Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 79.8% → 89.0%

Time: 14.0s

Alternatives: 17

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-213} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-213) (not (<= t_1 0.0)))
     t_1
     (+ t (/ (* (- t x) (- a y)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-213) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-2d-213)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = t_1
    else
        tmp = t + (((t - x) * (a - y)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-213) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -2e-213) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = t + (((t - x) * (a - y)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -2e-213) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -2e-213) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = t + (((t - x) * (a - y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-213], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.9999999999999999e-213 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 94.3%

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

   if -1.9999999999999999e-213 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.8%

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

   2. Taylor expanded in z around inf 89.3%

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

      1. +-commutative 89.3%

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

      2. associate--l+ 89.3%

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

      3. associate-*r/ 89.3%

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

      4. associate-*r/ 89.3%

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

      5. div-sub 89.4%

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

      6. distribute-lft-out-- 89.4%

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

      7. mul-1-neg 89.4%

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

      8. distribute-neg-frac 89.4%

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

      9. unsub-neg 89.4%

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

      10. distribute-rgt-out-- 89.5%

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

   4. Simplified 89.5%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-213} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]

Alternative 2: 36.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a}\\ \mathbf{if}\;a \leq -4.4 \cdot 10^{+160}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-256}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-237}:\\ \;\;\;\;y \cdot \frac{-t}{z}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+86}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+142}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) a))))
   (if (<= a -4.4e+160)
     x
     (if (<= a -3e-130)
       t_1
       (if (<= a -9e-256)
         t
         (if (<= a 7e-237)
           (* y (/ (- t) z))
           (if (<= a 1.5e+86) (+ x t) (if (<= a 5.5e+142) t_1 x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / a);
	double tmp;
	if (a <= -4.4e+160) {
		tmp = x;
	} else if (a <= -3e-130) {
		tmp = t_1;
	} else if (a <= -9e-256) {
		tmp = t;
	} else if (a <= 7e-237) {
		tmp = y * (-t / z);
	} else if (a <= 1.5e+86) {
		tmp = x + t;
	} else if (a <= 5.5e+142) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / a)
    if (a <= (-4.4d+160)) then
        tmp = x
    else if (a <= (-3d-130)) then
        tmp = t_1
    else if (a <= (-9d-256)) then
        tmp = t
    else if (a <= 7d-237) then
        tmp = y * (-t / z)
    else if (a <= 1.5d+86) then
        tmp = x + t
    else if (a <= 5.5d+142) then
        tmp = t_1
    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 t_1 = t * ((y - z) / a);
	double tmp;
	if (a <= -4.4e+160) {
		tmp = x;
	} else if (a <= -3e-130) {
		tmp = t_1;
	} else if (a <= -9e-256) {
		tmp = t;
	} else if (a <= 7e-237) {
		tmp = y * (-t / z);
	} else if (a <= 1.5e+86) {
		tmp = x + t;
	} else if (a <= 5.5e+142) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / a)
	tmp = 0
	if a <= -4.4e+160:
		tmp = x
	elif a <= -3e-130:
		tmp = t_1
	elif a <= -9e-256:
		tmp = t
	elif a <= 7e-237:
		tmp = y * (-t / z)
	elif a <= 1.5e+86:
		tmp = x + t
	elif a <= 5.5e+142:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / a))
	tmp = 0.0
	if (a <= -4.4e+160)
		tmp = x;
	elseif (a <= -3e-130)
		tmp = t_1;
	elseif (a <= -9e-256)
		tmp = t;
	elseif (a <= 7e-237)
		tmp = Float64(y * Float64(Float64(-t) / z));
	elseif (a <= 1.5e+86)
		tmp = Float64(x + t);
	elseif (a <= 5.5e+142)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / a);
	tmp = 0.0;
	if (a <= -4.4e+160)
		tmp = x;
	elseif (a <= -3e-130)
		tmp = t_1;
	elseif (a <= -9e-256)
		tmp = t;
	elseif (a <= 7e-237)
		tmp = y * (-t / z);
	elseif (a <= 1.5e+86)
		tmp = x + t;
	elseif (a <= 5.5e+142)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.4e+160], x, If[LessEqual[a, -3e-130], t$95$1, If[LessEqual[a, -9e-256], t, If[LessEqual[a, 7e-237], N[(y * N[((-t) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.5e+86], N[(x + t), $MachinePrecision], If[LessEqual[a, 5.5e+142], t$95$1, x]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -4.39999999999999984e160 or 5.50000000000000035e142 < a

   1. Initial program 93.1%

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

   2. Taylor expanded in a around inf 67.4%

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

   if -4.39999999999999984e160 < a < -2.99999999999999986e-130 or 1.49999999999999988e86 < a < 5.50000000000000035e142

