Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.6% → 91.2%

Time: 13.5s

Alternatives: 22

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: 80.6% 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: 91.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := x + \left(y - z\right) \cdot t\_1\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-271} \lor \neg \left(t\_2 \leq 2 \cdot 10^{-292}\right):\\ \;\;\;\;\mathsf{fma}\left(y - z, t\_1, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t x) (- a z))) (t_2 (+ x (* (- y z) t_1))))
   (if (or (<= t_2 -2e-271) (not (<= t_2 2e-292)))
     (fma (- y z) t_1 x)
     (+ t (* (/ (- t x) z) (- a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) / (a - z);
	double t_2 = x + ((y - z) * t_1);
	double tmp;
	if ((t_2 <= -2e-271) || !(t_2 <= 2e-292)) {
		tmp = fma((y - z), t_1, x);
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) / Float64(a - z))
	t_2 = Float64(x + Float64(Float64(y - z) * t_1))
	tmp = 0.0
	if ((t_2 <= -2e-271) || !(t_2 <= 2e-292))
		tmp = fma(Float64(y - z), t_1, 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[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -2e-271], N[Not[LessEqual[t$95$2, 2e-292]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t$95$1 + 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)))) < -1.99999999999999993e-271 or 2.0000000000000001e-292 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.2%

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

      1. +-commutative 90.2%

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

      2. fma-define 90.2%

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

   3. Simplified 90.2%

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

   if -1.99999999999999993e-271 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 2.0000000000000001e-292

   1. Initial program 3.5%

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

      1. +-commutative 3.5%

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

      2. fma-define 4.1%

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

   3. Simplified 4.1%

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

   5. Taylor expanded in z around inf 76.3%

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

      1. associate--l+ 76.3%

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

      2. distribute-lft-out-- 76.3%

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

      3. div-sub 76.4%

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

      4. mul-1-neg 76.4%

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

      5. unsub-neg 76.4%

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

      6. div-sub 76.3%

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

      7. associate-/l* 88.1%

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

      8. associate-/l* 96.8%

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

      9. distribute-rgt-out-- 96.8%

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

   7. Simplified 96.8%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-271} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 2 \cdot 10^{-292}\right):\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-271} \lor \neg \left(t\_1 \leq 2 \cdot 10^{-292}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-271) (not (<= t_1 2e-292)))
     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 <= -2e-271) || !(t_1 <= 2e-292)) {
		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 <= (-2d-271)) .or. (.not. (t_1 <= 2d-292))) 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 <= -2e-271) || !(t_1 <= 2e-292)) {
		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 <= -2e-271) or not (t_1 <= 2e-292):
		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 <= -2e-271) || !(t_1 <= 2e-292))
		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 <= -2e-271) || ~((t_1 <= 2e-292)))
		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, -2e-271], N[Not[LessEqual[t$95$1, 2e-292]], $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)))) < -1.99999999999999993e-271 or 2.0000000000000001e-292 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.2%

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

   if -1.99999999999999993e-271 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 2.0000000000000001e-292

   1. Initial program 3.5%

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

      1. +-commutative 3.5%

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

      2. fma-define 4.1%

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

   3. Simplified 4.1%

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

   5. Taylor expanded in z around inf 76.3%

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

      1. associate--l+ 76.3%

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

      2. distribute-lft-out-- 76.3%

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

      3. div-sub 76.4%

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

      4. mul-1-neg 76.4%

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

      5. unsub-neg 76.4%

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

      6. div-sub 76.3%

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

      7. associate-/l* 88.1%

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

      8. associate-/l* 96.8%

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

      9. distribute-rgt-out-- 96.8%

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

   7. Simplified 96.8%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-271} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 2 \cdot 10^{-292}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 42.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -2.1 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-280}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-93}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+75}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= a -2.1e-21)
     t_1
     (if (<= a 1.65e-280)
       (* x (/ (- y a) z))
       (if (<= a 5.5e-93) t (if (<= a 4.6e+75) (* y (/ t (- a z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -2.1e-21) {
		tmp = t_1;
	} else if (a <= 1.65e-280) {
		tmp = x * ((y - a) / z);
	} else if (a <= 5.5e-93) {
		tmp = t;
	} else if (a <= 4.6e+75) {
		tmp = y * (t / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (a <= (-2.1d-21)) then
        tmp = t_1
    else if (a <= 1.65d-280) then
        tmp = x * ((y - a) / z)
    else if (a <= 5.5d-93) then
        tmp = t
    else if (a <= 4.6d+75) then
        tmp = y * (t / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -2.1e-21) {
		tmp = t_1;
	} else if (a <= 1.65e-280) {
		tmp = x * ((y - a) / z);
	} else if (a <= 5.5e-93) {
		tmp = t;
	} else if (a <= 4.6e+75) {
		tmp = y * (t / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if a <= -2.1e-21:
		tmp = t_1
	elif a <= 1.65e-280:
		tmp = x * ((y - a) / z)
	elif a <= 5.5e-93:
		tmp = t
	elif a <= 4.6e+75:
		tmp = y * (t / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (a <= -2.1e-21)
		tmp = t_1;
	elseif (a <= 1.65e-280)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= 5.5e-93)
		tmp = t;
	elseif (a <= 4.6e+75)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (a <= -2.1e-21)
		tmp = t_1;
	elseif (a <= 1.65e-280)
		tmp = x * ((y - a) / z);
	elseif (a <= 5.5e-93)
		tmp = t;
	elseif (a <= 4.6e+75)
		tmp = y * (t / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.1e-21], t$95$1, If[LessEqual[a, 1.65e-280], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.5e-93], t, If[LessEqual[a, 4.6e+75], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.10000000000000013e-21 or 4.5999999999999997e75 < a

   1. Initial program 92.2%

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

      1. +-commutative 92.2%

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

      2. fma-define 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in t around 0 51.9%

