else if (a <= -5.4e-115) {
		tmp = t_1;
	} else if (a <= -3e-195) {
		tmp = -y / ((a - z) / x);
	} else if (a <= 136.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = -t / (z / (y - z))
    t_2 = x * (1.0d0 - (y / a))
    if (a <= (-6.5d+26)) then
        tmp = t_2
    else if (a <= (-5.4d-115)) then
        tmp = t_1
    else if (a <= (-3d-195)) then
        tmp = -y / ((a - z) / x)
    else if (a <= 136.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -t / (z / (y - z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -6.5e+26) {
		tmp = t_2;
	} else if (a <= -5.4e-115) {
		tmp = t_1;
	} else if (a <= -3e-195) {
		tmp = -y / ((a - z) / x);
	} else if (a <= 136.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -t / (z / (y - z))
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if a <= -6.5e+26:
		tmp = t_2
	elif a <= -5.4e-115:
		tmp = t_1
	elif a <= -3e-195:
		tmp = -y / ((a - z) / x)
	elif a <= 136.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-t) / Float64(z / Float64(y - z)))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (a <= -6.5e+26)
		tmp = t_2;
	elseif (a <= -5.4e-115)
		tmp = t_1;
	elseif (a <= -3e-195)
		tmp = Float64(Float64(-y) / Float64(Float64(a - z) / x));
	elseif (a <= 136.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -t / (z / (y - z));
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (a <= -6.5e+26)
		tmp = t_2;
	elseif (a <= -5.4e-115)
		tmp = t_1;
	elseif (a <= -3e-195)
		tmp = -y / ((a - z) / x);
	elseif (a <= 136.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-t) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.5e+26], t$95$2, If[LessEqual[a, -5.4e-115], t$95$1, If[LessEqual[a, -3e-195], N[((-y) / N[(N[(a - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 136.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.50000000000000022e26 or 136 < a

