Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.0% → 95.1%

Time: 17.7s

Alternatives: 20

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ t_2 := \frac{z}{t - x}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-294} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t - \frac{y}{t_2}\right) + \frac{a}{t_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z y) (/ (- x t) (- a z))))) (t_2 (/ z (- t x))))
   (if (or (<= t_1 -5e-294) (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 + ((z - y) * ((x - t) / (a - z)));
	double t_2 = z / (t - x);
	double tmp;
	if ((t_1 <= -5e-294) || !(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(z - y) * Float64(Float64(x - t) / Float64(a - z))))
	t_2 = Float64(z / Float64(t - x))
	tmp = 0.0
	if ((t_1 <= -5e-294) || !(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[(z - y), $MachinePrecision] * N[(N[(x - t), $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, -5e-294], 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)))) < -5.0000000000000003e-294 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 89.9%

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

      1. +-commutative 89.9%

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

      2. associate-*r/ 79.5%

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

      3. *-commutative 79.5%

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

      4. associate-*r/ 96.5%

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

      5. fma-def 96.4%

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

   3. Simplified 96.4%

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

   if -5.0000000000000003e-294 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.4%

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

      1. clear-num 3.3%

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

      2. associate-/r/ 3.1%

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

   3. Applied egg-rr 3.1%

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

   4. Taylor expanded in z around inf 86.4%

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

      1. sub-neg 86.4%

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

      2. +-commutative 86.4%

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

      3. mul-1-neg 86.4%

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

      4. unsub-neg 86.4%

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

      5. associate-/l* 91.9%

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

      6. mul-1-neg 91.9%

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

      7. remove-double-neg 91.9%

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

      8. associate-/l* 99.9%

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

   6. Simplified 99.9%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -5 \cdot 10^{-294} \lor \neg \left(x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t - \frac{y}{\frac{z}{t - x}}\right) + \frac{a}{\frac{z}{t - x}}\\ \end{array} \]

Alternative 2: 90.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ t_2 := \frac{z}{t - x}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-222} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(t - \frac{y}{t_2}\right) + \frac{a}{t_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z y) (/ (- x t) (- a z))))) (t_2 (/ z (- t x))))
   (if (or (<= t_1 -1e-222) (not (<= t_1 0.0)))
     t_1
     (+ (- t (/ y t_2)) (/ a t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((x - t) / (a - z)));
	double t_2 = z / (t - x);
	double tmp;
	if ((t_1 <= -1e-222) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = (t - (y / t_2)) + (a / t_2);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((z - y) * ((x - t) / (a - z)))
    t_2 = z / (t - x)
    if ((t_1 <= (-1d-222)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = t_1
    else
        tmp = (t - (y / t_2)) + (a / t_2)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((x - t) / (a - z)));
	double t_2 = z / (t - x);
	double tmp;
	if ((t_1 <= -1e-222) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = (t - (y / t_2)) + (a / t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - y) * ((x - t) / (a - z)))
	t_2 = z / (t - x)
	tmp = 0
	if (t_1 <= -1e-222) or not (t_1 <= 0.0):
		tmp = t_1
	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(z - y) * Float64(Float64(x - t) / Float64(a - z))))
	t_2 = Float64(z / Float64(t - x))
	tmp = 0.0
	if ((t_1 <= -1e-222) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(Float64(t - Float64(y / t_2)) + Float64(a / t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - y) * ((x - t) / (a - z)));
	t_2 = z / (t - x);
	tmp = 0.0;
	if ((t_1 <= -1e-222) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = (t - (y / t_2)) + (a / t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(x - t), $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-222], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, 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)))) < -1.00000000000000005e-222 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.0%

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

   if -1.00000000000000005e-222 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 6.1%

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

      1. clear-num 5.9%

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

      2. associate-/r/ 5.8%

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

   3. Applied egg-rr 5.8%

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

   4. Taylor expanded in z around inf 85.4%

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

      1. sub-neg 85.4%

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

      2. +-commutative 85.4%

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

      3. mul-1-neg 85.4%

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

      4. unsub-neg 85.4%

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

      5. associate-/l* 90.3%

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

      6. mul-1-neg 90.3%

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

      7. remove-double-neg 90.3%

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

      8. associate-/l* 97.4%

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

   6. Simplified 97.4%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -1 \cdot 10^{-222} \lor \neg \left(x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\left(t - \frac{y}{\frac{z}{t - x}}\right) + \frac{a}{\frac{z}{t - x}}\\ \end{array} \]

Alternative 3: 88.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-222} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z y) (/ (- x t) (- a z))))))
   (if (or (<= t_1 -1e-222) (not (<= t_1 0.0)))
     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 + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-222) || !(t_1 <= 0.0)) {
		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 + ((z - y) * ((x - t) / (a - z)))
    if ((t_1 <= (-1d-222)) .or. (.not. (t_1 <= 0.0d0))) 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 + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-222) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - y) * ((x - t) / (a - z)))
	tmp = 0
	if (t_1 <= -1e-222) or not (t_1 <= 0.0):
		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(z - y) * Float64(Float64(x - t) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -1e-222) || !(t_1 <= 0.0))
		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 + ((z - y) * ((x - t) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -1e-222) || ~((t_1 <= 0.0)))
		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[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-222], N[Not[LessEqual[t$95$1, 0.0]], $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)))) < -1.00000000000000005e-222 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.0%

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

   if -1.00000000000000005e-222 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 6.1%

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

   2. Taylor expanded in z around inf 85.4%

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

      1. +-commutative 85.4%

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

      2. associate--l+ 85.4%

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

      3. associate-*r/ 85.4%

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

      4. associate-*r/ 85.4%

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

      5. div-sub 85.4%

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

      6. distribute-lft-out-- 85.4%

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

      7. mul-1-neg 85.4%

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

      8. distribute-neg-frac 85.4%

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

      9. unsub-neg 85.4%

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

      10. distribute-rgt-out-- 85.5%

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

   4. Simplified 85.5%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -1 \cdot 10^{-222} \lor \neg \left(x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]

Alternative 4: 66.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{y}{z} \cdot \left(x - t\right)\\ t_2 := x + \frac{x - t}{\frac{a}{z} + -1}\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+200}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+41}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-158}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-54}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+73}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (/ y z) (- x t))))
        (t_2 (+ x (/ (- x t) (+ (/ a z) -1.0)))))
   (if (<= z -1.9e+200)
     t_1
     (if (<= z -1.1e+41)
       (+ t (/ (* (- t x) (- a y)) z))
       (if (<= z -1.95e-40)
         t_2
         (if (<= z -7.5e-158)
           (/ y (/ (- a z) (- t x)))
           (if (<= z 4.5e-54)
             (+ x (/ (* y (- t x)) a))
             (if (<= z 4.3e+73) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((y / z) * (x - t));
	double t_2 = x + ((x - t) / ((a / z) + -1.0));
	double tmp;
	if (z <= -1.9e+200) {
		tmp = t_1;
	} else if (z <= -1.1e+41) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (z <= -1.95e-40) {
		tmp = t_2;
	} else if (z <= -7.5e-158) {
		tmp = y / ((a - z) / (t - x));
	} else if (z <= 4.5e-54) {
		tmp = x + ((y * (t - x)) / a);
	} else if (z <= 4.3e+73) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = t + ((y / z) * (x - t))
    t_2 = x + ((x - t) / ((a / z) + (-1.0d0)))
    if (z <= (-1.9d+200)) then
        tmp = t_1
    else if (z <= (-1.1d+41)) then
        tmp = t + (((t - x) * (a - y)) / z)
    else if (z <= (-1.95d-40)) then
        tmp = t_2
    else if (z <= (-7.5d-158)) then
        tmp = y / ((a - z) / (t - x))
    else if (z <= 4.5d-54) then
        tmp = x + ((y * (t - x)) / a)
    else if (z <= 4.3d+73) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((y / z) * (x - t));
	double t_2 = x + ((x - t) / ((a / z) + -1.0));
	double tmp;
	if (z <= -1.9e+200) {
		tmp = t_1;
	} else if (z <= -1.1e+41) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (z <= -1.95e-40) {
		tmp = t_2;
	} else if (z <= -7.5e-158) {
		tmp = y / ((a - z) / (t - x));
	} else if (z <= 4.5e-54) {
		tmp = x + ((y * (t - x)) / a);
	} else if (z <= 4.3e+73) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((y / z) * (x - t))
	t_2 = x + ((x - t) / ((a / z) + -1.0))
	tmp = 0
	if z <= -1.9e+200:
		tmp = t_1
	elif z <= -1.1e+41:
		tmp = t + (((t - x) * (a - y)) / z)
	elif z <= -1.95e-40:
		tmp = t_2
	elif z <= -7.5e-158:
		tmp = y / ((a - z) / (t - x))
	elif z <= 4.5e-54:
		tmp = x + ((y * (t - x)) / a)
	elif z <= 4.3e+73:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(y / z) * Float64(x - t)))
	t_2 = Float64(x + Float64(Float64(x - t) / Float64(Float64(a / z) + -1.0)))
	tmp = 0.0
	if (z <= -1.9e+200)
		tmp = t_1;
	elseif (z <= -1.1e+41)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif (z <= -1.95e-40)
		tmp = t_2;
	elseif (z <= -7.5e-158)
		tmp = Float64(y / Float64(Float64(a - z) / Float64(t - x)));
	elseif (z <= 4.5e-54)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / a));
	elseif (z <= 4.3e+73)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((y / z) * (x - t));
	t_2 = x + ((x - t) / ((a / z) + -1.0));
	tmp = 0.0;
	if (z <= -1.9e+200)
		tmp = t_1;
	elseif (z <= -1.1e+41)
		tmp = t + (((t - x) * (a - y)) / z);
	elseif (z <= -1.95e-40)
		tmp = t_2;
	elseif (z <= -7.5e-158)
		tmp = y / ((a - z) / (t - x));
	elseif (z <= 4.5e-54)
		tmp = x + ((y * (t - x)) / a);
	elseif (z <= 4.3e+73)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(x - t), $MachinePrecision] / N[(N[(a / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.9e+200], t$95$1, If[LessEqual[z, -1.1e+41], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.95e-40], t$95$2, If[LessEqual[z, -7.5e-158], N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-54], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.3e+73], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.89999999999999991e200 or 4.30000000000000013e73 < z

   1. Initial program 51.9%

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

      1. +-commutative 51.9%

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

      2. fma-def 52.0%

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

   3. Simplified 52.0%

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

   4. Taylor expanded in z around inf 57.1%

      \[\leadsto \color{blue}{\frac{{a}^{2} \cdot \left(t - x\right)}{{z}^{2}} + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \left(t + \left(\frac{a \cdot \left(t - x\right)}{z} + -1 \cdot \frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-/l* 61.6%

         \[\leadsto \color{blue}{\frac{{a}^{2}}{\frac{{z}^{2}}{t - x}}} + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \left(t + \left(\frac{a \cdot \left(t - x\right)}{z} + -1 \cdot \frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)\right)\right) \]

