Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.5% → 95.0%

Time: 17.7s

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: 80.5% 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: 95.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ t_2 := \frac{z}{t - x}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-285} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t - \frac{y}{t_2}\right) + \frac{a}{t_2}\\ \end{array} \end{array} \]

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-285) (not (<= t_1 0.0)))
     (fma (- t x) (/ (- y z) (- a z)) x)
     (+ (- 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-285) || !(t_1 <= 0.0)) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} 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-285) || !(t_1 <= 0.0))
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	else
		tmp = Float64(Float64(t - Float64(y / t_2)) + Float64(a / t_2));
	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[Or[LessEqual[t$95$1, -1e-285], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(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)))) < -1.00000000000000007e-285 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   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. associate-*r/ 78.7%

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

      3. *-commutative 78.7%

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

      4. associate-*r/ 96.7%

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

      5. fma-def 96.7%

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

   3. Simplified 96.7%

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

   if -1.00000000000000007e-285 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 4.0%

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

      1. clear-num 3.9%

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

      2. un-div-inv 4.1%

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

   3. Applied egg-rr 4.1%

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

   4. Taylor expanded in z around inf 99.7%

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

      1. sub-neg 99.7%

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

      2. +-commutative 99.7%

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

      3. mul-1-neg 99.7%

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

      4. unsub-neg 99.7%

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

      5. associate-/l* 99.8%

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

      6. mul-1-neg 99.8%

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

      7. remove-double-neg 99.8%

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

      8. associate-/l* 99.8%

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

   6. Simplified 99.8%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-285} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t - \frac{y}{\frac{z}{t - x}}\right) + \frac{a}{\frac{z}{t - x}}\\ \end{array} \]

Alternative 2: 89.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-285} \lor \neg \left(t_1 \leq 10^{-256}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y \cdot \left(t - x\right) + a \cdot \left(x - t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -1e-285) (not (<= t_1 1e-256)))
     (+ x (/ (- y z) (/ (- a z) (- t x))))
     (- t (/ (+ (* y (- t x)) (* a (- x t))) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-285) || !(t_1 <= 1e-256)) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t - (((y * (t - x)) + (a * (x - t))) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-1d-285)) .or. (.not. (t_1 <= 1d-256))) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    else
        tmp = t - (((y * (t - x)) + (a * (x - t))) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-285) || !(t_1 <= 1e-256)) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t - (((y * (t - x)) + (a * (x - t))) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -1e-285) or not (t_1 <= 1e-256):
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t - (((y * (t - x)) + (a * (x - t))) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -1e-285) || !(t_1 <= 1e-256))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = Float64(t - Float64(Float64(Float64(y * Float64(t - x)) + Float64(a * Float64(x - t))) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -1e-285) || ~((t_1 <= 1e-256)))
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t - (((y * (t - x)) + (a * (x - t))) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-285], N[Not[LessEqual[t$95$1, 1e-256]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] + N[(a * N[(x - t), $MachinePrecision]), $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)))) < -1.00000000000000007e-285 or 9.99999999999999977e-257 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.5%

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

      1. clear-num 92.4%

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

      2. un-div-inv 92.8%

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

   3. Applied egg-rr 92.8%

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

   if -1.00000000000000007e-285 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 9.99999999999999977e-257

   1. Initial program 8.0%

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

   2. Taylor expanded in z around -inf 94.6%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-285} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 10^{-256}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y \cdot \left(t - x\right) + a \cdot \left(x - t\right)}{z}\\ \end{array} \]

Alternative 3: 89.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-285} \lor \neg \left(t_1 \leq 10^{-256}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -1e-285) (not (<= t_1 1e-256)))
     t_1
     (+ t (/ (* (- t x) (- a 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 tmp;
	if ((t_1 <= -1e-285) || !(t_1 <= 1e-256)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) * (a - y)) / 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-285)) .or. (.not. (t_1 <= 1d-256))) then
        tmp = t_1
    else
        tmp = t + (((t - x) * (a - y)) / 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-285) || !(t_1 <= 1e-256)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) * (a - y)) / 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-285) or not (t_1 <= 1e-256):
		tmp = t_1
	else:
		tmp = t + (((t - x) * (a - 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))))
	tmp = 0.0
	if ((t_1 <= -1e-285) || !(t_1 <= 1e-256))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / 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-285) || ~((t_1 <= 1e-256)))
		tmp = t_1;
	else
		tmp = t + (((t - x) * (a - y)) / 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-285], N[Not[LessEqual[t$95$1, 1e-256]], $MachinePrecision]], t$95$1, N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $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)))) < -1.00000000000000007e-285 or 9.99999999999999977e-257 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.5%

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

   if -1.00000000000000007e-285 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 9.99999999999999977e-257

   1. Initial program 8.0%

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

   2. Taylor expanded in z around inf 94.6%

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

      1. +-commutative 94.6%

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

      2. associate--l+ 94.6%

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

      3. associate-*r/ 94.6%

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

      4. associate-*r/ 94.6%

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

      5. div-sub 94.6%

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

      6. distribute-lft-out-- 94.6%

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

      7. mul-1-neg 94.6%

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

      8. distribute-neg-frac 94.6%

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

      9. unsub-neg 94.6%

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

      10. distribute-rgt-out-- 94.5%

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

   4. Simplified 94.5%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-285} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 10^{-256}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]

Alternative 4: 89.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-285} \lor \neg \left(t_1 \leq 10^{-256}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -1e-285) (not (<= t_1 1e-256)))
     (+ x (/ (- y z) (/ (- a z) (- t x))))
     (+ t (/ (* (- t x) (- a 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 tmp;
	if ((t_1 <= -1e-285) || !(t_1 <= 1e-256)) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t + (((t - x) * (a - y)) / 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-285)) .or. (.not. (t_1 <= 1d-256))) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    else
        tmp = t + (((t - x) * (a - y)) / 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-285) || !(t_1 <= 1e-256)) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t + (((t - x) * (a - y)) / 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-285) or not (t_1 <= 1e-256):
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t + (((t - x) * (a - 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))))
	tmp = 0.0
	if ((t_1 <= -1e-285) || !(t_1 <= 1e-256))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / 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-285) || ~((t_1 <= 1e-256)))
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t + (((t - x) * (a - y)) / 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-285], N[Not[LessEqual[t$95$1, 1e-256]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $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)))) < -1.00000000000000007e-285 or 9.99999999999999977e-257 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.5%

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

      1. clear-num 92.4%

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

      2. un-div-inv 92.8%

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

   3. Applied egg-rr 92.8%

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

   if -1.00000000000000007e-285 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 9.99999999999999977e-257

   1. Initial program 8.0%

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

   2. Taylor expanded in z around inf 94.6%

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

      1. +-commutative 94.6%

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

      2. associate--l+ 94.6%

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

      3. associate-*r/ 94.6%

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

      4. associate-*r/ 94.6%

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

      5. div-sub 94.6%

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

      6. distribute-lft-out-- 94.6%

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

      7. mul-1-neg 94.6%

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

      8. distribute-neg-frac 94.6%

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

      9. unsub-neg 94.6%

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

      10. distribute-rgt-out-- 94.5%

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

   4. Simplified 94.5%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-285} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 10^{-256}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]