   1. Initial program 88.5%

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

   2. Taylor expanded in y around 0 77.0%

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

      1. div-sub 77.0%

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

      2. associate-*r/ 77.0%

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

      3. mul-1-neg 77.0%

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

      4. distribute-lft-neg-out 77.0%

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

      5. associate-*r/ 88.5%

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

      6. *-commutative 88.5%

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

      7. distribute-lft-out 88.5%

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

      8. sub-neg 88.5%

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

      9. associate-/r/ 92.1%

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

   4. Simplified 92.1%

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

   5. Taylor expanded in z around 0 76.0%

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

   6. Taylor expanded in x around inf 60.5%

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

      1. *-commutative 60.5%

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

      2. mul-1-neg 60.5%

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

      3. unsub-neg 60.5%

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

   8. Simplified 60.5%

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

   if -6.50000000000000022e26 < a < -5.4e-115 or -3e-195 < a < 136

   1. Initial program 77.5%

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

   2. Taylor expanded in x around 0 54.4%

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

   3. Taylor expanded in a around 0 46.2%

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

      1. mul-1-neg 46.2%

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

      2. associate-/l* 58.1%

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

   5. Simplified 58.1%

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

   if -5.4e-115 < a < -3e-195

   1. Initial program 76.4%

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

   2. Taylor expanded in x around inf 56.9%

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

      1. *-commutative 56.9%

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

      2. distribute-rgt-in 56.9%

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

      3. *-lft-identity 56.9%

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

      4. mul-1-neg 56.9%

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

      5. distribute-lft-neg-in 56.9%

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

      6. distribute-rgt-neg-out 56.9%

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

      7. associate-*l/ 53.2%

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

      8. distribute-rgt-neg-out 53.2%

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

      9. mul-1-neg 53.2%

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

      10. associate-*r/ 53.2%

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

      11. mul-1-neg 53.2%

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

      12. unsub-neg 53.2%

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

      13. associate-/l* 52.1%

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

   4. Simplified 52.1%

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

   5. Taylor expanded in y around inf 46.7%

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

      1. associate-*r/ 46.7%

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

      2. associate-*r* 46.7%

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

      3. mul-1-neg 46.7%

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

   7. Simplified 46.7%

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

   8. Taylor expanded in y around 0 46.7%

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

      1. mul-1-neg 46.7%

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

      2. associate-/l* 50.9%

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

      3. distribute-neg-frac 50.9%

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

   10. Simplified 50.9%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-115}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-195}:\\ \;\;\;\;\frac{-y}{\frac{a - z}{x}}\\ \mathbf{elif}\;a \leq 136:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]

Alternative 10: 36.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-115}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-304}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-176}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-10}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.8e+23)
   x
   (if (<= a -2.1e-115)
     t
     (if (<= a -9.5e-304)
       (/ y (/ z x))
       (if (<= a 2e-176) t (if (<= a 6.5e-10) (* t (/ y a)) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.8e+23) {
		tmp = x;
	} else if (a <= -2.1e-115) {
		tmp = t;
	} else if (a <= -9.5e-304) {
		tmp = y / (z / x);
	} else if (a <= 2e-176) {
		tmp = t;
	} else if (a <= 6.5e-10) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5.8d+23)) then
        tmp = x
    else if (a <= (-2.1d-115)) then
        tmp = t
    else if (a <= (-9.5d-304)) then
        tmp = y / (z / x)
    else if (a <= 2d-176) then
        tmp = t
    else if (a <= 6.5d-10) then
        tmp = t * (y / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.8e+23) {
		tmp = x;
	} else if (a <= -2.1e-115) {
		tmp = t;
	} else if (a <= -9.5e-304) {
		tmp = y / (z / x);
	} else if (a <= 2e-176) {
		tmp = t;
	} else if (a <= 6.5e-10) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.8e+23:
		tmp = x
	elif a <= -2.1e-115:
		tmp = t
	elif a <= -9.5e-304:
		tmp = y / (z / x)
	elif a <= 2e-176:
		tmp = t
	elif a <= 6.5e-10:
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.8e+23)
		tmp = x;
	elseif (a <= -2.1e-115)
		tmp = t;
	elseif (a <= -9.5e-304)
		tmp = Float64(y / Float64(z / x));
	elseif (a <= 2e-176)
		tmp = t;
	elseif (a <= 6.5e-10)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.8e+23)
		tmp = x;
	elseif (a <= -2.1e-115)
		tmp = t;
	elseif (a <= -9.5e-304)
		tmp = y / (z / x);
	elseif (a <= 2e-176)
		tmp = t;
	elseif (a <= 6.5e-10)
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.8e+23], x, If[LessEqual[a, -2.1e-115], t, If[LessEqual[a, -9.5e-304], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2e-176], t, If[LessEqual[a, 6.5e-10], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.80000000000000025e23 or 6.5000000000000003e-10 < a

   1. Initial program 88.0%

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

   2. Taylor expanded in a around inf 49.8%

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

   if -5.80000000000000025e23 < a < -2.10000000000000002e-115 or -9.50000000000000023e-304 < a < 2e-176