   1. Initial program 83.4%

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

   2. Taylor expanded in t around inf 55.0%

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

      1. div-sub 55.0%

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

   4. Simplified 55.0%

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

   5. Taylor expanded in a around inf 38.5%

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

   if -2.99999999999999986e-130 < a < -9.0000000000000005e-256

   1. Initial program 62.7%

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

   2. Taylor expanded in z around inf 57.3%

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

   if -9.0000000000000005e-256 < a < 6.99999999999999966e-237

   1. Initial program 74.3%

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

   2. Taylor expanded in x around 0 64.4%

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

      1. associate-/l* 74.4%

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

   4. Simplified 74.4%

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

   5. Taylor expanded in y around inf 59.6%

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

   6. Taylor expanded in a around 0 54.6%

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

      1. mul-1-neg 54.6%

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

      2. associate-*r/ 59.6%

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

      3. distribute-rgt-neg-in 59.6%

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

      4. distribute-frac-neg 59.6%

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

   8. Simplified 59.6%

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

   if 6.99999999999999966e-237 < a < 1.49999999999999988e86

   1. Initial program 76.9%

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

   2. Taylor expanded in t around inf 58.5%

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

   3. Taylor expanded in z around inf 37.9%

      \[\leadsto \color{blue}{t + x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{+160}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-130}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-256}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-237}:\\ \;\;\;\;y \cdot \frac{-t}{z}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+86}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+142}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 48.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a}\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{+161}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-25}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+78}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+142}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) a))))
   (if (<= a -1.8e+161)
     x
     (if (<= a -6.5e+69)
       t_1
       (if (<= a -2.8e-25)
         (+ x t)
         (if (<= a 2.9e+78)
           (* t (- 1.0 (/ y z)))
           (if (<= a 6.2e+142) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / a);
	double tmp;
	if (a <= -1.8e+161) {
		tmp = x;
	} else if (a <= -6.5e+69) {
		tmp = t_1;
	} else if (a <= -2.8e-25) {
		tmp = x + t;
	} else if (a <= 2.9e+78) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= 6.2e+142) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / a)
    if (a <= (-1.8d+161)) then
        tmp = x
    else if (a <= (-6.5d+69)) then
        tmp = t_1
    else if (a <= (-2.8d-25)) then
        tmp = x + t
    else if (a <= 2.9d+78) then
        tmp = t * (1.0d0 - (y / z))
    else if (a <= 6.2d+142) then
        tmp = t_1
    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 t_1 = t * ((y - z) / a);
	double tmp;
	if (a <= -1.8e+161) {
		tmp = x;
	} else if (a <= -6.5e+69) {
		tmp = t_1;
	} else if (a <= -2.8e-25) {
		tmp = x + t;
	} else if (a <= 2.9e+78) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= 6.2e+142) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / a)
	tmp = 0
	if a <= -1.8e+161:
		tmp = x
	elif a <= -6.5e+69:
		tmp = t_1
	elif a <= -2.8e-25:
		tmp = x + t
	elif a <= 2.9e+78:
		tmp = t * (1.0 - (y / z))
	elif a <= 6.2e+142:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / a))
	tmp = 0.0
	if (a <= -1.8e+161)
		tmp = x;
	elseif (a <= -6.5e+69)
		tmp = t_1;
	elseif (a <= -2.8e-25)
		tmp = Float64(x + t);
	elseif (a <= 2.9e+78)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif (a <= 6.2e+142)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / a);
	tmp = 0.0;
	if (a <= -1.8e+161)
		tmp = x;
	elseif (a <= -6.5e+69)
		tmp = t_1;
	elseif (a <= -2.8e-25)
		tmp = x + t;
	elseif (a <= 2.9e+78)
		tmp = t * (1.0 - (y / z));
	elseif (a <= 6.2e+142)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.8e+161], x, If[LessEqual[a, -6.5e+69], t$95$1, If[LessEqual[a, -2.8e-25], N[(x + t), $MachinePrecision], If[LessEqual[a, 2.9e+78], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.2e+142], t$95$1, x]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.79999999999999992e161 or 6.1999999999999998e142 < a

   1. Initial program 93.1%

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

   2. Taylor expanded in a around inf 67.4%

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

   if -1.79999999999999992e161 < a < -6.5000000000000001e69 or 2.90000000000000017e78 < a < 6.1999999999999998e142