Alternative 5: 58.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{+216}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+152}:\\ \;\;\;\;\frac{y - a}{\frac{z}{x}}\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{+81}:\\ \;\;\;\;y \cdot \left(-\frac{x}{a - z}\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-82}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= x -4.5e+216)
     t_2
     (if (<= x -1.9e+152)
       (/ (- y a) (/ z x))
       (if (<= x -2.2e+81)
         (* y (- (/ x (- a z))))
         (if (<= x 1.05e-113)
           t_1
           (if (<= x 2.1e-82)
             (- x (/ y (/ a x)))
             (if (<= x 9e+50) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -4.5e+216) {
		tmp = t_2;
	} else if (x <= -1.9e+152) {
		tmp = (y - a) / (z / x);
	} else if (x <= -2.2e+81) {
		tmp = y * -(x / (a - z));
	} else if (x <= 1.05e-113) {
		tmp = t_1;
	} else if (x <= 2.1e-82) {
		tmp = x - (y / (a / x));
	} else if (x <= 9e+50) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x * (1.0d0 - (y / a))
    if (x <= (-4.5d+216)) then
        tmp = t_2
    else if (x <= (-1.9d+152)) then
        tmp = (y - a) / (z / x)
    else if (x <= (-2.2d+81)) then
        tmp = y * -(x / (a - z))
    else if (x <= 1.05d-113) then
        tmp = t_1
    else if (x <= 2.1d-82) then
        tmp = x - (y / (a / x))
    else if (x <= 9d+50) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -4.5e+216) {
		tmp = t_2;
	} else if (x <= -1.9e+152) {
		tmp = (y - a) / (z / x);
	} else if (x <= -2.2e+81) {
		tmp = y * -(x / (a - z));
	} else if (x <= 1.05e-113) {
		tmp = t_1;
	} else if (x <= 2.1e-82) {
		tmp = x - (y / (a / x));
	} else if (x <= 9e+50) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if x <= -4.5e+216:
		tmp = t_2
	elif x <= -1.9e+152:
		tmp = (y - a) / (z / x)
	elif x <= -2.2e+81:
		tmp = y * -(x / (a - z))
	elif x <= 1.05e-113:
		tmp = t_1
	elif x <= 2.1e-82:
		tmp = x - (y / (a / x))
	elif x <= 9e+50:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (x <= -4.5e+216)
		tmp = t_2;
	elseif (x <= -1.9e+152)
		tmp = Float64(Float64(y - a) / Float64(z / x));
	elseif (x <= -2.2e+81)
		tmp = Float64(y * Float64(-Float64(x / Float64(a - z))));
	elseif (x <= 1.05e-113)
		tmp = t_1;
	elseif (x <= 2.1e-82)
		tmp = Float64(x - Float64(y / Float64(a / x)));
	elseif (x <= 9e+50)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (x <= -4.5e+216)
		tmp = t_2;
	elseif (x <= -1.9e+152)
		tmp = (y - a) / (z / x);
	elseif (x <= -2.2e+81)
		tmp = y * -(x / (a - z));
	elseif (x <= 1.05e-113)
		tmp = t_1;
	elseif (x <= 2.1e-82)
		tmp = x - (y / (a / x));
	elseif (x <= 9e+50)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.5e+216], t$95$2, If[LessEqual[x, -1.9e+152], N[(N[(y - a), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.2e+81], N[(y * (-N[(x / N[(a - z), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], If[LessEqual[x, 1.05e-113], t$95$1, If[LessEqual[x, 2.1e-82], N[(x - N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9e+50], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -4.50000000000000025e216 or 9.00000000000000027e50 < x

   1. Initial program 86.2%

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

   2. Taylor expanded in z around 0 57.2%

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

   3. Taylor expanded in x around inf 67.6%

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

      1. *-commutative 67.6%

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

      2. mul-1-neg 67.6%

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

      3. unsub-neg 67.6%

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

   5. Simplified 67.6%

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

   if -4.50000000000000025e216 < x < -1.9e152

   1. Initial program 55.2%

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

   2. Taylor expanded in z around inf 84.9%

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

      1. +-commutative 84.9%

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

      2. associate--l+ 84.9%

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

      3. associate-*r/ 84.9%

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

      4. associate-*r/ 84.9%

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

      5. div-sub 85.2%

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

      6. distribute-lft-out-- 85.2%

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

      7. mul-1-neg 85.2%

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

      8. distribute-neg-frac 85.2%

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

      9. unsub-neg 85.2%

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

      10. distribute-rgt-out-- 85.2%

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

   4. Simplified 85.2%

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

   5. Taylor expanded in t around 0 85.2%

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

      1. associate-/l* 85.4%

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

   7. Simplified 85.4%

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

   if -1.9e152 < x < -2.19999999999999987e81

   1. Initial program 84.8%

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

   2. Taylor expanded in y around inf 62.7%

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

   3. Taylor expanded in t around 0 62.2%

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

      1. neg-mul-1 62.2%

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

      2. distribute-neg-frac 62.2%

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

   5. Simplified 62.2%

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

   if -2.19999999999999987e81 < x < 1.05e-113 or 2.1e-82 < x < 9.00000000000000027e50

   1. Initial program 85.2%

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

   2. Taylor expanded in t around inf 74.3%

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

      1. div-sub 74.3%

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

   4. Simplified 74.3%

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

   if 1.05e-113 < x < 2.1e-82

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 85.6%

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

   3. Taylor expanded in t around 0 83.4%

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

      1. +-commutative 83.4%

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

      2. mul-1-neg 83.4%

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

      3. unsub-neg 83.4%

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

      4. associate-/l* 83.6%

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

   5. Simplified 83.6%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+216}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+152}:\\ \;\;\;\;\frac{y - a}{\frac{z}{x}}\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{+81}:\\ \;\;\;\;y \cdot \left(-\frac{x}{a - z}\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-113}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-82}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+50}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]

Alternative 6: 59.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{+212}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3 \cdot 10^{+154}:\\ \;\;\;\;\frac{y - a}{\frac{z}{x}}\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{+80}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-82}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= x -4.2e+212)
     t_2
     (if (<= x -3e+154)
       (/ (- y a) (/ z x))
       (if (<= x -1.15e+80)
         (* (- t x) (/ y (- a z)))
         (if (<= x 1.05e-113)
           t_1
           (if (<= x 2.1e-82)
             (- x (/ y (/ a x)))
             (if (<= x 6.2e+50) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -4.2e+212) {
		tmp = t_2;
	} else if (x <= -3e+154) {
		tmp = (y - a) / (z / x);
	} else if (x <= -1.15e+80) {
		tmp = (t - x) * (y / (a - z));
	} else if (x <= 1.05e-113) {
		tmp = t_1;
	} else if (x <= 2.1e-82) {
		tmp = x - (y / (a / x));
	} else if (x <= 6.2e+50) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x * (1.0d0 - (y / a))
    if (x <= (-4.2d+212)) then
        tmp = t_2
    else if (x <= (-3d+154)) then
        tmp = (y - a) / (z / x)
    else if (x <= (-1.15d+80)) then
        tmp = (t - x) * (y / (a - z))
    else if (x <= 1.05d-113) then
        tmp = t_1
    else if (x <= 2.1d-82) then
        tmp = x - (y / (a / x))
    else if (x <= 6.2d+50) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -4.2e+212) {
		tmp = t_2;
	} else if (x <= -3e+154) {
		tmp = (y - a) / (z / x);
	} else if (x <= -1.15e+80) {
		tmp = (t - x) * (y / (a - z));
	} else if (x <= 1.05e-113) {
		tmp = t_1;
	} else if (x <= 2.1e-82) {
		tmp = x - (y / (a / x));
	} else if (x <= 6.2e+50) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if x <= -4.2e+212:
		tmp = t_2
	elif x <= -3e+154:
		tmp = (y - a) / (z / x)
	elif x <= -1.15e+80:
		tmp = (t - x) * (y / (a - z))
	elif x <= 1.05e-113:
		tmp = t_1
	elif x <= 2.1e-82:
		tmp = x - (y / (a / x))
	elif x <= 6.2e+50:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (x <= -4.2e+212)
		tmp = t_2;
	elseif (x <= -3e+154)
		tmp = Float64(Float64(y - a) / Float64(z / x));
	elseif (x <= -1.15e+80)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (x <= 1.05e-113)
		tmp = t_1;
	elseif (x <= 2.1e-82)
		tmp = Float64(x - Float64(y / Float64(a / x)));
	elseif (x <= 6.2e+50)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (x <= -4.2e+212)
		tmp = t_2;
	elseif (x <= -3e+154)
		tmp = (y - a) / (z / x);
	elseif (x <= -1.15e+80)
		tmp = (t - x) * (y / (a - z));
	elseif (x <= 1.05e-113)
		tmp = t_1;
	elseif (x <= 2.1e-82)
		tmp = x - (y / (a / x));
	elseif (x <= 6.2e+50)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.2e+212], t$95$2, If[LessEqual[x, -3e+154], N[(N[(y - a), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.15e+80], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.05e-113], t$95$1, If[LessEqual[x, 2.1e-82], N[(x - N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.2e+50], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -4.2e212 or 6.20000000000000006e50 < x