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

      1. mul-1-neg 51.9%

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

      2. *-rgt-identity 51.9%

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

      3. associate-/l* 60.9%

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

      4. distribute-rgt-neg-in 60.9%

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

      5. mul-1-neg 60.9%

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

      6. distribute-lft-in 60.9%

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

      7. mul-1-neg 60.9%

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

      8. unsub-neg 60.9%

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

   7. Simplified 60.9%

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

   8. Taylor expanded in z around 0 58.7%

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

   if -2.10000000000000013e-21 < a < 1.64999999999999995e-280

   1. Initial program 62.6%

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

      1. +-commutative 62.6%

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

      2. fma-define 62.7%

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

   3. Simplified 62.7%

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

   5. Taylor expanded in z around inf 77.0%

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

      1. associate--l+ 77.0%

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

      2. distribute-lft-out-- 77.0%

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

      3. div-sub 77.0%

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

      4. mul-1-neg 77.0%

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

      5. unsub-neg 77.0%

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

      6. div-sub 77.0%

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

      7. associate-/l* 79.8%

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

      8. associate-/l* 77.9%

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

      9. distribute-rgt-out-- 79.9%

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

   7. Simplified 79.9%

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

   8. Taylor expanded in t around 0 36.3%

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

      1. associate-/l* 46.7%

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

   10. Simplified 46.7%

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

   if 1.64999999999999995e-280 < a < 5.49999999999999968e-93

   1. Initial program 68.7%

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

      1. associate-*r/ 69.1%

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

      2. clear-num 68.8%

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

   4. Applied egg-rr 68.8%

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

      1. associate-/r/ 68.9%

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

      2. *-commutative 68.9%

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

   6. Simplified 68.9%

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

   7. Taylor expanded in z around inf 46.9%

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

   if 5.49999999999999968e-93 < a < 4.5999999999999997e75

   1. Initial program 80.8%

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

      1. +-commutative 80.8%

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

      2. fma-define 80.8%

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

   3. Simplified 80.8%

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

   5. Taylor expanded in y around inf 64.0%

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

   6. Taylor expanded in t around inf 44.0%

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

Alternative 4: 37.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.85 \cdot 10^{+228}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8.6 \cdot 10^{-119}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 0.000125:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+71}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.85e+228)
   x
   (if (<= a -8.6e-119)
     (+ x t)
     (if (<= a 0.000125) (* x (/ y z)) (if (<= a 2.5e+71) (* y (/ t a)) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.85e+228) {
		tmp = x;
	} else if (a <= -8.6e-119) {
		tmp = x + t;
	} else if (a <= 0.000125) {
		tmp = x * (y / z);
	} else if (a <= 2.5e+71) {
		tmp = y * (t / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.85d+228)) then
        tmp = x
    else if (a <= (-8.6d-119)) then
        tmp = x + t
    else if (a <= 0.000125d0) then
        tmp = x * (y / z)
    else if (a <= 2.5d+71) then
        tmp = y * (t / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.85e+228) {
		tmp = x;
	} else if (a <= -8.6e-119) {
		tmp = x + t;
	} else if (a <= 0.000125) {
		tmp = x * (y / z);
	} else if (a <= 2.5e+71) {
		tmp = y * (t / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.85e+228:
		tmp = x
	elif a <= -8.6e-119:
		tmp = x + t
	elif a <= 0.000125:
		tmp = x * (y / z)
	elif a <= 2.5e+71:
		tmp = y * (t / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.85e+228)
		tmp = x;
	elseif (a <= -8.6e-119)
		tmp = Float64(x + t);
	elseif (a <= 0.000125)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 2.5e+71)
		tmp = Float64(y * Float64(t / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.85e+228)
		tmp = x;
	elseif (a <= -8.6e-119)
		tmp = x + t;
	elseif (a <= 0.000125)
		tmp = x * (y / z);
	elseif (a <= 2.5e+71)
		tmp = y * (t / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.85e+228], x, If[LessEqual[a, -8.6e-119], N[(x + t), $MachinePrecision], If[LessEqual[a, 0.000125], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.5e+71], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.8500000000000001e228 or 2.49999999999999986e71 < a

   1. Initial program 98.4%

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

      1. +-commutative 98.4%

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

      2. fma-define 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in a around inf 63.1%

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

   if -2.8500000000000001e228 < a < -8.5999999999999999e-119

   1. Initial program 80.6%

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

   3. Taylor expanded in t around inf 69.2%

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

      1. associate-/l* 73.8%

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

   5. Simplified 73.8%

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

   6. Taylor expanded in z around inf 39.6%

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

   if -8.5999999999999999e-119 < a < 1.25e-4

   1. Initial program 67.2%

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

      1. +-commutative 67.2%

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

      2. fma-define 67.4%

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

   3. Simplified 67.4%

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

   5. Taylor expanded in t around 0 31.3%

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

      1. mul-1-neg 31.3%

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

      2. *-rgt-identity 31.3%

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

      3. associate-/l* 34.4%

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

      4. distribute-rgt-neg-in 34.4%

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

      5. mul-1-neg 34.4%

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

      6. distribute-lft-in 34.3%

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

      7. mul-1-neg 34.3%

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

      8. unsub-neg 34.3%

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

   7. Simplified 34.3%

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

   8. Taylor expanded in a around 0 40.5%

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

   if 1.25e-4 < a < 2.49999999999999986e71

   1. Initial program 77.0%

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

      1. +-commutative 77.0%

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

      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 y around inf 56.0%

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

   6. Taylor expanded in t around inf 50.7%

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

   7. Taylor expanded in a around inf 46.2%

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

Alternative 5: 38.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+228}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-119}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-280}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+77}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.2e+228)
   x
   (if (<= a -7.5e-119)
     (+ x t)
     (if (<= a 7.2e-280) (* x (/ y z)) (if (<= a 7e+77) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.2e+228) {
		tmp = x;
	} else if (a <= -7.5e-119) {
		tmp = x + t;
	} else if (a <= 7.2e-280) {
		tmp = x * (y / z);
	} else if (a <= 7e+77) {
		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 <= (-3.2d+228)) then
        tmp = x
    else if (a <= (-7.5d-119)) then
        tmp = x + t
    else if (a <= 7.2d-280) then
        tmp = x * (y / z)
    else if (a <= 7d+77) 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 <= -3.2e+228) {
		tmp = x;
	} else if (a <= -7.5e-119) {
		tmp = x + t;
	} else if (a <= 7.2e-280) {
		tmp = x * (y / z);
	} else if (a <= 7e+77) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.2e+228:
		tmp = x
	elif a <= -7.5e-119:
		tmp = x + t
	elif a <= 7.2e-280:
		tmp = x * (y / z)
	elif a <= 7e+77:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.2e+228)
		tmp = x;
	elseif (a <= -7.5e-119)
		tmp = Float64(x + t);
	elseif (a <= 7.2e-280)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 7e+77)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.2e+228)
		tmp = x;
	elseif (a <= -7.5e-119)
		tmp = x + t;
	elseif (a <= 7.2e-280)
		tmp = x * (y / z);
	elseif (a <= 7e+77)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.2e+228], x, If[LessEqual[a, -7.5e-119], N[(x + t), $MachinePrecision], If[LessEqual[a, 7.2e-280], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7e+77], t, x]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.2000000000000003e228 or 7.0000000000000003e77 < a

   1. Initial program 98.3%

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

      1. +-commutative 98.3%

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

      2. fma-define 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in a around inf 65.0%

