Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.9% → 89.4%

Time: 24.5s

Alternatives: 23

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.9% 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: 89.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := x + \left(y - z\right) \cdot t_1\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-281}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 10^{-159}:\\ \;\;\;\;t + \frac{1}{z} \cdot \frac{x - t}{\frac{1}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, t_1, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t x) (- a z))) (t_2 (+ x (* (- y z) t_1))))
   (if (<= t_2 -2e-281)
     t_2
     (if (<= t_2 1e-159)
       (+ t (* (/ 1.0 z) (/ (- x t) (/ 1.0 (- y a)))))
       (fma (- y z) t_1 x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) / (a - z);
	double t_2 = x + ((y - z) * t_1);
	double tmp;
	if (t_2 <= -2e-281) {
		tmp = t_2;
	} else if (t_2 <= 1e-159) {
		tmp = t + ((1.0 / z) * ((x - t) / (1.0 / (y - a))));
	} else {
		tmp = fma((y - z), t_1, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) / Float64(a - z))
	t_2 = Float64(x + Float64(Float64(y - z) * t_1))
	tmp = 0.0
	if (t_2 <= -2e-281)
		tmp = t_2;
	elseif (t_2 <= 1e-159)
		tmp = Float64(t + Float64(Float64(1.0 / z) * Float64(Float64(x - t) / Float64(1.0 / Float64(y - a)))));
	else
		tmp = fma(Float64(y - z), t_1, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-281], t$95$2, If[LessEqual[t$95$2, 1e-159], N[(t + N[(N[(1.0 / z), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(1.0 / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * t$95$1 + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2e-281

   1. Initial program 92.0%

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

   if -2e-281 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 9.99999999999999989e-160

   1. Initial program 3.4%

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

   2. Taylor expanded in z around inf 93.5%

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

      1. associate--l+ 93.5%

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

      2. distribute-lft-out-- 93.5%

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

      3. div-sub 93.5%

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

      4. mul-1-neg 93.5%

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

      5. unsub-neg 93.5%

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

      6. distribute-rgt-out-- 93.5%

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

      7. associate-/l* 87.6%

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

   4. Simplified 87.6%

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

      1. *-un-lft-identity 87.6%

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

      2. div-inv 87.6%

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

      3. times-frac 93.6%

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

   6. Applied egg-rr 93.6%

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

   if 9.99999999999999989e-160 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 95.9%

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

      1. +-commutative 95.9%

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

      2. fma-def 96.0%

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

   3. Simplified 96.0%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-281}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 10^{-159}:\\ \;\;\;\;t + \frac{1}{z} \cdot \frac{x - t}{\frac{1}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \end{array} \]

Alternative 2: 89.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-281} \lor \neg \left(t_1 \leq 10^{-159}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{1}{z} \cdot \frac{x - t}{\frac{1}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-281) (not (<= t_1 1e-159)))
     t_1
     (+ t (* (/ 1.0 z) (/ (- x t) (/ 1.0 (- y a))))))))

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-281) || !(t_1 <= 1e-159)) {
		tmp = t_1;
	} else {
		tmp = t + ((1.0 / z) * ((x - t) / (1.0 / (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) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-2d-281)) .or. (.not. (t_1 <= 1d-159))) then
        tmp = t_1
    else
        tmp = t + ((1.0d0 / z) * ((x - t) / (1.0d0 / (y - a))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-281) || !(t_1 <= 1e-159)) {
		tmp = t_1;
	} else {
		tmp = t + ((1.0 / z) * ((x - t) / (1.0 / (y - a))));
	}
	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-281) or not (t_1 <= 1e-159):
		tmp = t_1
	else:
		tmp = t + ((1.0 / z) * ((x - t) / (1.0 / (y - a))))
	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-281) || !(t_1 <= 1e-159))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(1.0 / z) * Float64(Float64(x - t) / Float64(1.0 / Float64(y - a)))));
	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-281) || ~((t_1 <= 1e-159)))
		tmp = t_1;
	else
		tmp = t + ((1.0 / z) * ((x - t) / (1.0 / (y - a))));
	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-281], N[Not[LessEqual[t$95$1, 1e-159]], $MachinePrecision]], t$95$1, N[(t + N[(N[(1.0 / z), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(1.0 / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2e-281 or 9.99999999999999989e-160 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 94.2%

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

   if -2e-281 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 9.99999999999999989e-160

   1. Initial program 3.4%

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

   2. Taylor expanded in z around inf 93.5%

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

      1. associate--l+ 93.5%

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

      2. distribute-lft-out-- 93.5%

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

      3. div-sub 93.5%

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

      4. mul-1-neg 93.5%

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

      5. unsub-neg 93.5%

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

      6. distribute-rgt-out-- 93.5%

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

      7. associate-/l* 87.6%

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

   4. Simplified 87.6%

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

      1. *-un-lft-identity 87.6%

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

      2. div-inv 87.6%

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

      3. times-frac 93.6%

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

   6. Applied egg-rr 93.6%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-281} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 10^{-159}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{1}{z} \cdot \frac{x - t}{\frac{1}{y - a}}\\ \end{array} \]

Alternative 3: 90.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-281} \lor \neg \left(t_1 \leq 10^{-159}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-281) (not (<= t_1 1e-159)))
     t_1
     (+ t (/ (- x t) (/ z (- y a)))))))

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-281) || !(t_1 <= 1e-159)) {
		tmp = t_1;
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-2d-281)) .or. (.not. (t_1 <= 1d-159))) then
        tmp = t_1
    else
        tmp = t + ((x - t) / (z / (y - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-281) || !(t_1 <= 1e-159)) {
		tmp = t_1;
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	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-281) or not (t_1 <= 1e-159):
		tmp = t_1
	else:
		tmp = t + ((x - t) / (z / (y - a)))
	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-281) || !(t_1 <= 1e-159))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	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-281) || ~((t_1 <= 1e-159)))
		tmp = t_1;
	else
		tmp = t + ((x - t) / (z / (y - a)));
	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-281], N[Not[LessEqual[t$95$1, 1e-159]], $MachinePrecision]], t$95$1, N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2e-281 or 9.99999999999999989e-160 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 94.2%