   1. Initial program 86.2%

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

   2. Taylor expanded in z around 0 57.2%

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

   3. Taylor expanded in x around inf 67.6%

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

      1. *-commutative 67.6%

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

      2. mul-1-neg 67.6%

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

      3. unsub-neg 67.6%

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

   5. Simplified 67.6%

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

   if -4.2e212 < x < -3.00000000000000026e154

   1. Initial program 55.2%

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

   2. Taylor expanded in z around inf 84.9%

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

      1. +-commutative 84.9%

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

      2. associate--l+ 84.9%

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

      3. associate-*r/ 84.9%

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

      4. associate-*r/ 84.9%

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

      5. div-sub 85.2%

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

      6. distribute-lft-out-- 85.2%

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

      7. mul-1-neg 85.2%

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

      8. distribute-neg-frac 85.2%

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

      9. unsub-neg 85.2%

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

      10. distribute-rgt-out-- 85.2%

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

   4. Simplified 85.2%

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

   5. Taylor expanded in t around 0 85.2%

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

      1. associate-/l* 85.4%

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

   7. Simplified 85.4%

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

   if -3.00000000000000026e154 < x < -1.15000000000000002e80

   1. Initial program 84.8%

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

      1. clear-num 84.8%

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

      2. un-div-inv 84.8%

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

   3. Applied egg-rr 84.8%

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

   4. Taylor expanded in y around inf 62.7%

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

      1. div-sub 62.7%

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

      2. associate-*l/ 55.7%

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

      3. associate-*r/ 62.8%

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

      4. *-commutative 62.8%

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

   6. Simplified 62.8%

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

   if -1.15000000000000002e80 < x < 1.05e-113 or 2.1e-82 < x < 6.20000000000000006e50

   1. Initial program 85.2%

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

   2. Taylor expanded in t around inf 74.3%

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

      1. div-sub 74.3%

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

   4. Simplified 74.3%

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

   if 1.05e-113 < x < 2.1e-82

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 85.6%

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

   3. Taylor expanded in t around 0 83.4%

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

      1. +-commutative 83.4%

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

      2. mul-1-neg 83.4%

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

      3. unsub-neg 83.4%

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

      4. associate-/l* 83.6%

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

   5. Simplified 83.6%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+212}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq -3 \cdot 10^{+154}:\\ \;\;\;\;\frac{y - a}{\frac{z}{x}}\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{+80}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-113}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-82}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+50}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]

Alternative 7: 46.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;z \leq -1.12 \cdot 10^{+196}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-270}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-252}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-150}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))))
   (if (<= z -1.12e+196)
     t
     (if (<= z -2.9e-270)
       t_1
       (if (<= z 3.3e-252)
         (* y (/ (- t x) a))
         (if (<= z 3.1e-203)
           t_1
           (if (<= z 4.5e-150)
             (* x (- 1.0 (/ y a)))
             (if (<= z 1.3e-69) t_1 t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (z <= -1.12e+196) {
		tmp = t;
	} else if (z <= -2.9e-270) {
		tmp = t_1;
	} else if (z <= 3.3e-252) {
		tmp = y * ((t - x) / a);
	} else if (z <= 3.1e-203) {
		tmp = t_1;
	} else if (z <= 4.5e-150) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.3e-69) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * t) / a)
    if (z <= (-1.12d+196)) then
        tmp = t
    else if (z <= (-2.9d-270)) then
        tmp = t_1
    else if (z <= 3.3d-252) then
        tmp = y * ((t - x) / a)
    else if (z <= 3.1d-203) then
        tmp = t_1
    else if (z <= 4.5d-150) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 1.3d-69) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (z <= -1.12e+196) {
		tmp = t;
	} else if (z <= -2.9e-270) {
		tmp = t_1;
	} else if (z <= 3.3e-252) {
		tmp = y * ((t - x) / a);
	} else if (z <= 3.1e-203) {
		tmp = t_1;
	} else if (z <= 4.5e-150) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.3e-69) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	tmp = 0
	if z <= -1.12e+196:
		tmp = t
	elif z <= -2.9e-270:
		tmp = t_1
	elif z <= 3.3e-252:
		tmp = y * ((t - x) / a)
	elif z <= 3.1e-203:
		tmp = t_1
	elif z <= 4.5e-150:
		tmp = x * (1.0 - (y / a))
	elif z <= 1.3e-69:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (z <= -1.12e+196)
		tmp = t;
	elseif (z <= -2.9e-270)
		tmp = t_1;
	elseif (z <= 3.3e-252)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 3.1e-203)
		tmp = t_1;
	elseif (z <= 4.5e-150)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 1.3e-69)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	tmp = 0.0;
	if (z <= -1.12e+196)
		tmp = t;
	elseif (z <= -2.9e-270)
		tmp = t_1;
	elseif (z <= 3.3e-252)
		tmp = y * ((t - x) / a);
	elseif (z <= 3.1e-203)
		tmp = t_1;
	elseif (z <= 4.5e-150)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 1.3e-69)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.12e+196], t, If[LessEqual[z, -2.9e-270], t$95$1, If[LessEqual[z, 3.3e-252], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e-203], t$95$1, If[LessEqual[z, 4.5e-150], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e-69], t$95$1, t]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.1199999999999999e196 or 1.3000000000000001e-69 < z

   1. Initial program 70.0%

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

   2. Taylor expanded in z around inf 50.4%

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

   if -1.1199999999999999e196 < z < -2.89999999999999983e-270 or 3.30000000000000009e-252 < z < 3.09999999999999977e-203 or 4.5000000000000002e-150 < z < 1.3000000000000001e-69

   1. Initial program 91.2%

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

   2. Taylor expanded in z around 0 55.7%

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

   3. Taylor expanded in t around inf 55.2%

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

   if -2.89999999999999983e-270 < z < 3.30000000000000009e-252

   1. Initial program 94.7%

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

   2. Taylor expanded in y around inf 79.6%

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

   3. Taylor expanded in a around inf 79.6%

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

   if 3.09999999999999977e-203 < z < 4.5000000000000002e-150

   1. Initial program 93.4%

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

   2. Taylor expanded in z around 0 62.6%

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

   3. Taylor expanded in x around inf 68.3%

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

      1. *-commutative 68.3%

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

      2. mul-1-neg 68.3%

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

      3. unsub-neg 68.3%

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

   5. Simplified 68.3%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+196}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-270}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-252}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-203}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-150}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-69}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8: 51.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ t_2 := t - \frac{y}{\frac{z}{t}}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+149}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-270}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-252}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-144}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))) (t_2 (- t (/ y (/ z t)))))
   (if (<= z -3.5e+149)
     t_2
     (if (<= z -2.6e-270)
       t_1
       (if (<= z 2.4e-252)
         (* y (/ (- t x) a))
         (if (<= z 1.7e-190)
           t_1
           (if (<= z 4.2e-144)
             (* x (- 1.0 (/ y a)))
             (if (<= z 1.8e-69) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double t_2 = t - (y / (z / t));
	double tmp;
	if (z <= -3.5e+149) {
		tmp = t_2;
	} else if (z <= -2.6e-270) {
		tmp = t_1;
	} else if (z <= 2.4e-252) {
		tmp = y * ((t - x) / a);
	} else if (z <= 1.7e-190) {
		tmp = t_1;
	} else if (z <= 4.2e-144) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.8e-69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((y * t) / a)
    t_2 = t - (y / (z / t))
    if (z <= (-3.5d+149)) then
        tmp = t_2
    else if (z <= (-2.6d-270)) then
        tmp = t_1
    else if (z <= 2.4d-252) then
        tmp = y * ((t - x) / a)
    else if (z <= 1.7d-190) then
        tmp = t_1
    else if (z <= 4.2d-144) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 1.8d-69) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double t_2 = t - (y / (z / t));
	double tmp;
	if (z <= -3.5e+149) {
		tmp = t_2;
	} else if (z <= -2.6e-270) {
		tmp = t_1;
	} else if (z <= 2.4e-252) {
		tmp = y * ((t - x) / a);
	} else if (z <= 1.7e-190) {
		tmp = t_1;
	} else if (z <= 4.2e-144) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.8e-69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	t_2 = t - (y / (z / t))
	tmp = 0
	if z <= -3.5e+149:
		tmp = t_2
	elif z <= -2.6e-270:
		tmp = t_1
	elif z <= 2.4e-252:
		tmp = y * ((t - x) / a)
	elif z <= 1.7e-190:
		tmp = t_1
	elif z <= 4.2e-144:
		tmp = x * (1.0 - (y / a))
	elif z <= 1.8e-69:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	t_2 = Float64(t - Float64(y / Float64(z / t)))
	tmp = 0.0
	if (z <= -3.5e+149)
		tmp = t_2;
	elseif (z <= -2.6e-270)
		tmp = t_1;
	elseif (z <= 2.4e-252)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 1.7e-190)
		tmp = t_1;
	elseif (z <= 4.2e-144)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 1.8e-69)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	t_2 = t - (y / (z / t));
	tmp = 0.0;
	if (z <= -3.5e+149)
		tmp = t_2;
	elseif (z <= -2.6e-270)
		tmp = t_1;
	elseif (z <= 2.4e-252)
		tmp = y * ((t - x) / a);
	elseif (z <= 1.7e-190)
		tmp = t_1;
	elseif (z <= 4.2e-144)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 1.8e-69)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+149], t$95$2, If[LessEqual[z, -2.6e-270], t$95$1, If[LessEqual[z, 2.4e-252], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e-190], t$95$1, If[LessEqual[z, 4.2e-144], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e-69], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.50000000000000011e149 or 1.80000000000000009e-69 < z

