Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3

Percentage Accurate: 68.1% → 90.7%

Time: 13.7s

Alternatives: 17

Speedup: 0.6×

Specification

Math

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

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(Float64(y - z) * 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[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 68.1% accurate, 1.0× speedup

Math

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

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(Float64(y - z) * 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[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 90.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-302}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ (- y z) (- a z)))))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 -1e-302)
     t_1
     (if (<= t_2 0.0) (+ t (/ (* (- t x) (- a y)) z)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * ((y - z) / (a - z)));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -1e-302) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((t - x) * ((y - z) / (a - z)))
    t_2 = x + (((y - z) * (t - x)) / (a - z))
    if (t_2 <= (-1d-302)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) then
        tmp = t + (((t - x) * (a - y)) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * ((y - z) / (a - z)));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -1e-302) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) * ((y - z) / (a - z)))
	t_2 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if t_2 <= -1e-302:
		tmp = t_1
	elif t_2 <= 0.0:
		tmp = t + (((t - x) * (a - y)) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / Float64(a - z))))
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= -1e-302)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) * ((y - z) / (a - z)));
	t_2 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if (t_2 <= -1e-302)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = t + (((t - x) * (a - y)) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-302], t$95$1, If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -9.9999999999999996e-303 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 72.4%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{\color{blue}{a} - z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y - z}{a - z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y - z}}{a - z}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 87.6%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   4. Applied egg-rr 87.6%

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

   if -9.9999999999999996e-303 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.2%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right), \color{blue}{z}\right)\right) \]

      8. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(\left(t - x\right) \cdot \left(y - a\right)\right), z\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(t - x\right), \left(y - a\right)\right), z\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(y - a\right)\right), z\right)\right) \]

      11. --lowering--.f64 99.5%

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{\_.f64}\left(y, a\right)\right), z\right)\right) \]

   5. Simplified 99.5%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -1 \cdot 10^{-302}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 59.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(\frac{a - y}{z} + 1\right)\\ t_2 := x + t \cdot \frac{y - z}{a}\\ t_3 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{+116}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -5.7 \cdot 10^{-106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.3 \cdot 10^{-145}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 2.85 \cdot 10^{-154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-8}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (+ (/ (- a y) z) 1.0)))
        (t_2 (+ x (* t (/ (- y z) a))))
        (t_3 (* y (/ (- t x) (- a z)))))
   (if (<= a -1.9e+116)
     t_2
     (if (<= a -5.7e-106)
       t_1
       (if (<= a -4.3e-145)
         t_3
         (if (<= a 2.85e-154) t_1 (if (<= a 7e-8) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (((a - y) / z) + 1.0);
	double t_2 = x + (t * ((y - z) / a));
	double t_3 = y * ((t - x) / (a - z));
	double tmp;
	if (a <= -1.9e+116) {
		tmp = t_2;
	} else if (a <= -5.7e-106) {
		tmp = t_1;
	} else if (a <= -4.3e-145) {
		tmp = t_3;
	} else if (a <= 2.85e-154) {
		tmp = t_1;
	} else if (a <= 7e-8) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t * (((a - y) / z) + 1.0d0)
    t_2 = x + (t * ((y - z) / a))
    t_3 = y * ((t - x) / (a - z))
    if (a <= (-1.9d+116)) then
        tmp = t_2
    else if (a <= (-5.7d-106)) then
        tmp = t_1
    else if (a <= (-4.3d-145)) then
        tmp = t_3
    else if (a <= 2.85d-154) then
        tmp = t_1
    else if (a <= 7d-8) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (((a - y) / z) + 1.0);
	double t_2 = x + (t * ((y - z) / a));
	double t_3 = y * ((t - x) / (a - z));
	double tmp;
	if (a <= -1.9e+116) {
		tmp = t_2;
	} else if (a <= -5.7e-106) {
		tmp = t_1;
	} else if (a <= -4.3e-145) {
		tmp = t_3;
	} else if (a <= 2.85e-154) {
		tmp = t_1;
	} else if (a <= 7e-8) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (((a - y) / z) + 1.0)
	t_2 = x + (t * ((y - z) / a))
	t_3 = y * ((t - x) / (a - z))
	tmp = 0
	if a <= -1.9e+116:
		tmp = t_2
	elif a <= -5.7e-106:
		tmp = t_1
	elif a <= -4.3e-145:
		tmp = t_3
	elif a <= 2.85e-154:
		tmp = t_1
	elif a <= 7e-8:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(Float64(a - y) / z) + 1.0))
	t_2 = Float64(x + Float64(t * Float64(Float64(y - z) / a)))
	t_3 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	tmp = 0.0
	if (a <= -1.9e+116)
		tmp = t_2;
	elseif (a <= -5.7e-106)
		tmp = t_1;
	elseif (a <= -4.3e-145)
		tmp = t_3;
	elseif (a <= 2.85e-154)
		tmp = t_1;
	elseif (a <= 7e-8)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (((a - y) / z) + 1.0);
	t_2 = x + (t * ((y - z) / a));
	t_3 = y * ((t - x) / (a - z));
	tmp = 0.0;
	if (a <= -1.9e+116)
		tmp = t_2;
	elseif (a <= -5.7e-106)
		tmp = t_1;
	elseif (a <= -4.3e-145)
		tmp = t_3;
	elseif (a <= 2.85e-154)
		tmp = t_1;
	elseif (a <= 7e-8)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.9e+116], t$95$2, If[LessEqual[a, -5.7e-106], t$95$1, If[LessEqual[a, -4.3e-145], t$95$3, If[LessEqual[a, 2.85e-154], t$95$1, If[LessEqual[a, 7e-8], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.8999999999999999e116 or 7.00000000000000048e-8 < a

   1. Initial program 68.8%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{\color{blue}{a} - z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y - z}{a - z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y - z}}{a - z}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 89.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   4. Applied egg-rr 89.9%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{t}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, z\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 77.7%

