Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.2% → 95.0%

Time: 15.9s

Alternatives: 17

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-289} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -1e-289) (not (<= t_1 0.0)))
     (fma (- t x) (/ (- y z) (- a z)) x)
     (+ t (* (/ (- t x) z) (- a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-289) || !(t_1 <= 0.0)) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -1e-289) || !(t_1 <= 0.0))
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-289], 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[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1e-289 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 86.3%

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

      1. +-commutative 86.3%

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

      2. remove-double-neg 86.3%

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

      3. unsub-neg 86.3%

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

      4. *-commutative 86.3%

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

      5. associate-*l/ 76.1%

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

      6. associate-/l* 95.5%

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

      7. fma-neg 95.5%

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

      8. remove-double-neg 95.5%

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

   3. Simplified 95.5%

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

   if -1e-289 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.2%

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

      1. +-commutative 3.2%

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

      2. fma-define 3.4%

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

   3. Simplified 3.4%

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

   5. Taylor expanded in z around inf 81.1%

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

      1. associate--l+ 81.1%

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

      2. distribute-lft-out-- 81.1%

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

      3. div-sub 81.1%

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

      4. mul-1-neg 81.1%

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

      5. unsub-neg 81.1%

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

      6. div-sub 81.1%

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

      7. associate-/l* 84.0%

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

      8. associate-/l* 99.8%

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

      9. distribute-rgt-out-- 99.8%

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

   7. Simplified 99.8%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-289} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-289} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{x - t}{\frac{a - z}{z - y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -1e-289) (not (<= t_1 0.0)))
     (+ x (/ (- x t) (/ (- a z) (- z y))))
     (+ t (* (/ (- t x) z) (- a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-289) || !(t_1 <= 0.0)) {
		tmp = x + ((x - t) / ((a - z) / (z - y)));
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-1d-289)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((x - t) / ((a - z) / (z - y)))
    else
        tmp = t + (((t - x) / z) * (a - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-289) || !(t_1 <= 0.0)) {
		tmp = x + ((x - t) / ((a - z) / (z - y)));
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -1e-289) or not (t_1 <= 0.0):
		tmp = x + ((x - t) / ((a - z) / (z - y)))
	else:
		tmp = t + (((t - x) / z) * (a - y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -1e-289) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(x - t) / Float64(Float64(a - z) / Float64(z - y))));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -1e-289) || ~((t_1 <= 0.0)))
		tmp = x + ((x - t) / ((a - z) / (z - y)));
	else
		tmp = t + (((t - x) / z) * (a - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-289], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(x - t), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1e-289 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 86.3%

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

      1. +-commutative 86.3%

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

      2. fma-define 86.3%

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

   3. Simplified 86.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 86.3%

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

      2. *-commutative 86.3%

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

      3. associate-*l/ 76.1%

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

      4. associate-*r/ 95.5%

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

      5. clear-num 95.4%

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

      6. un-div-inv 95.4%

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

   6. Applied egg-rr 95.4%

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

   if -1e-289 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.2%

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

      1. +-commutative 3.2%

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

      2. fma-define 3.4%

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

   3. Simplified 3.4%

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

   5. Taylor expanded in z around inf 81.1%

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

      1. associate--l+ 81.1%

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

      2. distribute-lft-out-- 81.1%

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

      3. div-sub 81.1%

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

      4. mul-1-neg 81.1%

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

      5. unsub-neg 81.1%

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

      6. div-sub 81.1%

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

      7. associate-/l* 84.0%

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

      8. associate-/l* 99.8%

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

      9. distribute-rgt-out-- 99.8%

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

   7. Simplified 99.8%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-289} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{x - t}{\frac{a - z}{z - y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-203} \lor \neg \left(t\_1 \leq 10^{-236}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -5e-203) (not (<= t_1 1e-236)))
     t_1
     (+ t (* (/ (- t x) z) (- a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-203) || !(t_1 <= 1e-236)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-5d-203)) .or. (.not. (t_1 <= 1d-236))) then
        tmp = t_1
    else
        tmp = t + (((t - x) / z) * (a - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-203) || !(t_1 <= 1e-236)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -5e-203) or not (t_1 <= 1e-236):
		tmp = t_1
	else:
		tmp = t + (((t - x) / z) * (a - y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -5e-203) || !(t_1 <= 1e-236))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -5e-203) || ~((t_1 <= 1e-236)))
		tmp = t_1;
	else
		tmp = t + (((t - x) / z) * (a - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-203], N[Not[LessEqual[t$95$1, 1e-236]], $MachinePrecision]], t$95$1, N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5.0000000000000002e-203 or 1e-236 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 89.7%

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

   if -5.0000000000000002e-203 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1e-236