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

   if -3.2000000000000003e228 < a < -7.50000000000000044e-119

   1. Initial program 80.6%

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

   3. Taylor expanded in t around inf 69.2%

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

      1. associate-/l* 73.8%

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

   5. Simplified 73.8%

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

   6. Taylor expanded in z around inf 39.6%

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

   if -7.50000000000000044e-119 < a < 7.19999999999999989e-280

   1. Initial program 60.0%

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

      1. +-commutative 60.0%

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

      2. fma-define 60.3%

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

   3. Simplified 60.3%

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

   5. Taylor expanded in t around 0 27.6%

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

      1. mul-1-neg 27.6%

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

      2. *-rgt-identity 27.6%

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

      3. associate-/l* 32.7%

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

      4. distribute-rgt-neg-in 32.7%

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

      5. mul-1-neg 32.7%

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

      6. distribute-lft-in 32.6%

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

      7. mul-1-neg 32.6%

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

      8. unsub-neg 32.6%

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

   7. Simplified 32.6%

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

   8. Taylor expanded in a around 0 50.3%

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

   if 7.19999999999999989e-280 < a < 7.0000000000000003e77

   1. Initial program 74.3%

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

      1. associate-*r/ 71.0%

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

      2. clear-num 70.8%

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

   4. Applied egg-rr 70.8%

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

      1. associate-/r/ 70.9%

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

      2. *-commutative 70.9%

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

   6. Simplified 70.9%

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

   7. Taylor expanded in z around inf 34.9%

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

Alternative 6: 74.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{-67} \lor \neg \left(a \leq 2.75 \cdot 10^{-5}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y \cdot \left(t - x\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -9.5e-67) (not (<= a 2.75e-5)))
   (+ x (* t (/ (- y z) (- a z))))
   (- t (/ (* y (- t x)) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -9.5e-67) || !(a <= 2.75e-5)) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = t - ((y * (t - x)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-9.5d-67)) .or. (.not. (a <= 2.75d-5))) then
        tmp = x + (t * ((y - z) / (a - z)))
    else
        tmp = t - ((y * (t - x)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -9.5e-67) || !(a <= 2.75e-5)) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = t - ((y * (t - x)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -9.5e-67) or not (a <= 2.75e-5):
		tmp = x + (t * ((y - z) / (a - z)))
	else:
		tmp = t - ((y * (t - x)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -9.5e-67) || !(a <= 2.75e-5))
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))));
	else
		tmp = Float64(t - Float64(Float64(y * Float64(t - x)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -9.5e-67) || ~((a <= 2.75e-5)))
		tmp = x + (t * ((y - z) / (a - z)));
	else
		tmp = t - ((y * (t - x)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -9.5e-67], N[Not[LessEqual[a, 2.75e-5]], $MachinePrecision]], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -9.4999999999999994e-67 or 2.7500000000000001e-5 < a

   1. Initial program 88.6%

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

   3. Taylor expanded in t around inf 71.2%

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

      1. associate-/l* 83.3%

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

   5. Simplified 83.3%

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

   if -9.4999999999999994e-67 < a < 2.7500000000000001e-5

   1. Initial program 67.5%

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

      1. +-commutative 67.5%

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

      2. fma-define 67.7%

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

   3. Simplified 67.7%

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

   5. Taylor expanded in z around inf 80.8%

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

      1. associate--l+ 80.8%

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

      2. distribute-lft-out-- 80.8%

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

      3. div-sub 81.6%

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

      4. mul-1-neg 81.6%

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

      5. unsub-neg 81.6%

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

      6. div-sub 80.8%

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

      7. associate-/l* 79.8%

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

      8. associate-/l* 78.7%

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

      9. distribute-rgt-out-- 80.7%

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

   7. Simplified 80.7%

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

   8. Taylor expanded in y around inf 78.1%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{-67} \lor \neg \left(a \leq 2.75 \cdot 10^{-5}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y \cdot \left(t - x\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-67}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-5}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7e-67)
   (+ x (* t (/ (- y z) (- a z))))
   (if (<= a 2.8e-5)
     (+ t (* (/ (- t x) z) (- a y)))
     (+ x (/ t (/ (- a z) (- y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7e-67) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else if (a <= 2.8e-5) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = x + (t / ((a - z) / (y - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-7d-67)) then
        tmp = x + (t * ((y - z) / (a - z)))
    else if (a <= 2.8d-5) then
        tmp = t + (((t - x) / z) * (a - y))
    else
        tmp = x + (t / ((a - z) / (y - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7e-67) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else if (a <= 2.8e-5) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = x + (t / ((a - z) / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7e-67:
		tmp = x + (t * ((y - z) / (a - z)))
	elif a <= 2.8e-5:
		tmp = t + (((t - x) / z) * (a - y))
	else:
		tmp = x + (t / ((a - z) / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7e-67)
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))));
	elseif (a <= 2.8e-5)
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	else
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7e-67)
		tmp = x + (t * ((y - z) / (a - z)));
	elseif (a <= 2.8e-5)
		tmp = t + (((t - x) / z) * (a - y));
	else
		tmp = x + (t / ((a - z) / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7e-67], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e-5], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.0000000000000001e-67

   1. Initial program 85.7%

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

   3. Taylor expanded in t around inf 73.3%

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

      1. associate-/l* 81.1%

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

   5. Simplified 81.1%

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

   if -7.0000000000000001e-67 < a < 2.79999999999999996e-5

   1. Initial program 67.5%

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

      1. +-commutative 67.5%

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

      2. fma-define 67.7%

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

   3. Simplified 67.7%

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

   5. Taylor expanded in z around inf 80.8%

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

      1. associate--l+ 80.8%

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

      2. distribute-lft-out-- 80.8%

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

      3. div-sub 81.6%

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

      4. mul-1-neg 81.6%

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

      5. unsub-neg 81.6%

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

      6. div-sub 80.8%

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

      7. associate-/l* 79.8%

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

      8. associate-/l* 78.7%

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

      9. distribute-rgt-out-- 80.7%

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

   7. Simplified 80.7%

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

   if 2.79999999999999996e-5 < a

   1. Initial program 91.7%

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

   3. Taylor expanded in t around inf 69.0%

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

      1. associate-/l* 85.6%

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

   5. Simplified 85.6%

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

      1. clear-num 85.5%

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

      2. un-div-inv 85.6%

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

   7. Applied egg-rr 85.6%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-67}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-5}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.3 \cdot 10^{-67}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 2.85 \cdot 10^{-5}:\\ \;\;\;\;t - \frac{y \cdot \left(t - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.3e-67)
   (+ x (* t (/ (- y z) (- a z))))
   (if (<= a 2.85e-5)
     (- t (/ (* y (- t x)) z))
     (+ x (/ t (/ (- a z) (- y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.3e-67) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else if (a <= 2.85e-5) {
		tmp = t - ((y * (t - x)) / z);
	} else {
		tmp = x + (t / ((a - z) / (y - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5.3d-67)) then
        tmp = x + (t * ((y - z) / (a - z)))
    else if (a <= 2.85d-5) then
        tmp = t - ((y * (t - x)) / z)
    else
        tmp = x + (t / ((a - z) / (y - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.3e-67) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else if (a <= 2.85e-5) {
		tmp = t - ((y * (t - x)) / z);
	} else {
		tmp = x + (t / ((a - z) / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.3e-67:
		tmp = x + (t * ((y - z) / (a - z)))
	elif a <= 2.85e-5:
		tmp = t - ((y * (t - x)) / z)
	else:
		tmp = x + (t / ((a - z) / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.3e-67)
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))));
	elseif (a <= 2.85e-5)
		tmp = Float64(t - Float64(Float64(y * Float64(t - x)) / z));
	else
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.3e-67)
		tmp = x + (t * ((y - z) / (a - z)));
	elseif (a <= 2.85e-5)
		tmp = t - ((y * (t - x)) / z);
	else
		tmp = x + (t / ((a - z) / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.3e-67], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.85e-5], N[(t - N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.29999999999999971e-67