      2. unpow2 61.6%

         \[\leadsto \frac{\color{blue}{a \cdot a}}{\frac{{z}^{2}}{t - x}} + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \left(t + \left(\frac{a \cdot \left(t - x\right)}{z} + -1 \cdot \frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)\right)\right) \]

      3. unpow2 61.6%

         \[\leadsto \frac{a \cdot a}{\frac{\color{blue}{z \cdot z}}{t - x}} + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \left(t + \left(\frac{a \cdot \left(t - x\right)}{z} + -1 \cdot \frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)\right)\right) \]

      4. fma-def 61.6%

         \[\leadsto \frac{a \cdot a}{\frac{z \cdot z}{t - x}} + \color{blue}{\mathsf{fma}\left(-1, \frac{y \cdot \left(t - x\right)}{z}, t + \left(\frac{a \cdot \left(t - x\right)}{z} + -1 \cdot \frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)\right)} \]

      5. associate-/l* 70.2%

         \[\leadsto \frac{a \cdot a}{\frac{z \cdot z}{t - x}} + \mathsf{fma}\left(-1, \color{blue}{\frac{y}{\frac{z}{t - x}}}, t + \left(\frac{a \cdot \left(t - x\right)}{z} + -1 \cdot \frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)\right) \]

      6. associate-/l* 69.5%

         \[\leadsto \frac{a \cdot a}{\frac{z \cdot z}{t - x}} + \mathsf{fma}\left(-1, \frac{y}{\frac{z}{t - x}}, t + \left(\color{blue}{\frac{a}{\frac{z}{t - x}}} + -1 \cdot \frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)\right) \]

      7. mul-1-neg 69.5%

         \[\leadsto \frac{a \cdot a}{\frac{z \cdot z}{t - x}} + \mathsf{fma}\left(-1, \frac{y}{\frac{z}{t - x}}, t + \left(\frac{a}{\frac{z}{t - x}} + \color{blue}{\left(-\frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)}\right)\right) \]

      8. associate-*r* 69.4%

         \[\leadsto \frac{a \cdot a}{\frac{z \cdot z}{t - x}} + \mathsf{fma}\left(-1, \frac{y}{\frac{z}{t - x}}, t + \left(\frac{a}{\frac{z}{t - x}} + \left(-\frac{\color{blue}{\left(y \cdot a\right) \cdot \left(t - x\right)}}{{z}^{2}}\right)\right)\right) \]

      9. unpow2 69.4%

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

   6. Simplified 69.4%

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

   7. Taylor expanded in a around 0 64.6%

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

      1. +-commutative 64.6%

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

      2. mul-1-neg 64.6%

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

      3. unsub-neg 64.6%

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

      4. associate-*l/ 83.2%

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

      5. *-commutative 83.2%

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

   9. Simplified 83.2%

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

   if -1.89999999999999991e200 < z < -1.09999999999999995e41

   1. Initial program 65.5%

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

   2. Taylor expanded in z around inf 65.1%

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

      1. +-commutative 65.1%

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

      2. associate--l+ 65.1%

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

      3. associate-*r/ 65.1%

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

      4. associate-*r/ 65.1%

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

      5. div-sub 65.1%

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

      6. distribute-lft-out-- 65.1%

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

      7. mul-1-neg 65.1%

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

      8. distribute-neg-frac 65.1%

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

      9. unsub-neg 65.1%

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

      10. distribute-rgt-out-- 67.7%

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

   4. Simplified 67.7%

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

   if -1.09999999999999995e41 < z < -1.9499999999999999e-40 or 4.4999999999999998e-54 < z < 4.30000000000000013e73

   1. Initial program 88.2%

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

   2. Taylor expanded in y around 0 64.8%

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

      1. mul-1-neg 64.8%

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

      2. unsub-neg 64.8%

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

      3. *-commutative 64.8%

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

      4. associate-/l* 72.6%

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

      5. div-sub 72.6%

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

      6. *-inverses 72.6%

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

   4. Simplified 72.6%

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

   if -1.9499999999999999e-40 < z < -7.5e-158

   1. Initial program 95.7%

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

   2. Taylor expanded in y around inf 67.4%

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

      1. div-sub 67.8%

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

      2. *-commutative 67.8%

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

      3. associate-*r/ 63.4%

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

      4. associate-/l* 67.7%

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

   4. Simplified 67.7%

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

   if -7.5e-158 < z < 4.4999999999999998e-54

   1. Initial program 93.7%

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

   2. Taylor expanded in z around 0 84.4%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+200}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+41}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-40}:\\ \;\;\;\;x + \frac{x - t}{\frac{a}{z} + -1}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-158}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-54}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+73}:\\ \;\;\;\;x + \frac{x - t}{\frac{a}{z} + -1}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \end{array} \]

Alternative 5: 37.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-t}{\frac{a - z}{z}}\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+247}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq -0.00172:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-289}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-86}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+205}:\\ \;\;\;\;\frac{-y}{\frac{a - z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t) (/ (- a z) z))))
   (if (<= y -8.2e+247)
     (* (/ y z) (- x t))
     (if (<= y -0.00172)
       (* y (/ t (- a z)))
       (if (<= y -6.5e-289)
         t_1
         (if (<= y 8.5e-86)
           x
           (if (<= y 2e+94)
             t_1
             (if (<= y 7e+205)
               (/ (- y) (/ (- a z) x))
               (* t (/ (- y z) a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -t / ((a - z) / z);
	double tmp;
	if (y <= -8.2e+247) {
		tmp = (y / z) * (x - t);
	} else if (y <= -0.00172) {
		tmp = y * (t / (a - z));
	} else if (y <= -6.5e-289) {
		tmp = t_1;
	} else if (y <= 8.5e-86) {
		tmp = x;
	} else if (y <= 2e+94) {
		tmp = t_1;
	} else if (y <= 7e+205) {
		tmp = -y / ((a - z) / x);
	} else {
		tmp = t * ((y - z) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -t / ((a - z) / z)
    if (y <= (-8.2d+247)) then
        tmp = (y / z) * (x - t)
    else if (y <= (-0.00172d0)) then
        tmp = y * (t / (a - z))
    else if (y <= (-6.5d-289)) then
        tmp = t_1
    else if (y <= 8.5d-86) then
        tmp = x
    else if (y <= 2d+94) then
        tmp = t_1
    else if (y <= 7d+205) then
        tmp = -y / ((a - z) / x)
    else
        tmp = t * ((y - z) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -t / ((a - z) / z);
	double tmp;
	if (y <= -8.2e+247) {
		tmp = (y / z) * (x - t);
	} else if (y <= -0.00172) {
		tmp = y * (t / (a - z));
	} else if (y <= -6.5e-289) {
		tmp = t_1;
	} else if (y <= 8.5e-86) {
		tmp = x;
	} else if (y <= 2e+94) {
		tmp = t_1;
	} else if (y <= 7e+205) {
		tmp = -y / ((a - z) / x);
	} else {
		tmp = t * ((y - z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -t / ((a - z) / z)
	tmp = 0
	if y <= -8.2e+247:
		tmp = (y / z) * (x - t)
	elif y <= -0.00172:
		tmp = y * (t / (a - z))
	elif y <= -6.5e-289:
		tmp = t_1
	elif y <= 8.5e-86:
		tmp = x
	elif y <= 2e+94:
		tmp = t_1
	elif y <= 7e+205:
		tmp = -y / ((a - z) / x)
	else:
		tmp = t * ((y - z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-t) / Float64(Float64(a - z) / z))
	tmp = 0.0
	if (y <= -8.2e+247)
		tmp = Float64(Float64(y / z) * Float64(x - t));
	elseif (y <= -0.00172)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	elseif (y <= -6.5e-289)
		tmp = t_1;
	elseif (y <= 8.5e-86)
		tmp = x;
	elseif (y <= 2e+94)
		tmp = t_1;
	elseif (y <= 7e+205)
		tmp = Float64(Float64(-y) / Float64(Float64(a - z) / x));
	else
		tmp = Float64(t * Float64(Float64(y - z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -t / ((a - z) / z);
	tmp = 0.0;
	if (y <= -8.2e+247)
		tmp = (y / z) * (x - t);
	elseif (y <= -0.00172)
		tmp = y * (t / (a - z));
	elseif (y <= -6.5e-289)
		tmp = t_1;
	elseif (y <= 8.5e-86)
		tmp = x;
	elseif (y <= 2e+94)
		tmp = t_1;
	elseif (y <= 7e+205)
		tmp = -y / ((a - z) / x);
	else
		tmp = t * ((y - z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-t) / N[(N[(a - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.2e+247], N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -0.00172], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.5e-289], t$95$1, If[LessEqual[y, 8.5e-86], x, If[LessEqual[y, 2e+94], t$95$1, If[LessEqual[y, 7e+205], N[((-y) / N[(N[(a - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -8.2000000000000004e247

   1. Initial program 85.1%

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

   2. Taylor expanded in y around inf 84.0%

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

      1. div-sub 84.0%

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

      2. *-commutative 84.0%

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

      3. associate-*r/ 92.1%

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

      4. associate-/l* 84.0%

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

   4. Simplified 84.0%

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

   5. Taylor expanded in a around 0 83.7%

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

      1. mul-1-neg 83.7%

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

      2. associate-*l/ 91.7%

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

      3. distribute-rgt-neg-in 91.7%

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

   7. Simplified 91.7%

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

   if -8.2000000000000004e247 < y < -0.00171999999999999996

   1. Initial program 97.6%

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

   2. Taylor expanded in y around inf 61.2%

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

      1. div-sub 63.2%

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

      2. *-commutative 63.2%

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

      3. associate-*r/ 55.8%

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

      4. associate-/l* 63.1%

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

   4. Simplified 63.1%

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

   5. Taylor expanded in t around inf 42.8%

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

      1. associate-/l* 48.3%

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

   7. Simplified 48.3%

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

   8. Taylor expanded in y around 0 42.8%

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

      1. associate-*r/ 48.3%

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

   10. Simplified 48.3%

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

   if -0.00171999999999999996 < y < -6.49999999999999974e-289 or 8.499999999999999e-86 < y < 2e94