   1. Initial program 9.5%

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

      1. +-commutative 9.5%

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

      2. fma-define 9.6%

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

   3. Simplified 9.6%

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

   5. Taylor expanded in z around inf 75.8%

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

      1. associate--l+ 75.8%

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

      2. distribute-lft-out-- 75.8%

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

      3. div-sub 75.8%

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

      4. mul-1-neg 75.8%

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

      5. unsub-neg 75.8%

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

      6. div-sub 75.8%

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

      7. associate-/l* 76.0%

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

      8. associate-/l* 88.0%

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

      9. distribute-rgt-out-- 88.0%

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

   7. Simplified 88.0%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-203} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 10^{-236}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 43.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a}\\ \mathbf{if}\;z \leq -2.55 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-191}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) a))))
   (if (<= z -2.55e+69)
     t
     (if (<= z -5.8e+27)
       x
       (if (<= z -5.3e-140)
         t_1
         (if (<= z -3.5e-191)
           x
           (if (<= z 1.6e-105) t_1 (if (<= z 3.2e-5) x t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / a);
	double tmp;
	if (z <= -2.55e+69) {
		tmp = t;
	} else if (z <= -5.8e+27) {
		tmp = x;
	} else if (z <= -5.3e-140) {
		tmp = t_1;
	} else if (z <= -3.5e-191) {
		tmp = x;
	} else if (z <= 1.6e-105) {
		tmp = t_1;
	} else if (z <= 3.2e-5) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((t - x) / a)
    if (z <= (-2.55d+69)) then
        tmp = t
    else if (z <= (-5.8d+27)) then
        tmp = x
    else if (z <= (-5.3d-140)) then
        tmp = t_1
    else if (z <= (-3.5d-191)) then
        tmp = x
    else if (z <= 1.6d-105) then
        tmp = t_1
    else if (z <= 3.2d-5) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / a);
	double tmp;
	if (z <= -2.55e+69) {
		tmp = t;
	} else if (z <= -5.8e+27) {
		tmp = x;
	} else if (z <= -5.3e-140) {
		tmp = t_1;
	} else if (z <= -3.5e-191) {
		tmp = x;
	} else if (z <= 1.6e-105) {
		tmp = t_1;
	} else if (z <= 3.2e-5) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / a)
	tmp = 0
	if z <= -2.55e+69:
		tmp = t
	elif z <= -5.8e+27:
		tmp = x
	elif z <= -5.3e-140:
		tmp = t_1
	elif z <= -3.5e-191:
		tmp = x
	elif z <= 1.6e-105:
		tmp = t_1
	elif z <= 3.2e-5:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / a))
	tmp = 0.0
	if (z <= -2.55e+69)
		tmp = t;
	elseif (z <= -5.8e+27)
		tmp = x;
	elseif (z <= -5.3e-140)
		tmp = t_1;
	elseif (z <= -3.5e-191)
		tmp = x;
	elseif (z <= 1.6e-105)
		tmp = t_1;
	elseif (z <= 3.2e-5)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / a);
	tmp = 0.0;
	if (z <= -2.55e+69)
		tmp = t;
	elseif (z <= -5.8e+27)
		tmp = x;
	elseif (z <= -5.3e-140)
		tmp = t_1;
	elseif (z <= -3.5e-191)
		tmp = x;
	elseif (z <= 1.6e-105)
		tmp = t_1;
	elseif (z <= 3.2e-5)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.55e+69], t, If[LessEqual[z, -5.8e+27], x, If[LessEqual[z, -5.3e-140], t$95$1, If[LessEqual[z, -3.5e-191], x, If[LessEqual[z, 1.6e-105], t$95$1, If[LessEqual[z, 3.2e-5], x, t]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.54999999999999999e69 or 3.19999999999999986e-5 < z

   1. Initial program 57.4%

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

      1. +-commutative 57.4%

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

      2. fma-define 57.3%

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

   3. Simplified 57.3%

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

   5. Taylor expanded in z around inf 48.1%

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

   if -2.54999999999999999e69 < z < -5.8000000000000002e27 or -5.29999999999999984e-140 < z < -3.50000000000000007e-191 or 1.59999999999999991e-105 < z < 3.19999999999999986e-5

   1. Initial program 89.0%

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

      1. +-commutative 89.0%

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

      2. fma-define 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in a around inf 64.3%

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

   if -5.8000000000000002e27 < z < -5.29999999999999984e-140 or -3.50000000000000007e-191 < z < 1.59999999999999991e-105

   1. Initial program 89.3%

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

      1. +-commutative 89.3%

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

      2. fma-define 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in y around inf 60.5%

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

      1. div-sub 60.5%

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

   7. Simplified 60.5%

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

   8. Taylor expanded in a around inf 51.4%

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

Alternative 5: 37.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-119}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{a}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-191}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-104}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.2e+69)
   t
   (if (<= z -5.6e+28)
     x
     (if (<= z -6.6e-119)
       (/ (* x (- y)) a)
       (if (<= z -1.15e-191)
         x
         (if (<= z 2.3e-104) (* t (/ y (- a z))) (if (<= z 1e-5) x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.2e+69) {
		tmp = t;
	} else if (z <= -5.6e+28) {
		tmp = x;
	} else if (z <= -6.6e-119) {
		tmp = (x * -y) / a;
	} else if (z <= -1.15e-191) {
		tmp = x;
	} else if (z <= 2.3e-104) {
		tmp = t * (y / (a - z));
	} else if (z <= 1e-5) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.2d+69)) then
        tmp = t
    else if (z <= (-5.6d+28)) then
        tmp = x
    else if (z <= (-6.6d-119)) then
        tmp = (x * -y) / a
    else if (z <= (-1.15d-191)) then
        tmp = x
    else if (z <= 2.3d-104) then
        tmp = t * (y / (a - z))
    else if (z <= 1d-5) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.2e+69) {
		tmp = t;
	} else if (z <= -5.6e+28) {
		tmp = x;
	} else if (z <= -6.6e-119) {
		tmp = (x * -y) / a;
	} else if (z <= -1.15e-191) {
		tmp = x;
	} else if (z <= 2.3e-104) {
		tmp = t * (y / (a - z));
	} else if (z <= 1e-5) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.2e+69:
		tmp = t
	elif z <= -5.6e+28:
		tmp = x
	elif z <= -6.6e-119:
		tmp = (x * -y) / a
	elif z <= -1.15e-191:
		tmp = x
	elif z <= 2.3e-104:
		tmp = t * (y / (a - z))
	elif z <= 1e-5:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.2e+69)
		tmp = t;
	elseif (z <= -5.6e+28)
		tmp = x;
	elseif (z <= -6.6e-119)
		tmp = Float64(Float64(x * Float64(-y)) / a);
	elseif (z <= -1.15e-191)
		tmp = x;
	elseif (z <= 2.3e-104)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 1e-5)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.2e+69)
		tmp = t;
	elseif (z <= -5.6e+28)
		tmp = x;
	elseif (z <= -6.6e-119)
		tmp = (x * -y) / a;
	elseif (z <= -1.15e-191)
		tmp = x;
	elseif (z <= 2.3e-104)
		tmp = t * (y / (a - z));
	elseif (z <= 1e-5)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.2e+69], t, If[LessEqual[z, -5.6e+28], x, If[LessEqual[z, -6.6e-119], N[(N[(x * (-y)), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, -1.15e-191], x, If[LessEqual[z, 2.3e-104], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e-5], x, t]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.2000000000000002e69 or 1.00000000000000008e-5 < z

   1. Initial program 57.4%

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

      1. +-commutative 57.4%

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

      2. fma-define 57.3%

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

   3. Simplified 57.3%

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

   5. Taylor expanded in z around inf 48.1%

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

   if -2.2000000000000002e69 < z < -5.6000000000000003e28 or -6.60000000000000017e-119 < z < -1.15000000000000005e-191 or 2.2999999999999999e-104 < z < 1.00000000000000008e-5

   1. Initial program 87.6%

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

      1. +-commutative 87.6%

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

      2. fma-define 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in a around inf 60.9%

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

   if -5.6000000000000003e28 < z < -6.60000000000000017e-119

   1. Initial program 96.2%

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

      1. +-commutative 96.2%

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

      2. fma-define 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in y around -inf 71.1%