   1. Initial program 87.2%

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

   2. Taylor expanded in t around inf 68.8%

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

      1. div-sub 68.8%

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

   4. Simplified 68.8%

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

   5. Taylor expanded in a around inf 50.2%

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

   if -6.5000000000000001e69 < a < -2.79999999999999988e-25

   1. Initial program 84.7%

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

   2. Taylor expanded in t around inf 60.2%

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

   3. Taylor expanded in z around inf 35.0%

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

   if -2.79999999999999988e-25 < a < 2.90000000000000017e78

   1. Initial program 73.1%

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

   2. Taylor expanded in x around 0 50.0%

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

      1. associate-/l* 62.6%

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

   4. Simplified 62.6%

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

   5. Taylor expanded in a around 0 57.0%

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

      1. associate-*r/ 57.0%

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

      2. mul-1-neg 57.0%

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

   7. Simplified 57.0%

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

   8. Taylor expanded in z around 0 52.8%

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

      1. +-commutative 52.8%

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

      2. mul-1-neg 52.8%

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

      3. unsub-neg 52.8%

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

      4. associate-*r/ 55.5%

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

   10. Simplified 55.5%

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

   11. Taylor expanded in t around 0 57.7%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+161}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{+69}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-25}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+78}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+142}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 69.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{a - z}{y - z}}\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-137}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+180}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (/ (- a z) (- y z)))))
   (if (<= z -9.5e-7)
     t_1
     (if (<= z 6e-137)
       (+ x (/ y (/ a (- t x))))
       (if (<= z 7e+180) (+ x (* (- y z) (/ t (- a z)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / ((a - z) / (y - z));
	double tmp;
	if (z <= -9.5e-7) {
		tmp = t_1;
	} else if (z <= 6e-137) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 7e+180) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / ((a - z) / (y - z))
    if (z <= (-9.5d-7)) then
        tmp = t_1
    else if (z <= 6d-137) then
        tmp = x + (y / (a / (t - x)))
    else if (z <= 7d+180) then
        tmp = x + ((y - z) * (t / (a - z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t / ((a - z) / (y - z));
	double tmp;
	if (z <= -9.5e-7) {
		tmp = t_1;
	} else if (z <= 6e-137) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 7e+180) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / ((a - z) / (y - z))
	tmp = 0
	if z <= -9.5e-7:
		tmp = t_1
	elif z <= 6e-137:
		tmp = x + (y / (a / (t - x)))
	elif z <= 7e+180:
		tmp = x + ((y - z) * (t / (a - z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(Float64(a - z) / Float64(y - z)))
	tmp = 0.0
	if (z <= -9.5e-7)
		tmp = t_1;
	elseif (z <= 6e-137)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif (z <= 7e+180)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t / ((a - z) / (y - z));
	tmp = 0.0;
	if (z <= -9.5e-7)
		tmp = t_1;
	elseif (z <= 6e-137)
		tmp = x + (y / (a / (t - x)));
	elseif (z <= 7e+180)
		tmp = x + ((y - z) * (t / (a - z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.5e-7], t$95$1, If[LessEqual[z, 6e-137], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e+180], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.5000000000000001e-7 or 6.9999999999999996e180 < z

   1. Initial program 58.9%

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

   2. Taylor expanded in x around 0 46.7%

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

      1. associate-/l* 70.7%

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

   4. Simplified 70.7%

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

   if -9.5000000000000001e-7 < z < 5.9999999999999996e-137

   1. Initial program 95.9%

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

   2. Taylor expanded in z around 0 79.9%

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

      1. +-commutative 79.9%

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

      2. associate-/l* 87.6%

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

   4. Simplified 87.6%

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

   if 5.9999999999999996e-137 < z < 6.9999999999999996e180

   1. Initial program 92.1%

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

   2. Taylor expanded in t around inf 70.9%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-7}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-137}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+180}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 5: 47.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -4 \cdot 10^{+160}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.35 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+70}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+142}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y z) (/ t a))))
   (if (<= a -4e+160)
     x
     (if (<= a -2.35e-46)
       t_1
       (if (<= a 9e+70) (* t (- 1.0 (/ y z))) (if (<= a 5.6e+142) t_1 x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) * (t / a);
	double tmp;
	if (a <= -4e+160) {
		tmp = x;
	} else if (a <= -2.35e-46) {
		tmp = t_1;
	} else if (a <= 9e+70) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= 5.6e+142) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (t / a)
    if (a <= (-4d+160)) then
        tmp = x
    else if (a <= (-2.35d-46)) then
        tmp = t_1
    else if (a <= 9d+70) then
        tmp = t * (1.0d0 - (y / z))
    else if (a <= 5.6d+142) then
        tmp = t_1
    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 t_1 = (y - z) * (t / a);
	double tmp;
	if (a <= -4e+160) {
		tmp = x;
	} else if (a <= -2.35e-46) {
		tmp = t_1;
	} else if (a <= 9e+70) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= 5.6e+142) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - z) * (t / a)
	tmp = 0
	if a <= -4e+160:
		tmp = x
	elif a <= -2.35e-46:
		tmp = t_1
	elif a <= 9e+70:
		tmp = t * (1.0 - (y / z))
	elif a <= 5.6e+142:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) * Float64(t / a))
	tmp = 0.0
	if (a <= -4e+160)
		tmp = x;
	elseif (a <= -2.35e-46)
		tmp = t_1;
	elseif (a <= 9e+70)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif (a <= 5.6e+142)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - z) * (t / a);
	tmp = 0.0;
	if (a <= -4e+160)
		tmp = x;
	elseif (a <= -2.35e-46)
		tmp = t_1;
	elseif (a <= 9e+70)
		tmp = t * (1.0 - (y / z));
	elseif (a <= 5.6e+142)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4e+160], x, If[LessEqual[a, -2.35e-46], t$95$1, If[LessEqual[a, 9e+70], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.6e+142], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.00000000000000003e160 or 5.6e142 < a