   1. Initial program 70.7%

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

   2. Taylor expanded in t around inf 61.1%

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

      1. div-sub 61.1%

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

   4. Simplified 61.1%

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

   5. Taylor expanded in y around 0 35.2%

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

      1. mul-1-neg 35.2%

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

      2. associate-/l* 47.1%

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

      3. distribute-neg-frac 47.1%

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

   7. Simplified 47.1%

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

   if -6.49999999999999974e-289 < y < 8.499999999999999e-86

   1. Initial program 64.1%

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

   2. Taylor expanded in a around inf 52.6%

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

   if 2e94 < y < 6.9999999999999996e205

   1. Initial program 79.0%

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

   2. Taylor expanded in y around inf 78.1%

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

      1. div-sub 78.1%

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

      2. *-commutative 78.1%

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

      3. associate-*r/ 58.3%

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

      4. associate-/l* 78.0%

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

   4. Simplified 78.0%

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

   5. Taylor expanded in t around 0 43.8%

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

      1. mul-1-neg 43.8%

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

      2. associate-/l* 55.3%

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

      3. distribute-neg-frac 55.3%

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

   7. Simplified 55.3%

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

   if 6.9999999999999996e205 < y

   1. Initial program 92.3%

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

   2. Taylor expanded in t around inf 74.1%

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

      1. div-sub 74.1%

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

   4. Simplified 74.1%

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

   5. Taylor expanded in a around inf 74.8%

      \[\leadsto t \cdot \color{blue}{\frac{y - z}{a}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+247}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq -0.00172:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-289}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-86}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+94}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+205}:\\ \;\;\;\;\frac{-y}{\frac{a - z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \end{array} \]

Alternative 6: 33.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t}{a - z}\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+249}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq -6.3 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-289}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-43}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+205}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ t (- a z)))))
   (if (<= y -2.7e+249)
     (* x (/ y z))
     (if (<= y -6.3e-7)
       t_1
       (if (<= y -3.3e-289)
         t
         (if (<= y 9.8e-43)
           x
           (if (<= y 2.6e+164)
             t_1
             (if (<= y 2.5e+205) (/ y (/ z x)) (* t (/ (- y z) a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / (a - z));
	double tmp;
	if (y <= -2.7e+249) {
		tmp = x * (y / z);
	} else if (y <= -6.3e-7) {
		tmp = t_1;
	} else if (y <= -3.3e-289) {
		tmp = t;
	} else if (y <= 9.8e-43) {
		tmp = x;
	} else if (y <= 2.6e+164) {
		tmp = t_1;
	} else if (y <= 2.5e+205) {
		tmp = y / (z / x);
	} else {
		tmp = t * ((y - z) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (t / (a - z))
    if (y <= (-2.7d+249)) then
        tmp = x * (y / z)
    else if (y <= (-6.3d-7)) then
        tmp = t_1
    else if (y <= (-3.3d-289)) then
        tmp = t
    else if (y <= 9.8d-43) then
        tmp = x
    else if (y <= 2.6d+164) then
        tmp = t_1
    else if (y <= 2.5d+205) then
        tmp = y / (z / x)
    else
        tmp = t * ((y - z) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / (a - z));
	double tmp;
	if (y <= -2.7e+249) {
		tmp = x * (y / z);
	} else if (y <= -6.3e-7) {
		tmp = t_1;
	} else if (y <= -3.3e-289) {
		tmp = t;
	} else if (y <= 9.8e-43) {
		tmp = x;
	} else if (y <= 2.6e+164) {
		tmp = t_1;
	} else if (y <= 2.5e+205) {
		tmp = y / (z / x);
	} else {
		tmp = t * ((y - z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (t / (a - z))
	tmp = 0
	if y <= -2.7e+249:
		tmp = x * (y / z)
	elif y <= -6.3e-7:
		tmp = t_1
	elif y <= -3.3e-289:
		tmp = t
	elif y <= 9.8e-43:
		tmp = x
	elif y <= 2.6e+164:
		tmp = t_1
	elif y <= 2.5e+205:
		tmp = y / (z / x)
	else:
		tmp = t * ((y - z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(t / Float64(a - z)))
	tmp = 0.0
	if (y <= -2.7e+249)
		tmp = Float64(x * Float64(y / z));
	elseif (y <= -6.3e-7)
		tmp = t_1;
	elseif (y <= -3.3e-289)
		tmp = t;
	elseif (y <= 9.8e-43)
		tmp = x;
	elseif (y <= 2.6e+164)
		tmp = t_1;
	elseif (y <= 2.5e+205)
		tmp = Float64(y / Float64(z / x));
	else
		tmp = Float64(t * Float64(Float64(y - z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (t / (a - z));
	tmp = 0.0;
	if (y <= -2.7e+249)
		tmp = x * (y / z);
	elseif (y <= -6.3e-7)
		tmp = t_1;
	elseif (y <= -3.3e-289)
		tmp = t;
	elseif (y <= 9.8e-43)
		tmp = x;
	elseif (y <= 2.6e+164)
		tmp = t_1;
	elseif (y <= 2.5e+205)
		tmp = y / (z / x);
	else
		tmp = t * ((y - z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7e+249], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.3e-7], t$95$1, If[LessEqual[y, -3.3e-289], t, If[LessEqual[y, 9.8e-43], x, If[LessEqual[y, 2.6e+164], t$95$1, If[LessEqual[y, 2.5e+205], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -2.70000000000000018e249

   1. Initial program 85.1%

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

   2. Taylor expanded in a around 0 76.8%

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

      1. associate-*r/ 76.8%

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

      2. neg-mul-1 76.8%

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

   4. Simplified 76.8%

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

   5. Taylor expanded in x around inf 75.4%

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

      1. associate-/l* 67.3%

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

   7. Simplified 67.3%

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

      1. associate-/r/ 83.3%

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

   9. Applied egg-rr 83.3%

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

   if -2.70000000000000018e249 < y < -6.30000000000000003e-7 or 9.79999999999999976e-43 < y < 2.5999999999999999e164

   1. Initial program 86.0%

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

   2. Taylor expanded in y around inf 55.2%

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

      1. div-sub 56.3%

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

      2. *-commutative 56.3%

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

      3. associate-*r/ 48.9%

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

      4. associate-/l* 56.3%

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

   4. Simplified 56.3%

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

   5. Taylor expanded in t around inf 36.7%

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

      1. associate-/l* 41.9%

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

   7. Simplified 41.9%

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

   8. Taylor expanded in y around 0 36.7%

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

      1. associate-*r/ 41.9%

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

   10. Simplified 41.9%

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

   if -6.30000000000000003e-7 < y < -3.29999999999999997e-289

   1. Initial program 74.1%

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

   2. Taylor expanded in z around inf 46.7%

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

   if -3.29999999999999997e-289 < y < 9.79999999999999976e-43

   1. Initial program 64.8%

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

   2. Taylor expanded in a around inf 47.0%

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

   if 2.5999999999999999e164 < y < 2.5000000000000001e205

   1. Initial program 73.4%

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

   2. Taylor expanded in a around 0 28.2%

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

      1. associate-*r/ 28.2%

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

      2. neg-mul-1 28.2%

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

   4. Simplified 28.2%

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

   5. Taylor expanded in x around inf 37.3%

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

      1. associate-/l* 52.9%

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

   7. Simplified 52.9%

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

   if 2.5000000000000001e205 < y

   1. Initial program 92.3%

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

   2. Taylor expanded in t around inf 74.1%

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

      1. div-sub 74.1%

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

   4. Simplified 74.1%

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

   5. Taylor expanded in a around inf 74.8%

      \[\leadsto t \cdot \color{blue}{\frac{y - z}{a}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+249}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq -6.3 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-289}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-43}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+164}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+205}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \end{array} \]

Alternative 7: 35.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+248}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-5}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-289}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+91}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+205}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -8e+248)
   (* x (/ y z))
   (if (<= y -1.3e-5)
     (* y (/ t (- a z)))
     (if (<= y -1.9e-289)
       t
       (if (<= y 1.8e-90)
         x
         (if (<= y 4.3e+91)
           t
           (if (<= y 3.2e+205) (* y (/ (- x t) z)) (* t (/ (- y z) a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -8e+248) {
		tmp = x * (y / z);
	} else if (y <= -1.3e-5) {
		tmp = y * (t / (a - z));
	} else if (y <= -1.9e-289) {
		tmp = t;
	} else if (y <= 1.8e-90) {
		tmp = x;
	} else if (y <= 4.3e+91) {
		tmp = t;
	} else if (y <= 3.2e+205) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t * ((y - z) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-8d+248)) then
        tmp = x * (y / z)
    else if (y <= (-1.3d-5)) then
        tmp = y * (t / (a - z))
    else if (y <= (-1.9d-289)) then
        tmp = t
    else if (y <= 1.8d-90) then
        tmp = x
    else if (y <= 4.3d+91) then
        tmp = t
    else if (y <= 3.2d+205) then
        tmp = y * ((x - t) / z)
    else
        tmp = t * ((y - z) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -8e+248) {
		tmp = x * (y / z);
	} else if (y <= -1.3e-5) {
		tmp = y * (t / (a - z));
	} else if (y <= -1.9e-289) {
		tmp = t;
	} else if (y <= 1.8e-90) {
		tmp = x;
	} else if (y <= 4.3e+91) {
		tmp = t;
	} else if (y <= 3.2e+205) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t * ((y - z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -8e+248:
		tmp = x * (y / z)
	elif y <= -1.3e-5:
		tmp = y * (t / (a - z))
	elif y <= -1.9e-289:
		tmp = t
	elif y <= 1.8e-90:
		tmp = x
	elif y <= 4.3e+91:
		tmp = t
	elif y <= 3.2e+205:
		tmp = y * ((x - t) / z)
	else:
		tmp = t * ((y - z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -8e+248)
		tmp = Float64(x * Float64(y / z));
	elseif (y <= -1.3e-5)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	elseif (y <= -1.9e-289)
		tmp = t;
	elseif (y <= 1.8e-90)
		tmp = x;
	elseif (y <= 4.3e+91)
		tmp = t;
	elseif (y <= 3.2e+205)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = Float64(t * Float64(Float64(y - z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -8e+248)
		tmp = x * (y / z);
	elseif (y <= -1.3e-5)
		tmp = y * (t / (a - z));
	elseif (y <= -1.9e-289)
		tmp = t;
	elseif (y <= 1.8e-90)
		tmp = x;
	elseif (y <= 4.3e+91)
		tmp = t;
	elseif (y <= 3.2e+205)
		tmp = y * ((x - t) / z);
	else
		tmp = t * ((y - z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -8e+248], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.3e-5], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.9e-289], t, If[LessEqual[y, 1.8e-90], x, If[LessEqual[y, 4.3e+91], t, If[LessEqual[y, 3.2e+205], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -8.00000000000000036e248