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

   8. Taylor expanded in a around inf

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{t \cdot \left(y - z\right)}{a}\right)}\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(t \cdot \color{blue}{\frac{y - z}{a}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{y - z}{a}\right)}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{a}\right)\right)\right) \]

      5. --lowering--.f64 67.1%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), a\right)\right)\right) \]

   10. Simplified 67.1%

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

   if -1.8999999999999999e116 < a < -5.7000000000000004e-106 or -4.2999999999999999e-145 < a < 2.8499999999999999e-154

   1. Initial program 60.0%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right), \color{blue}{z}\right)\right) \]

      8. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(\left(t - x\right) \cdot \left(y - a\right)\right), z\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(t - x\right), \left(y - a\right)\right), z\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(y - a\right)\right), z\right)\right) \]

      11. --lowering--.f64 76.7%

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{\_.f64}\left(y, a\right)\right), z\right)\right) \]

   5. Simplified 76.7%

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

   6. Taylor expanded in t around -inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(1 + -1 \cdot \frac{y - a}{z}\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(1 + \left(\mathsf{neg}\left(\frac{y - a}{z}\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(1 - \color{blue}{\frac{y - a}{z}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y - a}{z}\right)}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(y - a\right), \color{blue}{z}\right)\right)\right) \]

      6. --lowering--.f64 59.1%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, a\right), z\right)\right)\right) \]

   8. Simplified 59.1%

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

   if -5.7000000000000004e-106 < a < -4.2999999999999999e-145 or 2.8499999999999999e-154 < a < 7.00000000000000048e-8

   1. Initial program 83.9%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right)\right), \color{blue}{\left(a - z\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - x\right)\right), \left(\color{blue}{a} - z\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \left(a - z\right)\right) \]

      6. --lowering--.f64 68.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right) \]

   5. Simplified 68.7%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{t - x}{a - z}\right), \color{blue}{y}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(t - x\right), \left(a - z\right)\right), y\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(a - z\right)\right), y\right) \]

      6. --lowering--.f64 73.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{\_.f64}\left(a, z\right)\right), y\right) \]

   7. Applied egg-rr 73.5%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+116}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -5.7 \cdot 10^{-106}:\\ \;\;\;\;t \cdot \left(\frac{a - y}{z} + 1\right)\\ \mathbf{elif}\;a \leq -4.3 \cdot 10^{-145}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 2.85 \cdot 10^{-154}:\\ \;\;\;\;t \cdot \left(\frac{a - y}{z} + 1\right)\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{if}\;z \leq -4.7 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-163}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+38}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (/ (- t x) z) (- a y)))))
   (if (<= z -4.7e+54)
     t_1
     (if (<= z -5.2e-163)
       (+ x (* t (/ (- y z) (- a z))))
       (if (<= z 2.9e+38) (+ x (* (- y z) (/ (- t x) a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((t - x) / z) * (a - y));
	double tmp;
	if (z <= -4.7e+54) {
		tmp = t_1;
	} else if (z <= -5.2e-163) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else if (z <= 2.9e+38) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (((t - x) / z) * (a - y))
    if (z <= (-4.7d+54)) then
        tmp = t_1
    else if (z <= (-5.2d-163)) then
        tmp = x + (t * ((y - z) / (a - z)))
    else if (z <= 2.9d+38) then
        tmp = x + ((y - z) * ((t - x) / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((t - x) / z) * (a - y));
	double tmp;
	if (z <= -4.7e+54) {
		tmp = t_1;
	} else if (z <= -5.2e-163) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else if (z <= 2.9e+38) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (((t - x) / z) * (a - y))
	tmp = 0
	if z <= -4.7e+54:
		tmp = t_1
	elif z <= -5.2e-163:
		tmp = x + (t * ((y - z) / (a - z)))
	elif z <= 2.9e+38:
		tmp = x + ((y - z) * ((t - x) / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)))
	tmp = 0.0
	if (z <= -4.7e+54)
		tmp = t_1;
	elseif (z <= -5.2e-163)
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))));
	elseif (z <= 2.9e+38)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (((t - x) / z) * (a - y));
	tmp = 0.0;
	if (z <= -4.7e+54)
		tmp = t_1;
	elseif (z <= -5.2e-163)
		tmp = x + (t * ((y - z) / (a - z)));
	elseif (z <= 2.9e+38)
		tmp = x + ((y - z) * ((t - x) / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.7e+54], t$95$1, If[LessEqual[z, -5.2e-163], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+38], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.69999999999999993e54 or 2.90000000000000007e38 < z

   1. Initial program 38.9%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right), \color{blue}{z}\right)\right) \]

      8. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(\left(t - x\right) \cdot \left(y - a\right)\right), z\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(t - x\right), \left(y - a\right)\right), z\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(y - a\right)\right), z\right)\right) \]

      11. --lowering--.f64 60.6%

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{\_.f64}\left(y, a\right)\right), z\right)\right) \]

   5. Simplified 60.6%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(\frac{\left(y - a\right) \cdot \left(t - x\right)}{z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(\left(y - a\right) \cdot \color{blue}{\frac{t - x}{z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\left(y - a\right), \color{blue}{\left(\frac{t - x}{z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, a\right), \left(\frac{\color{blue}{t - x}}{z}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, a\right), \mathsf{/.f64}\left(\left(t - x\right), \color{blue}{z}\right)\right)\right) \]

      6. --lowering--.f64 76.9%

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, a\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), z\right)\right)\right) \]

   7. Applied egg-rr 76.9%

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

   if -4.69999999999999993e54 < z < -5.20000000000000003e-163

   1. Initial program 83.2%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{\color{blue}{a} - z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y - z}{a - z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y - z}}{a - z}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 90.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   4. Applied egg-rr 90.8%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{t}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, z\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 75.5%