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

   if -2e-281 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 9.99999999999999989e-160

   1. Initial program 3.4%

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

   2. Taylor expanded in z around inf 93.5%

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

      1. associate--l+ 93.5%

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

      2. distribute-lft-out-- 93.5%

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

      3. div-sub 93.5%

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

      4. mul-1-neg 93.5%

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

      5. unsub-neg 93.5%

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

      6. distribute-rgt-out-- 93.5%

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

      7. associate-/l* 87.6%

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

   4. Simplified 87.6%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-281} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 10^{-159}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 4: 89.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-281} \lor \neg \left(t_1 \leq 10^{-159}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{-1}{\frac{z}{\left(t - x\right) \cdot \left(y - a\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-281) (not (<= t_1 1e-159)))
     t_1
     (+ t (/ -1.0 (/ z (* (- t x) (- y a))))))))

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-281) || !(t_1 <= 1e-159)) {
		tmp = t_1;
	} else {
		tmp = t + (-1.0 / (z / ((t - x) * (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) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-2d-281)) .or. (.not. (t_1 <= 1d-159))) then
        tmp = t_1
    else
        tmp = t + ((-1.0d0) / (z / ((t - x) * (y - a))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-281) || !(t_1 <= 1e-159)) {
		tmp = t_1;
	} else {
		tmp = t + (-1.0 / (z / ((t - x) * (y - a))));
	}
	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-281) or not (t_1 <= 1e-159):
		tmp = t_1
	else:
		tmp = t + (-1.0 / (z / ((t - x) * (y - a))))
	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-281) || !(t_1 <= 1e-159))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(-1.0 / Float64(z / Float64(Float64(t - x) * Float64(y - a)))));
	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-281) || ~((t_1 <= 1e-159)))
		tmp = t_1;
	else
		tmp = t + (-1.0 / (z / ((t - x) * (y - a))));
	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-281], N[Not[LessEqual[t$95$1, 1e-159]], $MachinePrecision]], t$95$1, N[(t + N[(-1.0 / N[(z / N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2e-281 or 9.99999999999999989e-160 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 94.2%

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

   if -2e-281 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 9.99999999999999989e-160

   1. Initial program 3.4%

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

   2. Taylor expanded in z around inf 93.5%

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

      1. associate--l+ 93.5%

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

      2. distribute-lft-out-- 93.5%

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

      3. div-sub 93.5%

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

      4. mul-1-neg 93.5%

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

      5. unsub-neg 93.5%

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

      6. distribute-rgt-out-- 93.5%

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

      7. associate-/l* 87.6%

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

   4. Simplified 87.6%

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

      1. clear-num 87.5%

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

      2. inv-pow 87.5%

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

   6. Applied egg-rr 87.5%

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

      1. unpow-1 87.5%

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

      2. associate-/l/ 93.4%

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

   8. Simplified 93.4%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-281} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 10^{-159}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{-1}{\frac{z}{\left(t - x\right) \cdot \left(y - a\right)}}\\ \end{array} \]

Alternative 5: 37.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a}\\ \mathbf{if}\;z \leq -9 \cdot 10^{+123}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-233}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-262}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+146}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) a))))
   (if (<= z -9e+123)
     t
     (if (<= z -9.5e+53)
       (* x (/ (- y a) z))
       (if (<= z -4.8e-147)
         t_1
         (if (<= z -1.7e-233)
           x
           (if (<= z -9e-262)
             (* t (/ y a))
             (if (<= z 2.35e-35) x (if (<= z 1.3e+146) t_1 t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / a);
	double tmp;
	if (z <= -9e+123) {
		tmp = t;
	} else if (z <= -9.5e+53) {
		tmp = x * ((y - a) / z);
	} else if (z <= -4.8e-147) {
		tmp = t_1;
	} else if (z <= -1.7e-233) {
		tmp = x;
	} else if (z <= -9e-262) {
		tmp = t * (y / a);
	} else if (z <= 2.35e-35) {
		tmp = x;
	} else if (z <= 1.3e+146) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / a)
    if (z <= (-9d+123)) then
        tmp = t
    else if (z <= (-9.5d+53)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-4.8d-147)) then
        tmp = t_1
    else if (z <= (-1.7d-233)) then
        tmp = x
    else if (z <= (-9d-262)) then
        tmp = t * (y / a)
    else if (z <= 2.35d-35) then
        tmp = x
    else if (z <= 1.3d+146) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / a);
	double tmp;
	if (z <= -9e+123) {
		tmp = t;
	} else if (z <= -9.5e+53) {
		tmp = x * ((y - a) / z);
	} else if (z <= -4.8e-147) {
		tmp = t_1;
	} else if (z <= -1.7e-233) {
		tmp = x;
	} else if (z <= -9e-262) {
		tmp = t * (y / a);
	} else if (z <= 2.35e-35) {
		tmp = x;
	} else if (z <= 1.3e+146) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / a)
	tmp = 0
	if z <= -9e+123:
		tmp = t
	elif z <= -9.5e+53:
		tmp = x * ((y - a) / z)
	elif z <= -4.8e-147:
		tmp = t_1
	elif z <= -1.7e-233:
		tmp = x
	elif z <= -9e-262:
		tmp = t * (y / a)
	elif z <= 2.35e-35:
		tmp = x
	elif z <= 1.3e+146:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / a))
	tmp = 0.0
	if (z <= -9e+123)
		tmp = t;
	elseif (z <= -9.5e+53)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -4.8e-147)
		tmp = t_1;
	elseif (z <= -1.7e-233)
		tmp = x;
	elseif (z <= -9e-262)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 2.35e-35)
		tmp = x;
	elseif (z <= 1.3e+146)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / a);
	tmp = 0.0;
	if (z <= -9e+123)
		tmp = t;
	elseif (z <= -9.5e+53)
		tmp = x * ((y - a) / z);
	elseif (z <= -4.8e-147)
		tmp = t_1;
	elseif (z <= -1.7e-233)
		tmp = x;
	elseif (z <= -9e-262)
		tmp = t * (y / a);
	elseif (z <= 2.35e-35)
		tmp = x;
	elseif (z <= 1.3e+146)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e+123], t, If[LessEqual[z, -9.5e+53], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.8e-147], t$95$1, If[LessEqual[z, -1.7e-233], x, If[LessEqual[z, -9e-262], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.35e-35], x, If[LessEqual[z, 1.3e+146], t$95$1, t]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -8.99999999999999965e123 or 1.30000000000000007e146 < z