   1. Initial program 85.1%

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

   2. Taylor expanded in a around 0 76.8%

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

      1. associate-*r/ 76.8%

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

      2. neg-mul-1 76.8%

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

   4. Simplified 76.8%

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

   5. Taylor expanded in x around inf 75.4%

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

      1. associate-/l* 67.3%

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

   7. Simplified 67.3%

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

      1. associate-/r/ 83.3%

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

   9. Applied egg-rr 83.3%

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

   if -8.00000000000000036e248 < y < -1.29999999999999992e-5

   1. Initial program 97.6%

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

   2. Taylor expanded in y around inf 61.2%

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

      1. div-sub 63.2%

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

      2. *-commutative 63.2%

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

      3. associate-*r/ 55.8%

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

      4. associate-/l* 63.1%

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

   4. Simplified 63.1%

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

   5. Taylor expanded in t around inf 42.8%

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

      1. associate-/l* 48.3%

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

   7. Simplified 48.3%

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

   8. Taylor expanded in y around 0 42.8%

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

      1. associate-*r/ 48.3%

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

   10. Simplified 48.3%

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

   if -1.29999999999999992e-5 < y < -1.90000000000000005e-289 or 1.7999999999999999e-90 < y < 4.3000000000000001e91

   1. Initial program 70.7%

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

   2. Taylor expanded in z around inf 42.0%

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

   if -1.90000000000000005e-289 < y < 1.7999999999999999e-90

   1. Initial program 64.1%

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

   2. Taylor expanded in a around inf 52.6%

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

   if 4.3000000000000001e91 < y < 3.19999999999999996e205

   1. Initial program 79.0%

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

   2. Taylor expanded in a around 0 36.4%

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

      1. associate-*r/ 36.4%

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

      2. neg-mul-1 36.4%

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

   4. Simplified 36.4%

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

   5. Taylor expanded in y around inf 52.1%

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

      1. div-sub 52.1%

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

   7. Simplified 52.1%

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

   if 3.19999999999999996e205 < y

   1. Initial program 92.3%

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

   2. Taylor expanded in t around inf 74.1%

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

      1. div-sub 74.1%

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

   4. Simplified 74.1%

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

   5. Taylor expanded in a around inf 74.8%

      \[\leadsto t \cdot \color{blue}{\frac{y - z}{a}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+248}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-5}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-289}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+91}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+205}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \end{array} \]

Alternative 8: 36.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+242}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq -0.00172:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-289}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+88}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+205}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.05e+242)
   (* (/ y z) (- x t))
   (if (<= y -0.00172)
     (* y (/ t (- a z)))
     (if (<= y -3.9e-289)
       t
       (if (<= y 3e-90)
         x
         (if (<= y 3.2e+88)
           t
           (if (<= y 7.8e+205) (* y (/ (- x t) z)) (* t (/ (- y z) a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.05e+242) {
		tmp = (y / z) * (x - t);
	} else if (y <= -0.00172) {
		tmp = y * (t / (a - z));
	} else if (y <= -3.9e-289) {
		tmp = t;
	} else if (y <= 3e-90) {
		tmp = x;
	} else if (y <= 3.2e+88) {
		tmp = t;
	} else if (y <= 7.8e+205) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t * ((y - z) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.05d+242)) then
        tmp = (y / z) * (x - t)
    else if (y <= (-0.00172d0)) then
        tmp = y * (t / (a - z))
    else if (y <= (-3.9d-289)) then
        tmp = t
    else if (y <= 3d-90) then
        tmp = x
    else if (y <= 3.2d+88) then
        tmp = t
    else if (y <= 7.8d+205) then
        tmp = y * ((x - t) / z)
    else
        tmp = t * ((y - z) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.05e+242) {
		tmp = (y / z) * (x - t);
	} else if (y <= -0.00172) {
		tmp = y * (t / (a - z));
	} else if (y <= -3.9e-289) {
		tmp = t;
	} else if (y <= 3e-90) {
		tmp = x;
	} else if (y <= 3.2e+88) {
		tmp = t;
	} else if (y <= 7.8e+205) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t * ((y - z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.05e+242:
		tmp = (y / z) * (x - t)
	elif y <= -0.00172:
		tmp = y * (t / (a - z))
	elif y <= -3.9e-289:
		tmp = t
	elif y <= 3e-90:
		tmp = x
	elif y <= 3.2e+88:
		tmp = t
	elif y <= 7.8e+205:
		tmp = y * ((x - t) / z)
	else:
		tmp = t * ((y - z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.05e+242)
		tmp = Float64(Float64(y / z) * Float64(x - t));
	elseif (y <= -0.00172)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	elseif (y <= -3.9e-289)
		tmp = t;
	elseif (y <= 3e-90)
		tmp = x;
	elseif (y <= 3.2e+88)
		tmp = t;
	elseif (y <= 7.8e+205)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = Float64(t * Float64(Float64(y - z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.05e+242)
		tmp = (y / z) * (x - t);
	elseif (y <= -0.00172)
		tmp = y * (t / (a - z));
	elseif (y <= -3.9e-289)
		tmp = t;
	elseif (y <= 3e-90)
		tmp = x;
	elseif (y <= 3.2e+88)
		tmp = t;
	elseif (y <= 7.8e+205)
		tmp = y * ((x - t) / z);
	else
		tmp = t * ((y - z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.05e+242], N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -0.00172], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.9e-289], t, If[LessEqual[y, 3e-90], x, If[LessEqual[y, 3.2e+88], t, If[LessEqual[y, 7.8e+205], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.05e242

   1. Initial program 85.1%

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

   2. Taylor expanded in y around inf 84.0%

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

      1. div-sub 84.0%

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

      2. *-commutative 84.0%

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

      3. associate-*r/ 92.1%

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

      4. associate-/l* 84.0%

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

   4. Simplified 84.0%

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

   5. Taylor expanded in a around 0 83.7%

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

      1. mul-1-neg 83.7%

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

      2. associate-*l/ 91.7%

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

      3. distribute-rgt-neg-in 91.7%

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

   7. Simplified 91.7%

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

   if -1.05e242 < y < -0.00171999999999999996

   1. Initial program 97.6%

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

   2. Taylor expanded in y around inf 61.2%

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

      1. div-sub 63.2%

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

      2. *-commutative 63.2%

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

      3. associate-*r/ 55.8%

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

      4. associate-/l* 63.1%

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

   4. Simplified 63.1%

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

   5. Taylor expanded in t around inf 42.8%

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

      1. associate-/l* 48.3%

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

   7. Simplified 48.3%

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

   8. Taylor expanded in y around 0 42.8%

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

      1. associate-*r/ 48.3%

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

   10. Simplified 48.3%

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

   if -0.00171999999999999996 < y < -3.8999999999999998e-289 or 3.0000000000000002e-90 < y < 3.1999999999999999e88

   1. Initial program 70.7%

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

   2. Taylor expanded in z around inf 42.0%

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

   if -3.8999999999999998e-289 < y < 3.0000000000000002e-90

   1. Initial program 64.1%

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

   2. Taylor expanded in a around inf 52.6%

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

   if 3.1999999999999999e88 < y < 7.7999999999999997e205

   1. Initial program 79.0%

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

   2. Taylor expanded in a around 0 36.4%

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

      1. associate-*r/ 36.4%

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

      2. neg-mul-1 36.4%

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

   4. Simplified 36.4%

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

   5. Taylor expanded in y around inf 52.1%

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

      1. div-sub 52.1%

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

   7. Simplified 52.1%

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

   if 7.7999999999999997e205 < y

   1. Initial program 92.3%

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

   2. Taylor expanded in t around inf 74.1%

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

      1. div-sub 74.1%

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

   4. Simplified 74.1%

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

   5. Taylor expanded in a around inf 74.8%

      \[\leadsto t \cdot \color{blue}{\frac{y - z}{a}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+242}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq -0.00172:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-289}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+88}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+205}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \end{array} \]

Alternative 9: 38.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-t}{\frac{a - z}{z}}\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{+249}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq -0.0067:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-289}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-93}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+206}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t) (/ (- a z) z))))
   (if (<= y -1.25e+249)
     (* (/ y z) (- x t))
     (if (<= y -0.0067)
       (* y (/ t (- a z)))
       (if (<= y -1.95e-289)
         t_1
         (if (<= y 9.5e-93)
           x
           (if (<= y 6.8e+89)
             t_1
             (if (<= y 1.02e+206)
               (* y (/ (- x t) z))
               (* t (/ (- y z) a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -t / ((a - z) / z);
	double tmp;
	if (y <= -1.25e+249) {
		tmp = (y / z) * (x - t);
	} else if (y <= -0.0067) {
		tmp = y * (t / (a - z));
	} else if (y <= -1.95e-289) {
		tmp = t_1;
	} else if (y <= 9.5e-93) {
		tmp = x;
	} else if (y <= 6.8e+89) {
		tmp = t_1;
	} else if (y <= 1.02e+206) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t * ((y - z) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -t / ((a - z) / z)
    if (y <= (-1.25d+249)) then
        tmp = (y / z) * (x - t)
    else if (y <= (-0.0067d0)) then
        tmp = y * (t / (a - z))
    else if (y <= (-1.95d-289)) then
        tmp = t_1
    else if (y <= 9.5d-93) then
        tmp = x
    else if (y <= 6.8d+89) then
        tmp = t_1
    else if (y <= 1.02d+206) then
        tmp = y * ((x - t) / z)
    else
        tmp = t * ((y - z) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -t / ((a - z) / z);
	double tmp;
	if (y <= -1.25e+249) {
		tmp = (y / z) * (x - t);
	} else if (y <= -0.0067) {
		tmp = y * (t / (a - z));
	} else if (y <= -1.95e-289) {
		tmp = t_1;
	} else if (y <= 9.5e-93) {
		tmp = x;
	} else if (y <= 6.8e+89) {
		tmp = t_1;
	} else if (y <= 1.02e+206) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t * ((y - z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -t / ((a - z) / z)
	tmp = 0
	if y <= -1.25e+249:
		tmp = (y / z) * (x - t)
	elif y <= -0.0067:
		tmp = y * (t / (a - z))
	elif y <= -1.95e-289:
		tmp = t_1
	elif y <= 9.5e-93:
		tmp = x
	elif y <= 6.8e+89:
		tmp = t_1
	elif y <= 1.02e+206:
		tmp = y * ((x - t) / z)
	else:
		tmp = t * ((y - z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-t) / Float64(Float64(a - z) / z))
	tmp = 0.0
	if (y <= -1.25e+249)
		tmp = Float64(Float64(y / z) * Float64(x - t));
	elseif (y <= -0.0067)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	elseif (y <= -1.95e-289)
		tmp = t_1;
	elseif (y <= 9.5e-93)
		tmp = x;
	elseif (y <= 6.8e+89)
		tmp = t_1;
	elseif (y <= 1.02e+206)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = Float64(t * Float64(Float64(y - z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -t / ((a - z) / z);
	tmp = 0.0;
	if (y <= -1.25e+249)
		tmp = (y / z) * (x - t);
	elseif (y <= -0.0067)
		tmp = y * (t / (a - z));
	elseif (y <= -1.95e-289)
		tmp = t_1;
	elseif (y <= 9.5e-93)
		tmp = x;
	elseif (y <= 6.8e+89)
		tmp = t_1;
	elseif (y <= 1.02e+206)
		tmp = y * ((x - t) / z);
	else
		tmp = t * ((y - z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-t) / N[(N[(a - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.25e+249], N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -0.0067], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.95e-289], t$95$1, If[LessEqual[y, 9.5e-93], x, If[LessEqual[y, 6.8e+89], t$95$1, If[LessEqual[y, 1.02e+206], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.2499999999999999e249