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

   if -5.20000000000000003e-163 < z < 2.90000000000000007e38

   1. Initial program 93.6%

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

   3. Taylor expanded in a around inf

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{a}\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - z\right) \cdot \left(t - x\right)}{a}\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - z\right) \cdot \color{blue}{\frac{t - x}{a}}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(y - z\right), \color{blue}{\left(\frac{t - x}{a}\right)}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{\color{blue}{t - x}}{a}\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(\left(t - x\right), \color{blue}{a}\right)\right)\right) \]

      7. --lowering--.f64 82.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), a\right)\right)\right) \]

   5. Simplified 82.8%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+54}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-163}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+38}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-43}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+64}:\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z)))))
   (if (<= y -9.5e+129)
     t_1
     (if (<= y -9.5e-43)
       (+ x (* (- t x) (/ y a)))
       (if (<= y 2.2e+64) (+ x (* t (/ z (- z a)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -9.5e+129) {
		tmp = t_1;
	} else if (y <= -9.5e-43) {
		tmp = x + ((t - x) * (y / a));
	} else if (y <= 2.2e+64) {
		tmp = x + (t * (z / (z - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((t - x) / (a - z))
    if (y <= (-9.5d+129)) then
        tmp = t_1
    else if (y <= (-9.5d-43)) then
        tmp = x + ((t - x) * (y / a))
    else if (y <= 2.2d+64) then
        tmp = x + (t * (z / (z - a)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -9.5e+129) {
		tmp = t_1;
	} else if (y <= -9.5e-43) {
		tmp = x + ((t - x) * (y / a));
	} else if (y <= 2.2e+64) {
		tmp = x + (t * (z / (z - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	tmp = 0
	if y <= -9.5e+129:
		tmp = t_1
	elif y <= -9.5e-43:
		tmp = x + ((t - x) * (y / a))
	elif y <= 2.2e+64:
		tmp = x + (t * (z / (z - a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	tmp = 0.0
	if (y <= -9.5e+129)
		tmp = t_1;
	elseif (y <= -9.5e-43)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (y <= 2.2e+64)
		tmp = Float64(x + Float64(t * Float64(z / Float64(z - a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / (a - z));
	tmp = 0.0;
	if (y <= -9.5e+129)
		tmp = t_1;
	elseif (y <= -9.5e-43)
		tmp = x + ((t - x) * (y / a));
	elseif (y <= 2.2e+64)
		tmp = x + (t * (z / (z - a)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.5e+129], t$95$1, If[LessEqual[y, -9.5e-43], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e+64], N[(x + N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.5000000000000004e129 or 2.20000000000000002e64 < y

   1. Initial program 68.0%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right)\right), \color{blue}{\left(a - z\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - x\right)\right), \left(\color{blue}{a} - z\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \left(a - z\right)\right) \]

      6. --lowering--.f64 65.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right) \]

   5. Simplified 65.7%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{t - x}{a - z}\right), \color{blue}{y}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(t - x\right), \left(a - z\right)\right), y\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(a - z\right)\right), y\right) \]

      6. --lowering--.f64 79.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{\_.f64}\left(a, z\right)\right), y\right) \]

   7. Applied egg-rr 79.9%

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

   if -9.5000000000000004e129 < y < -9.50000000000000044e-43

   1. Initial program 68.3%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{\color{blue}{a} - z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y - z}{a - z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y - z}}{a - z}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 78.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   4. Applied egg-rr 78.9%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \color{blue}{\left(\frac{y}{a}\right)}\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 61.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right)\right) \]

   7. Simplified 61.0%

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

   if -9.50000000000000044e-43 < y < 2.20000000000000002e64

   1. Initial program 67.7%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{\color{blue}{a} - z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y - z}{a - z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y - z}}{a - z}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 80.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   4. Applied egg-rr 80.9%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{t}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, z\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 74.4%

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

   8. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{t \cdot z}{a - z}\right)}\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(t \cdot \color{blue}{\frac{z}{a - z}}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{z}{a - z}\right)}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, \color{blue}{\left(a - z\right)}\right)\right)\right) \]

      7. --lowering--.f64 69.0%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   10. Simplified 69.0%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+129}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-43}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+64}:\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+64}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z)))))
   (if (<= y -2.2e+130)
     t_1
     (if (<= y 7e+64) (+ x (* t (/ (- y z) (- a z)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -2.2e+130) {
		tmp = t_1;
	} else if (y <= 7e+64) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((t - x) / (a - z))
    if (y <= (-2.2d+130)) then
        tmp = t_1
    else if (y <= 7d+64) then
        tmp = x + (t * ((y - z) / (a - z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -2.2e+130) {
		tmp = t_1;
	} else if (y <= 7e+64) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	tmp = 0
	if y <= -2.2e+130:
		tmp = t_1
	elif y <= 7e+64:
		tmp = x + (t * ((y - z) / (a - z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	tmp = 0.0
	if (y <= -2.2e+130)
		tmp = t_1;
	elseif (y <= 7e+64)
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / (a - z));
	tmp = 0.0;
	if (y <= -2.2e+130)
		tmp = t_1;
	elseif (y <= 7e+64)
		tmp = x + (t * ((y - z) / (a - z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.2e+130], t$95$1, If[LessEqual[y, 7e+64], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.19999999999999993e130 or 6.9999999999999997e64 < y

   1. Initial program 68.0%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right)\right), \color{blue}{\left(a - z\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - x\right)\right), \left(\color{blue}{a} - z\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \left(a - z\right)\right) \]

      6. --lowering--.f64 65.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right) \]

   5. Simplified 65.7%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{t - x}{a - z}\right), \color{blue}{y}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(t - x\right), \left(a - z\right)\right), y\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(a - z\right)\right), y\right) \]