   1. Initial program 85.7%

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

   3. Taylor expanded in t around inf 73.3%

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

      1. associate-/l* 81.1%

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

   5. Simplified 81.1%

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

   if -5.29999999999999971e-67 < a < 2.8500000000000002e-5

   1. Initial program 67.5%

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

      1. +-commutative 67.5%

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

      2. fma-define 67.7%

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

   3. Simplified 67.7%

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

   5. Taylor expanded in z around inf 80.8%

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

      1. associate--l+ 80.8%

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

      2. distribute-lft-out-- 80.8%

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

      3. div-sub 81.6%

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

      4. mul-1-neg 81.6%

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

      5. unsub-neg 81.6%

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

      6. div-sub 80.8%

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

      7. associate-/l* 79.8%

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

      8. associate-/l* 78.7%

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

      9. distribute-rgt-out-- 80.7%

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

   7. Simplified 80.7%

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

   8. Taylor expanded in y around inf 78.1%

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

   if 2.8500000000000002e-5 < a

   1. Initial program 91.7%

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

   3. Taylor expanded in t around inf 69.0%

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

      1. associate-/l* 85.6%

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

   5. Simplified 85.6%

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

      1. clear-num 85.5%

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

      2. un-div-inv 85.6%

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

   7. Applied egg-rr 85.6%

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

Alternative 9: 67.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{-33} \lor \neg \left(a \leq 1.15 \cdot 10^{+48}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y \cdot \left(t - x\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.7e-33) (not (<= a 1.15e+48)))
   (+ x (* t (/ (- y z) a)))
   (- t (/ (* y (- t x)) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.7e-33) || !(a <= 1.15e+48)) {
		tmp = x + (t * ((y - z) / a));
	} else {
		tmp = t - ((y * (t - x)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-3.7d-33)) .or. (.not. (a <= 1.15d+48))) then
        tmp = x + (t * ((y - z) / a))
    else
        tmp = t - ((y * (t - x)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.7e-33) || !(a <= 1.15e+48)) {
		tmp = x + (t * ((y - z) / a));
	} else {
		tmp = t - ((y * (t - x)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.7e-33) or not (a <= 1.15e+48):
		tmp = x + (t * ((y - z) / a))
	else:
		tmp = t - ((y * (t - x)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.7e-33) || !(a <= 1.15e+48))
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / a)));
	else
		tmp = Float64(t - Float64(Float64(y * Float64(t - x)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.7e-33) || ~((a <= 1.15e+48)))
		tmp = x + (t * ((y - z) / a));
	else
		tmp = t - ((y * (t - x)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.7e-33], N[Not[LessEqual[a, 1.15e+48]], $MachinePrecision]], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.70000000000000014e-33 or 1.15e48 < a

   1. Initial program 89.2%

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

   3. Taylor expanded in t around inf 70.3%

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

      1. associate-/l* 82.5%

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

   5. Simplified 82.5%

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

   6. Taylor expanded in a around inf 64.4%

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

      1. +-commutative 64.4%

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

      2. associate-/l* 72.1%

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

   8. Simplified 72.1%

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

   if -3.70000000000000014e-33 < a < 1.15e48

   1. Initial program 69.7%

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

      1. +-commutative 69.7%

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

      2. fma-define 69.8%

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

   3. Simplified 69.8%

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

   5. Taylor expanded in z around inf 78.7%

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

      1. associate--l+ 78.7%

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

      2. distribute-lft-out-- 78.7%

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

      3. div-sub 80.2%

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

      4. mul-1-neg 80.2%

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

      5. unsub-neg 80.2%

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

      6. div-sub 78.7%

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

      7. associate-/l* 77.9%

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

      8. associate-/l* 77.6%

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

      9. distribute-rgt-out-- 80.1%

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

   7. Simplified 80.1%

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

   8. Taylor expanded in y around inf 77.3%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{-33} \lor \neg \left(a \leq 1.15 \cdot 10^{+48}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y \cdot \left(t - x\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.1 \cdot 10^{-42} \lor \neg \left(a \leq 1.75 \cdot 10^{+49}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 + \frac{a - y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.1e-42) (not (<= a 1.75e+49)))
   (+ x (* t (/ (- y z) a)))
   (* t (+ 1.0 (/ (- a y) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.1e-42) || !(a <= 1.75e+49)) {
		tmp = x + (t * ((y - z) / a));
	} else {
		tmp = t * (1.0 + ((a - y) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-5.1d-42)) .or. (.not. (a <= 1.75d+49))) then
        tmp = x + (t * ((y - z) / a))
    else
        tmp = t * (1.0d0 + ((a - y) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.1e-42) || !(a <= 1.75e+49)) {
		tmp = x + (t * ((y - z) / a));
	} else {
		tmp = t * (1.0 + ((a - y) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5.1e-42) or not (a <= 1.75e+49):
		tmp = x + (t * ((y - z) / a))
	else:
		tmp = t * (1.0 + ((a - y) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5.1e-42) || !(a <= 1.75e+49))
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / a)));
	else
		tmp = Float64(t * Float64(1.0 + Float64(Float64(a - y) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -5.1e-42) || ~((a <= 1.75e+49)))
		tmp = x + (t * ((y - z) / a));
	else
		tmp = t * (1.0 + ((a - y) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5.1e-42], N[Not[LessEqual[a, 1.75e+49]], $MachinePrecision]], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 + N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.1e-42 or 1.74999999999999987e49 < a