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

   6. Taylor expanded in a around inf 45.8%

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

   7. Taylor expanded in t around 0 38.8%

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

      1. neg-mul-1 63.6%

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

   9. Simplified 38.8%

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

   if -1.15000000000000005e-191 < z < 2.2999999999999999e-104

   1. Initial program 87.5%

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

      1. +-commutative 87.5%

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

      2. fma-define 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in y around -inf 62.2%

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

   6. Taylor expanded in t around inf 48.0%

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

      1. associate-/l* 50.4%

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

   8. Simplified 50.4%

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

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-119}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{a}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-191}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-104}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+69} \lor \neg \left(z \leq -3.55 \cdot 10^{+61} \lor \neg \left(z \leq -1.4 \cdot 10^{-25}\right) \land z \leq 6.2 \cdot 10^{+34}\right):\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.65e+69)
         (not
          (or (<= z -3.55e+61) (and (not (<= z -1.4e-25)) (<= z 6.2e+34)))))
   (+ t (* (- t x) (/ (- a y) z)))
   (+ x (* (- x t) (/ (- z y) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.65e+69) || !((z <= -3.55e+61) || (!(z <= -1.4e-25) && (z <= 6.2e+34)))) {
		tmp = t + ((t - x) * ((a - y) / z));
	} else {
		tmp = x + ((x - t) * ((z - y) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.65d+69)) .or. (.not. (z <= (-3.55d+61)) .or. (.not. (z <= (-1.4d-25))) .and. (z <= 6.2d+34))) then
        tmp = t + ((t - x) * ((a - y) / z))
    else
        tmp = x + ((x - t) * ((z - y) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.65e+69) || !((z <= -3.55e+61) || (!(z <= -1.4e-25) && (z <= 6.2e+34)))) {
		tmp = t + ((t - x) * ((a - y) / z));
	} else {
		tmp = x + ((x - t) * ((z - y) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.65e+69) or not ((z <= -3.55e+61) or (not (z <= -1.4e-25) and (z <= 6.2e+34))):
		tmp = t + ((t - x) * ((a - y) / z))
	else:
		tmp = x + ((x - t) * ((z - y) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.65e+69) || !((z <= -3.55e+61) || (!(z <= -1.4e-25) && (z <= 6.2e+34))))
		tmp = Float64(t + Float64(Float64(t - x) * Float64(Float64(a - y) / z)));
	else
		tmp = Float64(x + Float64(Float64(x - t) * Float64(Float64(z - y) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.65e+69) || ~(((z <= -3.55e+61) || (~((z <= -1.4e-25)) && (z <= 6.2e+34)))))
		tmp = t + ((t - x) * ((a - y) / z));
	else
		tmp = x + ((x - t) * ((z - y) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.65e+69], N[Not[Or[LessEqual[z, -3.55e+61], And[N[Not[LessEqual[z, -1.4e-25]], $MachinePrecision], LessEqual[z, 6.2e+34]]]], $MachinePrecision]], N[(t + N[(N[(t - x), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(x - t), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6499999999999999e69 or -3.55e61 < z < -1.39999999999999994e-25 or 6.19999999999999955e34 < z

   1. Initial program 61.0%

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

      1. clear-num 60.2%

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

      2. un-div-inv 60.2%

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

   4. Applied egg-rr 60.2%

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

   5. Taylor expanded in z around inf 66.6%

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

      1. associate--l+ 66.6%

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

      2. associate-*r/ 66.6%

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

      3. associate-*r/ 66.6%

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

      4. mul-1-neg 66.6%

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

      5. div-sub 66.6%

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

      6. mul-1-neg 66.6%

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

      7. distribute-lft-out-- 66.6%

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

      8. associate-*r/ 66.6%

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

      9. mul-1-neg 66.6%

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

      10. unsub-neg 66.6%

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

      11. distribute-rgt-out-- 67.4%

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

      12. *-lft-identity 67.4%

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

      13. times-frac 79.2%

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

   7. Simplified 79.2%

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

   if -1.6499999999999999e69 < z < -3.55e61 or -1.39999999999999994e-25 < z < 6.19999999999999955e34

   1. Initial program 89.4%

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

      1. +-commutative 89.4%

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

      2. fma-define 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in a around inf 81.6%

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

      1. associate-/l* 88.6%

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

   7. Simplified 88.6%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+69} \lor \neg \left(z \leq -3.55 \cdot 10^{+61} \lor \neg \left(z \leq -1.4 \cdot 10^{-25}\right) \land z \leq 6.2 \cdot 10^{+34}\right):\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -1.42 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{+51}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+34}:\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (/ y z) (- x t)))))
   (if (<= z -1.42e+69)
     t_1
     (if (<= z -2.35e+51)
       (+ x (* y (/ (- t x) a)))
       (if (<= z -2e-20)
         t_1
         (if (<= z 6.2e+34)
           (+ x (* (- x t) (/ (- z y) a)))
           (+ t (* x (/ (- y a) z)))))))))

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 <= -1.42e+69) {
		tmp = t_1;
	} else if (z <= -2.35e+51) {
		tmp = x + (y * ((t - x) / a));
	} else if (z <= -2e-20) {
		tmp = t_1;
	} else if (z <= 6.2e+34) {
		tmp = x + ((x - t) * ((z - y) / a));
	} else {
		tmp = t + (x * ((y - a) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((y / z) * (x - t))
    if (z <= (-1.42d+69)) then
        tmp = t_1
    else if (z <= (-2.35d+51)) then
        tmp = x + (y * ((t - x) / a))
    else if (z <= (-2d-20)) then
        tmp = t_1
    else if (z <= 6.2d+34) then
        tmp = x + ((x - t) * ((z - y) / a))
    else
        tmp = t + (x * ((y - a) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((y / z) * (x - t));
	double tmp;
	if (z <= -1.42e+69) {
		tmp = t_1;
	} else if (z <= -2.35e+51) {
		tmp = x + (y * ((t - x) / a));
	} else if (z <= -2e-20) {
		tmp = t_1;
	} else if (z <= 6.2e+34) {
		tmp = x + ((x - t) * ((z - y) / a));
	} else {
		tmp = t + (x * ((y - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((y / z) * (x - t))
	tmp = 0
	if z <= -1.42e+69:
		tmp = t_1
	elif z <= -2.35e+51:
		tmp = x + (y * ((t - x) / a))
	elif z <= -2e-20:
		tmp = t_1
	elif z <= 6.2e+34:
		tmp = x + ((x - t) * ((z - y) / a))
	else:
		tmp = t + (x * ((y - a) / z))
	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 <= -1.42e+69)
		tmp = t_1;
	elseif (z <= -2.35e+51)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	elseif (z <= -2e-20)
		tmp = t_1;
	elseif (z <= 6.2e+34)
		tmp = Float64(x + Float64(Float64(x - t) * Float64(Float64(z - y) / a)));
	else
		tmp = Float64(t + Float64(x * Float64(Float64(y - a) / z)));
	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 <= -1.42e+69)
		tmp = t_1;
	elseif (z <= -2.35e+51)
		tmp = x + (y * ((t - x) / a));
	elseif (z <= -2e-20)
		tmp = t_1;
	elseif (z <= 6.2e+34)
		tmp = x + ((x - t) * ((z - y) / a));
	else
		tmp = t + (x * ((y - a) / z));
	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, -1.42e+69], t$95$1, If[LessEqual[z, -2.35e+51], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2e-20], t$95$1, If[LessEqual[z, 6.2e+34], N[(x + N[(N[(x - t), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.42e69 or -2.3500000000000001e51 < z < -1.99999999999999989e-20