   1. Initial program 71.9%

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

   2. Taylor expanded in x around 0 47.1%

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

      1. associate-/l* 68.5%

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

   4. Simplified 68.5%

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

   5. Taylor expanded in a around 0 45.5%

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

      1. associate-*r/ 45.5%

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

      2. mul-1-neg 45.5%

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

   7. Simplified 45.5%

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

   8. Taylor expanded in y around 0 55.3%

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

      1. +-commutative 55.3%

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

      2. mul-1-neg 55.3%

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

      3. unsub-neg 55.3%

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

      4. associate-/l* 60.3%

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

   10. Simplified 60.3%

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

   if -3.50000000000000011e149 < z < -2.6000000000000002e-270 or 2.4000000000000002e-252 < z < 1.69999999999999991e-190 or 4.2000000000000002e-144 < z < 1.80000000000000009e-69

   1. Initial program 91.2%

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

   2. Taylor expanded in z around 0 57.1%

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

   3. Taylor expanded in t around inf 55.9%

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

   if -2.6000000000000002e-270 < z < 2.4000000000000002e-252

   1. Initial program 94.7%

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

   2. Taylor expanded in y around inf 79.6%

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

   3. Taylor expanded in a around inf 79.6%

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

   if 1.69999999999999991e-190 < z < 4.2000000000000002e-144

   1. Initial program 93.4%

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

   2. Taylor expanded in z around 0 62.6%

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

   3. Taylor expanded in x around inf 68.3%

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

      1. *-commutative 68.3%

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

      2. mul-1-neg 68.3%

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

      3. unsub-neg 68.3%

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

   5. Simplified 68.3%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+149}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-270}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-252}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-190}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-144}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-69}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \end{array} \]

Alternative 9: 51.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+149}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-269}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-252}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-207}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-154}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{z - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))))
   (if (<= z -3.5e+149)
     (- t (/ y (/ z t)))
     (if (<= z -1.25e-269)
       t_1
       (if (<= z 2.6e-252)
         (* y (/ (- t x) a))
         (if (<= z 1.45e-207)
           t_1
           (if (<= z 2.7e-154)
             (* x (- 1.0 (/ y a)))
             (if (<= z 1.6e-69) t_1 (/ t (/ z (- z y)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (z <= -3.5e+149) {
		tmp = t - (y / (z / t));
	} else if (z <= -1.25e-269) {
		tmp = t_1;
	} else if (z <= 2.6e-252) {
		tmp = y * ((t - x) / a);
	} else if (z <= 1.45e-207) {
		tmp = t_1;
	} else if (z <= 2.7e-154) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.6e-69) {
		tmp = t_1;
	} else {
		tmp = t / (z / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * t) / a)
    if (z <= (-3.5d+149)) then
        tmp = t - (y / (z / t))
    else if (z <= (-1.25d-269)) then
        tmp = t_1
    else if (z <= 2.6d-252) then
        tmp = y * ((t - x) / a)
    else if (z <= 1.45d-207) then
        tmp = t_1
    else if (z <= 2.7d-154) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 1.6d-69) then
        tmp = t_1
    else
        tmp = t / (z / (z - y))
    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 * t) / a);
	double tmp;
	if (z <= -3.5e+149) {
		tmp = t - (y / (z / t));
	} else if (z <= -1.25e-269) {
		tmp = t_1;
	} else if (z <= 2.6e-252) {
		tmp = y * ((t - x) / a);
	} else if (z <= 1.45e-207) {
		tmp = t_1;
	} else if (z <= 2.7e-154) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.6e-69) {
		tmp = t_1;
	} else {
		tmp = t / (z / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	tmp = 0
	if z <= -3.5e+149:
		tmp = t - (y / (z / t))
	elif z <= -1.25e-269:
		tmp = t_1
	elif z <= 2.6e-252:
		tmp = y * ((t - x) / a)
	elif z <= 1.45e-207:
		tmp = t_1
	elif z <= 2.7e-154:
		tmp = x * (1.0 - (y / a))
	elif z <= 1.6e-69:
		tmp = t_1
	else:
		tmp = t / (z / (z - y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (z <= -3.5e+149)
		tmp = Float64(t - Float64(y / Float64(z / t)));
	elseif (z <= -1.25e-269)
		tmp = t_1;
	elseif (z <= 2.6e-252)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 1.45e-207)
		tmp = t_1;
	elseif (z <= 2.7e-154)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 1.6e-69)
		tmp = t_1;
	else
		tmp = Float64(t / Float64(z / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	tmp = 0.0;
	if (z <= -3.5e+149)
		tmp = t - (y / (z / t));
	elseif (z <= -1.25e-269)
		tmp = t_1;
	elseif (z <= 2.6e-252)
		tmp = y * ((t - x) / a);
	elseif (z <= 1.45e-207)
		tmp = t_1;
	elseif (z <= 2.7e-154)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 1.6e-69)
		tmp = t_1;
	else
		tmp = t / (z / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+149], N[(t - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.25e-269], t$95$1, If[LessEqual[z, 2.6e-252], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e-207], t$95$1, If[LessEqual[z, 2.7e-154], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e-69], t$95$1, N[(t / N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.50000000000000011e149

   1. Initial program 79.4%

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

   2. Taylor expanded in x around 0 45.3%

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

      1. associate-/l* 74.2%

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

   4. Simplified 74.2%

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

   5. Taylor expanded in a around 0 45.8%

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

      1. associate-*r/ 45.8%

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

      2. mul-1-neg 45.8%

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

   7. Simplified 45.8%

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

   8. Taylor expanded in y around 0 59.1%

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

      1. +-commutative 59.1%

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

      2. mul-1-neg 59.1%

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

      3. unsub-neg 59.1%

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

      4. associate-/l* 71.8%

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

   10. Simplified 71.8%

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

   if -3.50000000000000011e149 < z < -1.24999999999999995e-269 or 2.5999999999999999e-252 < z < 1.45000000000000006e-207 or 2.69999999999999989e-154 < z < 1.59999999999999999e-69