   1. Initial program 85.1%

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

   2. Taylor expanded in y around inf 84.0%

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

      1. div-sub 84.0%

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

      2. *-commutative 84.0%

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

      3. associate-*r/ 92.1%

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

      4. associate-/l* 84.0%

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

   4. Simplified 84.0%

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

   5. Taylor expanded in a around 0 83.7%

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

      1. mul-1-neg 83.7%

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

      2. associate-*l/ 91.7%

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

      3. distribute-rgt-neg-in 91.7%

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

   7. Simplified 91.7%

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

   if -1.2499999999999999e249 < y < -0.00670000000000000023

   1. Initial program 97.6%

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

   2. Taylor expanded in y around inf 61.2%

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

      1. div-sub 63.2%

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

      2. *-commutative 63.2%

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

      3. associate-*r/ 55.8%

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

      4. associate-/l* 63.1%

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

   4. Simplified 63.1%

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

   5. Taylor expanded in t around inf 42.8%

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

      1. associate-/l* 48.3%

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

   7. Simplified 48.3%

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

   8. Taylor expanded in y around 0 42.8%

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

      1. associate-*r/ 48.3%

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

   10. Simplified 48.3%

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

   if -0.00670000000000000023 < y < -1.9499999999999999e-289 or 9.5000000000000001e-93 < y < 6.8000000000000004e89

   1. Initial program 70.7%

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

   2. Taylor expanded in t around inf 61.1%

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

      1. div-sub 61.1%

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

   4. Simplified 61.1%

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

   5. Taylor expanded in y around 0 35.2%

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

      1. mul-1-neg 35.2%

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

      2. associate-/l* 47.1%

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

      3. distribute-neg-frac 47.1%

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

   7. Simplified 47.1%

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

   if -1.9499999999999999e-289 < y < 9.5000000000000001e-93

   1. Initial program 64.1%

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

   2. Taylor expanded in a around inf 52.6%

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

   if 6.8000000000000004e89 < y < 1.02e206

   1. Initial program 79.0%

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

   2. Taylor expanded in a around 0 36.4%

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

      1. associate-*r/ 36.4%

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

      2. neg-mul-1 36.4%

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

   4. Simplified 36.4%

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

   5. Taylor expanded in y around inf 52.1%

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

      1. div-sub 52.1%

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

   7. Simplified 52.1%

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

   if 1.02e206 < y

   1. Initial program 92.3%

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

   2. Taylor expanded in t around inf 74.1%

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

      1. div-sub 74.1%

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

   4. Simplified 74.1%

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

   5. Taylor expanded in a around inf 74.8%

      \[\leadsto t \cdot \color{blue}{\frac{y - z}{a}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+249}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq -0.0067:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-289}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-93}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+89}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+206}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \end{array} \]

Alternative 10: 64.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+182}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{+95}:\\ \;\;\;\;t - \frac{a \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;z \leq -31000000 \lor \neg \left(z \leq 5.1 \cdot 10^{-24}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -1.9e+182)
     t_1
     (if (<= z -8.8e+95)
       (- t (/ (* a (- x t)) z))
       (if (or (<= z -31000000.0) (not (<= z 5.1e-24)))
         t_1
         (+ x (/ (* y (- t x)) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.9e+182) {
		tmp = t_1;
	} else if (z <= -8.8e+95) {
		tmp = t - ((a * (x - t)) / z);
	} else if ((z <= -31000000.0) || !(z <= 5.1e-24)) {
		tmp = t_1;
	} else {
		tmp = x + ((y * (t - x)) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (z <= (-1.9d+182)) then
        tmp = t_1
    else if (z <= (-8.8d+95)) then
        tmp = t - ((a * (x - t)) / z)
    else if ((z <= (-31000000.0d0)) .or. (.not. (z <= 5.1d-24))) then
        tmp = t_1
    else
        tmp = x + ((y * (t - x)) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.9e+182) {
		tmp = t_1;
	} else if (z <= -8.8e+95) {
		tmp = t - ((a * (x - t)) / z);
	} else if ((z <= -31000000.0) || !(z <= 5.1e-24)) {
		tmp = t_1;
	} else {
		tmp = x + ((y * (t - x)) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -1.9e+182:
		tmp = t_1
	elif z <= -8.8e+95:
		tmp = t - ((a * (x - t)) / z)
	elif (z <= -31000000.0) or not (z <= 5.1e-24):
		tmp = t_1
	else:
		tmp = x + ((y * (t - x)) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -1.9e+182)
		tmp = t_1;
	elseif (z <= -8.8e+95)
		tmp = Float64(t - Float64(Float64(a * Float64(x - t)) / z));
	elseif ((z <= -31000000.0) || !(z <= 5.1e-24))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -1.9e+182)
		tmp = t_1;
	elseif (z <= -8.8e+95)
		tmp = t - ((a * (x - t)) / z);
	elseif ((z <= -31000000.0) || ~((z <= 5.1e-24)))
		tmp = t_1;
	else
		tmp = x + ((y * (t - x)) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.9e+182], t$95$1, If[LessEqual[z, -8.8e+95], N[(t - N[(N[(a * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -31000000.0], N[Not[LessEqual[z, 5.1e-24]], $MachinePrecision]], t$95$1, N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.90000000000000006e182 or -8.7999999999999996e95 < z < -3.1e7 or 5.10000000000000025e-24 < z

   1. Initial program 63.2%

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

   2. Taylor expanded in t around inf 64.9%

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

      1. div-sub 64.9%

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

   4. Simplified 64.9%

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

   if -1.90000000000000006e182 < z < -8.7999999999999996e95

   1. Initial program 56.6%

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

      1. clear-num 56.4%

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

      2. associate-/r/ 56.1%

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

   3. Applied egg-rr 56.1%

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

   4. Taylor expanded in z around inf 75.7%

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

      1. sub-neg 75.7%

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

      2. +-commutative 75.7%

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

      3. mul-1-neg 75.7%

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

      4. unsub-neg 75.7%

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

      5. associate-/l* 80.4%

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

      6. mul-1-neg 80.4%

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

      7. remove-double-neg 80.4%

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

      8. associate-/l* 85.4%

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

   6. Simplified 85.4%

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

   7. Taylor expanded in y around 0 71.1%

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

   if -3.1e7 < z < 5.10000000000000025e-24

   1. Initial program 94.1%

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

   2. Taylor expanded in z around 0 75.6%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+182}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{+95}:\\ \;\;\;\;t - \frac{a \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;z \leq -31000000 \lor \neg \left(z \leq 5.1 \cdot 10^{-24}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \end{array} \]

Alternative 11: 66.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+210}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+96}:\\ \;\;\;\;t - \frac{a \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;z \leq -1350000:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-29}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (/ y z) (- x t)))))
   (if (<= z -2.2e+210)
     t_1
     (if (<= z -1.05e+96)
       (- t (/ (* a (- x t)) z))
       (if (<= z -1350000.0)
         (* t (/ (- y z) (- a z)))
         (if (<= z 8.5e-29) (+ x (/ (* y (- t x)) a)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((y / z) * (x - t));
	double tmp;
	if (z <= -2.2e+210) {
		tmp = t_1;
	} else if (z <= -1.05e+96) {
		tmp = t - ((a * (x - t)) / z);
	} else if (z <= -1350000.0) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 8.5e-29) {
		tmp = x + ((y * (t - x)) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((y / z) * (x - t))
    if (z <= (-2.2d+210)) then
        tmp = t_1
    else if (z <= (-1.05d+96)) then
        tmp = t - ((a * (x - t)) / z)
    else if (z <= (-1350000.0d0)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= 8.5d-29) then
        tmp = x + ((y * (t - x)) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((y / z) * (x - t));
	double tmp;
	if (z <= -2.2e+210) {
		tmp = t_1;
	} else if (z <= -1.05e+96) {
		tmp = t - ((a * (x - t)) / z);
	} else if (z <= -1350000.0) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 8.5e-29) {
		tmp = x + ((y * (t - x)) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((y / z) * (x - t))
	tmp = 0
	if z <= -2.2e+210:
		tmp = t_1
	elif z <= -1.05e+96:
		tmp = t - ((a * (x - t)) / z)
	elif z <= -1350000.0:
		tmp = t * ((y - z) / (a - z))
	elif z <= 8.5e-29:
		tmp = x + ((y * (t - x)) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(y / z) * Float64(x - t)))
	tmp = 0.0
	if (z <= -2.2e+210)
		tmp = t_1;
	elseif (z <= -1.05e+96)
		tmp = Float64(t - Float64(Float64(a * Float64(x - t)) / z));
	elseif (z <= -1350000.0)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 8.5e-29)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((y / z) * (x - t));
	tmp = 0.0;
	if (z <= -2.2e+210)
		tmp = t_1;
	elseif (z <= -1.05e+96)
		tmp = t - ((a * (x - t)) / z);
	elseif (z <= -1350000.0)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= 8.5e-29)
		tmp = x + ((y * (t - x)) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+210], t$95$1, If[LessEqual[z, -1.05e+96], N[(t - N[(N[(a * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1350000.0], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e-29], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.19999999999999987e210 or 8.5000000000000001e-29 < z

   1. Initial program 58.0%

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

      1. +-commutative 58.0%

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

      2. fma-def 58.2%

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

   3. Simplified 58.2%

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

   4. Taylor expanded in z around inf 52.9%

      \[\leadsto \color{blue}{\frac{{a}^{2} \cdot \left(t - x\right)}{{z}^{2}} + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \left(t + \left(\frac{a \cdot \left(t - x\right)}{z} + -1 \cdot \frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-/l* 56.4%

         \[\leadsto \color{blue}{\frac{{a}^{2}}{\frac{{z}^{2}}{t - x}}} + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \left(t + \left(\frac{a \cdot \left(t - x\right)}{z} + -1 \cdot \frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)\right)\right) \]