   1. Initial program 93.1%

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

   2. Taylor expanded in a around inf 67.4%

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

   if -4.00000000000000003e160 < a < -2.34999999999999983e-46 or 8.9999999999999999e70 < a < 5.6e142

   1. Initial program 84.1%

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

   2. Taylor expanded in t around inf 51.9%

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

      1. div-sub 51.9%

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

   4. Simplified 51.9%

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

   5. Taylor expanded in a around inf 34.5%

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

      1. associate-/l* 39.3%

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

      2. associate-/r/ 39.5%

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

   7. Simplified 39.5%

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

   if -2.34999999999999983e-46 < a < 8.9999999999999999e70

   1. Initial program 73.5%

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

   2. Taylor expanded in x around 0 50.3%

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

      1. associate-/l* 63.4%

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

   4. Simplified 63.4%

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

   5. Taylor expanded in a around 0 58.3%

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

      1. associate-*r/ 58.3%

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

      2. mul-1-neg 58.3%

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

   7. Simplified 58.3%

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

   8. Taylor expanded in z around 0 53.8%

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

      1. +-commutative 53.8%

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

      2. mul-1-neg 53.8%

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

      3. unsub-neg 53.8%

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

      4. associate-*r/ 56.7%

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

   10. Simplified 56.7%

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

   11. Taylor expanded in t around 0 59.0%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+160}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.35 \cdot 10^{-46}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+70}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+142}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 75.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.6 \cdot 10^{-27} \lor \neg \left(a \leq 4 \cdot 10^{-58}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -7.6e-27) (not (<= a 4e-58)))
   (+ x (* (- y z) (/ t (- a z))))
   (+ t (/ (* (- t x) (- a y)) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7.6e-27) || !(a <= 4e-58)) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-7.6d-27)) .or. (.not. (a <= 4d-58))) then
        tmp = x + ((y - z) * (t / (a - z)))
    else
        tmp = t + (((t - x) * (a - y)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7.6e-27) || !(a <= 4e-58)) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -7.6e-27) or not (a <= 4e-58):
		tmp = x + ((y - z) * (t / (a - z)))
	else:
		tmp = t + (((t - x) * (a - y)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -7.6e-27) || !(a <= 4e-58))
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -7.6e-27) || ~((a <= 4e-58)))
		tmp = x + ((y - z) * (t / (a - z)));
	else
		tmp = t + (((t - x) * (a - y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -7.6e-27], N[Not[LessEqual[a, 4e-58]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.60000000000000001e-27 or 4.0000000000000001e-58 < a

   1. Initial program 87.9%

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

   2. Taylor expanded in t around inf 76.6%

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

   if -7.60000000000000001e-27 < a < 4.0000000000000001e-58

   1. Initial program 71.0%

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

   2. Taylor expanded in z around inf 81.5%

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

      1. +-commutative 81.5%

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

      2. associate--l+ 81.5%

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

      3. associate-*r/ 81.5%

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

      4. associate-*r/ 81.5%

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

      5. div-sub 82.5%

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

      6. distribute-lft-out-- 82.5%

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

      7. mul-1-neg 82.5%

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

      8. distribute-neg-frac 82.5%

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

      9. unsub-neg 82.5%

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

      10. distribute-rgt-out-- 82.5%

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

   4. Simplified 82.5%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.6 \cdot 10^{-27} \lor \neg \left(a \leq 4 \cdot 10^{-58}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]

Alternative 7: 60.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+18} \lor \neg \left(z \leq 6.5 \cdot 10^{-128}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.05e+18) (not (<= z 6.5e-128)))
   (* t (/ (- y z) (- a z)))
   (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.05e+18) || !(z <= 6.5e-128)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.05d+18)) .or. (.not. (z <= 6.5d-128))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.05e+18) || !(z <= 6.5e-128)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.05e+18) or not (z <= 6.5e-128):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.05e+18) || !(z <= 6.5e-128))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.05e+18) || ~((z <= 6.5e-128)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.05e+18], N[Not[LessEqual[z, 6.5e-128]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.05e18 or 6.49999999999999977e-128 < z