   1. Initial program 78.3%

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

   2. Taylor expanded in z around inf 54.4%

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

   if -2.10000000000000002e-115 < a < -9.50000000000000023e-304

   1. Initial program 72.4%

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

   2. Taylor expanded in x around inf 46.2%

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

      1. *-commutative 46.2%

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

      2. distribute-rgt-in 46.2%

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

      3. *-lft-identity 46.2%

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

      4. mul-1-neg 46.2%

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

      5. distribute-lft-neg-in 46.2%

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

      6. distribute-rgt-neg-out 46.2%

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

      7. associate-*l/ 41.9%

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

      8. distribute-rgt-neg-out 41.9%

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

      9. mul-1-neg 41.9%

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

      10. associate-*r/ 41.9%

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

      11. mul-1-neg 41.9%

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

      12. unsub-neg 41.9%

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

      13. associate-/l* 41.1%

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

   4. Simplified 41.1%

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

   5. Taylor expanded in y around inf 42.1%

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

      1. associate-*r/ 42.1%

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

      2. associate-*r* 42.1%

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

      3. mul-1-neg 42.1%

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

   7. Simplified 42.1%

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

   8. Taylor expanded in a around 0 41.3%

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

      1. associate-/l* 44.8%

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

   10. Simplified 44.8%

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

   if 2e-176 < a < 6.5000000000000003e-10

   1. Initial program 80.8%

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

   2. Taylor expanded in x around 0 61.3%

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

   3. Taylor expanded in z around 0 27.2%

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

      1. associate-/l* 25.4%

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

   5. Simplified 25.4%

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

      1. associate-/r/ 29.3%

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

   7. Applied egg-rr 29.3%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-115}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-304}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-176}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-10}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 39.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;x \leq -1.16 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-251}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq 1.36 \cdot 10^{-14}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= x -1.16e-113)
     t_1
     (if (<= x -2e-251) (* t (/ y a)) (if (<= x 1.36e-14) t t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -1.16e-113) {
		tmp = t_1;
	} else if (x <= -2e-251) {
		tmp = t * (y / a);
	} else if (x <= 1.36e-14) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (x <= (-1.16d-113)) then
        tmp = t_1
    else if (x <= (-2d-251)) then
        tmp = t * (y / a)
    else if (x <= 1.36d-14) then
        tmp = t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -1.16e-113) {
		tmp = t_1;
	} else if (x <= -2e-251) {
		tmp = t * (y / a);
	} else if (x <= 1.36e-14) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if x <= -1.16e-113:
		tmp = t_1
	elif x <= -2e-251:
		tmp = t * (y / a)
	elif x <= 1.36e-14:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (x <= -1.16e-113)
		tmp = t_1;
	elseif (x <= -2e-251)
		tmp = Float64(t * Float64(y / a));
	elseif (x <= 1.36e-14)
		tmp = t;
	else
		tmp = t_1;
	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 (x <= -1.16e-113)
		tmp = t_1;
	elseif (x <= -2e-251)
		tmp = t * (y / a);
	elseif (x <= 1.36e-14)
		tmp = t;
	else
		tmp = t_1;
	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[x, -1.16e-113], t$95$1, If[LessEqual[x, -2e-251], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.36e-14], t, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.15999999999999999e-113 or 1.36e-14 < x

   1. Initial program 81.1%

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

   2. Taylor expanded in y around 0 64.2%

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

      1. div-sub 64.8%

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

      2. associate-*r/ 64.8%

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

      3. mul-1-neg 64.8%

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

      4. distribute-lft-neg-out 64.8%

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

      5. associate-*r/ 78.5%

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

      6. *-commutative 78.5%

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

      7. distribute-lft-out 81.1%

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

      8. sub-neg 81.1%

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

      9. associate-/r/ 83.0%

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

   4. Simplified 83.0%

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

   5. Taylor expanded in z around 0 56.4%

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

   6. Taylor expanded in x around inf 52.6%

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

      1. *-commutative 52.6%

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

      2. mul-1-neg 52.6%

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

      3. unsub-neg 52.6%

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

   8. Simplified 52.6%

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

   if -1.15999999999999999e-113 < x < -2.00000000000000003e-251

   1. Initial program 85.2%

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

   2. Taylor expanded in x around 0 65.4%

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

   3. Taylor expanded in z around 0 41.0%

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

      1. associate-/l* 41.2%

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

   5. Simplified 41.2%

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

      1. associate-/r/ 44.6%

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

   7. Applied egg-rr 44.6%

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

   if -2.00000000000000003e-251 < x < 1.36e-14

   1. Initial program 84.3%

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

   2. Taylor expanded in z around inf 38.5%

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

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.16 \cdot 10^{-113}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-251}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq 1.36 \cdot 10^{-14}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]