   1. Initial program 62.2%

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

   2. Taylor expanded in z around inf 60.0%

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

   if -8.99999999999999965e123 < z < -9.5000000000000006e53

   1. Initial program 66.9%

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

   2. Taylor expanded in z around inf 62.3%

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

      1. associate--l+ 62.3%

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

      2. distribute-lft-out-- 62.3%

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

      3. div-sub 62.3%

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

      4. mul-1-neg 62.3%

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

      5. unsub-neg 62.3%

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

      6. distribute-rgt-out-- 62.3%

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

      7. associate-/l* 68.4%

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

   4. Simplified 68.4%

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

   5. Taylor expanded in t around 0 41.6%

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

      1. expm1-log1p-u 19.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x \cdot \left(y - a\right)}{z}\right)\right)} \]

      2. expm1-udef 13.0%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x \cdot \left(y - a\right)}{z}\right)} - 1} \]

      3. associate-/l* 13.0%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{x}{\frac{z}{y - a}}}\right)} - 1 \]

   7. Applied egg-rr 13.0%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{\frac{z}{y - a}}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 19.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{\frac{z}{y - a}}\right)\right)} \]

      2. expm1-log1p 47.7%

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

      3. associate-/r/ 47.7%

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

      4. *-commutative 47.7%

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

      5. associate-*r/ 41.6%

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

      6. *-commutative 41.6%

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

      7. associate-*r/ 48.0%

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

   9. Simplified 48.0%

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

   if -9.5000000000000006e53 < z < -4.79999999999999997e-147 or 2.35e-35 < z < 1.30000000000000007e146

   1. Initial program 88.1%

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

      1. +-commutative 88.1%

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

      2. fma-def 88.3%

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

   3. Simplified 88.3%

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

   4. Taylor expanded in a around inf 62.2%

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

   5. Taylor expanded in t around inf 33.4%

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

      1. div-sub 33.4%

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

   7. Simplified 33.4%

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

   if -4.79999999999999997e-147 < z < -1.7000000000000001e-233 or -8.99999999999999997e-262 < z < 2.35e-35

   1. Initial program 96.4%

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

   2. Taylor expanded in a around inf 49.8%

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

   if -1.7000000000000001e-233 < z < -8.99999999999999997e-262

   1. Initial program 89.5%

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

   2. Taylor expanded in x around 0 68.0%

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

      1. associate-/l* 77.6%

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

   4. Simplified 77.6%

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

   5. Taylor expanded in z around 0 77.6%

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

   6. Taylor expanded in t around 0 68.0%

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

      1. associate-*r/ 77.8%

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

   8. Simplified 77.8%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+123}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-147}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-233}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-262}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+146}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 6: 37.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a}\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+115}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-233}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-262}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+146}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) a))))
   (if (<= z -3.6e+115)
     t
     (if (<= z -3.8e-144)
       t_1
       (if (<= z -2e-233)
         x
         (if (<= z -4.2e-262)
           (* t (/ y a))
           (if (<= z 7.6e-36) x (if (<= z 1.6e+146) t_1 t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / a);
	double tmp;
	if (z <= -3.6e+115) {
		tmp = t;
	} else if (z <= -3.8e-144) {
		tmp = t_1;
	} else if (z <= -2e-233) {
		tmp = x;
	} else if (z <= -4.2e-262) {
		tmp = t * (y / a);
	} else if (z <= 7.6e-36) {
		tmp = x;
	} else if (z <= 1.6e+146) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / a)
    if (z <= (-3.6d+115)) then
        tmp = t
    else if (z <= (-3.8d-144)) then
        tmp = t_1
    else if (z <= (-2d-233)) then
        tmp = x
    else if (z <= (-4.2d-262)) then
        tmp = t * (y / a)
    else if (z <= 7.6d-36) then
        tmp = x
    else if (z <= 1.6d+146) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / a);
	double tmp;
	if (z <= -3.6e+115) {
		tmp = t;
	} else if (z <= -3.8e-144) {
		tmp = t_1;
	} else if (z <= -2e-233) {
		tmp = x;
	} else if (z <= -4.2e-262) {
		tmp = t * (y / a);
	} else if (z <= 7.6e-36) {
		tmp = x;
	} else if (z <= 1.6e+146) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / a)
	tmp = 0
	if z <= -3.6e+115:
		tmp = t
	elif z <= -3.8e-144:
		tmp = t_1
	elif z <= -2e-233:
		tmp = x
	elif z <= -4.2e-262:
		tmp = t * (y / a)
	elif z <= 7.6e-36:
		tmp = x
	elif z <= 1.6e+146:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / a))
	tmp = 0.0
	if (z <= -3.6e+115)
		tmp = t;
	elseif (z <= -3.8e-144)
		tmp = t_1;
	elseif (z <= -2e-233)
		tmp = x;
	elseif (z <= -4.2e-262)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 7.6e-36)
		tmp = x;
	elseif (z <= 1.6e+146)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / a);
	tmp = 0.0;
	if (z <= -3.6e+115)
		tmp = t;
	elseif (z <= -3.8e-144)
		tmp = t_1;
	elseif (z <= -2e-233)
		tmp = x;
	elseif (z <= -4.2e-262)
		tmp = t * (y / a);
	elseif (z <= 7.6e-36)
		tmp = x;
	elseif (z <= 1.6e+146)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.6e+115], t, If[LessEqual[z, -3.8e-144], t$95$1, If[LessEqual[z, -2e-233], x, If[LessEqual[z, -4.2e-262], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.6e-36], x, If[LessEqual[z, 1.6e+146], t$95$1, t]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.6000000000000001e115 or 1.6e146 < z