   1. Initial program 89.3%

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

   3. Taylor expanded in t around inf 69.7%

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

      1. associate-/l* 81.9%

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

   5. Simplified 81.9%

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

   6. Taylor expanded in a around inf 64.0%

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

      1. +-commutative 64.0%

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

      2. associate-/l* 72.3%

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

   8. Simplified 72.3%

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

   if -5.1e-42 < a < 1.74999999999999987e49

   1. Initial program 69.4%

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

      1. +-commutative 69.4%

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

      2. fma-define 69.6%

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

   3. Simplified 69.6%

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

   5. Taylor expanded in z around inf 78.5%

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

      1. associate--l+ 78.5%

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

      2. distribute-lft-out-- 78.5%

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

      3. div-sub 80.0%

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

      4. mul-1-neg 80.0%

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

      5. unsub-neg 80.0%

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

      6. div-sub 78.5%

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

      7. associate-/l* 77.7%

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

      8. associate-/l* 77.5%

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

      9. distribute-rgt-out-- 80.0%

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

   7. Simplified 80.0%

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

   8. Taylor expanded in t around inf 53.7%

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

      1. associate--l+ 53.7%

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

      2. div-sub 54.4%

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

   10. Simplified 54.4%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.1 \cdot 10^{-42} \lor \neg \left(a \leq 1.75 \cdot 10^{+49}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 + \frac{a - y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+30} \lor \neg \left(a \leq 1.12 \cdot 10^{+48}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 + \frac{a - y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.2e+30) (not (<= a 1.12e+48)))
   (+ x (* (- y z) (/ t a)))
   (* t (+ 1.0 (/ (- a y) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.2e+30) || !(a <= 1.12e+48)) {
		tmp = x + ((y - z) * (t / a));
	} else {
		tmp = t * (1.0 + ((a - y) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.2d+30)) .or. (.not. (a <= 1.12d+48))) then
        tmp = x + ((y - z) * (t / a))
    else
        tmp = t * (1.0d0 + ((a - y) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.2e+30) || !(a <= 1.12e+48)) {
		tmp = x + ((y - z) * (t / a));
	} else {
		tmp = t * (1.0 + ((a - y) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.2e+30) or not (a <= 1.12e+48):
		tmp = x + ((y - z) * (t / a))
	else:
		tmp = t * (1.0 + ((a - y) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.2e+30) || !(a <= 1.12e+48))
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / a)));
	else
		tmp = Float64(t * Float64(1.0 + Float64(Float64(a - y) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.2e+30) || ~((a <= 1.12e+48)))
		tmp = x + ((y - z) * (t / a));
	else
		tmp = t * (1.0 + ((a - y) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.2e+30], N[Not[LessEqual[a, 1.12e+48]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 + N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.2e30 or 1.11999999999999995e48 < a

   1. Initial program 90.1%

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

   3. Taylor expanded in t around inf 80.8%

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

   4. Taylor expanded in a around inf 74.5%

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

   if -1.2e30 < a < 1.11999999999999995e48

   1. Initial program 70.4%

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

      1. +-commutative 70.4%

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

      2. fma-define 70.6%

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

   3. Simplified 70.6%

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

   5. Taylor expanded in z around inf 74.9%

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

      1. associate--l+ 74.9%

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

      2. distribute-lft-out-- 74.9%

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

      3. div-sub 76.3%

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

      4. mul-1-neg 76.3%

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

      5. unsub-neg 76.3%

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

      6. div-sub 74.9%

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

      7. associate-/l* 75.5%

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

      8. associate-/l* 75.9%

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

      9. distribute-rgt-out-- 78.3%

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

   7. Simplified 78.3%

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

   8. Taylor expanded in t around inf 52.7%

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

      1. associate--l+ 52.7%

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

      2. div-sub 53.4%

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

   10. Simplified 53.4%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+30} \lor \neg \left(a \leq 1.12 \cdot 10^{+48}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 + \frac{a - y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.75 \cdot 10^{-36} \lor \neg \left(a \leq 1.02 \cdot 10^{+48}\right):\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 + \frac{a - y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.75e-36) (not (<= a 1.02e+48)))
   (+ x (* y (/ (- t x) a)))
   (* t (+ 1.0 (/ (- a y) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.75e-36) || !(a <= 1.02e+48)) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t * (1.0 + ((a - y) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.75d-36)) .or. (.not. (a <= 1.02d+48))) then
        tmp = x + (y * ((t - x) / a))
    else
        tmp = t * (1.0d0 + ((a - y) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.75e-36) || !(a <= 1.02e+48)) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t * (1.0 + ((a - y) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.75e-36) or not (a <= 1.02e+48):
		tmp = x + (y * ((t - x) / a))
	else:
		tmp = t * (1.0 + ((a - y) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.75e-36) || !(a <= 1.02e+48))
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	else
		tmp = Float64(t * Float64(1.0 + Float64(Float64(a - y) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.75e-36) || ~((a <= 1.02e+48)))
		tmp = x + (y * ((t - x) / a));
	else
		tmp = t * (1.0 + ((a - y) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.75e-36], N[Not[LessEqual[a, 1.02e+48]], $MachinePrecision]], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 + N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.74999999999999992e-36 or 1.02e48 < a

   1. Initial program 89.2%

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

   3. Taylor expanded in z around 0 62.1%

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

      1. associate-/l* 70.7%

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

   5. Simplified 70.7%

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

   if -2.74999999999999992e-36 < a < 1.02e48

   1. Initial program 69.7%

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

      1. +-commutative 69.7%

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

      2. fma-define 69.8%

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

   3. Simplified 69.8%

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

   5. Taylor expanded in z around inf 78.7%

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

      1. associate--l+ 78.7%

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

      2. distribute-lft-out-- 78.7%

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

      3. div-sub 80.2%

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

      4. mul-1-neg 80.2%

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

      5. unsub-neg 80.2%

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

      6. div-sub 78.7%

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

      7. associate-/l* 77.9%

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

      8. associate-/l* 77.6%

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

      9. distribute-rgt-out-- 80.1%

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

   7. Simplified 80.1%

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

   8. Taylor expanded in t around inf 53.3%

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

      1. associate--l+ 53.3%

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

      2. div-sub 54.0%

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

   10. Simplified 54.0%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.75 \cdot 10^{-36} \lor \neg \left(a \leq 1.02 \cdot 10^{+48}\right):\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 + \frac{a - y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 56.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-42}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+48}:\\ \;\;\;\;t \cdot \left(1 + \frac{a - y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.5e-42)
   (+ x (* t (/ y a)))
   (if (<= a 1.05e+48) (* t (+ 1.0 (/ (- a y) z))) (+ x (/ t (/ a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.5e-42) {
		tmp = x + (t * (y / a));
	} else if (a <= 1.05e+48) {
		tmp = t * (1.0 + ((a - y) / z));
	} else {
		tmp = x + (t / (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 (a <= (-4.5d-42)) then
        tmp = x + (t * (y / a))
    else if (a <= 1.05d+48) then
        tmp = t * (1.0d0 + ((a - y) / z))
    else
        tmp = x + (t / (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 (a <= -4.5e-42) {
		tmp = x + (t * (y / a));
	} else if (a <= 1.05e+48) {
		tmp = t * (1.0 + ((a - y) / z));
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.5e-42:
		tmp = x + (t * (y / a))
	elif a <= 1.05e+48:
		tmp = t * (1.0 + ((a - y) / z))
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.5e-42)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (a <= 1.05e+48)
		tmp = Float64(t * Float64(1.0 + Float64(Float64(a - y) / z)));
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.5e-42)
		tmp = x + (t * (y / a));
	elseif (a <= 1.05e+48)
		tmp = t * (1.0 + ((a - y) / z));
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.5e-42], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e+48], N[(t * N[(1.0 + N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.5e-42