Alternative 12: 40.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;x \leq -5.5 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-303}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-12}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= x -5.5e-112)
     t_1
     (if (<= x 2.55e-303) (* (- y z) (/ t a)) (if (<= x 3.5e-12) t t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -5.5e-112) {
		tmp = t_1;
	} else if (x <= 2.55e-303) {
		tmp = (y - z) * (t / a);
	} else if (x <= 3.5e-12) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (x <= (-5.5d-112)) then
        tmp = t_1
    else if (x <= 2.55d-303) then
        tmp = (y - z) * (t / a)
    else if (x <= 3.5d-12) then
        tmp = t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -5.5e-112) {
		tmp = t_1;
	} else if (x <= 2.55e-303) {
		tmp = (y - z) * (t / a);
	} else if (x <= 3.5e-12) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if x <= -5.5e-112:
		tmp = t_1
	elif x <= 2.55e-303:
		tmp = (y - z) * (t / a)
	elif x <= 3.5e-12:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (x <= -5.5e-112)
		tmp = t_1;
	elseif (x <= 2.55e-303)
		tmp = Float64(Float64(y - z) * Float64(t / a));
	elseif (x <= 3.5e-12)
		tmp = t;
	else
		tmp = t_1;
	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 (x <= -5.5e-112)
		tmp = t_1;
	elseif (x <= 2.55e-303)
		tmp = (y - z) * (t / a);
	elseif (x <= 3.5e-12)
		tmp = t;
	else
		tmp = t_1;
	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[x, -5.5e-112], t$95$1, If[LessEqual[x, 2.55e-303], N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.5e-12], t, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.5e-112 or 3.5e-12 < x

   1. Initial program 81.1%

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

   2. Taylor expanded in y around 0 64.2%

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

      1. div-sub 64.8%

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

      2. associate-*r/ 64.8%

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

      3. mul-1-neg 64.8%

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

      4. distribute-lft-neg-out 64.8%

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

      5. associate-*r/ 78.5%

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

      6. *-commutative 78.5%

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

      7. distribute-lft-out 81.1%

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

      8. sub-neg 81.1%

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

      9. associate-/r/ 83.0%

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

   4. Simplified 83.0%

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

   5. Taylor expanded in z around 0 56.4%

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

   6. Taylor expanded in x around inf 52.6%

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

      1. *-commutative 52.6%

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

      2. mul-1-neg 52.6%

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

      3. unsub-neg 52.6%

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

   8. Simplified 52.6%

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

   if -5.5e-112 < x < 2.55e-303

   1. Initial program 87.3%

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

   2. Taylor expanded in x around 0 68.8%

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

   3. Taylor expanded in a around inf 46.8%

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

      1. expm1-log1p-u 30.5%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{t \cdot \left(y - z\right)}{a}\right)\right)} \]

      2. expm1-udef 20.9%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{t \cdot \left(y - z\right)}{a}\right)} - 1} \]

      3. associate-/l* 23.0%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{t}{\frac{a}{y - z}}}\right)} - 1 \]

   5. Applied egg-rr 23.0%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{t}{\frac{a}{y - z}}\right)} - 1} \]
   6. Step-by-step derivation

      1. expm1-def 32.7%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{t}{\frac{a}{y - z}}\right)\right)} \]

      2. expm1-log1p 49.5%

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

      3. associate-/r/ 46.9%

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

      4. *-commutative 46.9%

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

   7. Simplified 46.9%

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

   if 2.55e-303 < x < 3.5e-12

   1. Initial program 82.7%

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

   2. Taylor expanded in z around inf 37.6%

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

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-112}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-303}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-12}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]