   1. Initial program 64.0%

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

      1. clear-num 63.5%

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

      2. un-div-inv 63.5%

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

   4. Applied egg-rr 63.5%

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

   5. Taylor expanded in z around inf 64.9%

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

      1. associate--l+ 64.9%

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

      2. associate-*r/ 64.9%

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

      3. associate-*r/ 64.9%

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

      4. mul-1-neg 64.9%

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

      5. div-sub 64.9%

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

      6. mul-1-neg 64.9%

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

      7. distribute-lft-out-- 64.9%

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

      8. associate-*r/ 64.9%

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

      9. mul-1-neg 64.9%

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

      10. unsub-neg 64.9%

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

      11. distribute-rgt-out-- 66.2%

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

      12. *-lft-identity 66.2%

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

      13. times-frac 74.6%

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

   7. Simplified 74.6%

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

   8. Taylor expanded in y around inf 68.3%

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

   if -1.42e69 < z < -2.3500000000000001e51

   1. Initial program 86.5%

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

      1. +-commutative 86.5%

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

      2. fma-define 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in z around 0 73.6%

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

      1. associate-/l* 86.4%

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

   7. Simplified 86.4%

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

   if -1.99999999999999989e-20 < z < 6.19999999999999955e34

   1. Initial program 89.0%

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

      1. +-commutative 89.0%

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

      2. fma-define 89.1%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in a around inf 82.5%

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

      1. associate-/l* 88.1%

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

   7. Simplified 88.1%

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

   if 6.19999999999999955e34 < z

   1. Initial program 57.3%

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

      1. clear-num 56.0%

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

      2. un-div-inv 56.0%

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

   4. Applied egg-rr 56.0%

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

   5. Taylor expanded in z around inf 69.2%

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

      1. associate--l+ 69.2%

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

      2. associate-*r/ 69.2%

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

      3. associate-*r/ 69.2%

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

      4. mul-1-neg 69.2%

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

      5. div-sub 69.2%

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

      6. mul-1-neg 69.2%

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

      7. distribute-lft-out-- 69.2%

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

      8. associate-*r/ 69.2%

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

      9. mul-1-neg 69.2%

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

      10. unsub-neg 69.2%

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

      11. distribute-rgt-out-- 69.5%

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

      12. *-lft-identity 69.5%

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

      13. times-frac 86.2%

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

   7. Simplified 86.2%

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

   8. Taylor expanded in t around 0 79.5%

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

      1. neg-mul-1 79.5%

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

   10. Simplified 79.5%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{+69}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{+51}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-20}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+34}:\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -2.55 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{+51}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-25} \lor \neg \left(z \leq 6.8 \cdot 10^{-9}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (/ y z) (- x t)))))
   (if (<= z -2.55e+69)
     t_1
     (if (<= z -1.35e+51)
       (+ x (* y (/ (- t x) a)))
       (if (or (<= z -6.5e-25) (not (<= z 6.8e-9)))
         t_1
         (+ x (/ (- t x) (/ a y))))))))

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 <= -2.55e+69) {
		tmp = t_1;
	} else if (z <= -1.35e+51) {
		tmp = x + (y * ((t - x) / a));
	} else if ((z <= -6.5e-25) || !(z <= 6.8e-9)) {
		tmp = t_1;
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((y / z) * (x - t))
    if (z <= (-2.55d+69)) then
        tmp = t_1
    else if (z <= (-1.35d+51)) then
        tmp = x + (y * ((t - x) / a))
    else if ((z <= (-6.5d-25)) .or. (.not. (z <= 6.8d-9))) then
        tmp = t_1
    else
        tmp = x + ((t - x) / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((y / z) * (x - t));
	double tmp;
	if (z <= -2.55e+69) {
		tmp = t_1;
	} else if (z <= -1.35e+51) {
		tmp = x + (y * ((t - x) / a));
	} else if ((z <= -6.5e-25) || !(z <= 6.8e-9)) {
		tmp = t_1;
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((y / z) * (x - t))
	tmp = 0
	if z <= -2.55e+69:
		tmp = t_1
	elif z <= -1.35e+51:
		tmp = x + (y * ((t - x) / a))
	elif (z <= -6.5e-25) or not (z <= 6.8e-9):
		tmp = t_1
	else:
		tmp = x + ((t - x) / (a / y))
	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 <= -2.55e+69)
		tmp = t_1;
	elseif (z <= -1.35e+51)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	elseif ((z <= -6.5e-25) || !(z <= 6.8e-9))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((y / z) * (x - t));
	tmp = 0.0;
	if (z <= -2.55e+69)
		tmp = t_1;
	elseif (z <= -1.35e+51)
		tmp = x + (y * ((t - x) / a));
	elseif ((z <= -6.5e-25) || ~((z <= 6.8e-9)))
		tmp = t_1;
	else
		tmp = x + ((t - x) / (a / y));
	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, -2.55e+69], t$95$1, If[LessEqual[z, -1.35e+51], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -6.5e-25], N[Not[LessEqual[z, 6.8e-9]], $MachinePrecision]], t$95$1, N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.54999999999999999e69 or -1.34999999999999996e51 < z < -6.5e-25 or 6.7999999999999997e-9 < z