      6. --lowering--.f64 79.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{\_.f64}\left(a, z\right)\right), y\right) \]

   7. Applied egg-rr 79.9%

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

   if -2.19999999999999993e130 < y < 6.9999999999999997e64

   1. Initial program 67.8%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{\color{blue}{a} - z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y - z}{a - z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y - z}}{a - z}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 80.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   4. Applied egg-rr 80.5%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{t}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, z\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 72.4%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+130}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+64}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-74}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+47}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{a - y}{z} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.5e-74)
   (* t (- 1.0 (/ y z)))
   (if (<= z 2e+47) (+ x (* (- t x) (/ y a))) (* t (+ (/ (- a y) z) 1.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e-74) {
		tmp = t * (1.0 - (y / z));
	} else if (z <= 2e+47) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t * (((a - y) / z) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.5d-74)) then
        tmp = t * (1.0d0 - (y / z))
    else if (z <= 2d+47) then
        tmp = x + ((t - x) * (y / a))
    else
        tmp = t * (((a - y) / z) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e-74) {
		tmp = t * (1.0 - (y / z));
	} else if (z <= 2e+47) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t * (((a - y) / z) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.5e-74:
		tmp = t * (1.0 - (y / z))
	elif z <= 2e+47:
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t * (((a - y) / z) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.5e-74)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif (z <= 2e+47)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = Float64(t * Float64(Float64(Float64(a - y) / z) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.5e-74)
		tmp = t * (1.0 - (y / z));
	elseif (z <= 2e+47)
		tmp = x + ((t - x) * (y / a));
	else
		tmp = t * (((a - y) / z) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.5e-74], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+47], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.49999999999999999e-74

   1. Initial program 53.2%

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

   3. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{z}\right)}\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{z}}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y - z}{z}\right)}\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y - z}}{z}\right)\right)\right) \]

      7. div-sub N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{y}{z} - \color{blue}{\frac{z}{z}}\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{y}{z} + \color{blue}{\left(\mathsf{neg}\left(\frac{z}{z}\right)\right)}\right)\right)\right) \]

      9. *-inverses N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{y}{z} + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{y}{z} + -1\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(-1 + \color{blue}{\frac{y}{z}}\right)\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{+.f64}\left(-1, \color{blue}{\left(\frac{y}{z}\right)}\right)\right)\right) \]

      13. /-lowering-/.f64 46.6%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   5. Simplified 46.6%

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

   6. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. distribute-rgt-neg-in N/A

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

      3. mul-1-neg N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \left(\frac{y}{z} - 1\right)\right)}\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(\frac{y}{z} + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(\frac{y}{z} + -1\right)\right)\right) \]

      7. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \frac{y}{z} + \color{blue}{-1 \cdot -1}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \frac{y}{z} + 1\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(1 + \color{blue}{-1 \cdot \frac{y}{z}}\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(t, \left(1 + \left(\mathsf{neg}\left(\frac{y}{z}\right)\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(t, \left(1 - \color{blue}{\frac{y}{z}}\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      13. /-lowering-/.f64 46.7%

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   8. Simplified 46.7%

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

   if -2.49999999999999999e-74 < z < 2.0000000000000001e47

   1. Initial program 90.1%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{\color{blue}{a} - z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y - z}{a - z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y - z}}{a - z}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 93.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   4. Applied egg-rr 93.5%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \color{blue}{\left(\frac{y}{a}\right)}\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 78.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right)\right) \]

   7. Simplified 78.4%

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

   if 2.0000000000000001e47 < z

   1. Initial program 41.3%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right), \color{blue}{z}\right)\right) \]

      8. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(\left(t - x\right) \cdot \left(y - a\right)\right), z\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(t - x\right), \left(y - a\right)\right), z\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(y - a\right)\right), z\right)\right) \]

      11. --lowering--.f64 59.4%

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{\_.f64}\left(y, a\right)\right), z\right)\right) \]

   5. Simplified 59.4%

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

   6. Taylor expanded in t around -inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(1 + -1 \cdot \frac{y - a}{z}\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(1 + \left(\mathsf{neg}\left(\frac{y - a}{z}\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(1 - \color{blue}{\frac{y - a}{z}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y - a}{z}\right)}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(y - a\right), \color{blue}{z}\right)\right)\right) \]

      6. --lowering--.f64 53.5%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, a\right), z\right)\right)\right) \]

   8. Simplified 53.5%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-74}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+47}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{a - y}{z} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 56.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{-42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+63}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z)))))
   (if (<= y -2.4e-42) t_1 (if (<= y 7e+63) (+ x t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -2.4e-42) {
		tmp = t_1;
	} else if (y <= 7e+63) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((t - x) / (a - z))
    if (y <= (-2.4d-42)) then
        tmp = t_1
    else if (y <= 7d+63) then
        tmp = x + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -2.4e-42) {
		tmp = t_1;
	} else if (y <= 7e+63) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	tmp = 0
	if y <= -2.4e-42:
		tmp = t_1
	elif y <= 7e+63:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	tmp = 0.0
	if (y <= -2.4e-42)
		tmp = t_1;
	elseif (y <= 7e+63)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / (a - z));
	tmp = 0.0;
	if (y <= -2.4e-42)
		tmp = t_1;
	elseif (y <= 7e+63)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.4e-42], t$95$1, If[LessEqual[y, 7e+63], N[(x + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.40000000000000003e-42 or 7.00000000000000059e63 < y

   1. Initial program 68.1%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right)\right), \color{blue}{\left(a - z\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - x\right)\right), \left(\color{blue}{a} - z\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \left(a - z\right)\right) \]

      6. --lowering--.f64 57.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right) \]

   5. Simplified 57.8%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{t - x}{a - z}\right), \color{blue}{y}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(t - x\right), \left(a - z\right)\right), y\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(a - z\right)\right), y\right) \]