Alternative 13: 41.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{-116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-294}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-12}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= x -2.8e-116)
     t_1
     (if (<= x 1.2e-294) (/ t (/ a (- y z))) (if (<= x 2.7e-12) t t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -2.8e-116) {
		tmp = t_1;
	} else if (x <= 1.2e-294) {
		tmp = t / (a / (y - z));
	} else if (x <= 2.7e-12) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (x <= (-2.8d-116)) then
        tmp = t_1
    else if (x <= 1.2d-294) then
        tmp = t / (a / (y - z))
    else if (x <= 2.7d-12) then
        tmp = t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -2.8e-116) {
		tmp = t_1;
	} else if (x <= 1.2e-294) {
		tmp = t / (a / (y - z));
	} else if (x <= 2.7e-12) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if x <= -2.8e-116:
		tmp = t_1
	elif x <= 1.2e-294:
		tmp = t / (a / (y - z))
	elif x <= 2.7e-12:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (x <= -2.8e-116)
		tmp = t_1;
	elseif (x <= 1.2e-294)
		tmp = Float64(t / Float64(a / Float64(y - z)));
	elseif (x <= 2.7e-12)
		tmp = t;
	else
		tmp = t_1;
	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 (x <= -2.8e-116)
		tmp = t_1;
	elseif (x <= 1.2e-294)
		tmp = t / (a / (y - z));
	elseif (x <= 2.7e-12)
		tmp = t;
	else
		tmp = t_1;
	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[x, -2.8e-116], t$95$1, If[LessEqual[x, 1.2e-294], N[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.7e-12], t, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.7999999999999999e-116 or 2.6999999999999998e-12 < x

   1. Initial program 81.1%

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

   2. Taylor expanded in y around 0 64.2%

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

      1. div-sub 64.8%

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

      2. associate-*r/ 64.8%

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

      3. mul-1-neg 64.8%

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

      4. distribute-lft-neg-out 64.8%

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

      5. associate-*r/ 78.5%

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

      6. *-commutative 78.5%

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

      7. distribute-lft-out 81.1%

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

      8. sub-neg 81.1%

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

      9. associate-/r/ 83.0%

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

   4. Simplified 83.0%

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

   5. Taylor expanded in z around 0 56.4%

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

   6. Taylor expanded in x around inf 52.6%

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

      1. *-commutative 52.6%

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

      2. mul-1-neg 52.6%

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

      3. unsub-neg 52.6%

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

   8. Simplified 52.6%

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

   if -2.7999999999999999e-116 < x < 1.19999999999999999e-294

   1. Initial program 86.4%

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

   2. Taylor expanded in x around 0 70.2%

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

   3. Taylor expanded in a around inf 47.1%

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

      1. associate-/l* 49.6%

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

   5. Simplified 49.6%

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

   if 1.19999999999999999e-294 < x < 2.6999999999999998e-12

   1. Initial program 83.2%

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

   2. Taylor expanded in z around inf 37.1%

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

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-116}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-294}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-12}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]

Alternative 14: 41.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;x \leq -4.4 \cdot 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-162}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t}}\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-12}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= x -4.4e-111)
     t_1
     (if (<= x 1.4e-162) (/ y (/ (- a z) t)) (if (<= x 1.25e-12) t t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -4.4e-111) {
		tmp = t_1;
	} else if (x <= 1.4e-162) {
		tmp = y / ((a - z) / t);
	} else if (x <= 1.25e-12) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (x <= (-4.4d-111)) then
        tmp = t_1
    else if (x <= 1.4d-162) then
        tmp = y / ((a - z) / t)
    else if (x <= 1.25d-12) then
        tmp = t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -4.4e-111) {
		tmp = t_1;
	} else if (x <= 1.4e-162) {
		tmp = y / ((a - z) / t);
	} else if (x <= 1.25e-12) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if x <= -4.4e-111:
		tmp = t_1
	elif x <= 1.4e-162:
		tmp = y / ((a - z) / t)
	elif x <= 1.25e-12:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (x <= -4.4e-111)
		tmp = t_1;
	elseif (x <= 1.4e-162)
		tmp = Float64(y / Float64(Float64(a - z) / t));
	elseif (x <= 1.25e-12)
		tmp = t;
	else
		tmp = t_1;
	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 (x <= -4.4e-111)
		tmp = t_1;
	elseif (x <= 1.4e-162)
		tmp = y / ((a - z) / t);
	elseif (x <= 1.25e-12)
		tmp = t;
	else
		tmp = t_1;
	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[x, -4.4e-111], t$95$1, If[LessEqual[x, 1.4e-162], N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.25e-12], t, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.4e-111 or 1.24999999999999992e-12 < x