   1. Initial program 61.7%

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

      1. clear-num 60.9%

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

      2. un-div-inv 60.9%

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

   4. Applied egg-rr 60.9%

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

   5. Taylor expanded in z around inf 66.5%

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

      1. associate--l+ 66.5%

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

      2. associate-*r/ 66.5%

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

      3. associate-*r/ 66.5%

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

      4. mul-1-neg 66.5%

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

      5. div-sub 66.5%

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

      6. mul-1-neg 66.5%

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

      7. distribute-lft-out-- 66.5%

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

      8. associate-*r/ 66.5%

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

      9. mul-1-neg 66.5%

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

      10. unsub-neg 66.5%

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

      11. distribute-rgt-out-- 67.4%

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

      12. *-lft-identity 67.4%

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

      13. times-frac 79.1%

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

   7. Simplified 79.1%

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

   8. Taylor expanded in y around inf 71.6%

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

   if -2.54999999999999999e69 < z < -1.34999999999999996e51

   1. Initial program 86.5%

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

      1. +-commutative 86.5%

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

      2. fma-define 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in z around 0 73.6%

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

      1. associate-/l* 86.4%

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

   7. Simplified 86.4%

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

   if -6.5e-25 < z < 6.7999999999999997e-9

   1. Initial program 88.8%

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

      1. +-commutative 88.8%

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

      2. fma-define 88.9%

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

   3. Simplified 88.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 88.8%

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

      2. *-commutative 88.8%

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

      3. associate-*l/ 89.8%

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

      4. associate-*r/ 95.6%

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

      5. clear-num 95.6%

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

      6. un-div-inv 95.6%

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

   6. Applied egg-rr 95.6%

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

   7. Taylor expanded in z around 0 85.4%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+69}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{+51}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-25} \lor \neg \left(z \leq 6.8 \cdot 10^{-9}\right):\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 70.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -2.15 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{+51}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-6}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (/ y z) (- x t)))))
   (if (<= z -2.15e+69)
     t_1
     (if (<= z -1.35e+51)
       (+ x (* y (/ (- t x) a)))
       (if (<= z -1.1e-21)
         t_1
         (if (<= z 5.6e-6)
           (+ x (/ (- t x) (/ a y)))
           (+ t (* x (/ (- y a) z)))))))))

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 <= -2.15e+69) {
		tmp = t_1;
	} else if (z <= -1.35e+51) {
		tmp = x + (y * ((t - x) / a));
	} else if (z <= -1.1e-21) {
		tmp = t_1;
	} else if (z <= 5.6e-6) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t + (x * ((y - a) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((y / z) * (x - t))
    if (z <= (-2.15d+69)) then
        tmp = t_1
    else if (z <= (-1.35d+51)) then
        tmp = x + (y * ((t - x) / a))
    else if (z <= (-1.1d-21)) then
        tmp = t_1
    else if (z <= 5.6d-6) then
        tmp = x + ((t - x) / (a / y))
    else
        tmp = t + (x * ((y - a) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((y / z) * (x - t));
	double tmp;
	if (z <= -2.15e+69) {
		tmp = t_1;
	} else if (z <= -1.35e+51) {
		tmp = x + (y * ((t - x) / a));
	} else if (z <= -1.1e-21) {
		tmp = t_1;
	} else if (z <= 5.6e-6) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t + (x * ((y - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((y / z) * (x - t))
	tmp = 0
	if z <= -2.15e+69:
		tmp = t_1
	elif z <= -1.35e+51:
		tmp = x + (y * ((t - x) / a))
	elif z <= -1.1e-21:
		tmp = t_1
	elif z <= 5.6e-6:
		tmp = x + ((t - x) / (a / y))
	else:
		tmp = t + (x * ((y - a) / z))
	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 <= -2.15e+69)
		tmp = t_1;
	elseif (z <= -1.35e+51)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	elseif (z <= -1.1e-21)
		tmp = t_1;
	elseif (z <= 5.6e-6)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	else
		tmp = Float64(t + Float64(x * Float64(Float64(y - a) / z)));
	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 <= -2.15e+69)
		tmp = t_1;
	elseif (z <= -1.35e+51)
		tmp = x + (y * ((t - x) / a));
	elseif (z <= -1.1e-21)
		tmp = t_1;
	elseif (z <= 5.6e-6)
		tmp = x + ((t - x) / (a / y));
	else
		tmp = t + (x * ((y - a) / z));
	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, -2.15e+69], t$95$1, If[LessEqual[z, -1.35e+51], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.1e-21], t$95$1, If[LessEqual[z, 5.6e-6], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.14999999999999996e69 or -1.34999999999999996e51 < z < -1.1e-21

   1. Initial program 64.0%

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

      1. clear-num 63.5%

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

      2. un-div-inv 63.5%

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

   4. Applied egg-rr 63.5%

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

   5. Taylor expanded in z around inf 64.9%

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

      1. associate--l+ 64.9%

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

      2. associate-*r/ 64.9%

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

      3. associate-*r/ 64.9%

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

      4. mul-1-neg 64.9%

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

      5. div-sub 64.9%

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

      6. mul-1-neg 64.9%

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

      7. distribute-lft-out-- 64.9%

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

      8. associate-*r/ 64.9%

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

      9. mul-1-neg 64.9%

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

      10. unsub-neg 64.9%

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

      11. distribute-rgt-out-- 66.2%

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

      12. *-lft-identity 66.2%

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

      13. times-frac 74.6%

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

   7. Simplified 74.6%

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

   8. Taylor expanded in y around inf 68.3%

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

   if -2.14999999999999996e69 < z < -1.34999999999999996e51

   1. Initial program 86.5%

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

      1. +-commutative 86.5%

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

      2. fma-define 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in z around 0 73.6%