      2. unpow2 56.4%

         \[\leadsto \frac{\color{blue}{a \cdot a}}{\frac{{z}^{2}}{t - x}} + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \left(t + \left(\frac{a \cdot \left(t - x\right)}{z} + -1 \cdot \frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)\right)\right) \]

      3. unpow2 56.4%

         \[\leadsto \frac{a \cdot a}{\frac{\color{blue}{z \cdot z}}{t - x}} + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \left(t + \left(\frac{a \cdot \left(t - x\right)}{z} + -1 \cdot \frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)\right)\right) \]

      4. fma-def 56.4%

         \[\leadsto \frac{a \cdot a}{\frac{z \cdot z}{t - x}} + \color{blue}{\mathsf{fma}\left(-1, \frac{y \cdot \left(t - x\right)}{z}, t + \left(\frac{a \cdot \left(t - x\right)}{z} + -1 \cdot \frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)\right)} \]

      5. associate-/l* 61.9%

         \[\leadsto \frac{a \cdot a}{\frac{z \cdot z}{t - x}} + \mathsf{fma}\left(-1, \color{blue}{\frac{y}{\frac{z}{t - x}}}, t + \left(\frac{a \cdot \left(t - x\right)}{z} + -1 \cdot \frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)\right) \]

      6. associate-/l* 61.4%

         \[\leadsto \frac{a \cdot a}{\frac{z \cdot z}{t - x}} + \mathsf{fma}\left(-1, \frac{y}{\frac{z}{t - x}}, t + \left(\color{blue}{\frac{a}{\frac{z}{t - x}}} + -1 \cdot \frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)\right) \]

      7. mul-1-neg 61.4%

         \[\leadsto \frac{a \cdot a}{\frac{z \cdot z}{t - x}} + \mathsf{fma}\left(-1, \frac{y}{\frac{z}{t - x}}, t + \left(\frac{a}{\frac{z}{t - x}} + \color{blue}{\left(-\frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)}\right)\right) \]

      8. associate-*r* 62.4%

         \[\leadsto \frac{a \cdot a}{\frac{z \cdot z}{t - x}} + \mathsf{fma}\left(-1, \frac{y}{\frac{z}{t - x}}, t + \left(\frac{a}{\frac{z}{t - x}} + \left(-\frac{\color{blue}{\left(y \cdot a\right) \cdot \left(t - x\right)}}{{z}^{2}}\right)\right)\right) \]

      9. unpow2 62.4%

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

   6. Simplified 62.4%

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

   7. Taylor expanded in a around 0 59.1%

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

      1. +-commutative 59.1%

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

      2. mul-1-neg 59.1%

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

      3. unsub-neg 59.1%

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

      4. associate-*l/ 72.4%

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

      5. *-commutative 72.4%

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

   9. Simplified 72.4%

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

   if -2.19999999999999987e210 < z < -1.0500000000000001e96

   1. Initial program 53.8%

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

      1. clear-num 53.7%

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

      2. associate-/r/ 53.4%

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

   3. Applied egg-rr 53.4%

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

   4. Taylor expanded in z around inf 71.2%

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

      1. sub-neg 71.2%

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

      2. +-commutative 71.2%

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

      3. mul-1-neg 71.2%

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

      4. unsub-neg 71.2%

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

      5. associate-/l* 78.4%

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

      6. mul-1-neg 78.4%

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

      7. remove-double-neg 78.4%

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

      8. associate-/l* 82.2%

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

   6. Simplified 82.2%

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

   7. Taylor expanded in y around 0 71.3%

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

   if -1.0500000000000001e96 < z < -1.35e6

   1. Initial program 90.7%

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

   2. Taylor expanded in t around inf 55.5%

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

      1. div-sub 55.5%

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

   4. Simplified 55.5%

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

   if -1.35e6 < z < 8.5000000000000001e-29

   1. Initial program 94.7%

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

   2. Taylor expanded in z around 0 76.6%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+210}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+96}:\\ \;\;\;\;t - \frac{a \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;z \leq -1350000:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-29}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \end{array} \]

Alternative 12: 66.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -9 \cdot 10^{+209}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+96}:\\ \;\;\;\;t - \frac{a \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;z \leq -5800:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-32}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (/ y z) (- x t)))))
   (if (<= z -9e+209)
     t_1
     (if (<= z -1.15e+96)
       (- t (/ (* a (- x t)) z))
       (if (<= z -5800.0)
         (/ t (/ (- a z) (- y z)))
         (if (<= z 9.8e-32) (+ x (/ (* y (- t x)) a)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((y / z) * (x - t));
	double tmp;
	if (z <= -9e+209) {
		tmp = t_1;
	} else if (z <= -1.15e+96) {
		tmp = t - ((a * (x - t)) / z);
	} else if (z <= -5800.0) {
		tmp = t / ((a - z) / (y - z));
	} else if (z <= 9.8e-32) {
		tmp = x + ((y * (t - x)) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((y / z) * (x - t))
    if (z <= (-9d+209)) then
        tmp = t_1
    else if (z <= (-1.15d+96)) then
        tmp = t - ((a * (x - t)) / z)
    else if (z <= (-5800.0d0)) then
        tmp = t / ((a - z) / (y - z))
    else if (z <= 9.8d-32) then
        tmp = x + ((y * (t - x)) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((y / z) * (x - t));
	double tmp;
	if (z <= -9e+209) {
		tmp = t_1;
	} else if (z <= -1.15e+96) {
		tmp = t - ((a * (x - t)) / z);
	} else if (z <= -5800.0) {
		tmp = t / ((a - z) / (y - z));
	} else if (z <= 9.8e-32) {
		tmp = x + ((y * (t - x)) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((y / z) * (x - t))
	tmp = 0
	if z <= -9e+209:
		tmp = t_1
	elif z <= -1.15e+96:
		tmp = t - ((a * (x - t)) / z)
	elif z <= -5800.0:
		tmp = t / ((a - z) / (y - z))
	elif z <= 9.8e-32:
		tmp = x + ((y * (t - x)) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(y / z) * Float64(x - t)))
	tmp = 0.0
	if (z <= -9e+209)
		tmp = t_1;
	elseif (z <= -1.15e+96)
		tmp = Float64(t - Float64(Float64(a * Float64(x - t)) / z));
	elseif (z <= -5800.0)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (z <= 9.8e-32)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((y / z) * (x - t));
	tmp = 0.0;
	if (z <= -9e+209)
		tmp = t_1;
	elseif (z <= -1.15e+96)
		tmp = t - ((a * (x - t)) / z);
	elseif (z <= -5800.0)
		tmp = t / ((a - z) / (y - z));
	elseif (z <= 9.8e-32)
		tmp = x + ((y * (t - x)) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e+209], t$95$1, If[LessEqual[z, -1.15e+96], N[(t - N[(N[(a * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5800.0], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.8e-32], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.0000000000000007e209 or 9.7999999999999996e-32 < z

   1. Initial program 58.0%

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

      1. +-commutative 58.0%

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

      2. fma-def 58.2%

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

   3. Simplified 58.2%

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

   4. Taylor expanded in z around inf 52.9%

      \[\leadsto \color{blue}{\frac{{a}^{2} \cdot \left(t - x\right)}{{z}^{2}} + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \left(t + \left(\frac{a \cdot \left(t - x\right)}{z} + -1 \cdot \frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-/l* 56.4%

         \[\leadsto \color{blue}{\frac{{a}^{2}}{\frac{{z}^{2}}{t - x}}} + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \left(t + \left(\frac{a \cdot \left(t - x\right)}{z} + -1 \cdot \frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)\right)\right) \]

      2. unpow2 56.4%

         \[\leadsto \frac{\color{blue}{a \cdot a}}{\frac{{z}^{2}}{t - x}} + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \left(t + \left(\frac{a \cdot \left(t - x\right)}{z} + -1 \cdot \frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)\right)\right) \]

      3. unpow2 56.4%

         \[\leadsto \frac{a \cdot a}{\frac{\color{blue}{z \cdot z}}{t - x}} + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \left(t + \left(\frac{a \cdot \left(t - x\right)}{z} + -1 \cdot \frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)\right)\right) \]

      4. fma-def 56.4%

         \[\leadsto \frac{a \cdot a}{\frac{z \cdot z}{t - x}} + \color{blue}{\mathsf{fma}\left(-1, \frac{y \cdot \left(t - x\right)}{z}, t + \left(\frac{a \cdot \left(t - x\right)}{z} + -1 \cdot \frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)\right)} \]

      5. associate-/l* 61.9%

         \[\leadsto \frac{a \cdot a}{\frac{z \cdot z}{t - x}} + \mathsf{fma}\left(-1, \color{blue}{\frac{y}{\frac{z}{t - x}}}, t + \left(\frac{a \cdot \left(t - x\right)}{z} + -1 \cdot \frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)\right) \]

      6. associate-/l* 61.4%

         \[\leadsto \frac{a \cdot a}{\frac{z \cdot z}{t - x}} + \mathsf{fma}\left(-1, \frac{y}{\frac{z}{t - x}}, t + \left(\color{blue}{\frac{a}{\frac{z}{t - x}}} + -1 \cdot \frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)\right) \]

      7. mul-1-neg 61.4%

         \[\leadsto \frac{a \cdot a}{\frac{z \cdot z}{t - x}} + \mathsf{fma}\left(-1, \frac{y}{\frac{z}{t - x}}, t + \left(\frac{a}{\frac{z}{t - x}} + \color{blue}{\left(-\frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)}\right)\right) \]

      8. associate-*r* 62.4%

         \[\leadsto \frac{a \cdot a}{\frac{z \cdot z}{t - x}} + \mathsf{fma}\left(-1, \frac{y}{\frac{z}{t - x}}, t + \left(\frac{a}{\frac{z}{t - x}} + \left(-\frac{\color{blue}{\left(y \cdot a\right) \cdot \left(t - x\right)}}{{z}^{2}}\right)\right)\right) \]

      9. unpow2 62.4%

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

   6. Simplified 62.4%

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

   7. Taylor expanded in a around 0 59.1%

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

      1. +-commutative 59.1%

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

      2. mul-1-neg 59.1%

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

      3. unsub-neg 59.1%

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

      4. associate-*l/ 72.4%

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

      5. *-commutative 72.4%

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

   9. Simplified 72.4%

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

   if -9.0000000000000007e209 < z < -1.15000000000000008e96

   1. Initial program 53.8%

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

      1. clear-num 53.7%

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

      2. associate-/r/ 53.4%

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

   3. Applied egg-rr 53.4%

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

   4. Taylor expanded in z around inf 71.2%

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

      1. sub-neg 71.2%

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

      2. +-commutative 71.2%

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

      3. mul-1-neg 71.2%

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

      4. unsub-neg 71.2%

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

      5. associate-/l* 78.4%

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

      6. mul-1-neg 78.4%

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

      7. remove-double-neg 78.4%

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

      8. associate-/l* 82.2%

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

   6. Simplified 82.2%

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

   7. Taylor expanded in y around 0 71.3%

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

   if -1.15000000000000008e96 < z < -5800

   1. Initial program 90.7%

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

   2. Taylor expanded in x around 0 47.0%

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

      1. associate-/l* 55.5%

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

   4. Simplified 55.5%

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

   if -5800 < z < 9.7999999999999996e-32

   1. Initial program 94.7%

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

   2. Taylor expanded in z around 0 76.6%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+209}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+96}:\\ \;\;\;\;t - \frac{a \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;z \leq -5800:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-32}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \end{array} \]