   1. Initial program 61.3%

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

   2. Taylor expanded in z around inf 59.2%

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

   if -3.6000000000000001e115 < z < -3.79999999999999993e-144 or 7.59999999999999942e-36 < z < 1.6e146

   1. Initial program 85.7%

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

      1. +-commutative 85.7%

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

      2. fma-def 86.1%

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

   3. Simplified 86.1%

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

   4. Taylor expanded in a around inf 57.6%

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

   5. Taylor expanded in t around inf 31.1%

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

      1. div-sub 31.1%

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

   7. Simplified 31.1%

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

   if -3.79999999999999993e-144 < z < -1.99999999999999992e-233 or -4.1999999999999999e-262 < z < 7.59999999999999942e-36

   1. Initial program 96.4%

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

   2. Taylor expanded in a around inf 49.8%

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

   if -1.99999999999999992e-233 < z < -4.1999999999999999e-262

   1. Initial program 89.5%

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

   2. Taylor expanded in x around 0 68.0%

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

      1. associate-/l* 77.6%

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

   4. Simplified 77.6%

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

   5. Taylor expanded in z around 0 77.6%

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

   6. Taylor expanded in t around 0 68.0%

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

      1. associate-*r/ 77.8%

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

   8. Simplified 77.8%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+115}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-144}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-233}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-262}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+146}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7: 65.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{a - z}{y - z}}\\ \mathbf{if}\;z \leq -1 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-151}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-39}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+174}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{-z}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (/ (- a z) (- y z)))))
   (if (<= z -1e+24)
     t_1
     (if (<= z -7e-151)
       (* (- t x) (/ y (- a z)))
       (if (<= z 5.5e-39)
         (+ x (* (- t x) (/ y a)))
         (if (<= z 1.25e+174) t_1 (- t (/ (- t x) (/ (- z) a)))))))))

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 <= -1e+24) {
		tmp = t_1;
	} else if (z <= -7e-151) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= 5.5e-39) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 1.25e+174) {
		tmp = t_1;
	} else {
		tmp = t - ((t - x) / (-z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / ((a - z) / (y - z))
    if (z <= (-1d+24)) then
        tmp = t_1
    else if (z <= (-7d-151)) then
        tmp = (t - x) * (y / (a - z))
    else if (z <= 5.5d-39) then
        tmp = x + ((t - x) * (y / a))
    else if (z <= 1.25d+174) then
        tmp = t_1
    else
        tmp = t - ((t - x) / (-z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t / ((a - z) / (y - z));
	double tmp;
	if (z <= -1e+24) {
		tmp = t_1;
	} else if (z <= -7e-151) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= 5.5e-39) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 1.25e+174) {
		tmp = t_1;
	} else {
		tmp = t - ((t - x) / (-z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / ((a - z) / (y - z))
	tmp = 0
	if z <= -1e+24:
		tmp = t_1
	elif z <= -7e-151:
		tmp = (t - x) * (y / (a - z))
	elif z <= 5.5e-39:
		tmp = x + ((t - x) * (y / a))
	elif z <= 1.25e+174:
		tmp = t_1
	else:
		tmp = t - ((t - x) / (-z / a))
	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 <= -1e+24)
		tmp = t_1;
	elseif (z <= -7e-151)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (z <= 5.5e-39)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (z <= 1.25e+174)
		tmp = t_1;
	else
		tmp = Float64(t - Float64(Float64(t - x) / Float64(Float64(-z) / a)));
	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 <= -1e+24)
		tmp = t_1;
	elseif (z <= -7e-151)
		tmp = (t - x) * (y / (a - z));
	elseif (z <= 5.5e-39)
		tmp = x + ((t - x) * (y / a));
	elseif (z <= 1.25e+174)
		tmp = t_1;
	else
		tmp = t - ((t - x) / (-z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1e+24], t$95$1, If[LessEqual[z, -7e-151], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e-39], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+174], t$95$1, N[(t - N[(N[(t - x), $MachinePrecision] / N[((-z) / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.9999999999999998e23 or 5.50000000000000018e-39 < z < 1.2499999999999999e174

   1. Initial program 72.9%

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

   2. Taylor expanded in x around 0 44.6%

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

      1. associate-/l* 60.2%

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

   4. Simplified 60.2%

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

   if -9.9999999999999998e23 < z < -6.99999999999999991e-151

   1. Initial program 97.1%

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

   2. Taylor expanded in y around inf 70.5%

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

      1. div-sub 73.2%

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

      2. associate-*r/ 63.2%

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

      3. associate-/l* 73.1%

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

      4. associate-/r/ 70.6%

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

   4. Simplified 70.6%

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

   if -6.99999999999999991e-151 < z < 5.50000000000000018e-39

   1. Initial program 96.7%

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

   2. Taylor expanded in z around 0 89.1%

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

      1. associate-/l* 92.6%

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

      2. associate-/r/ 93.8%

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

   4. Simplified 93.8%

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

   if 1.2499999999999999e174 < z

   1. Initial program 54.3%

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

   2. Taylor expanded in z around inf 65.5%

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

      1. associate--l+ 65.5%

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

      2. distribute-lft-out-- 65.5%

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

      3. div-sub 65.5%

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

      4. mul-1-neg 65.5%

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

      5. unsub-neg 65.5%

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

      6. distribute-rgt-out-- 65.6%

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

      7. associate-/l* 85.6%

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

   4. Simplified 85.6%

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

   5. Taylor expanded in y around 0 82.2%

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

      1. associate-*r/ 82.2%

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

      2. neg-mul-1 82.2%

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

   7. Simplified 82.2%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+24}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-151}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-39}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+174}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{-z}{a}}\\ \end{array} \]