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

      1. associate-/l* 86.4%

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

   7. Simplified 86.4%

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

   if -1.1e-21 < z < 5.59999999999999975e-6

   1. Initial program 88.8%

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

      1. +-commutative 88.8%

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

      2. fma-define 88.9%

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

   3. Simplified 88.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 88.8%

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

      2. *-commutative 88.8%

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

      3. associate-*l/ 89.8%

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

      4. associate-*r/ 95.6%

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

      5. clear-num 95.6%

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

      6. un-div-inv 95.6%

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

   6. Applied egg-rr 95.6%

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

   7. Taylor expanded in z around 0 85.4%

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

   if 5.59999999999999975e-6 < z

   1. Initial program 58.7%

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

      1. clear-num 57.5%

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

      2. un-div-inv 57.5%

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

   4. Applied egg-rr 57.5%

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

   5. Taylor expanded in z around inf 68.6%

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

      1. associate--l+ 68.6%

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

      2. associate-*r/ 68.6%

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

      3. associate-*r/ 68.6%

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

      4. mul-1-neg 68.6%

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

      5. div-sub 68.6%

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

      6. mul-1-neg 68.6%

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

      7. distribute-lft-out-- 68.6%

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

      8. associate-*r/ 68.6%

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

      9. mul-1-neg 68.6%

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

      10. unsub-neg 68.6%

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

      11. distribute-rgt-out-- 68.9%

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

      12. *-lft-identity 68.9%

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

      13. times-frac 85.0%

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

   7. Simplified 85.0%

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

   8. Taylor expanded in t around 0 78.6%

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

      1. neg-mul-1 78.6%

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

   10. Simplified 78.6%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+69}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{+51}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-21}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-6}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 48.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ t_2 := t \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+129}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-274}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-222}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* x (/ y a)))) (t_2 (* t (/ z (- z a)))))
   (if (<= z -1.8e+129)
     t_2
     (if (<= z -5.6e-274)
       t_1
       (if (<= z 2.1e-222)
         (* t (/ y (- a z)))
         (if (<= z 1.18e+92) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (y / a));
	double t_2 = t * (z / (z - a));
	double tmp;
	if (z <= -1.8e+129) {
		tmp = t_2;
	} else if (z <= -5.6e-274) {
		tmp = t_1;
	} else if (z <= 2.1e-222) {
		tmp = t * (y / (a - z));
	} else if (z <= 1.18e+92) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (x * (y / a))
    t_2 = t * (z / (z - a))
    if (z <= (-1.8d+129)) then
        tmp = t_2
    else if (z <= (-5.6d-274)) then
        tmp = t_1
    else if (z <= 2.1d-222) then
        tmp = t * (y / (a - z))
    else if (z <= 1.18d+92) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (y / a));
	double t_2 = t * (z / (z - a));
	double tmp;
	if (z <= -1.8e+129) {
		tmp = t_2;
	} else if (z <= -5.6e-274) {
		tmp = t_1;
	} else if (z <= 2.1e-222) {
		tmp = t * (y / (a - z));
	} else if (z <= 1.18e+92) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x * (y / a))
	t_2 = t * (z / (z - a))
	tmp = 0
	if z <= -1.8e+129:
		tmp = t_2
	elif z <= -5.6e-274:
		tmp = t_1
	elif z <= 2.1e-222:
		tmp = t * (y / (a - z))
	elif z <= 1.18e+92:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x * Float64(y / a)))
	t_2 = Float64(t * Float64(z / Float64(z - a)))
	tmp = 0.0
	if (z <= -1.8e+129)
		tmp = t_2;
	elseif (z <= -5.6e-274)
		tmp = t_1;
	elseif (z <= 2.1e-222)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 1.18e+92)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x * (y / a));
	t_2 = t * (z / (z - a));
	tmp = 0.0;
	if (z <= -1.8e+129)
		tmp = t_2;
	elseif (z <= -5.6e-274)
		tmp = t_1;
	elseif (z <= 2.1e-222)
		tmp = t * (y / (a - z));
	elseif (z <= 1.18e+92)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+129], t$95$2, If[LessEqual[z, -5.6e-274], t$95$1, If[LessEqual[z, 2.1e-222], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.18e+92], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8000000000000001e129 or 1.18e92 < z

   1. Initial program 53.1%

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

      1. clear-num 52.3%

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

      2. un-div-inv 52.2%

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

   4. Applied egg-rr 52.2%

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

   5. Taylor expanded in y around 0 28.2%

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

      1. associate-*r/ 44.8%

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

      2. neg-mul-1 44.8%

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

      3. unsub-neg 44.8%

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

   7. Simplified 44.8%

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

   8. Taylor expanded in x around 0 34.0%

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

      1. mul-1-neg 34.0%

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

      2. associate-/l* 58.3%

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

      3. distribute-rgt-neg-in 58.3%

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

      4. distribute-frac-neg2 58.3%

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

      5. sub-neg 58.3%

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

      6. distribute-neg-in 58.3%

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

      7. remove-double-neg 58.3%

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

   10. Simplified 58.3%

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

   if -1.8000000000000001e129 < z < -5.5999999999999995e-274 or 2.0999999999999999e-222 < z < 1.18e92

   1. Initial program 86.7%

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

   3. Taylor expanded in t around 0 51.7%

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

      1. mul-1-neg 51.7%

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

      2. associate-/l* 57.3%

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

      3. distribute-rgt-neg-in 57.3%

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

      4. mul-1-neg 57.3%

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

      5. associate-*r/ 57.3%

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

      6. neg-mul-1 57.3%

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

      7. neg-sub0 57.3%

         \[\leadsto x + x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{a - z} \]

      8. sub-neg 57.3%

         \[\leadsto x + x \cdot \frac{0 - \color{blue}{\left(y + \left(-z\right)\right)}}{a - z} \]

      9. +-commutative 57.3%

         \[\leadsto x + x \cdot \frac{0 - \color{blue}{\left(\left(-z\right) + y\right)}}{a - z} \]

      10. associate--r+ 57.3%

          \[\leadsto x + x \cdot \frac{\color{blue}{\left(0 - \left(-z\right)\right) - y}}{a - z} \]