      6. --lowering--.f64 68.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{\_.f64}\left(a, z\right)\right), y\right) \]

   7. Applied egg-rr 68.9%

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

   if -2.40000000000000003e-42 < y < 7.00000000000000059e63

   1. Initial program 67.7%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{\color{blue}{a} - z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y - z}{a - z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y - z}}{a - z}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 80.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   4. Applied egg-rr 80.9%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{t}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, z\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 74.4%

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

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{t}\right) \]
   9. Step-by-step derivation

   10. Simplified 50.0%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-42}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+63}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 56.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+63}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- t x) (/ y (- a z)))))
   (if (<= y -1.2e-43) t_1 (if (<= y 9.2e+63) (+ x t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / (a - z));
	double tmp;
	if (y <= -1.2e-43) {
		tmp = t_1;
	} else if (y <= 9.2e+63) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - x) * (y / (a - z))
    if (y <= (-1.2d-43)) then
        tmp = t_1
    else if (y <= 9.2d+63) then
        tmp = x + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / (a - z));
	double tmp;
	if (y <= -1.2e-43) {
		tmp = t_1;
	} else if (y <= 9.2e+63) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - x) * (y / (a - z))
	tmp = 0
	if y <= -1.2e-43:
		tmp = t_1
	elif y <= 9.2e+63:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (y <= -1.2e-43)
		tmp = t_1;
	elseif (y <= 9.2e+63)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - x) * (y / (a - z));
	tmp = 0.0;
	if (y <= -1.2e-43)
		tmp = t_1;
	elseif (y <= 9.2e+63)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.2e-43], t$95$1, If[LessEqual[y, 9.2e+63], N[(x + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2000000000000001e-43 or 9.19999999999999973e63 < y

   1. Initial program 68.1%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right)\right), \color{blue}{\left(a - z\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - x\right)\right), \left(\color{blue}{a} - z\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \left(a - z\right)\right) \]

      6. --lowering--.f64 57.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right) \]

   5. Simplified 57.8%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y}{a - z}\right)}\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y}}{a - z}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(y, \color{blue}{\left(a - z\right)}\right)\right) \]

      6. --lowering--.f64 67.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   7. Applied egg-rr 67.9%

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

   if -1.2000000000000001e-43 < y < 9.19999999999999973e63

   1. Initial program 67.7%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{\color{blue}{a} - z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y - z}{a - z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y - z}}{a - z}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 80.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   4. Applied egg-rr 80.9%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{t}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, z\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 74.4%

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

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{t}\right) \]
   9. Step-by-step derivation

   10. Simplified 50.0%

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

Alternative 9: 51.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+116}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-36}:\\ \;\;\;\;t \cdot \left(\frac{a - y}{z} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.9e+116)
   x
   (if (<= a 1.95e-36) (* t (+ (/ (- a y) z) 1.0)) (+ x (/ (* y t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.9e+116) {
		tmp = x;
	} else if (a <= 1.95e-36) {
		tmp = t * (((a - y) / z) + 1.0);
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.9d+116)) then
        tmp = x
    else if (a <= 1.95d-36) then
        tmp = t * (((a - y) / z) + 1.0d0)
    else
        tmp = x + ((y * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.9e+116) {
		tmp = x;
	} else if (a <= 1.95e-36) {
		tmp = t * (((a - y) / z) + 1.0);
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.9e+116:
		tmp = x
	elif a <= 1.95e-36:
		tmp = t * (((a - y) / z) + 1.0)
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.9e+116)
		tmp = x;
	elseif (a <= 1.95e-36)
		tmp = Float64(t * Float64(Float64(Float64(a - y) / z) + 1.0));
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.9e+116)
		tmp = x;
	elseif (a <= 1.95e-36)
		tmp = t * (((a - y) / z) + 1.0);
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.9e+116], x, If[LessEqual[a, 1.95e-36], N[(t * N[(N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.8999999999999999e116

   1. Initial program 60.9%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 55.1%

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

   if -1.8999999999999999e116 < a < 1.95e-36

   1. Initial program 65.8%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right), \color{blue}{z}\right)\right) \]

      8. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(\left(t - x\right) \cdot \left(y - a\right)\right), z\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(t - x\right), \left(y - a\right)\right), z\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(y - a\right)\right), z\right)\right) \]

      11. --lowering--.f64 69.4%

          \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{\_.f64}\left(y, a\right)\right), z\right)\right) \]

   5. Simplified 69.4%

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

   6. Taylor expanded in t around -inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(1 + -1 \cdot \frac{y - a}{z}\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(1 + \left(\mathsf{neg}\left(\frac{y - a}{z}\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(1 - \color{blue}{\frac{y - a}{z}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y - a}{z}\right)}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(y - a\right), \color{blue}{z}\right)\right)\right) \]

      6. --lowering--.f64 51.3%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, a\right), z\right)\right)\right) \]

   8. Simplified 51.3%

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

   if 1.95e-36 < a

   1. Initial program 73.0%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{\color{blue}{a} - z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y - z}{a - z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y - z}}{a - z}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 90.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   4. Applied egg-rr 90.5%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{t}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, z\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 77.4%

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

   8. Taylor expanded in z around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{t \cdot y}{a}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(t \cdot y\right), \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 55.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, y\right), a\right)\right) \]

   10. Simplified 55.0%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+116}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-36}:\\ \;\;\;\;t \cdot \left(\frac{a - y}{z} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+116}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-36}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.9e+116)
   x
   (if (<= a 2.1e-36) (* t (- 1.0 (/ y z))) (+ x (/ (* y t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.9e+116) {
		tmp = x;
	} else if (a <= 2.1e-36) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.9d+116)) then
        tmp = x
    else if (a <= 2.1d-36) then
        tmp = t * (1.0d0 - (y / z))
    else
        tmp = x + ((y * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.9e+116) {
		tmp = x;
	} else if (a <= 2.1e-36) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.9e+116:
		tmp = x
	elif a <= 2.1e-36:
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.9e+116)
		tmp = x;
	elseif (a <= 2.1e-36)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.9e+116)
		tmp = x;
	elseif (a <= 2.1e-36)
		tmp = t * (1.0 - (y / z));
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.9e+116], x, If[LessEqual[a, 2.1e-36], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.8999999999999999e116