   1. Initial program 81.1%

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

   2. Taylor expanded in y around 0 64.2%

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

      1. div-sub 64.8%

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

      2. associate-*r/ 64.8%

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

      3. mul-1-neg 64.8%

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

      4. distribute-lft-neg-out 64.8%

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

      5. associate-*r/ 78.5%

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

      6. *-commutative 78.5%

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

      7. distribute-lft-out 81.1%

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

      8. sub-neg 81.1%

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

      9. associate-/r/ 83.0%

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

   4. Simplified 83.0%

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

   5. Taylor expanded in z around 0 56.4%

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

   6. Taylor expanded in x around inf 52.6%

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

      1. *-commutative 52.6%

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

      2. mul-1-neg 52.6%

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

      3. unsub-neg 52.6%

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

   8. Simplified 52.6%

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

   if -4.4e-111 < x < 1.40000000000000011e-162

   1. Initial program 85.6%

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

   2. Taylor expanded in x around 0 72.4%

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

   3. Taylor expanded in y around inf 46.2%

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

      1. associate-/l* 45.3%

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

   5. Simplified 45.3%

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

   if 1.40000000000000011e-162 < x < 1.24999999999999992e-12

   1. Initial program 82.4%

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

   2. Taylor expanded in z around inf 42.0%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{-111}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-162}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t}}\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-12}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]

Alternative 15: 61.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+89} \lor \neg \left(x \leq 8 \cdot 10^{+80}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -3.9e+89) (not (<= x 8e+80)))
   (* x (- 1.0 (/ y a)))
   (* t (/ (- y z) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -3.9e+89) || !(x <= 8e+80)) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-3.9d+89)) .or. (.not. (x <= 8d+80))) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t * ((y - z) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -3.9e+89) || !(x <= 8e+80)) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -3.9e+89) or not (x <= 8e+80):
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -3.9e+89) || !(x <= 8e+80))
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -3.9e+89) || ~((x <= 8e+80)))
		tmp = x * (1.0 - (y / a));
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -3.9e+89], N[Not[LessEqual[x, 8e+80]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.90000000000000011e89 or 8e80 < x