   1. Initial program 91.2%

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

   2. Taylor expanded in z around 0 57.1%

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

   3. Taylor expanded in t around inf 55.9%

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

   if -1.24999999999999995e-269 < z < 2.5999999999999999e-252

   1. Initial program 94.7%

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

   2. Taylor expanded in y around inf 79.6%

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

   3. Taylor expanded in a around inf 79.6%

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

   if 1.45000000000000006e-207 < z < 2.69999999999999989e-154

   1. Initial program 93.4%

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

   2. Taylor expanded in z around 0 62.6%

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

   3. Taylor expanded in x around inf 68.3%

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

      1. *-commutative 68.3%

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

      2. mul-1-neg 68.3%

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

      3. unsub-neg 68.3%

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

   5. Simplified 68.3%

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

   if 1.59999999999999999e-69 < z

   1. Initial program 69.5%

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

   2. Taylor expanded in x around 0 47.7%

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

      1. associate-/l* 66.7%

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

   4. Simplified 66.7%

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

   5. Taylor expanded in a around 0 45.4%

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

      1. associate-*r/ 45.4%

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

      2. mul-1-neg 45.4%

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

   7. Simplified 45.4%

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

   8. Taylor expanded in t around inf 45.4%

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

      1. associate-/l* 57.5%

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

   10. Simplified 57.5%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+149}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-269}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-252}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-207}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-154}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-69}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{z - y}}\\ \end{array} \]

Alternative 10: 52.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;z \leq -6 \cdot 10^{+27}:\\ \;\;\;\;\frac{t}{\frac{z - a}{z}}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-270}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-252}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-209}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-154}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{z - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))))
   (if (<= z -6e+27)
     (/ t (/ (- z a) z))
     (if (<= z -2.6e-270)
       t_1
       (if (<= z 3e-252)
         (* y (/ (- t x) a))
         (if (<= z 4.2e-209)
           t_1
           (if (<= z 2.6e-154)
             (* x (- 1.0 (/ y a)))
             (if (<= z 1.75e-69) t_1 (/ t (/ z (- z y)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (z <= -6e+27) {
		tmp = t / ((z - a) / z);
	} else if (z <= -2.6e-270) {
		tmp = t_1;
	} else if (z <= 3e-252) {
		tmp = y * ((t - x) / a);
	} else if (z <= 4.2e-209) {
		tmp = t_1;
	} else if (z <= 2.6e-154) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.75e-69) {
		tmp = t_1;
	} else {
		tmp = t / (z / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * t) / a)
    if (z <= (-6d+27)) then
        tmp = t / ((z - a) / z)
    else if (z <= (-2.6d-270)) then
        tmp = t_1
    else if (z <= 3d-252) then
        tmp = y * ((t - x) / a)
    else if (z <= 4.2d-209) then
        tmp = t_1
    else if (z <= 2.6d-154) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 1.75d-69) then
        tmp = t_1
    else
        tmp = t / (z / (z - y))
    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 * t) / a);
	double tmp;
	if (z <= -6e+27) {
		tmp = t / ((z - a) / z);
	} else if (z <= -2.6e-270) {
		tmp = t_1;
	} else if (z <= 3e-252) {
		tmp = y * ((t - x) / a);
	} else if (z <= 4.2e-209) {
		tmp = t_1;
	} else if (z <= 2.6e-154) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.75e-69) {
		tmp = t_1;
	} else {
		tmp = t / (z / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	tmp = 0
	if z <= -6e+27:
		tmp = t / ((z - a) / z)
	elif z <= -2.6e-270:
		tmp = t_1
	elif z <= 3e-252:
		tmp = y * ((t - x) / a)
	elif z <= 4.2e-209:
		tmp = t_1
	elif z <= 2.6e-154:
		tmp = x * (1.0 - (y / a))
	elif z <= 1.75e-69:
		tmp = t_1
	else:
		tmp = t / (z / (z - y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (z <= -6e+27)
		tmp = Float64(t / Float64(Float64(z - a) / z));
	elseif (z <= -2.6e-270)
		tmp = t_1;
	elseif (z <= 3e-252)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 4.2e-209)
		tmp = t_1;
	elseif (z <= 2.6e-154)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 1.75e-69)
		tmp = t_1;
	else
		tmp = Float64(t / Float64(z / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	tmp = 0.0;
	if (z <= -6e+27)
		tmp = t / ((z - a) / z);
	elseif (z <= -2.6e-270)
		tmp = t_1;
	elseif (z <= 3e-252)
		tmp = y * ((t - x) / a);
	elseif (z <= 4.2e-209)
		tmp = t_1;
	elseif (z <= 2.6e-154)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 1.75e-69)
		tmp = t_1;
	else
		tmp = t / (z / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e+27], N[(t / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.6e-270], t$95$1, If[LessEqual[z, 3e-252], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e-209], t$95$1, If[LessEqual[z, 2.6e-154], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e-69], t$95$1, N[(t / N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.99999999999999953e27

   1. Initial program 83.0%

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

   2. Taylor expanded in x around 0 41.2%

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

      1. associate-/l* 64.2%

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

   4. Simplified 64.2%

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

   5. Taylor expanded in y around 0 52.7%

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

      1. associate-*r/ 52.7%

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

      2. neg-mul-1 52.7%

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

   7. Simplified 52.7%

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

   if -5.99999999999999953e27 < z < -2.6000000000000002e-270 or 2.99999999999999995e-252 < z < 4.19999999999999991e-209 or 2.6e-154 < z < 1.7500000000000001e-69

   1. Initial program 91.9%

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

   2. Taylor expanded in z around 0 63.4%

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

   3. Taylor expanded in t around inf 60.8%

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

   if -2.6000000000000002e-270 < z < 2.99999999999999995e-252

   1. Initial program 94.7%

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

   2. Taylor expanded in y around inf 79.6%

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

   3. Taylor expanded in a around inf 79.6%

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

   if 4.19999999999999991e-209 < z < 2.6e-154

   1. Initial program 93.4%

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

   2. Taylor expanded in z around 0 62.6%

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

   3. Taylor expanded in x around inf 68.3%

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

      1. *-commutative 68.3%

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

      2. mul-1-neg 68.3%

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

      3. unsub-neg 68.3%

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

   5. Simplified 68.3%

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

   if 1.7500000000000001e-69 < z

   1. Initial program 69.5%

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

   2. Taylor expanded in x around 0 47.7%

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

      1. associate-/l* 66.7%

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

   4. Simplified 66.7%

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

   5. Taylor expanded in a around 0 45.4%

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

      1. associate-*r/ 45.4%

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

      2. mul-1-neg 45.4%

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

   7. Simplified 45.4%

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

   8. Taylor expanded in t around inf 45.4%

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

      1. associate-/l* 57.5%

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

   10. Simplified 57.5%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+27}:\\ \;\;\;\;\frac{t}{\frac{z - a}{z}}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-270}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-252}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-209}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-154}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-69}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{z - y}}\\ \end{array} \]

Alternative 11: 72.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{if}\;a \leq -4.5 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-125}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+70} \lor \neg \left(a \leq 2.8 \cdot 10^{+105}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y z) (/ (- a z) t)))))
   (if (<= a -4.5e-40)
     t_1
     (if (<= a 6.4e-125)
       (+ t (/ (* y (- x t)) z))
       (if (or (<= a 1.15e+70) (not (<= a 2.8e+105)))
         t_1
         (+ x (/ y (/ a (- t x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / ((a - z) / t));
	double tmp;
	if (a <= -4.5e-40) {
		tmp = t_1;
	} else if (a <= 6.4e-125) {
		tmp = t + ((y * (x - t)) / z);
	} else if ((a <= 1.15e+70) || !(a <= 2.8e+105)) {
		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 = x + ((y - z) / ((a - z) / t))
    if (a <= (-4.5d-40)) then
        tmp = t_1
    else if (a <= 6.4d-125) then
        tmp = t + ((y * (x - t)) / z)
    else if ((a <= 1.15d+70) .or. (.not. (a <= 2.8d+105))) 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 = x + ((y - z) / ((a - z) / t));
	double tmp;
	if (a <= -4.5e-40) {
		tmp = t_1;
	} else if (a <= 6.4e-125) {
		tmp = t + ((y * (x - t)) / z);
	} else if ((a <= 1.15e+70) || !(a <= 2.8e+105)) {
		tmp = t_1;
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) / ((a - z) / t))
	tmp = 0
	if a <= -4.5e-40:
		tmp = t_1
	elif a <= 6.4e-125:
		tmp = t + ((y * (x - t)) / z)
	elif (a <= 1.15e+70) or not (a <= 2.8e+105):
		tmp = t_1
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)))
	tmp = 0.0
	if (a <= -4.5e-40)
		tmp = t_1;
	elseif (a <= 6.4e-125)
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	elseif ((a <= 1.15e+70) || !(a <= 2.8e+105))
		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 = x + ((y - z) / ((a - z) / t));
	tmp = 0.0;
	if (a <= -4.5e-40)
		tmp = t_1;
	elseif (a <= 6.4e-125)
		tmp = t + ((y * (x - t)) / z);
	elseif ((a <= 1.15e+70) || ~((a <= 2.8e+105)))
		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[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.5e-40], t$95$1, If[LessEqual[a, 6.4e-125], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 1.15e+70], N[Not[LessEqual[a, 2.8e+105]], $MachinePrecision]], t$95$1, N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.5000000000000001e-40 or 6.3999999999999997e-125 < a < 1.14999999999999997e70 or 2.8000000000000001e105 < a