Alternative 8: 39.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+119}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-195}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+146}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.1e+119)
   t
   (if (<= z -2.7e+45)
     (* x (/ (- y a) z))
     (if (<= z 8.5e-195)
       (* y (/ (- t x) a))
       (if (<= z 4.8e-36) x (if (<= z 1.25e+146) (* t (/ (- y z) a)) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.1e+119) {
		tmp = t;
	} else if (z <= -2.7e+45) {
		tmp = x * ((y - a) / z);
	} else if (z <= 8.5e-195) {
		tmp = y * ((t - x) / a);
	} else if (z <= 4.8e-36) {
		tmp = x;
	} else if (z <= 1.25e+146) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.1d+119)) then
        tmp = t
    else if (z <= (-2.7d+45)) then
        tmp = x * ((y - a) / z)
    else if (z <= 8.5d-195) then
        tmp = y * ((t - x) / a)
    else if (z <= 4.8d-36) then
        tmp = x
    else if (z <= 1.25d+146) then
        tmp = t * ((y - z) / a)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.1e+119) {
		tmp = t;
	} else if (z <= -2.7e+45) {
		tmp = x * ((y - a) / z);
	} else if (z <= 8.5e-195) {
		tmp = y * ((t - x) / a);
	} else if (z <= 4.8e-36) {
		tmp = x;
	} else if (z <= 1.25e+146) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.1e+119:
		tmp = t
	elif z <= -2.7e+45:
		tmp = x * ((y - a) / z)
	elif z <= 8.5e-195:
		tmp = y * ((t - x) / a)
	elif z <= 4.8e-36:
		tmp = x
	elif z <= 1.25e+146:
		tmp = t * ((y - z) / a)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.1e+119)
		tmp = t;
	elseif (z <= -2.7e+45)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= 8.5e-195)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 4.8e-36)
		tmp = x;
	elseif (z <= 1.25e+146)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.1e+119)
		tmp = t;
	elseif (z <= -2.7e+45)
		tmp = x * ((y - a) / z);
	elseif (z <= 8.5e-195)
		tmp = y * ((t - x) / a);
	elseif (z <= 4.8e-36)
		tmp = x;
	elseif (z <= 1.25e+146)
		tmp = t * ((y - z) / a);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.1e+119], t, If[LessEqual[z, -2.7e+45], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e-195], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e-36], x, If[LessEqual[z, 1.25e+146], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.09999999999999983e119 or 1.25e146 < z

   1. Initial program 62.2%

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

   2. Taylor expanded in z around inf 60.0%

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

   if -2.09999999999999983e119 < z < -2.69999999999999984e45

   1. Initial program 70.8%

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

   2. Taylor expanded in z around inf 60.9%

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

      1. associate--l+ 60.9%

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

      2. distribute-lft-out-- 60.9%

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

      3. div-sub 60.9%

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

      4. mul-1-neg 60.9%

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

      5. unsub-neg 60.9%

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

      6. distribute-rgt-out-- 60.9%

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

      7. associate-/l* 66.2%

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

   4. Simplified 66.2%

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

   5. Taylor expanded in t around 0 36.9%

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

      1. expm1-log1p-u 17.7%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x \cdot \left(y - a\right)}{z}\right)\right)} \]

      2. expm1-udef 11.8%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x \cdot \left(y - a\right)}{z}\right)} - 1} \]

      3. associate-/l* 11.8%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{x}{\frac{z}{y - a}}}\right)} - 1 \]

   7. Applied egg-rr 11.8%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{\frac{z}{y - a}}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 17.7%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{\frac{z}{y - a}}\right)\right)} \]

      2. expm1-log1p 42.3%

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

      3. associate-/r/ 42.3%

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

      4. *-commutative 42.3%

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

      5. associate-*r/ 36.9%

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

      6. *-commutative 36.9%

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

      7. associate-*r/ 42.5%

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

   9. Simplified 42.5%

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

   if -2.69999999999999984e45 < z < 8.50000000000000023e-195

   1. Initial program 98.0%

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

      1. +-commutative 98.0%

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

      2. fma-def 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in a around inf 84.1%