Alternative 13: 37.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a}\\ \mathbf{if}\;z \leq -1500:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-158}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) a))))
   (if (<= z -1500.0)
     t
     (if (<= z 1.7e-169) t_1 (if (<= z 1.1e-158) x (if (<= z 3e+31) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / a);
	double tmp;
	if (z <= -1500.0) {
		tmp = t;
	} else if (z <= 1.7e-169) {
		tmp = t_1;
	} else if (z <= 1.1e-158) {
		tmp = x;
	} else if (z <= 3e+31) {
		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 = t * ((y - z) / a)
    if (z <= (-1500.0d0)) then
        tmp = t
    else if (z <= 1.7d-169) then
        tmp = t_1
    else if (z <= 1.1d-158) then
        tmp = x
    else if (z <= 3d+31) 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 = t * ((y - z) / a);
	double tmp;
	if (z <= -1500.0) {
		tmp = t;
	} else if (z <= 1.7e-169) {
		tmp = t_1;
	} else if (z <= 1.1e-158) {
		tmp = x;
	} else if (z <= 3e+31) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / a)
	tmp = 0
	if z <= -1500.0:
		tmp = t
	elif z <= 1.7e-169:
		tmp = t_1
	elif z <= 1.1e-158:
		tmp = x
	elif z <= 3e+31:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / a))
	tmp = 0.0
	if (z <= -1500.0)
		tmp = t;
	elseif (z <= 1.7e-169)
		tmp = t_1;
	elseif (z <= 1.1e-158)
		tmp = x;
	elseif (z <= 3e+31)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / a);
	tmp = 0.0;
	if (z <= -1500.0)
		tmp = t;
	elseif (z <= 1.7e-169)
		tmp = t_1;
	elseif (z <= 1.1e-158)
		tmp = x;
	elseif (z <= 3e+31)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1500.0], t, If[LessEqual[z, 1.7e-169], t$95$1, If[LessEqual[z, 1.1e-158], x, If[LessEqual[z, 3e+31], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1500 or 2.99999999999999989e31 < z

   1. Initial program 60.4%

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

   2. Taylor expanded in z around inf 48.8%

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

   if -1500 < z < 1.7e-169 or 1.1000000000000001e-158 < z < 2.99999999999999989e31

   1. Initial program 92.4%

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

   2. Taylor expanded in t around inf 50.4%

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

      1. div-sub 50.4%

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

   4. Simplified 50.4%

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

   5. Taylor expanded in a around inf 42.1%

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

   if 1.7e-169 < z < 1.1000000000000001e-158

   1. Initial program 97.2%

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

   2. Taylor expanded in a around inf 97.2%

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

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1500:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-169}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-158}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+31}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 14: 55.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{-167}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.1 \cdot 10^{-205}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{a - z}\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{-119}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= t -2.2e-167)
     t_1
     (if (<= t -7.1e-205)
       (/ (* x (- y)) (- a z))
       (if (<= t 1.16e-119) x t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -2.2e-167) {
		tmp = t_1;
	} else if (t <= -7.1e-205) {
		tmp = (x * -y) / (a - z);
	} else if (t <= 1.16e-119) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (t <= (-2.2d-167)) then
        tmp = t_1
    else if (t <= (-7.1d-205)) then
        tmp = (x * -y) / (a - z)
    else if (t <= 1.16d-119) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -2.2e-167) {
		tmp = t_1;
	} else if (t <= -7.1e-205) {
		tmp = (x * -y) / (a - z);
	} else if (t <= 1.16e-119) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -2.2e-167:
		tmp = t_1
	elif t <= -7.1e-205:
		tmp = (x * -y) / (a - z)
	elif t <= 1.16e-119:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (t <= -2.2e-167)
		tmp = t_1;
	elseif (t <= -7.1e-205)
		tmp = Float64(Float64(x * Float64(-y)) / Float64(a - z));
	elseif (t <= 1.16e-119)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -2.2e-167)
		tmp = t_1;
	elseif (t <= -7.1e-205)
		tmp = (x * -y) / (a - z);
	elseif (t <= 1.16e-119)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.2e-167], t$95$1, If[LessEqual[t, -7.1e-205], N[(N[(x * (-y)), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.16e-119], x, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.2e-167 or 1.16e-119 < t

   1. Initial program 82.7%

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

   2. Taylor expanded in t around inf 67.9%

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

      1. div-sub 67.9%

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

   4. Simplified 67.9%

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

   if -2.2e-167 < t < -7.1000000000000003e-205

   1. Initial program 78.4%

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

      1. +-commutative 78.4%

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

      2. associate-*r/ 92.6%

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

      3. add-cube-cbrt 91.6%

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

      4. times-frac 91.4%

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

      5. fma-def 91.5%

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

      6. pow2 91.5%

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

   3. Applied egg-rr 91.5%

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

   4. Taylor expanded in y around inf 77.8%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \frac{y \cdot \left(t - x\right)}{a - z}} \]
   5. Step-by-step derivation

      1. pow-base-1 77.8%

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

      2. associate-*r/ 77.8%

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

      3. *-lft-identity 77.8%

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

      4. *-commutative 77.8%

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

   6. Simplified 77.8%

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

   7. Taylor expanded in t around 0 63.7%

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

      1. associate-*r/ 63.7%

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

      2. mul-1-neg 63.7%

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

      3. distribute-rgt-neg-out 63.7%

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

   9. Simplified 63.7%

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

   if -7.1000000000000003e-205 < t < 1.16e-119

   1. Initial program 63.1%

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

   2. Taylor expanded in a around inf 48.1%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-167}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -7.1 \cdot 10^{-205}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{a - z}\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{-119}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 15: 67.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+200}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -450000:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-29}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (/ y z) (- x t)))))
   (if (<= z -2.2e+200)
     t_1
     (if (<= z -450000.0)
       (+ t (/ (* (- t x) (- a y)) z))
       (if (<= z 5.8e-29) (+ x (/ (* y (- t x)) a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((y / z) * (x - t));
	double tmp;
	if (z <= -2.2e+200) {
		tmp = t_1;
	} else if (z <= -450000.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (z <= 5.8e-29) {
		tmp = x + ((y * (t - x)) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((y / z) * (x - t))
    if (z <= (-2.2d+200)) then
        tmp = t_1
    else if (z <= (-450000.0d0)) then
        tmp = t + (((t - x) * (a - y)) / z)
    else if (z <= 5.8d-29) then
        tmp = x + ((y * (t - x)) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((y / z) * (x - t));
	double tmp;
	if (z <= -2.2e+200) {
		tmp = t_1;
	} else if (z <= -450000.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (z <= 5.8e-29) {
		tmp = x + ((y * (t - x)) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((y / z) * (x - t))
	tmp = 0
	if z <= -2.2e+200:
		tmp = t_1
	elif z <= -450000.0:
		tmp = t + (((t - x) * (a - y)) / z)
	elif z <= 5.8e-29:
		tmp = x + ((y * (t - x)) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(y / z) * Float64(x - t)))
	tmp = 0.0
	if (z <= -2.2e+200)
		tmp = t_1;
	elseif (z <= -450000.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif (z <= 5.8e-29)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((y / z) * (x - t));
	tmp = 0.0;
	if (z <= -2.2e+200)
		tmp = t_1;
	elseif (z <= -450000.0)
		tmp = t + (((t - x) * (a - y)) / z);
	elseif (z <= 5.8e-29)
		tmp = x + ((y * (t - x)) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+200], t$95$1, If[LessEqual[z, -450000.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e-29], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2e200 or 5.80000000000000048e-29 < z

   1. Initial program 58.4%

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

      1. +-commutative 58.4%

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

      2. fma-def 58.5%

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

   3. Simplified 58.5%

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

   4. Taylor expanded in z around inf 53.4%

      \[\leadsto \color{blue}{\frac{{a}^{2} \cdot \left(t - x\right)}{{z}^{2}} + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \left(t + \left(\frac{a \cdot \left(t - x\right)}{z} + -1 \cdot \frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-/l* 56.7%

         \[\leadsto \color{blue}{\frac{{a}^{2}}{\frac{{z}^{2}}{t - x}}} + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \left(t + \left(\frac{a \cdot \left(t - x\right)}{z} + -1 \cdot \frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)\right)\right) \]

      2. unpow2 56.7%

         \[\leadsto \frac{\color{blue}{a \cdot a}}{\frac{{z}^{2}}{t - x}} + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \left(t + \left(\frac{a \cdot \left(t - x\right)}{z} + -1 \cdot \frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)\right)\right) \]

      3. unpow2 56.7%

         \[\leadsto \frac{a \cdot a}{\frac{\color{blue}{z \cdot z}}{t - x}} + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \left(t + \left(\frac{a \cdot \left(t - x\right)}{z} + -1 \cdot \frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)\right)\right) \]

      4. fma-def 56.7%

         \[\leadsto \frac{a \cdot a}{\frac{z \cdot z}{t - x}} + \color{blue}{\mathsf{fma}\left(-1, \frac{y \cdot \left(t - x\right)}{z}, t + \left(\frac{a \cdot \left(t - x\right)}{z} + -1 \cdot \frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)\right)} \]

      5. associate-/l* 63.2%

         \[\leadsto \frac{a \cdot a}{\frac{z \cdot z}{t - x}} + \mathsf{fma}\left(-1, \color{blue}{\frac{y}{\frac{z}{t - x}}}, t + \left(\frac{a \cdot \left(t - x\right)}{z} + -1 \cdot \frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)\right) \]

      6. associate-/l* 62.7%

         \[\leadsto \frac{a \cdot a}{\frac{z \cdot z}{t - x}} + \mathsf{fma}\left(-1, \frac{y}{\frac{z}{t - x}}, t + \left(\color{blue}{\frac{a}{\frac{z}{t - x}}} + -1 \cdot \frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)\right) \]