   1. Initial program 89.4%

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

      1. clear-num 89.3%

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

      2. un-div-inv 89.4%

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

   3. Applied egg-rr 89.4%

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

   4. Taylor expanded in t around inf 77.6%

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

   if -4.5000000000000001e-40 < a < 6.3999999999999997e-125

   1. Initial program 73.0%

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

   2. Taylor expanded in z around inf 84.7%

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

      1. +-commutative 84.7%

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

      2. associate--l+ 84.7%

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

      3. associate-*r/ 84.7%

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

      4. associate-*r/ 84.7%

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

      5. div-sub 84.7%

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

      6. distribute-lft-out-- 84.7%

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

      7. mul-1-neg 84.7%

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

      8. distribute-neg-frac 84.7%

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

      9. unsub-neg 84.7%

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

      10. distribute-rgt-out-- 84.7%

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

   4. Simplified 84.7%

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

   5. Taylor expanded in y around inf 80.2%

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

   if 1.14999999999999997e70 < a < 2.8000000000000001e105

   1. Initial program 99.6%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in z around 0 60.9%

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

      1. +-commutative 60.9%

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

      2. associate-/l* 99.8%

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

   6. Simplified 99.8%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-40}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-125}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+70} \lor \neg \left(a \leq 2.8 \cdot 10^{+105}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 12: 73.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{if}\;a \leq -8.2 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-126}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+69} \lor \neg \left(a \leq 7 \cdot 10^{+105}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y z) (/ (- a z) t)))))
   (if (<= a -8.2e-37)
     t_1
     (if (<= a 3e-126)
       (+ t (/ (* (- t x) (- a y)) z))
       (if (or (<= a 9.2e+69) (not (<= a 7e+105)))
         t_1
         (+ x (/ y (/ a (- t x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / ((a - z) / t));
	double tmp;
	if (a <= -8.2e-37) {
		tmp = t_1;
	} else if (a <= 3e-126) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if ((a <= 9.2e+69) || !(a <= 7e+105)) {
		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 = x + ((y - z) / ((a - z) / t))
    if (a <= (-8.2d-37)) then
        tmp = t_1
    else if (a <= 3d-126) then
        tmp = t + (((t - x) * (a - y)) / z)
    else if ((a <= 9.2d+69) .or. (.not. (a <= 7d+105))) 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 = x + ((y - z) / ((a - z) / t));
	double tmp;
	if (a <= -8.2e-37) {
		tmp = t_1;
	} else if (a <= 3e-126) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if ((a <= 9.2e+69) || !(a <= 7e+105)) {
		tmp = t_1;
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) / ((a - z) / t))
	tmp = 0
	if a <= -8.2e-37:
		tmp = t_1
	elif a <= 3e-126:
		tmp = t + (((t - x) * (a - y)) / z)
	elif (a <= 9.2e+69) or not (a <= 7e+105):
		tmp = t_1
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)))
	tmp = 0.0
	if (a <= -8.2e-37)
		tmp = t_1;
	elseif (a <= 3e-126)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif ((a <= 9.2e+69) || !(a <= 7e+105))
		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 = x + ((y - z) / ((a - z) / t));
	tmp = 0.0;
	if (a <= -8.2e-37)
		tmp = t_1;
	elseif (a <= 3e-126)
		tmp = t + (((t - x) * (a - y)) / z);
	elseif ((a <= 9.2e+69) || ~((a <= 7e+105)))
		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[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.2e-37], t$95$1, If[LessEqual[a, 3e-126], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 9.2e+69], N[Not[LessEqual[a, 7e+105]], $MachinePrecision]], t$95$1, N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.1999999999999996e-37 or 3.0000000000000002e-126 < a < 9.20000000000000067e69 or 6.99999999999999982e105 < a

   1. Initial program 89.4%

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

      1. clear-num 89.3%

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

      2. un-div-inv 89.4%

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

   3. Applied egg-rr 89.4%

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

   4. Taylor expanded in t around inf 77.6%

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

   if -8.1999999999999996e-37 < a < 3.0000000000000002e-126

   1. Initial program 73.0%

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

   2. Taylor expanded in z around inf 84.7%

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

      1. +-commutative 84.7%

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

      2. associate--l+ 84.7%

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

      3. associate-*r/ 84.7%

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

      4. associate-*r/ 84.7%

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

      5. div-sub 84.7%

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

      6. distribute-lft-out-- 84.7%

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

      7. mul-1-neg 84.7%

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

      8. distribute-neg-frac 84.7%

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

      9. unsub-neg 84.7%

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

      10. distribute-rgt-out-- 84.7%

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

   4. Simplified 84.7%

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

   if 9.20000000000000067e69 < a < 6.99999999999999982e105

   1. Initial program 99.6%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in z around 0 60.9%

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

      1. +-commutative 60.9%

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

      2. associate-/l* 99.8%

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

   6. Simplified 99.8%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{-37}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-126}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+69} \lor \neg \left(a \leq 7 \cdot 10^{+105}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 13: 65.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -118 \lor \neg \left(z \leq -5.4 \cdot 10^{-74} \lor \neg \left(z \leq -7.4 \cdot 10^{-91}\right) \land z \leq 8.2 \cdot 10^{-38}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -118.0)
         (not (or (<= z -5.4e-74) (and (not (<= z -7.4e-91)) (<= z 8.2e-38)))))
   (* 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 <= -118.0) || !((z <= -5.4e-74) || (!(z <= -7.4e-91) && (z <= 8.2e-38)))) {
		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 <= (-118.0d0)) .or. (.not. (z <= (-5.4d-74)) .or. (.not. (z <= (-7.4d-91))) .and. (z <= 8.2d-38))) 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 <= -118.0) || !((z <= -5.4e-74) || (!(z <= -7.4e-91) && (z <= 8.2e-38)))) {
		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 <= -118.0) or not ((z <= -5.4e-74) or (not (z <= -7.4e-91) and (z <= 8.2e-38))):
		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 <= -118.0) || !((z <= -5.4e-74) || (!(z <= -7.4e-91) && (z <= 8.2e-38))))
		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 <= -118.0) || ~(((z <= -5.4e-74) || (~((z <= -7.4e-91)) && (z <= 8.2e-38)))))
		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, -118.0], N[Not[Or[LessEqual[z, -5.4e-74], And[N[Not[LessEqual[z, -7.4e-91]], $MachinePrecision], LessEqual[z, 8.2e-38]]]], $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 < -118 or -5.40000000000000036e-74 < z < -7.4000000000000004e-91 or 8.1999999999999996e-38 < z

   1. Initial program 75.2%

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

   2. Taylor expanded in t around inf 66.6%

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

      1. div-sub 66.6%

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

   4. Simplified 66.6%

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

   if -118 < z < -5.40000000000000036e-74 or -7.4000000000000004e-91 < z < 8.1999999999999996e-38