   1. Initial program 60.9%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 55.1%

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

   if -1.8999999999999999e116 < a < 2.09999999999999991e-36

   1. Initial program 65.8%

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

   3. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{z}\right)}\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{z}}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y - z}{z}\right)}\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y - z}}{z}\right)\right)\right) \]

      7. div-sub N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{y}{z} - \color{blue}{\frac{z}{z}}\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{y}{z} + \color{blue}{\left(\mathsf{neg}\left(\frac{z}{z}\right)\right)}\right)\right)\right) \]

      9. *-inverses N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{y}{z} + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{y}{z} + -1\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(-1 + \color{blue}{\frac{y}{z}}\right)\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{+.f64}\left(-1, \color{blue}{\left(\frac{y}{z}\right)}\right)\right)\right) \]

      13. /-lowering-/.f64 52.9%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   5. Simplified 52.9%

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

   6. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. distribute-rgt-neg-in N/A

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

      3. mul-1-neg N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \left(\frac{y}{z} - 1\right)\right)}\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(\frac{y}{z} + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(\frac{y}{z} + -1\right)\right)\right) \]

      7. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \frac{y}{z} + \color{blue}{-1 \cdot -1}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \frac{y}{z} + 1\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(1 + \color{blue}{-1 \cdot \frac{y}{z}}\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(t, \left(1 + \left(\mathsf{neg}\left(\frac{y}{z}\right)\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(t, \left(1 - \color{blue}{\frac{y}{z}}\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      13. /-lowering-/.f64 51.2%

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   8. Simplified 51.2%

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

   if 2.09999999999999991e-36 < a

   1. Initial program 73.0%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{\color{blue}{a} - z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y - z}{a - z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y - z}}{a - z}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 90.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   4. Applied egg-rr 90.5%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{t}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, z\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 77.4%

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

   8. Taylor expanded in z around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{t \cdot y}{a}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(t \cdot y\right), \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 55.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, y\right), a\right)\right) \]

   10. Simplified 55.0%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+116}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-36}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 44.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a}\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+106}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) a))))
   (if (<= y -5.8e+117) t_1 (if (<= y 3.3e+106) (+ x t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / a);
	double tmp;
	if (y <= -5.8e+117) {
		tmp = t_1;
	} else if (y <= 3.3e+106) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((t - x) / a)
    if (y <= (-5.8d+117)) then
        tmp = t_1
    else if (y <= 3.3d+106) then
        tmp = x + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / a);
	double tmp;
	if (y <= -5.8e+117) {
		tmp = t_1;
	} else if (y <= 3.3e+106) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / a)
	tmp = 0
	if y <= -5.8e+117:
		tmp = t_1
	elif y <= 3.3e+106:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / a))
	tmp = 0.0
	if (y <= -5.8e+117)
		tmp = t_1;
	elseif (y <= 3.3e+106)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / a);
	tmp = 0.0;
	if (y <= -5.8e+117)
		tmp = t_1;
	elseif (y <= 3.3e+106)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e+117], t$95$1, If[LessEqual[y, 3.3e+106], N[(x + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.80000000000000055e117 or 3.30000000000000008e106 < y

   1. Initial program 67.5%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right)\right), \color{blue}{\left(a - z\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - x\right)\right), \left(\color{blue}{a} - z\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \left(a - z\right)\right) \]

      6. --lowering--.f64 65.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right) \]

   5. Simplified 65.1%

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

   6. Taylor expanded in a around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right)\right), \color{blue}{a}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - x\right)\right), a\right) \]

      3. --lowering--.f64 50.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), a\right) \]

   8. Simplified 50.1%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{t - x}{a}\right), \color{blue}{y}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(t - x\right), a\right), y\right) \]

      5. --lowering--.f64 57.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), a\right), y\right) \]

   10. Applied egg-rr 57.9%

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

   if -5.80000000000000055e117 < y < 3.30000000000000008e106

   1. Initial program 68.0%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{\color{blue}{a} - z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y - z}{a - z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y - z}}{a - z}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 80.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   4. Applied egg-rr 80.7%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{t}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, z\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 71.8%

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

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{t}\right) \]
   9. Step-by-step derivation

   10. Simplified 47.2%

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

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+117}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+106}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 48.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.3 \cdot 10^{+116}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 0.0048:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.3e+116) x (if (<= a 0.0048) (* t (- 1.0 (/ y z))) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.3e+116) {
		tmp = x;
	} else if (a <= 0.0048) {
		tmp = t * (1.0 - (y / z));
	} 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 <= (-4.3d+116)) then
        tmp = x
    else if (a <= 0.0048d0) then
        tmp = t * (1.0d0 - (y / z))
    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 <= -4.3e+116) {
		tmp = x;
	} else if (a <= 0.0048) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.3e+116:
		tmp = x
	elif a <= 0.0048:
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.3e+116)
		tmp = x;
	elseif (a <= 0.0048)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.3e+116)
		tmp = x;
	elseif (a <= 0.0048)
		tmp = t * (1.0 - (y / z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.3e+116], x, If[LessEqual[a, 0.0048], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -4.3e116 or 0.00479999999999999958 < a

   1. Initial program 68.8%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 46.8%

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

   if -4.3e116 < a < 0.00479999999999999958

   1. Initial program 67.1%

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

   3. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{z}\right)}\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{z}}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y - z}{z}\right)}\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y - z}}{z}\right)\right)\right) \]