   1. Initial program 79.7%

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

   2. Taylor expanded in y around 0 63.5%

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

      1. div-sub 64.6%

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

      2. associate-*r/ 64.6%

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

      3. mul-1-neg 64.6%

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

      4. distribute-lft-neg-out 64.6%

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

      5. associate-*r/ 76.7%

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

      6. *-commutative 76.7%

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

      7. distribute-lft-out 79.7%

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

      8. sub-neg 79.7%

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

      9. associate-/r/ 82.7%

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

   4. Simplified 82.7%

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

   5. Taylor expanded in z around 0 62.9%

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

   6. Taylor expanded in x around inf 61.1%

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

      1. *-commutative 61.1%

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

      2. mul-1-neg 61.1%

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

      3. unsub-neg 61.1%

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

   8. Simplified 61.1%

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

   if -3.90000000000000011e89 < x < 8e80

   1. Initial program 84.2%

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

   2. Taylor expanded in x around 0 57.3%

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

      1. associate-*r/ 72.7%

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

   4. Simplified 72.7%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+89} \lor \neg \left(x \leq 8 \cdot 10^{+80}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 16: 65.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-14} \lor \neg \left(z \leq 7 \cdot 10^{+130}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.7e-14) (not (<= z 7e+130)))
   (* t (/ (- y z) (- a z)))
   (+ x (/ y (/ a (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.7e-14) || !(z <= 7e+130)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.7d-14)) .or. (.not. (z <= 7d+130))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + (y / (a / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.7e-14) || !(z <= 7e+130)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.7e-14) or not (z <= 7e+130):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.7e-14) || !(z <= 7e+130))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.7e-14) || ~((z <= 7e+130)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.7e-14], N[Not[LessEqual[z, 7e+130]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6999999999999999e-14 or 7.0000000000000002e130 < z

   1. Initial program 68.0%

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

   2. Taylor expanded in x around 0 45.1%

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

      1. associate-*r/ 66.2%

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

   4. Simplified 66.2%

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

   if -2.6999999999999999e-14 < z < 7.0000000000000002e130

   1. Initial program 91.4%

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

   2. Taylor expanded in z around 0 64.4%

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

      1. +-commutative 64.4%

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

      2. associate-/l* 69.0%

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

   4. Simplified 69.0%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-14} \lor \neg \left(z \leq 7 \cdot 10^{+130}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 17: 66.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{-13} \lor \neg \left(z \leq 2.5 \cdot 10^{+130}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.08e-13) (not (<= z 2.5e+130)))
   (* t (/ (- y z) (- a z)))
   (+ x (/ (- t x) (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.08e-13) || !(z <= 2.5e+130)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((t - x) / (a / 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 ((z <= (-1.08d-13)) .or. (.not. (z <= 2.5d+130))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + ((t - x) / (a / 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 ((z <= -1.08e-13) || !(z <= 2.5e+130)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.08e-13) or not (z <= 2.5e+130):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + ((t - x) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.08e-13) || !(z <= 2.5e+130))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.08e-13) || ~((z <= 2.5e+130)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + ((t - x) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.08e-13], N[Not[LessEqual[z, 2.5e+130]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0799999999999999e-13 or 2.4999999999999998e130 < z

   1. Initial program 68.0%

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

   2. Taylor expanded in x around 0 45.1%

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

      1. associate-*r/ 66.2%

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

   4. Simplified 66.2%

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

   if -1.0799999999999999e-13 < z < 2.4999999999999998e130

   1. Initial program 91.4%

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

   2. Taylor expanded in y around 0 87.0%

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

      1. div-sub 87.6%

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

      2. associate-*r/ 87.6%

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

      3. mul-1-neg 87.6%

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

      4. distribute-lft-neg-out 87.6%

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

      5. associate-*r/ 88.0%

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

      6. *-commutative 88.0%

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

      7. distribute-lft-out 91.4%

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

      8. sub-neg 91.4%

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

      9. associate-/r/ 94.9%

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

   4. Simplified 94.9%

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

   5. Taylor expanded in z around 0 71.2%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{-13} \lor \neg \left(z \leq 2.5 \cdot 10^{+130}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \]

Alternative 18: 37.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-176}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-11}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.9e+23)
   x
   (if (<= a 1.9e-176) t (if (<= a 3.4e-11) (* t (/ y a)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.9e+23) {
		tmp = x;
	} else if (a <= 1.9e-176) {
		tmp = t;
	} else if (a <= 3.4e-11) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.9d+23)) then
        tmp = x
    else if (a <= 1.9d-176) then
        tmp = t
    else if (a <= 3.4d-11) then
        tmp = t * (y / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.9e+23) {
		tmp = x;
	} else if (a <= 1.9e-176) {
		tmp = t;
	} else if (a <= 3.4e-11) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.9e+23:
		tmp = x
	elif a <= 1.9e-176:
		tmp = t
	elif a <= 3.4e-11:
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.9e+23)
		tmp = x;
	elseif (a <= 1.9e-176)
		tmp = t;
	elseif (a <= 3.4e-11)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.9e+23)
		tmp = x;
	elseif (a <= 1.9e-176)
		tmp = t;
	elseif (a <= 3.4e-11)
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.9e+23], x, If[LessEqual[a, 1.9e-176], t, If[LessEqual[a, 3.4e-11], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.90000000000000013e23 or 3.3999999999999999e-11 < a