      11. neg-sub0 57.3%

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

      12. remove-double-neg 57.3%

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

   5. Simplified 57.3%

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

   6. Taylor expanded in z around 0 48.8%

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

      1. mul-1-neg 48.8%

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

      2. unsub-neg 48.8%

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

      3. associate-/l* 52.2%

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

   8. Simplified 52.2%

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

   if -5.5999999999999995e-274 < z < 2.0999999999999999e-222

   1. Initial program 83.1%

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

      1. +-commutative 83.1%

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

      2. fma-define 83.1%

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

   3. Simplified 83.1%

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

   5. Taylor expanded in y around -inf 67.0%

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

   6. Taylor expanded in t around inf 63.6%

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

      1. associate-/l* 66.7%

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

   8. Simplified 66.7%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+129}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-274}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-222}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{+92}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 47.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+130}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-275}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-222}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* x (/ y a)))))
   (if (<= z -3.5e+130)
     t
     (if (<= z -3e-275)
       t_1
       (if (<= z 3.6e-222) (* t (/ y (- a z))) (if (<= z 1.15e+92) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (y / a));
	double tmp;
	if (z <= -3.5e+130) {
		tmp = t;
	} else if (z <= -3e-275) {
		tmp = t_1;
	} else if (z <= 3.6e-222) {
		tmp = t * (y / (a - z));
	} else if (z <= 1.15e+92) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (x * (y / a))
    if (z <= (-3.5d+130)) then
        tmp = t
    else if (z <= (-3d-275)) then
        tmp = t_1
    else if (z <= 3.6d-222) then
        tmp = t * (y / (a - z))
    else if (z <= 1.15d+92) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (y / a));
	double tmp;
	if (z <= -3.5e+130) {
		tmp = t;
	} else if (z <= -3e-275) {
		tmp = t_1;
	} else if (z <= 3.6e-222) {
		tmp = t * (y / (a - z));
	} else if (z <= 1.15e+92) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x * (y / a))
	tmp = 0
	if z <= -3.5e+130:
		tmp = t
	elif z <= -3e-275:
		tmp = t_1
	elif z <= 3.6e-222:
		tmp = t * (y / (a - z))
	elif z <= 1.15e+92:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x * Float64(y / a)))
	tmp = 0.0
	if (z <= -3.5e+130)
		tmp = t;
	elseif (z <= -3e-275)
		tmp = t_1;
	elseif (z <= 3.6e-222)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 1.15e+92)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x * (y / a));
	tmp = 0.0;
	if (z <= -3.5e+130)
		tmp = t;
	elseif (z <= -3e-275)
		tmp = t_1;
	elseif (z <= 3.6e-222)
		tmp = t * (y / (a - z));
	elseif (z <= 1.15e+92)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+130], t, If[LessEqual[z, -3e-275], t$95$1, If[LessEqual[z, 3.6e-222], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e+92], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.5000000000000001e130 or 1.14999999999999999e92 < z

   1. Initial program 53.1%

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

      1. +-commutative 53.1%

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

      2. fma-define 53.2%

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

   3. Simplified 53.2%

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

   5. Taylor expanded in z around inf 54.4%

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

   if -3.5000000000000001e130 < z < -3e-275 or 3.59999999999999974e-222 < z < 1.14999999999999999e92

   1. Initial program 86.7%

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

   3. Taylor expanded in t around 0 51.7%

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

      1. mul-1-neg 51.7%

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

      2. associate-/l* 57.3%

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

      3. distribute-rgt-neg-in 57.3%

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

      4. mul-1-neg 57.3%

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

      5. associate-*r/ 57.3%

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

      6. neg-mul-1 57.3%

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

      7. neg-sub0 57.3%

         \[\leadsto x + x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{a - z} \]

      8. sub-neg 57.3%

         \[\leadsto x + x \cdot \frac{0 - \color{blue}{\left(y + \left(-z\right)\right)}}{a - z} \]

      9. +-commutative 57.3%

         \[\leadsto x + x \cdot \frac{0 - \color{blue}{\left(\left(-z\right) + y\right)}}{a - z} \]

      10. associate--r+ 57.3%

          \[\leadsto x + x \cdot \frac{\color{blue}{\left(0 - \left(-z\right)\right) - y}}{a - z} \]

      11. neg-sub0 57.3%

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

      12. remove-double-neg 57.3%

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

   5. Simplified 57.3%

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

   6. Taylor expanded in z around 0 48.8%

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

      1. mul-1-neg 48.8%

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

      2. unsub-neg 48.8%

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

      3. associate-/l* 52.2%

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

   8. Simplified 52.2%

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

   if -3e-275 < z < 3.59999999999999974e-222

   1. Initial program 83.1%

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

      1. +-commutative 83.1%

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

      2. fma-define 83.1%

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

   3. Simplified 83.1%

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

   5. Taylor expanded in y around -inf 67.0%

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

   6. Taylor expanded in t around inf 63.6%

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

      1. associate-/l* 66.7%

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

   8. Simplified 66.7%

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

Alternative 12: 68.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+69} \lor \neg \left(z \leq 5 \cdot 10^{-6}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.5e+69) (not (<= z 5e-6)))
   (* t (/ (- y z) (- a z)))
   (+ x (/ (- t x) (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.5e+69) || !(z <= 5e-6)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.5d+69)) .or. (.not. (z <= 5d-6))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + ((t - x) / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.5e+69) || !(z <= 5e-6)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.5e+69) or not (z <= 5e-6):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + ((t - x) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.5e+69) || !(z <= 5e-6))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.5e+69) || ~((z <= 5e-6)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + ((t - x) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.5e+69], N[Not[LessEqual[z, 5e-6]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.49999999999999992e69 or 5.00000000000000041e-6 < z

   1. Initial program 57.4%

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

      1. +-commutative 57.4%

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

      2. fma-define 57.3%

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

   3. Simplified 57.3%

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

   5. Taylor expanded in t around inf 59.7%

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

      1. div-sub 59.8%

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

   7. Simplified 59.8%

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

   if -1.49999999999999992e69 < z < 5.00000000000000041e-6

   1. Initial program 89.3%

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

      1. +-commutative 89.3%

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

      2. fma-define 89.4%

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

   3. Simplified 89.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 89.3%

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

      2. *-commutative 89.3%

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

      3. associate-*l/ 88.0%

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

      4. associate-*r/ 94.9%

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

      5. clear-num 94.9%

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

      6. un-div-inv 94.9%

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

   6. Applied egg-rr 94.9%

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

   7. Taylor expanded in z around 0 80.7%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+69} \lor \neg \left(z \leq 5 \cdot 10^{-6}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 67.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+69} \lor \neg \left(z \leq 1.25 \cdot 10^{-5}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.45e+69) (not (<= z 1.25e-5)))
   (* t (/ (- y z) (- a z)))
   (+ x (* y (/ (- t x) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.45e+69) || !(z <= 1.25e-5)) {
		tmp = t * ((y - z) / (a - z));
	} 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) :: tmp
    if ((z <= (-1.45d+69)) .or. (.not. (z <= 1.25d-5))) then
        tmp = t * ((y - z) / (a - z))
    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 tmp;
	if ((z <= -1.45e+69) || !(z <= 1.25e-5)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y * ((t - x) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.45e+69) or not (z <= 1.25e-5):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + (y * ((t - x) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.45e+69) || !(z <= 1.25e-5))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.45e+69) || ~((z <= 1.25e-5)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + (y * ((t - x) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.45e+69], N[Not[LessEqual[z, 1.25e-5]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4499999999999999e69 or 1.25000000000000006e-5 < z