   1. Initial program 72.4%

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

   2. Taylor expanded in t around inf 62.4%

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

      1. div-sub 62.3%

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

   4. Simplified 62.3%

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

   if -2.05e18 < z < 6.49999999999999977e-128

   1. Initial program 95.0%

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

   2. Taylor expanded in t around inf 79.1%

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

   3. Taylor expanded in z around 0 69.7%

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

      1. +-commutative 69.7%

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

      2. associate-/l* 75.4%

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

   5. Simplified 75.4%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+18} \lor \neg \left(z \leq 6.5 \cdot 10^{-128}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 8: 62.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -19000 \lor \neg \left(z \leq 5.8 \cdot 10^{-29}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -19000.0) (not (<= z 5.8e-29)))
   (* t (/ (- y z) (- a z)))
   (+ x (* (- y z) (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -19000.0) || !(z <= 5.8e-29)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((y - z) * (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 ((z <= (-19000.0d0)) .or. (.not. (z <= 5.8d-29))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + ((y - z) * (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 ((z <= -19000.0) || !(z <= 5.8e-29)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((y - z) * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -19000.0) or not (z <= 5.8e-29):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + ((y - z) * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -19000.0) || !(z <= 5.8e-29))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -19000.0) || ~((z <= 5.8e-29)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + ((y - z) * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -19000.0], N[Not[LessEqual[z, 5.8e-29]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -19000 or 5.80000000000000048e-29 < z

   1. Initial program 69.3%

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

   2. Taylor expanded in t around inf 64.9%

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

      1. div-sub 64.9%

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

   4. Simplified 64.9%

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

   if -19000 < z < 5.80000000000000048e-29

   1. Initial program 94.9%

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

      1. clear-num 94.9%

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

      2. inv-pow 94.9%

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

   3. Applied egg-rr 94.9%

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

      1. unpow-1 94.9%

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

   5. Simplified 94.9%

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

   6. Taylor expanded in t around inf 78.1%

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

   7. Taylor expanded in a around inf 72.8%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -19000 \lor \neg \left(z \leq 5.8 \cdot 10^{-29}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \end{array} \]

Alternative 9: 66.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0037 \lor \neg \left(z \leq 5.7 \cdot 10^{-30}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -0.0037) (not (<= z 5.7e-30)))
   (* t (/ (- y z) (- a z)))
   (+ x (/ y (/ a (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -0.0037) || !(z <= 5.7e-30)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-0.0037d0)) .or. (.not. (z <= 5.7d-30))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + (y / (a / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -0.0037) || !(z <= 5.7e-30)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -0.0037) or not (z <= 5.7e-30):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -0.0037) || !(z <= 5.7e-30))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -0.0037) || ~((z <= 5.7e-30)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -0.0037], N[Not[LessEqual[z, 5.7e-30]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.0037000000000000002 or 5.69999999999999977e-30 < z

   1. Initial program 68.9%

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

   2. Taylor expanded in t around inf 64.5%

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

      1. div-sub 64.5%

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

   4. Simplified 64.5%

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

   if -0.0037000000000000002 < z < 5.69999999999999977e-30

   1. Initial program 95.7%

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

   2. Taylor expanded in z around 0 75.8%

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

      1. +-commutative 75.8%

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

      2. associate-/l* 82.2%

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

   4. Simplified 82.2%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0037 \lor \neg \left(z \leq 5.7 \cdot 10^{-30}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 10: 67.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{-6} \lor \neg \left(z \leq 650\right):\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.1e-6) (not (<= z 650.0)))
   (/ t (/ (- a z) (- y z)))
   (+ x (/ y (/ a (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.1e-6) || !(z <= 650.0)) {
		tmp = t / ((a - z) / (y - z));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-5.1d-6)) .or. (.not. (z <= 650.0d0))) then
        tmp = t / ((a - z) / (y - z))
    else
        tmp = x + (y / (a / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.1e-6) || !(z <= 650.0)) {
		tmp = t / ((a - z) / (y - z));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.1e-6) or not (z <= 650.0):
		tmp = t / ((a - z) / (y - z))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.1e-6) || !(z <= 650.0))
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.1e-6) || ~((z <= 650.0)))
		tmp = t / ((a - z) / (y - z));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.1e-6], N[Not[LessEqual[z, 650.0]], $MachinePrecision]], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.1000000000000003e-6 or 650 < z