   1. Initial program 93.2%

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

      1. clear-num 93.2%

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

      2. un-div-inv 93.7%

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

   3. Applied egg-rr 93.7%

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

   4. Taylor expanded in z around 0 70.2%

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

      1. +-commutative 70.2%

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

      2. associate-/l* 78.2%

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

   6. Simplified 78.2%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -118 \lor \neg \left(z \leq -5.4 \cdot 10^{-74} \lor \neg \left(z \leq -7.4 \cdot 10^{-91}\right) \land z \leq 8.2 \cdot 10^{-38}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 14: 46.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+159}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-236}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-189}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -1.45e+159)
     t
     (if (<= z 1.15e-236)
       t_1
       (if (<= z 2.45e-189) (* y (/ t (- a z))) (if (<= z 8.8e-37) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -1.45e+159) {
		tmp = t;
	} else if (z <= 1.15e-236) {
		tmp = t_1;
	} else if (z <= 2.45e-189) {
		tmp = y * (t / (a - z));
	} else if (z <= 8.8e-37) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (z <= (-1.45d+159)) then
        tmp = t
    else if (z <= 1.15d-236) then
        tmp = t_1
    else if (z <= 2.45d-189) then
        tmp = y * (t / (a - z))
    else if (z <= 8.8d-37) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -1.45e+159) {
		tmp = t;
	} else if (z <= 1.15e-236) {
		tmp = t_1;
	} else if (z <= 2.45e-189) {
		tmp = y * (t / (a - z));
	} else if (z <= 8.8e-37) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -1.45e+159:
		tmp = t
	elif z <= 1.15e-236:
		tmp = t_1
	elif z <= 2.45e-189:
		tmp = y * (t / (a - z))
	elif z <= 8.8e-37:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -1.45e+159)
		tmp = t;
	elseif (z <= 1.15e-236)
		tmp = t_1;
	elseif (z <= 2.45e-189)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	elseif (z <= 8.8e-37)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -1.45e+159)
		tmp = t;
	elseif (z <= 1.15e-236)
		tmp = t_1;
	elseif (z <= 2.45e-189)
		tmp = y * (t / (a - z));
	elseif (z <= 8.8e-37)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.45e+159], t, If[LessEqual[z, 1.15e-236], t$95$1, If[LessEqual[z, 2.45e-189], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.8e-37], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.45000000000000007e159 or 8.80000000000000008e-37 < z

   1. Initial program 70.8%

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

   2. Taylor expanded in z around inf 51.5%

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

   if -1.45000000000000007e159 < z < 1.15000000000000003e-236 or 2.4499999999999999e-189 < z < 8.80000000000000008e-37

   1. Initial program 91.1%

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

   2. Taylor expanded in z around 0 60.7%

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

   3. Taylor expanded in x around inf 52.2%

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

      1. *-commutative 52.2%

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

      2. mul-1-neg 52.2%

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

      3. unsub-neg 52.2%

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

   5. Simplified 52.2%

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

   if 1.15000000000000003e-236 < z < 2.4499999999999999e-189

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 78.6%

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

   3. Taylor expanded in t around inf 68.4%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+159}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-236}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-189}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 15: 68.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{if}\;a \leq -6.6 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-139}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a (- t x))))))
   (if (<= a -6.6e-40)
     t_1
     (if (<= a 4.6e-139)
       (+ t (/ (* y (- x t)) z))
       (if (<= a 1.85e+68) (* t (/ (- y z) (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / (t - x)));
	double tmp;
	if (a <= -6.6e-40) {
		tmp = t_1;
	} else if (a <= 4.6e-139) {
		tmp = t + ((y * (x - t)) / z);
	} else if (a <= 1.85e+68) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (a / (t - x)))
    if (a <= (-6.6d-40)) then
        tmp = t_1
    else if (a <= 4.6d-139) then
        tmp = t + ((y * (x - t)) / z)
    else if (a <= 1.85d+68) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / (t - x)));
	double tmp;
	if (a <= -6.6e-40) {
		tmp = t_1;
	} else if (a <= 4.6e-139) {
		tmp = t + ((y * (x - t)) / z);
	} else if (a <= 1.85e+68) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / (t - x)))
	tmp = 0
	if a <= -6.6e-40:
		tmp = t_1
	elif a <= 4.6e-139:
		tmp = t + ((y * (x - t)) / z)
	elif a <= 1.85e+68:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / Float64(t - x))))
	tmp = 0.0
	if (a <= -6.6e-40)
		tmp = t_1;
	elseif (a <= 4.6e-139)
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	elseif (a <= 1.85e+68)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / (t - x)));
	tmp = 0.0;
	if (a <= -6.6e-40)
		tmp = t_1;
	elseif (a <= 4.6e-139)
		tmp = t + ((y * (x - t)) / z);
	elseif (a <= 1.85e+68)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.6e-40], t$95$1, If[LessEqual[a, 4.6e-139], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.85e+68], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.59999999999999986e-40 or 1.84999999999999999e68 < a

   1. Initial program 94.0%

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

      1. clear-num 93.9%

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

      2. un-div-inv 93.9%

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

   3. Applied egg-rr 93.9%

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

   4. Taylor expanded in z around 0 58.2%

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

      1. +-commutative 58.2%

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

      2. associate-/l* 77.1%

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

   6. Simplified 77.1%

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

   if -6.59999999999999986e-40 < a < 4.60000000000000025e-139

   1. Initial program 73.9%

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

   2. Taylor expanded in z around inf 84.5%

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

      1. +-commutative 84.5%

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

      2. associate--l+ 84.5%

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

      3. associate-*r/ 84.5%

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

      4. associate-*r/ 84.5%

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

      5. div-sub 84.5%

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

      6. distribute-lft-out-- 84.5%

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

      7. mul-1-neg 84.5%

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

      8. distribute-neg-frac 84.5%

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

      9. unsub-neg 84.5%

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

      10. distribute-rgt-out-- 84.5%

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

   4. Simplified 84.5%

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

   5. Taylor expanded in y around inf 80.0%

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

   if 4.60000000000000025e-139 < a < 1.84999999999999999e68

   1. Initial program 80.3%

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

   2. Taylor expanded in t around inf 62.9%

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

      1. div-sub 62.9%

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

   4. Simplified 62.9%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.6 \cdot 10^{-40}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-139}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 16: 68.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{if}\;a \leq -9 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-136}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+69}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a (- t x))))))
   (if (<= a -9e-37)
     t_1
     (if (<= a 5.8e-136)
       (+ t (/ (* y (- x t)) z))
       (if (<= a 2.6e+69) (/ t (/ (- a z) (- y z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / (t - x)));
	double tmp;
	if (a <= -9e-37) {
		tmp = t_1;
	} else if (a <= 5.8e-136) {
		tmp = t + ((y * (x - t)) / z);
	} else if (a <= 2.6e+69) {
		tmp = t / ((a - z) / (y - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (a / (t - x)))
    if (a <= (-9d-37)) then
        tmp = t_1
    else if (a <= 5.8d-136) then
        tmp = t + ((y * (x - t)) / z)
    else if (a <= 2.6d+69) then
        tmp = t / ((a - z) / (y - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / (t - x)));
	double tmp;
	if (a <= -9e-37) {
		tmp = t_1;
	} else if (a <= 5.8e-136) {
		tmp = t + ((y * (x - t)) / z);
	} else if (a <= 2.6e+69) {
		tmp = t / ((a - z) / (y - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / (t - x)))
	tmp = 0
	if a <= -9e-37:
		tmp = t_1
	elif a <= 5.8e-136:
		tmp = t + ((y * (x - t)) / z)
	elif a <= 2.6e+69:
		tmp = t / ((a - z) / (y - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / Float64(t - x))))
	tmp = 0.0
	if (a <= -9e-37)
		tmp = t_1;
	elseif (a <= 5.8e-136)
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	elseif (a <= 2.6e+69)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / (t - x)));
	tmp = 0.0;
	if (a <= -9e-37)
		tmp = t_1;
	elseif (a <= 5.8e-136)
		tmp = t + ((y * (x - t)) / z);
	elseif (a <= 2.6e+69)
		tmp = t / ((a - z) / (y - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9e-37], t$95$1, If[LessEqual[a, 5.8e-136], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.6e+69], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.00000000000000081e-37 or 2.6000000000000002e69 < a