   1. Initial program 57.4%

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

      1. +-commutative 57.4%

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

      2. fma-define 57.3%

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

   3. Simplified 57.3%

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

   5. Taylor expanded in t around inf 59.7%

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

      1. div-sub 59.8%

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

   7. Simplified 59.8%

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

   if -1.4499999999999999e69 < z < 1.25000000000000006e-5

   1. Initial program 89.3%

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

      1. +-commutative 89.3%

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

      2. fma-define 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in z around 0 76.0%

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

      1. associate-/l* 76.4%

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

   7. Simplified 76.4%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+69} \lor \neg \left(z \leq 1.25 \cdot 10^{-5}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 60.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -380 \lor \neg \left(x \leq 2.2 \cdot 10^{+118}\right):\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -380.0) (not (<= x 2.2e+118)))
   (- x (* x (/ y a)))
   (* t (/ (- y z) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -380.0) || !(x <= 2.2e+118)) {
		tmp = x - (x * (y / a));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-380.0d0)) .or. (.not. (x <= 2.2d+118))) then
        tmp = x - (x * (y / a))
    else
        tmp = t * ((y - z) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -380.0) || !(x <= 2.2e+118)) {
		tmp = x - (x * (y / a));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -380.0) or not (x <= 2.2e+118):
		tmp = x - (x * (y / a))
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -380.0) || !(x <= 2.2e+118))
		tmp = Float64(x - Float64(x * Float64(y / a)));
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -380.0) || ~((x <= 2.2e+118)))
		tmp = x - (x * (y / a));
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -380.0], N[Not[LessEqual[x, 2.2e+118]], $MachinePrecision]], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -380 or 2.19999999999999986e118 < x

   1. Initial program 70.8%

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

   3. Taylor expanded in t around 0 52.1%

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

      1. mul-1-neg 52.1%

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

      2. associate-/l* 62.7%

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

      3. distribute-rgt-neg-in 62.7%

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

      4. mul-1-neg 62.7%

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

      5. associate-*r/ 62.7%

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

      6. neg-mul-1 62.7%

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

      7. neg-sub0 62.7%

         \[\leadsto x + x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{a - z} \]

      8. sub-neg 62.7%

         \[\leadsto x + x \cdot \frac{0 - \color{blue}{\left(y + \left(-z\right)\right)}}{a - z} \]

      9. +-commutative 62.7%

         \[\leadsto x + x \cdot \frac{0 - \color{blue}{\left(\left(-z\right) + y\right)}}{a - z} \]

      10. associate--r+ 62.7%

          \[\leadsto x + x \cdot \frac{\color{blue}{\left(0 - \left(-z\right)\right) - y}}{a - z} \]

      11. neg-sub0 62.7%

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

      12. remove-double-neg 62.7%

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

   5. Simplified 62.7%

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

   6. Taylor expanded in z around 0 52.7%

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

      1. mul-1-neg 52.7%

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

      2. unsub-neg 52.7%

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

      3. associate-/l* 57.0%

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

   8. Simplified 57.0%

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

   if -380 < x < 2.19999999999999986e118

   1. Initial program 76.8%

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

      1. +-commutative 76.8%

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

      2. fma-define 76.9%

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

   3. Simplified 76.9%

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

   5. Taylor expanded in t around inf 72.1%

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

      1. div-sub 72.2%

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

   7. Simplified 72.2%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -380 \lor \neg \left(x \leq 2.2 \cdot 10^{+118}\right):\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 39.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+72}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+56}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.8e+72) x (if (<= a 3.6e+56) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.8e+72) {
		tmp = x;
	} else if (a <= 3.6e+56) {
		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 <= (-3.8d+72)) then
        tmp = x
    else if (a <= 3.6d+56) 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 <= -3.8e+72) {
		tmp = x;
	} else if (a <= 3.6e+56) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.8e+72:
		tmp = x
	elif a <= 3.6e+56:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.8e+72)
		tmp = x;
	elseif (a <= 3.6e+56)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.8e+72)
		tmp = x;
	elseif (a <= 3.6e+56)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.8e+72], x, If[LessEqual[a, 3.6e+56], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -3.80000000000000006e72 or 3.59999999999999998e56 < a

   1. Initial program 86.1%

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

      1. +-commutative 86.1%

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

      2. fma-define 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in a around inf 56.6%

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

   if -3.80000000000000006e72 < a < 3.59999999999999998e56

   1. Initial program 67.6%

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

      1. +-commutative 67.6%

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

      2. fma-define 67.6%

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

   3. Simplified 67.6%

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

   5. Taylor expanded in z around inf 34.8%

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

Alternative 16: 26.0% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 74.3%

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

   1. +-commutative 74.3%

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

   2. fma-define 74.4%

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

3. Simplified 74.4%

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

5. Taylor expanded in z around inf 26.6%

   \[\leadsto \color{blue}{t} \]
6. Add Preprocessing

Alternative 17: 2.8% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = 0.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 74.3%

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

3. Taylor expanded in t around 0 37.4%

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

   1. mul-1-neg 37.4%

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

   2. associate-/l* 41.8%

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

   3. distribute-rgt-neg-in 41.8%

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

   4. mul-1-neg 41.8%

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

   5. associate-*r/ 41.8%

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

   6. neg-mul-1 41.8%

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

   7. neg-sub0 41.8%

      \[\leadsto x + x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{a - z} \]

   8. sub-neg 41.8%

      \[\leadsto x + x \cdot \frac{0 - \color{blue}{\left(y + \left(-z\right)\right)}}{a - z} \]

   9. +-commutative 41.8%

      \[\leadsto x + x \cdot \frac{0 - \color{blue}{\left(\left(-z\right) + y\right)}}{a - z} \]

   10. associate--r+ 41.8%

       \[\leadsto x + x \cdot \frac{\color{blue}{\left(0 - \left(-z\right)\right) - y}}{a - z} \]

   11. neg-sub0 41.8%

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

   12. remove-double-neg 41.8%

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

5. Simplified 41.8%

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

6. Taylor expanded in z around inf 2.9%

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

   1. distribute-rgt1-in 2.9%

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

   2. metadata-eval 2.9%

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

   3. mul0-lft 2.9%

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

8. Simplified 2.9%

   \[\leadsto \color{blue}{0} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024111 
(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)))))