   1. Initial program 67.4%

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

   2. Taylor expanded in x around 0 45.0%

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

      1. associate-/l* 64.4%

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

   4. Simplified 64.4%

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

   if -5.1000000000000003e-6 < z < 650

   1. Initial program 95.9%

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

   2. Taylor expanded in z around 0 75.4%

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

      1. +-commutative 75.4%

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

      2. associate-/l* 81.5%

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

   4. Simplified 81.5%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{-6} \lor \neg \left(z \leq 650\right):\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 11: 39.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -70000000000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-259}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-204}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+147}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -70000000000.0)
   t
   (if (<= z 4.5e-259)
     x
     (if (<= z 5.4e-204) (* y (/ t a)) (if (<= z 1.3e+147) x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -70000000000.0) {
		tmp = t;
	} else if (z <= 4.5e-259) {
		tmp = x;
	} else if (z <= 5.4e-204) {
		tmp = y * (t / a);
	} else if (z <= 1.3e+147) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-70000000000.0d0)) then
        tmp = t
    else if (z <= 4.5d-259) then
        tmp = x
    else if (z <= 5.4d-204) then
        tmp = y * (t / a)
    else if (z <= 1.3d+147) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -70000000000.0) {
		tmp = t;
	} else if (z <= 4.5e-259) {
		tmp = x;
	} else if (z <= 5.4e-204) {
		tmp = y * (t / a);
	} else if (z <= 1.3e+147) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -70000000000.0:
		tmp = t
	elif z <= 4.5e-259:
		tmp = x
	elif z <= 5.4e-204:
		tmp = y * (t / a)
	elif z <= 1.3e+147:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -70000000000.0)
		tmp = t;
	elseif (z <= 4.5e-259)
		tmp = x;
	elseif (z <= 5.4e-204)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 1.3e+147)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -70000000000.0)
		tmp = t;
	elseif (z <= 4.5e-259)
		tmp = x;
	elseif (z <= 5.4e-204)
		tmp = y * (t / a);
	elseif (z <= 1.3e+147)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -70000000000.0], t, If[LessEqual[z, 4.5e-259], x, If[LessEqual[z, 5.4e-204], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+147], x, t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7e10 or 1.2999999999999999e147 < z

   1. Initial program 61.2%

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

   2. Taylor expanded in z around inf 49.3%

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

   if -7e10 < z < 4.49999999999999974e-259 or 5.39999999999999983e-204 < z < 1.2999999999999999e147

   1. Initial program 94.1%

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

   2. Taylor expanded in a around inf 43.2%

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

   if 4.49999999999999974e-259 < z < 5.39999999999999983e-204

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 60.5%

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

      1. associate-/l* 60.2%

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

   4. Simplified 60.2%

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

   5. Taylor expanded in z around 0 54.9%

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

      1. associate-/r/ 55.0%

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

   7. Applied egg-rr 55.0%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -70000000000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-259}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-204}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+147}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12: 39.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+15}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-259}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-204}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+148}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.8e+15)
   t
   (if (<= z 2.8e-259)
     x
     (if (<= z 5.5e-204) (/ y (/ a t)) (if (<= z 1.2e+148) x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.8e+15) {
		tmp = t;
	} else if (z <= 2.8e-259) {
		tmp = x;
	} else if (z <= 5.5e-204) {
		tmp = y / (a / t);
	} else if (z <= 1.2e+148) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6.8d+15)) then
        tmp = t
    else if (z <= 2.8d-259) then
        tmp = x
    else if (z <= 5.5d-204) then
        tmp = y / (a / t)
    else if (z <= 1.2d+148) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.8e+15) {
		tmp = t;
	} else if (z <= 2.8e-259) {
		tmp = x;
	} else if (z <= 5.5e-204) {
		tmp = y / (a / t);
	} else if (z <= 1.2e+148) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.8e+15:
		tmp = t
	elif z <= 2.8e-259:
		tmp = x
	elif z <= 5.5e-204:
		tmp = y / (a / t)
	elif z <= 1.2e+148:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.8e+15)
		tmp = t;
	elseif (z <= 2.8e-259)
		tmp = x;
	elseif (z <= 5.5e-204)
		tmp = Float64(y / Float64(a / t));
	elseif (z <= 1.2e+148)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.8e+15)
		tmp = t;
	elseif (z <= 2.8e-259)
		tmp = x;
	elseif (z <= 5.5e-204)
		tmp = y / (a / t);
	elseif (z <= 1.2e+148)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.8e+15], t, If[LessEqual[z, 2.8e-259], x, If[LessEqual[z, 5.5e-204], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e+148], x, t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.8e15 or 1.19999999999999997e148 < z

   1. Initial program 61.2%

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

   2. Taylor expanded in z around inf 49.3%

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

   if -6.8e15 < z < 2.8e-259 or 5.4999999999999999e-204 < z < 1.19999999999999997e148