   1. Initial program 87.3%

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

   3. Taylor expanded in t around inf 70.9%

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

      1. associate-/l* 79.4%

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

   5. Simplified 79.4%

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

   6. Taylor expanded in z around 0 58.9%

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

      1. +-commutative 58.9%

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

      2. associate-/l* 59.0%

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

   8. Simplified 59.0%

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

   if -4.5e-42 < a < 1.0499999999999999e48

   1. Initial program 69.4%

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

      1. +-commutative 69.4%

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

      2. fma-define 69.6%

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

   3. Simplified 69.6%

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

   5. Taylor expanded in z around inf 78.5%

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

      1. associate--l+ 78.5%

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

      2. distribute-lft-out-- 78.5%

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

      3. div-sub 80.0%

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

      4. mul-1-neg 80.0%

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

      5. unsub-neg 80.0%

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

      6. div-sub 78.5%

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

      7. associate-/l* 77.7%

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

      8. associate-/l* 77.5%

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

      9. distribute-rgt-out-- 80.0%

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

   7. Simplified 80.0%

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

   8. Taylor expanded in t around inf 53.7%

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

      1. associate--l+ 53.7%

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

      2. div-sub 54.4%

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

   10. Simplified 54.4%

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

   if 1.0499999999999999e48 < a

   1. Initial program 91.6%

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

   3. Taylor expanded in t around inf 68.5%

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

      1. associate-/l* 84.7%

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

   5. Simplified 84.7%

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

      1. clear-num 84.6%

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

      2. un-div-inv 84.7%

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

   7. Applied egg-rr 84.7%

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

   8. Taylor expanded in z around 0 71.0%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-42}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+48}:\\ \;\;\;\;t \cdot \left(1 + \frac{a - y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 46.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-67} \lor \neg \left(a \leq 2.75 \cdot 10^{-5}\right):\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -8e-67) (not (<= a 2.75e-5)))
   (+ x (/ t (/ a y)))
   (* x (/ (- y a) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8e-67) || !(a <= 2.75e-5)) {
		tmp = x + (t / (a / y));
	} else {
		tmp = 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) :: tmp
    if ((a <= (-8d-67)) .or. (.not. (a <= 2.75d-5))) then
        tmp = x + (t / (a / y))
    else
        tmp = 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 tmp;
	if ((a <= -8e-67) || !(a <= 2.75e-5)) {
		tmp = x + (t / (a / y));
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -8e-67) or not (a <= 2.75e-5):
		tmp = x + (t / (a / y))
	else:
		tmp = x * ((y - a) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -8e-67) || !(a <= 2.75e-5))
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = Float64(x * Float64(Float64(y - a) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -8e-67) || ~((a <= 2.75e-5)))
		tmp = x + (t / (a / y));
	else
		tmp = x * ((y - a) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -8e-67], N[Not[LessEqual[a, 2.75e-5]], $MachinePrecision]], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.99999999999999954e-67 or 2.7500000000000001e-5 < a

   1. Initial program 88.6%

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

   3. Taylor expanded in t around inf 71.2%

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

      1. associate-/l* 83.3%

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

   5. Simplified 83.3%

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

      1. clear-num 83.2%

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

      2. un-div-inv 83.3%

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

   7. Applied egg-rr 83.3%

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

   8. Taylor expanded in z around 0 60.5%

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

   if -7.99999999999999954e-67 < a < 2.7500000000000001e-5

   1. Initial program 67.5%

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

      1. +-commutative 67.5%

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

      2. fma-define 67.7%

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

   3. Simplified 67.7%

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

   5. Taylor expanded in z around inf 80.8%

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

      1. associate--l+ 80.8%

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

      2. distribute-lft-out-- 80.8%

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

      3. div-sub 81.6%

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

      4. mul-1-neg 81.6%

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

      5. unsub-neg 81.6%

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

      6. div-sub 80.8%

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

      7. associate-/l* 79.8%

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

      8. associate-/l* 78.7%

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

      9. distribute-rgt-out-- 80.7%

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

   7. Simplified 80.7%

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

   8. Taylor expanded in t around 0 37.1%

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

      1. associate-/l* 42.7%

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

   10. Simplified 42.7%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-67} \lor \neg \left(a \leq 2.75 \cdot 10^{-5}\right):\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 42.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{-18} \lor \neg \left(a \leq 4.7 \cdot 10^{+70}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.6e-18) (not (<= a 4.7e+70)))
   (* x (- 1.0 (/ y a)))
   (* x (/ (- y a) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.6e-18) || !(a <= 4.7e+70)) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = 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) :: tmp
    if ((a <= (-4.6d-18)) .or. (.not. (a <= 4.7d+70))) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = 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 tmp;
	if ((a <= -4.6e-18) || !(a <= 4.7e+70)) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.6e-18) or not (a <= 4.7e+70):
		tmp = x * (1.0 - (y / a))
	else:
		tmp = x * ((y - a) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.6e-18) || !(a <= 4.7e+70))
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = Float64(x * Float64(Float64(y - a) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.6e-18) || ~((a <= 4.7e+70)))
		tmp = x * (1.0 - (y / a));
	else
		tmp = x * ((y - a) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.6e-18], N[Not[LessEqual[a, 4.7e+70]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.6000000000000002e-18 or 4.6999999999999998e70 < a

   1. Initial program 92.4%

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

      1. +-commutative 92.4%

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

      2. fma-define 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in t around 0 50.6%