   1. Initial program 88.0%

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

   2. Taylor expanded in a around inf 49.8%

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

   if -2.90000000000000013e23 < a < 1.90000000000000006e-176

   1. Initial program 75.7%

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

   2. Taylor expanded in z around inf 40.8%

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

   if 1.90000000000000006e-176 < a < 3.3999999999999999e-11

   1. Initial program 80.8%

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

   2. Taylor expanded in x around 0 61.3%

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

   3. Taylor expanded in z around 0 27.2%

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

      1. associate-/l* 25.4%

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

   5. Simplified 25.4%

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

      1. associate-/r/ 29.3%

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

   7. Applied egg-rr 29.3%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-176}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-11}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19: 38.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.3 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-13}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.3e+20) x (if (<= a 2.8e-13) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.3e+20) {
		tmp = x;
	} else if (a <= 2.8e-13) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5.3d+20)) then
        tmp = x
    else if (a <= 2.8d-13) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.3e+20) {
		tmp = x;
	} else if (a <= 2.8e-13) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.3e+20:
		tmp = x
	elif a <= 2.8e-13:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.3e+20)
		tmp = x;
	elseif (a <= 2.8e-13)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.3e+20)
		tmp = x;
	elseif (a <= 2.8e-13)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.3e+20], x, If[LessEqual[a, 2.8e-13], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -5.3e20 or 2.8000000000000002e-13 < a

   1. Initial program 88.1%

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

   2. Taylor expanded in a around inf 49.4%

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

   if -5.3e20 < a < 2.8000000000000002e-13

   1. Initial program 77.2%

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

   2. Taylor expanded in z around inf 34.0%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.3 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-13}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20: 2.8% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 0.0)

C

double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

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 = 0.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Python

def code(x, y, z, t, a):
	return 0.0

Julia

function code(x, y, z, t, a)
	return 0.0
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := 0.0

Derivation

1. Initial program 82.4%

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

2. Taylor expanded in x around inf 44.8%

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

   1. *-commutative 44.8%

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

   2. distribute-rgt-in 44.8%

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

   3. *-lft-identity 44.8%

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

   4. mul-1-neg 44.8%

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

   5. distribute-lft-neg-in 44.8%

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

   6. distribute-rgt-neg-out 44.8%

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

   7. associate-*l/ 37.4%

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

   8. distribute-rgt-neg-out 37.4%

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

   9. mul-1-neg 37.4%

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

   10. associate-*r/ 37.4%

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

   11. mul-1-neg 37.4%

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

   12. unsub-neg 37.4%

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

   13. associate-/l* 44.0%

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

4. Simplified 44.0%

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

5. Taylor expanded in a around 0 14.2%

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

   1. sub-neg 14.2%

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

   2. mul-1-neg 14.2%

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

   3. remove-double-neg 14.2%

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

   4. associate-/l* 15.4%

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

7. Simplified 15.4%

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

8. Taylor expanded in y around 0 2.7%

   \[\leadsto \color{blue}{-1 \cdot x + x} \]
9. Step-by-step derivation

   1. distribute-lft1-in 2.7%

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

   2. metadata-eval 2.7%

      \[\leadsto \color{blue}{0} \cdot x \]

   3. mul0-lft 2.7%

      \[\leadsto \color{blue}{0} \]

10. Simplified 2.7%

    \[\leadsto \color{blue}{0} \]

11. Final simplification 2.7%

    \[\leadsto 0 \]

Alternative 21: 25.2% 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 82.4%

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

2. Taylor expanded in z around inf 23.1%

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

3. Final simplification 23.1%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023274 
(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)))))