   1. Initial program 94.1%

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

   2. Taylor expanded in a around inf 43.2%

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

   if 2.8e-259 < z < 5.4999999999999999e-204

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 60.5%

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

      1. associate-/l* 60.2%

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

   4. Simplified 60.2%

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

   5. Taylor expanded in z around 0 55.0%

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

      1. associate-/l* 55.1%

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

   7. Simplified 55.1%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+15}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-259}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-204}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+148}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 13: 56.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+17} \lor \neg \left(z \leq 190000000\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2e+17) (not (<= z 190000000.0)))
   (* t (- 1.0 (/ y z)))
   (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2e+17) || !(z <= 190000000.0)) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2d+17)) .or. (.not. (z <= 190000000.0d0))) then
        tmp = t * (1.0d0 - (y / z))
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2e+17) || !(z <= 190000000.0)) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2e+17) or not (z <= 190000000.0):
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2e+17) || !(z <= 190000000.0))
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2e+17) || ~((z <= 190000000.0)))
		tmp = t * (1.0 - (y / z));
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2e+17], N[Not[LessEqual[z, 190000000.0]], $MachinePrecision]], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2e17 or 1.9e8 < z

   1. Initial program 67.7%

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

   2. Taylor expanded in x around 0 45.6%

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

      1. associate-/l* 64.6%

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

   4. Simplified 64.6%

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

   5. Taylor expanded in a around 0 57.1%

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

      1. associate-*r/ 57.1%

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

      2. mul-1-neg 57.1%

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

   7. Simplified 57.1%

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

   8. Taylor expanded in z around 0 52.1%

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

      1. +-commutative 52.1%

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

      2. mul-1-neg 52.1%

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

      3. unsub-neg 52.1%

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

      4. associate-*r/ 56.3%

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

   10. Simplified 56.3%

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

   11. Taylor expanded in t around 0 57.1%

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

   if -2e17 < z < 1.9e8

   1. Initial program 95.2%

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

   2. Taylor expanded in t around inf 77.9%

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

   3. Taylor expanded in z around 0 64.4%

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

      1. +-commutative 64.4%

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

      2. associate-/l* 69.6%

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

   5. Simplified 69.6%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+17} \lor \neg \left(z \leq 190000000\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 14: 56.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -41000000:\\ \;\;\;\;t - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 205000000:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -41000000.0)
   (- t (* y (/ t z)))
   (if (<= z 205000000.0) (+ x (/ y (/ a t))) (* t (- 1.0 (/ y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -41000000.0) {
		tmp = t - (y * (t / z));
	} else if (z <= 205000000.0) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-41000000.0d0)) then
        tmp = t - (y * (t / z))
    else if (z <= 205000000.0d0) then
        tmp = x + (y / (a / t))
    else
        tmp = t * (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -41000000.0) {
		tmp = t - (y * (t / z));
	} else if (z <= 205000000.0) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -41000000.0:
		tmp = t - (y * (t / z))
	elif z <= 205000000.0:
		tmp = x + (y / (a / t))
	else:
		tmp = t * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -41000000.0)
		tmp = Float64(t - Float64(y * Float64(t / z)));
	elseif (z <= 205000000.0)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -41000000.0)
		tmp = t - (y * (t / z));
	elseif (z <= 205000000.0)
		tmp = x + (y / (a / t));
	else
		tmp = t * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -41000000.0], N[(t - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 205000000.0], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.1e7