   1. Initial program 94.0%

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

      1. clear-num 93.9%

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

      2. un-div-inv 93.9%

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

   3. Applied egg-rr 93.9%

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

   4. Taylor expanded in z around 0 58.2%

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

      1. +-commutative 58.2%

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

      2. associate-/l* 77.1%

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

   6. Simplified 77.1%

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

   if -9.00000000000000081e-37 < a < 5.79999999999999989e-136

   1. Initial program 73.9%

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

   2. Taylor expanded in z around inf 84.5%

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

      1. +-commutative 84.5%

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

      2. associate--l+ 84.5%

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

      3. associate-*r/ 84.5%

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

      4. associate-*r/ 84.5%

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

      5. div-sub 84.5%

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

      6. distribute-lft-out-- 84.5%

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

      7. mul-1-neg 84.5%

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

      8. distribute-neg-frac 84.5%

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

      9. unsub-neg 84.5%

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

      10. distribute-rgt-out-- 84.5%

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

   4. Simplified 84.5%

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

   5. Taylor expanded in y around inf 80.0%

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

   if 5.79999999999999989e-136 < a < 2.6000000000000002e69

   1. Initial program 80.3%

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

   2. Taylor expanded in x around 0 55.3%

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

      1. associate-/l* 62.9%

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

   4. Simplified 62.9%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{-37}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-136}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+69}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 17: 37.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+149}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.95 \cdot 10^{-269}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{-291}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.5e+149)
   t
   (if (<= z -2.95e-269)
     x
     (if (<= z 5.9e-291) (* y (/ t a)) (if (<= z 2.1e-77) x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.5e+149) {
		tmp = t;
	} else if (z <= -2.95e-269) {
		tmp = x;
	} else if (z <= 5.9e-291) {
		tmp = y * (t / a);
	} else if (z <= 2.1e-77) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.5d+149)) then
        tmp = t
    else if (z <= (-2.95d-269)) then
        tmp = x
    else if (z <= 5.9d-291) then
        tmp = y * (t / a)
    else if (z <= 2.1d-77) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.5e+149) {
		tmp = t;
	} else if (z <= -2.95e-269) {
		tmp = x;
	} else if (z <= 5.9e-291) {
		tmp = y * (t / a);
	} else if (z <= 2.1e-77) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.5e+149:
		tmp = t
	elif z <= -2.95e-269:
		tmp = x
	elif z <= 5.9e-291:
		tmp = y * (t / a)
	elif z <= 2.1e-77:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.5e+149)
		tmp = t;
	elseif (z <= -2.95e-269)
		tmp = x;
	elseif (z <= 5.9e-291)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 2.1e-77)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.5e+149)
		tmp = t;
	elseif (z <= -2.95e-269)
		tmp = x;
	elseif (z <= 5.9e-291)
		tmp = y * (t / a);
	elseif (z <= 2.1e-77)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.5e+149], t, If[LessEqual[z, -2.95e-269], x, If[LessEqual[z, 5.9e-291], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e-77], x, t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.50000000000000011e149 or 2.10000000000000015e-77 < z

   1. Initial program 72.7%

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

   2. Taylor expanded in z around inf 48.5%

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

   if -3.50000000000000011e149 < z < -2.95e-269 or 5.89999999999999972e-291 < z < 2.10000000000000015e-77

   1. Initial program 91.7%

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

   2. Taylor expanded in a around inf 37.4%

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

   if -2.95e-269 < z < 5.89999999999999972e-291

   1. Initial program 92.3%

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

   2. Taylor expanded in x around 0 40.4%

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

      1. associate-/l* 54.8%

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

   4. Simplified 54.8%

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

   5. Taylor expanded in z around 0 50.8%

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

      1. associate-/r/ 54.7%

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

   7. Applied egg-rr 54.7%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+149}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.95 \cdot 10^{-269}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{-291}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 18: 37.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+149}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-268}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-291}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7e+149)
   t
   (if (<= z -4.5e-268)
     x
     (if (<= z 2.7e-291) (/ y (/ a t)) (if (<= z 2.1e-77) x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7e+149) {
		tmp = t;
	} else if (z <= -4.5e-268) {
		tmp = x;
	} else if (z <= 2.7e-291) {
		tmp = y / (a / t);
	} else if (z <= 2.1e-77) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-7d+149)) then
        tmp = t
    else if (z <= (-4.5d-268)) then
        tmp = x
    else if (z <= 2.7d-291) then
        tmp = y / (a / t)
    else if (z <= 2.1d-77) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7e+149) {
		tmp = t;
	} else if (z <= -4.5e-268) {
		tmp = x;
	} else if (z <= 2.7e-291) {
		tmp = y / (a / t);
	} else if (z <= 2.1e-77) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7e+149:
		tmp = t
	elif z <= -4.5e-268:
		tmp = x
	elif z <= 2.7e-291:
		tmp = y / (a / t)
	elif z <= 2.1e-77:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7e+149)
		tmp = t;
	elseif (z <= -4.5e-268)
		tmp = x;
	elseif (z <= 2.7e-291)
		tmp = Float64(y / Float64(a / t));
	elseif (z <= 2.1e-77)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7e+149)
		tmp = t;
	elseif (z <= -4.5e-268)
		tmp = x;
	elseif (z <= 2.7e-291)
		tmp = y / (a / t);
	elseif (z <= 2.1e-77)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7e+149], t, If[LessEqual[z, -4.5e-268], x, If[LessEqual[z, 2.7e-291], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e-77], x, t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.00000000000000023e149 or 2.10000000000000015e-77 < z

   1. Initial program 72.7%

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

   2. Taylor expanded in z around inf 48.5%

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

   if -7.00000000000000023e149 < z < -4.5000000000000001e-268 or 2.69999999999999992e-291 < z < 2.10000000000000015e-77

   1. Initial program 91.7%

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

   2. Taylor expanded in a around inf 37.4%

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

   if -4.5000000000000001e-268 < z < 2.69999999999999992e-291

   1. Initial program 92.3%

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

   2. Taylor expanded in x around 0 40.4%

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

      1. associate-/l* 54.8%

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

   4. Simplified 54.8%

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

   5. Taylor expanded in z around 0 36.4%

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

      1. associate-/l* 54.8%

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

   7. Simplified 54.8%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+149}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-268}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-291}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 19: 47.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+159}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.45e+159) t (if (<= z 1.12e-37) (* x (- 1.0 (/ y a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.45e+159) {
		tmp = t;
	} else if (z <= 1.12e-37) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.45d+159)) then
        tmp = t
    else if (z <= 1.12d-37) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.45e+159) {
		tmp = t;
	} else if (z <= 1.12e-37) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.45e+159:
		tmp = t
	elif z <= 1.12e-37:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.45e+159)
		tmp = t;
	elseif (z <= 1.12e-37)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.45e+159)
		tmp = t;
	elseif (z <= 1.12e-37)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.45e+159], t, If[LessEqual[z, 1.12e-37], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.45000000000000007e159 or 1.12e-37 < z

   1. Initial program 70.8%

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

   2. Taylor expanded in z around inf 51.5%

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

   if -1.45000000000000007e159 < z < 1.12e-37

   1. Initial program 91.6%

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

   2. Taylor expanded in z around 0 60.6%

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

   3. Taylor expanded in x around inf 50.2%

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

      1. *-commutative 50.2%

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

      2. mul-1-neg 50.2%

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

      3. unsub-neg 50.2%

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

   5. Simplified 50.2%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+159}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 20: 37.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+149}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.5e+149) t (if (<= z 2.05e-77) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.5e+149) {
		tmp = t;
	} else if (z <= 2.05e-77) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.5d+149)) then
        tmp = t
    else if (z <= 2.05d-77) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.5e+149) {
		tmp = t;
	} else if (z <= 2.05e-77) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.5e+149:
		tmp = t
	elif z <= 2.05e-77:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.5e+149)
		tmp = t;
	elseif (z <= 2.05e-77)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.5e+149)
		tmp = t;
	elseif (z <= 2.05e-77)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.5e+149], t, If[LessEqual[z, 2.05e-77], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -3.50000000000000011e149 or 2.04999999999999981e-77 < z

   1. Initial program 72.7%

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

   2. Taylor expanded in z around inf 48.5%

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

   if -3.50000000000000011e149 < z < 2.04999999999999981e-77

   1. Initial program 91.7%

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

   2. Taylor expanded in a around inf 35.3%

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

4. Final simplification 40.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+149}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 21: 25.6% 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 84.3%

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

2. Taylor expanded in z around inf 23.8%

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

3. Final simplification 23.8%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023238 
(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)))))