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

      1. mul-1-neg 50.6%

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

      2. *-rgt-identity 50.6%

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

      3. associate-/l* 59.3%

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

      4. distribute-rgt-neg-in 59.3%

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

      5. mul-1-neg 59.3%

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

      6. distribute-lft-in 59.3%

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

      7. mul-1-neg 59.3%

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

      8. unsub-neg 59.3%

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

   7. Simplified 59.3%

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

   8. Taylor expanded in z around 0 57.2%

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

   if -4.6000000000000002e-18 < a < 4.6999999999999998e70

   1. Initial program 68.7%

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

      1. +-commutative 68.7%

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

      2. fma-define 68.8%

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

   3. Simplified 68.8%

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

   5. Taylor expanded in z around inf 74.9%

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

      1. associate--l+ 74.9%

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

      2. distribute-lft-out-- 74.9%

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

      3. div-sub 76.3%

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

      4. mul-1-neg 76.3%

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

      5. unsub-neg 76.3%

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

      6. div-sub 74.9%

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

      7. associate-/l* 75.5%

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

      8. associate-/l* 75.9%

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

      9. distribute-rgt-out-- 78.2%

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

   7. Simplified 78.2%

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

   8. Taylor expanded in t around 0 32.5%

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

      1. associate-/l* 39.7%

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

   10. Simplified 39.7%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{-18} \lor \neg \left(a \leq 4.7 \cdot 10^{+70}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 49.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{-35}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 0.000108:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.8e-35)
   (+ x (/ (* y t) a))
   (if (<= a 0.000108) (* y (/ (- x t) z)) (+ x (/ t (/ a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.8e-35) {
		tmp = x + ((y * t) / a);
	} else if (a <= 0.000108) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = x + (t / (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 (a <= (-6.8d-35)) then
        tmp = x + ((y * t) / a)
    else if (a <= 0.000108d0) then
        tmp = y * ((x - t) / z)
    else
        tmp = x + (t / (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 (a <= -6.8e-35) {
		tmp = x + ((y * t) / a);
	} else if (a <= 0.000108) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.8e-35:
		tmp = x + ((y * t) / a)
	elif a <= 0.000108:
		tmp = y * ((x - t) / z)
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.8e-35)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (a <= 0.000108)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.8e-35)
		tmp = x + ((y * t) / a);
	elseif (a <= 0.000108)
		tmp = y * ((x - t) / z);
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.8e-35], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.000108], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.8000000000000005e-35

   1. Initial program 87.1%

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

   3. Taylor expanded in t around inf 72.0%

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

      1. associate-/l* 80.6%

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

   5. Simplified 80.6%

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

   6. Taylor expanded in z around 0 59.7%

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

   if -6.8000000000000005e-35 < a < 1.08e-4

   1. Initial program 67.8%

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

      1. +-commutative 67.8%

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

      2. fma-define 68.0%

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

   3. Simplified 68.0%

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

   5. Taylor expanded in y around inf 57.0%

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

   6. Taylor expanded in a around 0 47.5%

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

      1. distribute-lft-out-- 47.5%

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

      2. div-sub 48.4%

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

      3. neg-mul-1 48.4%

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

      4. distribute-neg-frac2 48.4%

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

   8. Simplified 48.4%

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

   if 1.08e-4 < a

   1. Initial program 91.7%

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

   3. Taylor expanded in t around inf 69.0%

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

      1. associate-/l* 85.6%

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

   5. Simplified 85.6%

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

      1. clear-num 85.5%

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

      2. un-div-inv 85.6%

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

   7. Applied egg-rr 85.6%

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

   8. Taylor expanded in z around 0 66.8%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{-35}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 0.000108:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 47.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-116}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.8e-116)
   (+ x (* t (/ y a)))
   (if (<= a 8.4e-60) (* x (/ y (- z a))) (+ x (/ t (/ a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.8e-116) {
		tmp = x + (t * (y / a));
	} else if (a <= 8.4e-60) {
		tmp = x * (y / (z - a));
	} else {
		tmp = x + (t / (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 (a <= (-2.8d-116)) then
        tmp = x + (t * (y / a))
    else if (a <= 8.4d-60) then
        tmp = x * (y / (z - a))
    else
        tmp = x + (t / (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 (a <= -2.8e-116) {
		tmp = x + (t * (y / a));
	} else if (a <= 8.4e-60) {
		tmp = x * (y / (z - a));
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.8e-116:
		tmp = x + (t * (y / a))
	elif a <= 8.4e-60:
		tmp = x * (y / (z - a))
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.8e-116)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (a <= 8.4e-60)
		tmp = Float64(x * Float64(y / Float64(z - a)));
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.8e-116)
		tmp = x + (t * (y / a));
	elseif (a <= 8.4e-60)
		tmp = x * (y / (z - a));
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.8e-116], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.4e-60], N[(x * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.7999999999999999e-116

   1. Initial program 84.5%

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

   3. Taylor expanded in t around inf 71.9%

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

      1. associate-/l* 79.0%

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

   5. Simplified 79.0%

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

   6. Taylor expanded in z around 0 52.4%

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

      1. +-commutative 52.4%

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

      2. associate-/l* 52.4%

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

   8. Simplified 52.4%

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

   if -2.7999999999999999e-116 < a < 8.39999999999999964e-60

   1. Initial program 66.8%

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

      1. +-commutative 66.8%

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

      2. fma-define 67.0%

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

   3. Simplified 67.0%

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

   5. Taylor expanded in t around 0 31.2%

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

      1. mul-1-neg 31.2%

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

      2. *-rgt-identity 31.2%

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

      3. associate-/l* 34.6%

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

      4. distribute-rgt-neg-in 34.6%

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

      5. mul-1-neg 34.6%

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

      6. distribute-lft-in 34.5%

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

      7. mul-1-neg 34.5%

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

      8. unsub-neg 34.5%

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

   7. Simplified 34.5%

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

   8. Taylor expanded in y around inf 47.4%

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

      1. associate-*r/ 47.4%

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

      2. mul-1-neg 47.4%

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

   10. Simplified 47.4%

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

   if 8.39999999999999964e-60 < a

   1. Initial program 89.1%

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

   3. Taylor expanded in t around inf 65.8%

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

      1. associate-/l* 81.4%

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

   5. Simplified 81.4%

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

      1. clear-num 81.4%

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

      2. un-div-inv 81.4%

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

   7. Applied egg-rr 81.4%

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

   8. Taylor expanded in z around 0 62.5%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-116}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 46.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{-67}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4e-67)
   (+ x (* t (/ y a)))
   (if (<= a 3.5e-5) (* x (/ (- y a) z)) (+ x (/ t (/ a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4e-67) {
		tmp = x + (t * (y / a));
	} else if (a <= 3.5e-5) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = x + (t / (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 (a <= (-4d-67)) then
        tmp = x + (t * (y / a))
    else if (a <= 3.5d-5) then
        tmp = x * ((y - a) / z)
    else
        tmp = x + (t / (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 (a <= -4e-67) {
		tmp = x + (t * (y / a));
	} else if (a <= 3.5e-5) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4e-67:
		tmp = x + (t * (y / a))
	elif a <= 3.5e-5:
		tmp = x * ((y - a) / z)
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4e-67)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (a <= 3.5e-5)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4e-67)
		tmp = x + (t * (y / a));
	elseif (a <= 3.5e-5)
		tmp = x * ((y - a) / z);
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4e-67], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.5e-5], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.99999999999999977e-67

   1. Initial program 85.7%

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

   3. Taylor expanded in t around inf 73.3%

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

      1. associate-/l* 81.1%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in z around 0 55.8%