      7. div-sub N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{y}{z} - \color{blue}{\frac{z}{z}}\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{y}{z} + \color{blue}{\left(\mathsf{neg}\left(\frac{z}{z}\right)\right)}\right)\right)\right) \]

      9. *-inverses N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{y}{z} + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{y}{z} + -1\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(-1 + \color{blue}{\frac{y}{z}}\right)\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{+.f64}\left(-1, \color{blue}{\left(\frac{y}{z}\right)}\right)\right)\right) \]

      13. /-lowering-/.f64 51.4%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   5. Simplified 51.4%

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

   6. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. distribute-rgt-neg-in N/A

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

      3. mul-1-neg N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \left(\frac{y}{z} - 1\right)\right)}\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(\frac{y}{z} + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(\frac{y}{z} + -1\right)\right)\right) \]

      7. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \frac{y}{z} + \color{blue}{-1 \cdot -1}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \frac{y}{z} + 1\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(1 + \color{blue}{-1 \cdot \frac{y}{z}}\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(t, \left(1 + \left(\mathsf{neg}\left(\frac{y}{z}\right)\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(t, \left(1 - \color{blue}{\frac{y}{z}}\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      13. /-lowering-/.f64 49.3%

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   8. Simplified 49.3%

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

Alternative 13: 38.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+122}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+155}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(0 - y\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.1e+122)
   (/ t (/ a y))
   (if (<= y 6.6e+155) (+ x t) (/ (* x (- 0.0 y)) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.1e+122) {
		tmp = t / (a / y);
	} else if (y <= 6.6e+155) {
		tmp = x + t;
	} else {
		tmp = (x * (0.0 - y)) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-2.1d+122)) then
        tmp = t / (a / y)
    else if (y <= 6.6d+155) then
        tmp = x + t
    else
        tmp = (x * (0.0d0 - y)) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.1e+122) {
		tmp = t / (a / y);
	} else if (y <= 6.6e+155) {
		tmp = x + t;
	} else {
		tmp = (x * (0.0 - y)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.1e+122:
		tmp = t / (a / y)
	elif y <= 6.6e+155:
		tmp = x + t
	else:
		tmp = (x * (0.0 - y)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.1e+122)
		tmp = Float64(t / Float64(a / y));
	elseif (y <= 6.6e+155)
		tmp = Float64(x + t);
	else
		tmp = Float64(Float64(x * Float64(0.0 - y)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.1e+122)
		tmp = t / (a / y);
	elseif (y <= 6.6e+155)
		tmp = x + t;
	else
		tmp = (x * (0.0 - y)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.1e+122], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.6e+155], N[(x + t), $MachinePrecision], N[(N[(x * N[(0.0 - y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.10000000000000016e122

   1. Initial program 66.6%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right)\right), \color{blue}{\left(a - z\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - x\right)\right), \left(\color{blue}{a} - z\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \left(a - z\right)\right) \]

      6. --lowering--.f64 63.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right) \]

   5. Simplified 63.9%

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

   6. Taylor expanded in a around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right)\right), \color{blue}{a}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - x\right)\right), a\right) \]

      3. --lowering--.f64 43.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), a\right) \]

   8. Simplified 43.4%

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

   9. Taylor expanded in t around inf

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

       1. associate-/l* N/A

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

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{y}{a}\right)}\right) \]

       3. /-lowering-/.f64 34.2%

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right) \]

   11. Simplified 34.2%

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

       1. clear-num N/A

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

       2. un-div-inv N/A

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

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(t, \color{blue}{\left(\frac{a}{y}\right)}\right) \]

       4. /-lowering-/.f64 34.2%

          \[\leadsto \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(a, \color{blue}{y}\right)\right) \]

   13. Applied egg-rr 34.2%

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

   if -2.10000000000000016e122 < y < 6.5999999999999997e155

   1. Initial program 67.5%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{\color{blue}{a} - z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y - z}{a - z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y - z}}{a - z}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 81.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   4. Applied egg-rr 81.3%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{t}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, z\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 71.2%

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

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{t}\right) \]
   9. Step-by-step derivation

   10. Simplified 46.9%

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

   if 6.5999999999999997e155 < y

   1. Initial program 71.2%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right)\right), \color{blue}{\left(a - z\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - x\right)\right), \left(\color{blue}{a} - z\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \left(a - z\right)\right) \]

      6. --lowering--.f64 71.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right) \]

   5. Simplified 71.3%

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

   6. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{\left(\mathsf{neg}\left(\left(a - z\right)\right)\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot x\right), \left(\mathsf{neg}\left(\color{blue}{\left(a - z\right)}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(\mathsf{neg}\left(\color{blue}{\left(a - z\right)}\right)\right)\right) \]

      6. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{neg.f64}\left(\left(a - z\right)\right)\right) \]

      7. --lowering--.f64 50.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{neg.f64}\left(\mathsf{\_.f64}\left(a, z\right)\right)\right) \]

   8. Simplified 50.2%

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

   9. Taylor expanded in a around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{neg.f64}\left(\color{blue}{a}\right)\right) \]
   10. Step-by-step derivation

   11. Simplified 43.7%

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

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+122}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+155}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(0 - y\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 39.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;y \leq -8 \cdot 10^{+122}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+138}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (/ a y))))
   (if (<= y -8e+122) t_1 (if (<= y 4.5e+138) (+ x t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (a / y);
	double tmp;
	if (y <= -8e+122) {
		tmp = t_1;
	} else if (y <= 4.5e+138) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / (a / y)
    if (y <= (-8d+122)) then
        tmp = t_1
    else if (y <= 4.5d+138) then
        tmp = x + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (a / y);
	double tmp;
	if (y <= -8e+122) {
		tmp = t_1;
	} else if (y <= 4.5e+138) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / (a / y)
	tmp = 0
	if y <= -8e+122:
		tmp = t_1
	elif y <= 4.5e+138:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(a / y))
	tmp = 0.0
	if (y <= -8e+122)
		tmp = t_1;
	elseif (y <= 4.5e+138)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t / (a / y);
	tmp = 0.0;
	if (y <= -8e+122)
		tmp = t_1;
	elseif (y <= 4.5e+138)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8e+122], t$95$1, If[LessEqual[y, 4.5e+138], N[(x + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.00000000000000012e122 or 4.49999999999999982e138 < y