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

   5. Taylor expanded in y around inf 48.5%

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

      1. div-sub 50.5%

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

   7. Simplified 50.5%

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

   if 8.50000000000000023e-195 < z < 4.8e-36

   1. Initial program 90.5%

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

   2. Taylor expanded in a around inf 47.3%

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

   if 4.8e-36 < z < 1.25e146

   1. Initial program 77.2%

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

      1. +-commutative 77.2%

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

      2. fma-def 77.3%

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

   3. Simplified 77.3%

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

   4. Taylor expanded in a around inf 56.4%

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

   5. Taylor expanded in t around inf 33.2%

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

      1. div-sub 33.2%

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

   7. Simplified 33.2%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+119}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-195}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+146}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9: 40.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+119}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 10^{-192}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-38}:\\ \;\;\;\;x + \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+146}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8e+119)
   t
   (if (<= z -2.7e+45)
     (* x (/ (- y a) z))
     (if (<= z 1e-192)
       (* y (/ (- t x) a))
       (if (<= z 6.8e-38)
         (+ x (/ x (/ a z)))
         (if (<= z 1.2e+146) (* t (/ (- y z) a)) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8e+119) {
		tmp = t;
	} else if (z <= -2.7e+45) {
		tmp = x * ((y - a) / z);
	} else if (z <= 1e-192) {
		tmp = y * ((t - x) / a);
	} else if (z <= 6.8e-38) {
		tmp = x + (x / (a / z));
	} else if (z <= 1.2e+146) {
		tmp = t * ((y - z) / a);
	} 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 <= (-8d+119)) then
        tmp = t
    else if (z <= (-2.7d+45)) then
        tmp = x * ((y - a) / z)
    else if (z <= 1d-192) then
        tmp = y * ((t - x) / a)
    else if (z <= 6.8d-38) then
        tmp = x + (x / (a / z))
    else if (z <= 1.2d+146) then
        tmp = t * ((y - z) / a)
    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 <= -8e+119) {
		tmp = t;
	} else if (z <= -2.7e+45) {
		tmp = x * ((y - a) / z);
	} else if (z <= 1e-192) {
		tmp = y * ((t - x) / a);
	} else if (z <= 6.8e-38) {
		tmp = x + (x / (a / z));
	} else if (z <= 1.2e+146) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8e+119:
		tmp = t
	elif z <= -2.7e+45:
		tmp = x * ((y - a) / z)
	elif z <= 1e-192:
		tmp = y * ((t - x) / a)
	elif z <= 6.8e-38:
		tmp = x + (x / (a / z))
	elif z <= 1.2e+146:
		tmp = t * ((y - z) / a)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8e+119)
		tmp = t;
	elseif (z <= -2.7e+45)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= 1e-192)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 6.8e-38)
		tmp = Float64(x + Float64(x / Float64(a / z)));
	elseif (z <= 1.2e+146)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8e+119)
		tmp = t;
	elseif (z <= -2.7e+45)
		tmp = x * ((y - a) / z);
	elseif (z <= 1e-192)
		tmp = y * ((t - x) / a);
	elseif (z <= 6.8e-38)
		tmp = x + (x / (a / z));
	elseif (z <= 1.2e+146)
		tmp = t * ((y - z) / a);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8e+119], t, If[LessEqual[z, -2.7e+45], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e-192], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e-38], N[(x + N[(x / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e+146], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -7.99999999999999955e119 or 1.2000000000000001e146 < z

   1. Initial program 62.2%

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

   2. Taylor expanded in z around inf 60.0%

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

   if -7.99999999999999955e119 < z < -2.69999999999999984e45

   1. Initial program 70.8%

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

   2. Taylor expanded in z around inf 60.9%

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

      1. associate--l+ 60.9%

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

      2. distribute-lft-out-- 60.9%

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

      3. div-sub 60.9%

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

      4. mul-1-neg 60.9%

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

      5. unsub-neg 60.9%

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

      6. distribute-rgt-out-- 60.9%

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

      7. associate-/l* 66.2%

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

   4. Simplified 66.2%

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

   5. Taylor expanded in t around 0 36.9%

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

      1. expm1-log1p-u 17.7%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x \cdot \left(y - a\right)}{z}\right)\right)} \]

      2. expm1-udef 11.8%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x \cdot \left(y - a\right)}{z}\right)} - 1} \]

      3. associate-/l* 11.8%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{x}{\frac{z}{y - a}}}\right)} - 1 \]

   7. Applied egg-rr 11.8%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{\frac{z}{y - a}}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 17.7%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{\frac{z}{y - a}}\right)\right)} \]

      2. expm1-log1p 42.3%

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

      3. associate-/r/ 42.3%

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

      4. *-commutative 42.3%

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

      5. associate-*r/ 36.9%

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

      6. *-commutative 36.9%

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

      7. associate-*r/ 42.5%

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

   9. Simplified 42.5%

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

   if -2.69999999999999984e45 < z < 1.0000000000000001e-192

   1. Initial program 98.0%

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

      1. +-commutative 98.0%

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

      2. fma-def 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in a around inf 84.1%

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

   5. Taylor expanded in y around inf 48.5%

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

      1. div-sub 50.5%

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

   7. Simplified 50.5%

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

   if 1.0000000000000001e-192 < z < 6.8000000000000004e-38

   1. Initial program 93.5%

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

      1. +-commutative 93.5%

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

      2. fma-def 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in a around inf 85.6%

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

   5. Taylor expanded in t around 0 65.3%

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

      1. mul-1-neg 65.3%

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

      2. unsub-neg 65.3%

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

      3. associate-/l* 68.4%

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

   7. Simplified 68.4%

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

   8. Taylor expanded in y around 0 51.9%

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

      1. sub-neg 51.9%

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

      2. mul-1-neg 51.9%

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

      3. remove-double-neg 51.9%

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

      4. associate-/l* 51.9%

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

   10. Simplified 51.9%

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

   if 6.8000000000000004e-38 < z < 1.2000000000000001e146

   1. Initial program 75.3%

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

      1. +-commutative 75.3%

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

      2. fma-def 75.4%

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

   3. Simplified 75.4%

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

   4. Taylor expanded in a around inf 55.0%

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

   5. Taylor expanded in t around inf 32.4%

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

      1. div-sub 32.5%

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

   7. Simplified 32.5%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+119}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 10^{-192}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-38}:\\ \;\;\;\;x + \frac{x}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+146}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 10: 65.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{a - z}{y - z}}\\ \mathbf{if}\;z \leq -2.45 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-149}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-41}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+173}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t - a \cdot \frac{x - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (/ (- a z) (- y z)))))
   (if (<= z -2.45e+24)
     t_1
     (if (<= z -2.6e-149)
       (* (- t x) (/ y (- a z)))
       (if (<= z 1.2e-41)
         (+ x (* (- t x) (/ y a)))
         (if (<= z 7.5e+173) t_1 (- t (* a (/ (- x t) z)))))))))