      7. mul-1-neg 62.7%

         \[\leadsto \frac{a \cdot a}{\frac{z \cdot z}{t - x}} + \mathsf{fma}\left(-1, \frac{y}{\frac{z}{t - x}}, t + \left(\frac{a}{\frac{z}{t - x}} + \color{blue}{\left(-\frac{y \cdot \left(a \cdot \left(t - x\right)\right)}{{z}^{2}}\right)}\right)\right) \]

      8. associate-*r* 63.7%

         \[\leadsto \frac{a \cdot a}{\frac{z \cdot z}{t - x}} + \mathsf{fma}\left(-1, \frac{y}{\frac{z}{t - x}}, t + \left(\frac{a}{\frac{z}{t - x}} + \left(-\frac{\color{blue}{\left(y \cdot a\right) \cdot \left(t - x\right)}}{{z}^{2}}\right)\right)\right) \]

      9. unpow2 63.7%

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

   6. Simplified 63.7%

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

   7. Taylor expanded in a around 0 59.3%

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

      1. +-commutative 59.3%

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

      2. mul-1-neg 59.3%

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

      3. unsub-neg 59.3%

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

      4. associate-*l/ 73.3%

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

      5. *-commutative 73.3%

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

   9. Simplified 73.3%

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

   if -2.2e200 < z < -4.5e5

   1. Initial program 70.1%

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

   2. Taylor expanded in z around inf 65.5%

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

      1. +-commutative 65.5%

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

      2. associate--l+ 65.5%

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

      3. associate-*r/ 65.5%

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

      4. associate-*r/ 65.5%

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

      5. div-sub 65.5%

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

      6. distribute-lft-out-- 65.5%

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

      7. mul-1-neg 65.5%

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

      8. distribute-neg-frac 65.5%

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

      9. unsub-neg 65.5%

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

      10. distribute-rgt-out-- 67.7%

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

   4. Simplified 67.7%

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

   if -4.5e5 < z < 5.80000000000000048e-29

   1. Initial program 94.7%

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

   2. Taylor expanded in z around 0 76.6%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+200}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -450000:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-29}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \end{array} \]

Alternative 16: 55.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.26 \cdot 10^{+172} \lor \neg \left(x \leq 7500000\right):\\ \;\;\;\;\left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.26e+172) (not (<= x 7500000.0)))
   (* (- y a) (/ (- x t) z))
   (* t (/ (- y z) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.26e+172) || !(x <= 7500000.0)) {
		tmp = (y - a) * ((x - t) / z);
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-1.26d+172)) .or. (.not. (x <= 7500000.0d0))) then
        tmp = (y - a) * ((x - t) / z)
    else
        tmp = t * ((y - z) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.26e+172) || !(x <= 7500000.0)) {
		tmp = (y - a) * ((x - t) / z);
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1.26e+172) or not (x <= 7500000.0):
		tmp = (y - a) * ((x - t) / z)
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.26e+172) || !(x <= 7500000.0))
		tmp = Float64(Float64(y - a) * Float64(Float64(x - t) / z));
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -1.26e+172) || ~((x <= 7500000.0)))
		tmp = (y - a) * ((x - t) / z);
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.26e+172], N[Not[LessEqual[x, 7500000.0]], $MachinePrecision]], N[(N[(y - a), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.2600000000000001e172 or 7.5e6 < x

   1. Initial program 67.2%

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

      1. clear-num 67.1%

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

      2. associate-/r/ 67.2%

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

   3. Applied egg-rr 67.2%

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

   4. Taylor expanded in z around inf 47.6%

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

      1. sub-neg 47.6%

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

      2. +-commutative 47.6%

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

      3. mul-1-neg 47.6%

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

      4. unsub-neg 47.6%

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

      5. associate-/l* 55.0%

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

      6. mul-1-neg 55.0%

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

      7. remove-double-neg 55.0%

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

      8. associate-/l* 58.0%

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

   6. Simplified 58.0%

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

   7. Taylor expanded in z around 0 40.5%

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

      1. div-sub 40.3%

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

      2. associate-*r/ 42.4%

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

      3. associate-*r/ 49.4%

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

      4. distribute-rgt-out-- 50.8%

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

   9. Simplified 50.8%

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

   if -1.2600000000000001e172 < x < 7.5e6

   1. Initial program 83.6%

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

   2. Taylor expanded in t around inf 70.2%

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

      1. div-sub 70.2%

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

   4. Simplified 70.2%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.26 \cdot 10^{+172} \lor \neg \left(x \leq 7500000\right):\\ \;\;\;\;\left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 17: 38.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -13200000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-153}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.45 \cdot 10^{-133}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+98}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -13200000000.0)
   x
   (if (<= a 2.3e-153)
     t
     (if (<= a 3.45e-133) (* x (/ y z)) (if (<= a 1.15e+98) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -13200000000.0) {
		tmp = x;
	} else if (a <= 2.3e-153) {
		tmp = t;
	} else if (a <= 3.45e-133) {
		tmp = x * (y / z);
	} else if (a <= 1.15e+98) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-13200000000.0d0)) then
        tmp = x
    else if (a <= 2.3d-153) then
        tmp = t
    else if (a <= 3.45d-133) then
        tmp = x * (y / z)
    else if (a <= 1.15d+98) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -13200000000.0) {
		tmp = x;
	} else if (a <= 2.3e-153) {
		tmp = t;
	} else if (a <= 3.45e-133) {
		tmp = x * (y / z);
	} else if (a <= 1.15e+98) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -13200000000.0:
		tmp = x
	elif a <= 2.3e-153:
		tmp = t
	elif a <= 3.45e-133:
		tmp = x * (y / z)
	elif a <= 1.15e+98:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -13200000000.0)
		tmp = x;
	elseif (a <= 2.3e-153)
		tmp = t;
	elseif (a <= 3.45e-133)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 1.15e+98)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -13200000000.0)
		tmp = x;
	elseif (a <= 2.3e-153)
		tmp = t;
	elseif (a <= 3.45e-133)
		tmp = x * (y / z);
	elseif (a <= 1.15e+98)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -13200000000.0], x, If[LessEqual[a, 2.3e-153], t, If[LessEqual[a, 3.45e-133], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.15e+98], t, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.32e10 or 1.15000000000000007e98 < a

   1. Initial program 84.6%

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

   2. Taylor expanded in a around inf 49.1%

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

   if -1.32e10 < a < 2.29999999999999997e-153 or 3.45e-133 < a < 1.15000000000000007e98

   1. Initial program 73.5%

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

   2. Taylor expanded in z around inf 39.8%

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

   if 2.29999999999999997e-153 < a < 3.45e-133

   1. Initial program 58.9%

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

   2. Taylor expanded in a around 0 60.1%

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

      1. associate-*r/ 60.1%

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

      2. neg-mul-1 60.1%

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

   4. Simplified 60.1%

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

   5. Taylor expanded in x around inf 57.5%

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

      1. associate-/l* 69.4%

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

   7. Simplified 69.4%

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

      1. associate-/r/ 69.2%

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

   9. Applied egg-rr 69.2%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -13200000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-153}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.45 \cdot 10^{-133}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+98}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18: 38.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -12000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-153}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.15 \cdot 10^{-127}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{+98}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -12000000000.0)
   x
   (if (<= a 2.2e-153)
     t
     (if (<= a 3.15e-127) (/ y (/ z x)) (if (<= a 5.3e+98) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -12000000000.0) {
		tmp = x;
	} else if (a <= 2.2e-153) {
		tmp = t;
	} else if (a <= 3.15e-127) {
		tmp = y / (z / x);
	} else if (a <= 5.3e+98) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-12000000000.0d0)) then
        tmp = x
    else if (a <= 2.2d-153) then
        tmp = t
    else if (a <= 3.15d-127) then
        tmp = y / (z / x)
    else if (a <= 5.3d+98) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -12000000000.0) {
		tmp = x;
	} else if (a <= 2.2e-153) {
		tmp = t;
	} else if (a <= 3.15e-127) {
		tmp = y / (z / x);
	} else if (a <= 5.3e+98) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -12000000000.0:
		tmp = x
	elif a <= 2.2e-153:
		tmp = t
	elif a <= 3.15e-127:
		tmp = y / (z / x)
	elif a <= 5.3e+98:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -12000000000.0)
		tmp = x;
	elseif (a <= 2.2e-153)
		tmp = t;
	elseif (a <= 3.15e-127)
		tmp = Float64(y / Float64(z / x));
	elseif (a <= 5.3e+98)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -12000000000.0)
		tmp = x;
	elseif (a <= 2.2e-153)
		tmp = t;
	elseif (a <= 3.15e-127)
		tmp = y / (z / x);
	elseif (a <= 5.3e+98)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -12000000000.0], x, If[LessEqual[a, 2.2e-153], t, If[LessEqual[a, 3.15e-127], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.3e+98], t, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.2e10 or 5.29999999999999997e98 < a

   1. Initial program 84.6%

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

   2. Taylor expanded in a around inf 49.1%

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

   if -1.2e10 < a < 2.20000000000000001e-153 or 3.1499999999999999e-127 < a < 5.29999999999999997e98

   1. Initial program 73.5%

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

   2. Taylor expanded in z around inf 39.8%

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

   if 2.20000000000000001e-153 < a < 3.1499999999999999e-127

   1. Initial program 58.9%

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

   2. Taylor expanded in a around 0 60.1%

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

      1. associate-*r/ 60.1%

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

      2. neg-mul-1 60.1%

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

   4. Simplified 60.1%

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

   5. Taylor expanded in x around inf 57.5%

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

      1. associate-/l* 69.4%

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

   7. Simplified 69.4%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -12000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-153}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.15 \cdot 10^{-127}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{+98}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19: 38.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -12000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+98}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -12000000000.0) x (if (<= a 1.9e+98) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -12000000000.0) {
		tmp = x;
	} else if (a <= 1.9e+98) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-12000000000.0d0)) then
        tmp = x
    else if (a <= 1.9d+98) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -12000000000.0) {
		tmp = x;
	} else if (a <= 1.9e+98) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -12000000000.0:
		tmp = x
	elif a <= 1.9e+98:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -12000000000.0)
		tmp = x;
	elseif (a <= 1.9e+98)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -12000000000.0)
		tmp = x;
	elseif (a <= 1.9e+98)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -12000000000.0], x, If[LessEqual[a, 1.9e+98], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.2e10 or 1.89999999999999995e98 < a

   1. Initial program 84.6%

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

   2. Taylor expanded in a around inf 49.1%

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

   if -1.2e10 < a < 1.89999999999999995e98

   1. Initial program 72.7%

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

   2. Taylor expanded in z around inf 38.4%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -12000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+98}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20: 25.0% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 77.8%

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

2. Taylor expanded in z around inf 26.9%

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

3. Final simplification 26.9%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023173 
(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)))))