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

      1. +-commutative 55.8%

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

      2. associate-/l* 55.9%

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

   8. Simplified 55.9%

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

   if -3.99999999999999977e-67 < a < 3.4999999999999997e-5

   1. Initial program 67.5%

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

      1. +-commutative 67.5%

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

      2. fma-define 67.7%

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

   3. Simplified 67.7%

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

   5. Taylor expanded in z around inf 80.8%

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

      1. associate--l+ 80.8%

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

      2. distribute-lft-out-- 80.8%

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

      3. div-sub 81.6%

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

      4. mul-1-neg 81.6%

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

      5. unsub-neg 81.6%

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

      6. div-sub 80.8%

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

      7. associate-/l* 79.8%

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

      8. associate-/l* 78.7%

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

      9. distribute-rgt-out-- 80.7%

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

   7. Simplified 80.7%

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

   8. Taylor expanded in t around 0 37.1%

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

      1. associate-/l* 42.7%

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

   10. Simplified 42.7%

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

   if 3.4999999999999997e-5 < a

   1. Initial program 91.7%

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

   3. Taylor expanded in t around inf 69.0%

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

      1. associate-/l* 85.6%

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

   5. Simplified 85.6%

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

      1. clear-num 85.5%

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

      2. un-div-inv 85.6%

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

   7. Applied egg-rr 85.6%

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

   8. Taylor expanded in z around 0 66.8%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{-67}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 45.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{-67}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.1e-67)
   (+ x (/ (* y t) a))
   (if (<= a 2.75e-5) (* x (/ (- y a) z)) (+ x (/ t (/ a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.1e-67) {
		tmp = x + ((y * t) / a);
	} else if (a <= 2.75e-5) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = x + (t / (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 (a <= (-4.1d-67)) then
        tmp = x + ((y * t) / a)
    else if (a <= 2.75d-5) then
        tmp = x * ((y - a) / z)
    else
        tmp = x + (t / (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 (a <= -4.1e-67) {
		tmp = x + ((y * t) / a);
	} else if (a <= 2.75e-5) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.1e-67:
		tmp = x + ((y * t) / a)
	elif a <= 2.75e-5:
		tmp = x * ((y - a) / z)
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.1e-67)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (a <= 2.75e-5)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.1e-67)
		tmp = x + ((y * t) / a);
	elseif (a <= 2.75e-5)
		tmp = x * ((y - a) / z);
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.1e-67], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.75e-5], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.0999999999999997e-67

   1. Initial program 85.7%

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

   3. Taylor expanded in t around inf 73.3%

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

      1. associate-/l* 81.1%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in z around 0 55.8%

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

   if -4.0999999999999997e-67 < a < 2.7500000000000001e-5

   1. Initial program 67.5%

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

      1. +-commutative 67.5%

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

      2. fma-define 67.7%

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

   3. Simplified 67.7%

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

   5. Taylor expanded in z around inf 80.8%

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

      1. associate--l+ 80.8%

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

      2. distribute-lft-out-- 80.8%

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

      3. div-sub 81.6%

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

      4. mul-1-neg 81.6%

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

      5. unsub-neg 81.6%

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

      6. div-sub 80.8%

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

      7. associate-/l* 79.8%

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

      8. associate-/l* 78.7%

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

      9. distribute-rgt-out-- 80.7%

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

   7. Simplified 80.7%

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

   8. Taylor expanded in t around 0 37.1%

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

      1. associate-/l* 42.7%

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

   10. Simplified 42.7%

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

   if 2.7500000000000001e-5 < a

   1. Initial program 91.7%

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

   3. Taylor expanded in t around inf 69.0%

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

      1. associate-/l* 85.6%

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

   5. Simplified 85.6%

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

      1. clear-num 85.5%

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

      2. un-div-inv 85.6%

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

   7. Applied egg-rr 85.6%

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

   8. Taylor expanded in z around 0 66.8%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{-67}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 46.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+47}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-92}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.15e+47) t (if (<= z 5.2e-92) (* x (- 1.0 (/ y a))) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e+47) {
		tmp = t;
	} else if (z <= 5.2e-92) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.15d+47)) then
        tmp = t
    else if (z <= 5.2d-92) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e+47) {
		tmp = t;
	} else if (z <= 5.2e-92) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.15e+47:
		tmp = t
	elif z <= 5.2e-92:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.15e+47)
		tmp = t;
	elseif (z <= 5.2e-92)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.15e+47)
		tmp = t;
	elseif (z <= 5.2e-92)
		tmp = x * (1.0 - (y / a));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.15e+47], t, If[LessEqual[z, 5.2e-92], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1499999999999999e47

   1. Initial program 68.4%

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

      1. associate-*r/ 49.2%

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

      2. clear-num 49.0%

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

   4. Applied egg-rr 49.0%

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

      1. associate-/r/ 49.0%

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

      2. *-commutative 49.0%

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

   6. Simplified 49.0%

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

   7. Taylor expanded in z around inf 46.1%

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

   if -1.1499999999999999e47 < z < 5.2e-92

   1. Initial program 86.6%

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

      1. +-commutative 86.6%

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

      2. fma-define 86.6%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in t around 0 52.6%

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

      1. mul-1-neg 52.6%

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

      2. *-rgt-identity 52.6%

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

      3. associate-/l* 57.2%

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

      4. distribute-rgt-neg-in 57.2%

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

      5. mul-1-neg 57.2%

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

      6. distribute-lft-in 57.2%

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

      7. mul-1-neg 57.2%

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

      8. unsub-neg 57.2%

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

   7. Simplified 57.2%

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

   8. Taylor expanded in z around 0 46.5%

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

   if 5.2e-92 < z

   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 inf 56.9%

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

      1. associate-/l* 71.4%

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

   5. Simplified 71.4%

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

   6. Taylor expanded in z around inf 46.0%

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

Alternative 21: 38.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{+30}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+79}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.45e+30) x (if (<= a 3.6e+79) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.45e+30) {
		tmp = x;
	} else if (a <= 3.6e+79) {
		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 <= (-1.45d+30)) then
        tmp = x
    else if (a <= 3.6d+79) 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 <= -1.45e+30) {
		tmp = x;
	} else if (a <= 3.6e+79) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.45e+30:
		tmp = x
	elif a <= 3.6e+79:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.45e+30)
		tmp = x;
	elseif (a <= 3.6e+79)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.45e+30)
		tmp = x;
	elseif (a <= 3.6e+79)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.45e+30], x, If[LessEqual[a, 3.6e+79], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.4499999999999999e30 or 3.5999999999999999e79 < a

   1. Initial program 92.8%

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

      1. +-commutative 92.8%

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

      2. fma-define 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in a around inf 54.1%

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

   if -1.4499999999999999e30 < a < 3.5999999999999999e79

   1. Initial program 70.2%

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

      1. associate-*r/ 68.8%

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

      2. clear-num 68.7%

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

   4. Applied egg-rr 68.7%

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

      1. associate-/r/ 68.7%

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

      2. *-commutative 68.7%

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

   6. Simplified 68.7%

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

   7. Taylor expanded in z around inf 33.9%

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

Alternative 22: 24.5% 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 79.0%

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

   1. associate-*r/ 70.7%

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

   2. clear-num 70.6%

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

4. Applied egg-rr 70.6%

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

   1. associate-/r/ 70.6%

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

   2. *-commutative 70.6%

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

6. Simplified 70.6%

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

7. Taylor expanded in z around inf 23.7%

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

Reproduce

herbie shell --seed 2024165 
(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)))))