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 <= -2.45e+24) {
		tmp = t_1;
	} else if (z <= -2.6e-149) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= 1.2e-41) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 7.5e+173) {
		tmp = t_1;
	} else {
		tmp = t - (a * ((x - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / ((a - z) / (y - z))
    if (z <= (-2.45d+24)) then
        tmp = t_1
    else if (z <= (-2.6d-149)) then
        tmp = (t - x) * (y / (a - z))
    else if (z <= 1.2d-41) then
        tmp = x + ((t - x) * (y / a))
    else if (z <= 7.5d+173) then
        tmp = t_1
    else
        tmp = t - (a * ((x - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t / ((a - z) / (y - z));
	double tmp;
	if (z <= -2.45e+24) {
		tmp = t_1;
	} else if (z <= -2.6e-149) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= 1.2e-41) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 7.5e+173) {
		tmp = t_1;
	} else {
		tmp = t - (a * ((x - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / ((a - z) / (y - z))
	tmp = 0
	if z <= -2.45e+24:
		tmp = t_1
	elif z <= -2.6e-149:
		tmp = (t - x) * (y / (a - z))
	elif z <= 1.2e-41:
		tmp = x + ((t - x) * (y / a))
	elif z <= 7.5e+173:
		tmp = t_1
	else:
		tmp = t - (a * ((x - t) / z))
	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 <= -2.45e+24)
		tmp = t_1;
	elseif (z <= -2.6e-149)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (z <= 1.2e-41)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (z <= 7.5e+173)
		tmp = t_1;
	else
		tmp = Float64(t - Float64(a * Float64(Float64(x - t) / z)));
	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 <= -2.45e+24)
		tmp = t_1;
	elseif (z <= -2.6e-149)
		tmp = (t - x) * (y / (a - z));
	elseif (z <= 1.2e-41)
		tmp = x + ((t - x) * (y / a));
	elseif (z <= 7.5e+173)
		tmp = t_1;
	else
		tmp = t - (a * ((x - t) / z));
	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, -2.45e+24], t$95$1, If[LessEqual[z, -2.6e-149], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e-41], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e+173], t$95$1, N[(t - N[(a * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.45000000000000015e24 or 1.20000000000000011e-41 < z < 7.5e173

   1. Initial program 72.9%

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

   2. Taylor expanded in x around 0 44.6%

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

      1. associate-/l* 60.2%

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

   4. Simplified 60.2%

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

   if -2.45000000000000015e24 < z < -2.59999999999999999e-149

   1. Initial program 97.1%

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

   2. Taylor expanded in y around inf 70.5%

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

      1. div-sub 73.2%

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

      2. associate-*r/ 63.2%

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

      3. associate-/l* 73.1%

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

      4. associate-/r/ 70.6%

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

   4. Simplified 70.6%

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

   if -2.59999999999999999e-149 < z < 1.20000000000000011e-41

   1. Initial program 96.7%

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

   2. Taylor expanded in z around 0 89.1%

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

      1. associate-/l* 92.6%

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

      2. associate-/r/ 93.8%

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

   4. Simplified 93.8%

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

   if 7.5e173 < z

   1. Initial program 54.3%

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

   2. Taylor expanded in z around inf 65.5%

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

      1. associate--l+ 65.5%

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

      2. distribute-lft-out-- 65.5%

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

      3. div-sub 65.5%

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

      4. mul-1-neg 65.5%

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

      5. unsub-neg 65.5%

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

      6. distribute-rgt-out-- 65.6%

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

      7. associate-/l* 85.6%

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

   4. Simplified 85.6%

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

   5. Taylor expanded in y around 0 58.4%

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

      1. sub-neg 58.4%

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

      2. associate-*r/ 58.4%

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

      3. associate-*r* 58.4%

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

      4. neg-mul-1 58.4%

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

      5. associate-*r/ 81.8%

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

      6. distribute-lft-neg-out 81.8%

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

      7. remove-double-neg 81.8%

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

   7. Simplified 81.8%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+24}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-149}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-41}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+173}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t - a \cdot \frac{x - t}{z}\\ \end{array} \]

Alternative 11: 46.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+119}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-144}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+115}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.8e+119)
   t
   (if (<= z -3.6e+45)
     (* x (/ (- y a) z))
     (if (<= z -2.55e-144)
       (* y (/ (- t x) a))
       (if (<= z 3.7e+115) (- x (/ x (/ a y))) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.8e+119) {
		tmp = t;
	} else if (z <= -3.6e+45) {
		tmp = x * ((y - a) / z);
	} else if (z <= -2.55e-144) {
		tmp = y * ((t - x) / a);
	} else if (z <= 3.7e+115) {
		tmp = x - (x / (a / y));
	} 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 <= (-9.8d+119)) then
        tmp = t
    else if (z <= (-3.6d+45)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-2.55d-144)) then
        tmp = y * ((t - x) / a)
    else if (z <= 3.7d+115) then
        tmp = x - (x / (a / y))
    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 <= -9.8e+119) {
		tmp = t;
	} else if (z <= -3.6e+45) {
		tmp = x * ((y - a) / z);
	} else if (z <= -2.55e-144) {
		tmp = y * ((t - x) / a);
	} else if (z <= 3.7e+115) {
		tmp = x - (x / (a / y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.8e+119:
		tmp = t
	elif z <= -3.6e+45:
		tmp = x * ((y - a) / z)
	elif z <= -2.55e-144:
		tmp = y * ((t - x) / a)
	elif z <= 3.7e+115:
		tmp = x - (x / (a / y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.8e+119)
		tmp = t;
	elseif (z <= -3.6e+45)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -2.55e-144)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 3.7e+115)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.8e+119)
		tmp = t;
	elseif (z <= -3.6e+45)
		tmp = x * ((y - a) / z);
	elseif (z <= -2.55e-144)
		tmp = y * ((t - x) / a);
	elseif (z <= 3.7e+115)
		tmp = x - (x / (a / y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.8e+119], t, If[LessEqual[z, -3.6e+45], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.55e-144], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e+115], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.79999999999999992e119 or 3.70000000000000006e115 < z