   1. Initial program 60.3%

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

   2. Taylor expanded in x around 0 51.1%

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

      1. associate-/l* 68.3%

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

   4. Simplified 68.3%

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

   5. Taylor expanded in a around 0 59.4%

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

      1. associate-*r/ 59.4%

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

      2. mul-1-neg 59.4%

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

   7. Simplified 59.4%

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

   8. Taylor expanded in z around 0 56.4%

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

      1. +-commutative 56.4%

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

      2. mul-1-neg 56.4%

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

      3. unsub-neg 56.4%

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

      4. associate-*r/ 59.5%

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

   10. Simplified 59.5%

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

   if -4.1e7 < z < 2.05e8

   1. Initial program 95.2%

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

   2. Taylor expanded in t around inf 77.9%

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

   3. Taylor expanded in z around 0 64.4%

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

      1. +-commutative 64.4%

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

      2. associate-/l* 69.6%

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

   5. Simplified 69.6%

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

   if 2.05e8 < z

   1. Initial program 75.5%

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

   2. Taylor expanded in x around 0 39.8%

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

      1. associate-/l* 60.7%

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

   4. Simplified 60.7%

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

   5. Taylor expanded in a around 0 54.6%

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

      1. associate-*r/ 54.6%

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

      2. mul-1-neg 54.6%

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

   7. Simplified 54.6%

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

   8. Taylor expanded in z around 0 47.5%

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

      1. +-commutative 47.5%

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

      2. mul-1-neg 47.5%

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

      3. unsub-neg 47.5%

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

      4. associate-*r/ 53.0%

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

   10. Simplified 53.0%

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

   11. Taylor expanded in t around 0 54.6%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -41000000:\\ \;\;\;\;t - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 205000000:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 15: 56.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+20}:\\ \;\;\;\;t - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 48000:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{z - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3e+20)
   (- t (* y (/ t z)))
   (if (<= z 48000.0) (+ x (/ y (/ a t))) (/ t (/ z (- z y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3e+20) {
		tmp = t - (y * (t / z));
	} else if (z <= 48000.0) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t / (z / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3d+20)) then
        tmp = t - (y * (t / z))
    else if (z <= 48000.0d0) then
        tmp = x + (y / (a / t))
    else
        tmp = t / (z / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3e+20) {
		tmp = t - (y * (t / z));
	} else if (z <= 48000.0) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t / (z / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3e+20:
		tmp = t - (y * (t / z))
	elif z <= 48000.0:
		tmp = x + (y / (a / t))
	else:
		tmp = t / (z / (z - y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3e+20)
		tmp = Float64(t - Float64(y * Float64(t / z)));
	elseif (z <= 48000.0)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(t / Float64(z / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3e+20)
		tmp = t - (y * (t / z));
	elseif (z <= 48000.0)
		tmp = x + (y / (a / t));
	else
		tmp = t / (z / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3e+20], N[(t - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 48000.0], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3e20

   1. Initial program 60.3%

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

   2. Taylor expanded in x around 0 51.1%

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

      1. associate-/l* 68.3%

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

   4. Simplified 68.3%

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

   5. Taylor expanded in a around 0 59.4%

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

      1. associate-*r/ 59.4%

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

      2. mul-1-neg 59.4%

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

   7. Simplified 59.4%

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

   8. Taylor expanded in z around 0 56.4%

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

      1. +-commutative 56.4%

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

      2. mul-1-neg 56.4%

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

      3. unsub-neg 56.4%

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

      4. associate-*r/ 59.5%

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

   10. Simplified 59.5%

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

   if -3e20 < z < 48000

   1. Initial program 95.2%

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

   2. Taylor expanded in t around inf 77.9%

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

   3. Taylor expanded in z around 0 64.4%

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

      1. +-commutative 64.4%

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

      2. associate-/l* 69.6%

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

   5. Simplified 69.6%

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

   if 48000 < z

   1. Initial program 75.5%

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

   2. Taylor expanded in x around 0 39.8%

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

      1. associate-/l* 60.7%

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

   4. Simplified 60.7%

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

   5. Taylor expanded in a around 0 54.6%

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

      1. associate-*r/ 54.6%

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

      2. mul-1-neg 54.6%

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

   7. Simplified 54.6%

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

      1. frac-2neg 54.6%

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

      2. div-inv 54.5%

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

      3. remove-double-neg 54.5%

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

      4. sub-neg 54.5%

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

      5. distribute-neg-in 54.5%

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

      6. remove-double-neg 54.5%

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

   9. Applied egg-rr 54.5%

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

       1. associate-*r/ 54.6%

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

       2. *-rgt-identity 54.6%

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

       3. +-commutative 54.6%

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

       4. unsub-neg 54.6%

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

   11. Simplified 54.6%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+20}:\\ \;\;\;\;t - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 48000:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{z - y}}\\ \end{array} \]

Alternative 16: 39.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+23}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+149}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.2e+23) t (if (<= z 1.65e+149) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.2e+23) {
		tmp = t;
	} else if (z <= 1.65e+149) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-7.2d+23)) then
        tmp = t
    else if (z <= 1.65d+149) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.2e+23) {
		tmp = t;
	} else if (z <= 1.65e+149) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.2e+23:
		tmp = t
	elif z <= 1.65e+149:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.2e+23)
		tmp = t;
	elseif (z <= 1.65e+149)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.2e+23)
		tmp = t;
	elseif (z <= 1.65e+149)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.2e+23], t, If[LessEqual[z, 1.65e+149], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -7.1999999999999997e23 or 1.65e149 < z

   1. Initial program 61.2%

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

   2. Taylor expanded in z around inf 49.3%

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

   if -7.1999999999999997e23 < z < 1.65e149

   1. Initial program 94.7%

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

   2. Taylor expanded in a around inf 41.3%

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

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+23}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+149}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 17: 26.3% 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 81.2%

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

2. Taylor expanded in z around inf 24.5%

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

3. Final simplification 24.5%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023195 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))