   1. Initial program 67.9%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right)\right), \color{blue}{\left(a - z\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - x\right)\right), \left(\color{blue}{a} - z\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \left(a - z\right)\right) \]

      6. --lowering--.f64 66.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right) \]

   5. Simplified 66.7%

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

   6. Taylor expanded in a around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right)\right), \color{blue}{a}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - x\right)\right), a\right) \]

      3. --lowering--.f64 51.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), a\right) \]

   8. Simplified 51.9%

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

   9. Taylor expanded in t around inf

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

       1. associate-/l* N/A

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

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{y}{a}\right)}\right) \]

       3. /-lowering-/.f64 34.1%

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right) \]

   11. Simplified 34.1%

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

       1. clear-num N/A

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

       2. un-div-inv N/A

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

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(t, \color{blue}{\left(\frac{a}{y}\right)}\right) \]

       4. /-lowering-/.f64 34.1%

          \[\leadsto \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(a, \color{blue}{y}\right)\right) \]

   13. Applied egg-rr 34.1%

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

   if -8.00000000000000012e122 < y < 4.49999999999999982e138

   1. Initial program 67.9%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{\color{blue}{a} - z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y - z}{a - z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y - z}}{a - z}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 81.2%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   4. Applied egg-rr 81.2%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{t}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, z\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 71.0%

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

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{t}\right) \]
   9. Step-by-step derivation

   10. Simplified 47.1%

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

Alternative 15: 39.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+138}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= y -8.2e+121) t_1 (if (<= y 2.65e+138) (+ x t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (y <= -8.2e+121) {
		tmp = t_1;
	} else if (y <= 2.65e+138) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (y <= (-8.2d+121)) then
        tmp = t_1
    else if (y <= 2.65d+138) then
        tmp = x + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (y <= -8.2e+121) {
		tmp = t_1;
	} else if (y <= 2.65e+138) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if y <= -8.2e+121:
		tmp = t_1
	elif y <= 2.65e+138:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (y <= -8.2e+121)
		tmp = t_1;
	elseif (y <= 2.65e+138)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (y <= -8.2e+121)
		tmp = t_1;
	elseif (y <= 2.65e+138)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.2e+121], t$95$1, If[LessEqual[y, 2.65e+138], N[(x + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.2e121 or 2.64999999999999992e138 < y

   1. Initial program 67.9%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right)\right), \color{blue}{\left(a - z\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - x\right)\right), \left(\color{blue}{a} - z\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \left(a - z\right)\right) \]

      6. --lowering--.f64 66.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right) \]

   5. Simplified 66.7%

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

   6. Taylor expanded in a around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(t - x\right)\right), \color{blue}{a}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - x\right)\right), a\right) \]

      3. --lowering--.f64 51.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, x\right)\right), a\right) \]

   8. Simplified 51.9%

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

   9. Taylor expanded in t around inf

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

       1. associate-/l* N/A

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

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{y}{a}\right)}\right) \]

       3. /-lowering-/.f64 34.1%

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right) \]

   11. Simplified 34.1%

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

   if -8.2e121 < y < 2.64999999999999992e138

   1. Initial program 67.9%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(t - x\right) \cdot \left(y - z\right)}{\color{blue}{a} - z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y - z}{a - z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y - z}}{a - z}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(a - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{a} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 81.2%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right)\right) \]

   4. Applied egg-rr 81.2%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{t}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, z\right)\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 71.0%

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

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{t}\right) \]
   9. Step-by-step derivation

   10. Simplified 47.1%

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

Alternative 16: 38.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+116}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 0.09:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.9e+116) x (if (<= a 0.09) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.9e+116) {
		tmp = x;
	} else if (a <= 0.09) {
		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 <= (-1.9d+116)) then
        tmp = x
    else if (a <= 0.09d0) 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 <= -1.9e+116) {
		tmp = x;
	} else if (a <= 0.09) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.9e+116:
		tmp = x
	elif a <= 0.09:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.9e+116)
		tmp = x;
	elseif (a <= 0.09)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.9e+116)
		tmp = x;
	elseif (a <= 0.09)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.9e+116], x, If[LessEqual[a, 0.09], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.8999999999999999e116 or 0.089999999999999997 < a

   1. Initial program 68.8%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 46.8%

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

   if -1.8999999999999999e116 < a < 0.089999999999999997

   1. Initial program 67.1%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 38.0%

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

Alternative 17: 24.9% 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 67.9%

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

3. Taylor expanded in z around inf

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

5. Simplified 27.8%

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

Developer Target 1: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ y z) (- t x)))))
   (if (< z -1.2536131056095036e+188)
     t_1
     (if (< z 4.446702369113811e+64)
       (+ x (/ (- y z) (/ (- a z) (- t x))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y / z) * (t - x))
	tmp = 0
	if z < -1.2536131056095036e+188:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y / z) * Float64(t - x)))
	tmp = 0.0
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y / z) * (t - x));
	tmp = 0.0;
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y / z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.2536131056095036e+188], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024152 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -125361310560950360000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- t (* (/ y z) (- t x))) (if (< z 44467023691138110000000000000000000000000000000000000000000000000) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x))))))

  (+ x (/ (* (- y z) (- t x)) (- a z))))