   1. Initial program 61.6%

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

   2. Taylor expanded in z around inf 56.8%

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

   if -9.79999999999999992e119 < z < -3.6e45

   1. Initial program 70.8%

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

   2. Taylor expanded in z around inf 60.9%

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

      1. associate--l+ 60.9%

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

      2. distribute-lft-out-- 60.9%

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

      3. div-sub 60.9%

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

      4. mul-1-neg 60.9%

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

      5. unsub-neg 60.9%

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

      6. distribute-rgt-out-- 60.9%

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

      7. associate-/l* 66.2%

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

   4. Simplified 66.2%

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

   5. Taylor expanded in t around 0 36.9%

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

      1. expm1-log1p-u 17.7%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x \cdot \left(y - a\right)}{z}\right)\right)} \]

      2. expm1-udef 11.8%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x \cdot \left(y - a\right)}{z}\right)} - 1} \]

      3. associate-/l* 11.8%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{x}{\frac{z}{y - a}}}\right)} - 1 \]

   7. Applied egg-rr 11.8%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{\frac{z}{y - a}}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 17.7%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{\frac{z}{y - a}}\right)\right)} \]

      2. expm1-log1p 42.3%

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

      3. associate-/r/ 42.3%

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

      4. *-commutative 42.3%

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

      5. associate-*r/ 36.9%

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

      6. *-commutative 36.9%

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

      7. associate-*r/ 42.5%

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

   9. Simplified 42.5%

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

   if -3.6e45 < z < -2.55e-144

   1. Initial program 97.4%

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

      1. +-commutative 97.4%

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

      2. fma-def 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in a around inf 67.9%

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

   5. Taylor expanded in y around inf 47.6%

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

      1. div-sub 47.6%

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

   7. Simplified 47.6%

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

   if -2.55e-144 < z < 3.70000000000000006e115

   1. Initial program 91.6%

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

      1. +-commutative 91.6%

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

      2. fma-def 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in a around inf 81.9%

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

   5. Taylor expanded in t around 0 56.4%

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

      1. mul-1-neg 56.4%

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

      2. unsub-neg 56.4%

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

      3. associate-/l* 60.7%

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

   7. Simplified 60.7%

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

   8. Taylor expanded in y around inf 57.3%

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

      1. associate-/l* 60.9%

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

   10. Simplified 60.9%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+119}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-144}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+115}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12: 46.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+119}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-147}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+117}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7e+119)
   t
   (if (<= z -7.2e+45)
     (* x (/ (- y a) z))
     (if (<= z -8.5e-147)
       (/ y (/ a (- t x)))
       (if (<= z 4.3e+117) (- x (/ x (/ a y))) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7e+119) {
		tmp = t;
	} else if (z <= -7.2e+45) {
		tmp = x * ((y - a) / z);
	} else if (z <= -8.5e-147) {
		tmp = y / (a / (t - x));
	} else if (z <= 4.3e+117) {
		tmp = x - (x / (a / y));
	} 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 <= (-7d+119)) then
        tmp = t
    else if (z <= (-7.2d+45)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-8.5d-147)) then
        tmp = y / (a / (t - x))
    else if (z <= 4.3d+117) then
        tmp = x - (x / (a / y))
    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 <= -7e+119) {
		tmp = t;
	} else if (z <= -7.2e+45) {
		tmp = x * ((y - a) / z);
	} else if (z <= -8.5e-147) {
		tmp = y / (a / (t - x));
	} else if (z <= 4.3e+117) {
		tmp = x - (x / (a / y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7e+119:
		tmp = t
	elif z <= -7.2e+45:
		tmp = x * ((y - a) / z)
	elif z <= -8.5e-147:
		tmp = y / (a / (t - x))
	elif z <= 4.3e+117:
		tmp = x - (x / (a / y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7e+119)
		tmp = t;
	elseif (z <= -7.2e+45)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -8.5e-147)
		tmp = Float64(y / Float64(a / Float64(t - x)));
	elseif (z <= 4.3e+117)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7e+119)
		tmp = t;
	elseif (z <= -7.2e+45)
		tmp = x * ((y - a) / z);
	elseif (z <= -8.5e-147)
		tmp = y / (a / (t - x));
	elseif (z <= 4.3e+117)
		tmp = x - (x / (a / y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7e+119], t, If[LessEqual[z, -7.2e+45], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8.5e-147], N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.3e+117], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.0000000000000001e119 or 4.29999999999999998e117 < z

   1. Initial program 61.6%

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

   2. Taylor expanded in z around inf 56.8%

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

   if -7.0000000000000001e119 < z < -7.2e45

   1. Initial program 70.8%

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

   2. Taylor expanded in z around inf 60.9%

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

      1. associate--l+ 60.9%

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

      2. distribute-lft-out-- 60.9%

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

      3. div-sub 60.9%

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

      4. mul-1-neg 60.9%

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

      5. unsub-neg 60.9%

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

      6. distribute-rgt-out-- 60.9%

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

      7. associate-/l* 66.2%

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

   4. Simplified 66.2%

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

   5. Taylor expanded in t around 0 36.9%

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

      1. expm1-log1p-u 17.7%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x \cdot \left(y - a\right)}{z}\right)\right)} \]

      2. expm1-udef 11.8%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x \cdot \left(y - a\right)}{z}\right)} - 1} \]

      3. associate-/l* 11.8%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{x}{\frac{z}{y - a}}}\right)} - 1 \]

   7. Applied egg-rr 11.8%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{\frac{z}{y - a}}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 17.7%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{\frac{z}{y - a}}\right)\right)} \]

      2. expm1-log1p 42.3%

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

      3. associate-/r/ 42.3%

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

      4. *-commutative 42.3%

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

      5. associate-*r/ 36.9%

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

      6. *-commutative 36.9%

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

      7. associate-*r/ 42.5%

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

   9. Simplified 42.5%

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

   if -7.2e45 < z < -8.5000000000000002e-147

   1. Initial program 97.4%

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

      1. +-commutative 97.4%

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

      2. fma-def 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in a around inf 67.9%

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

   5. Taylor expanded in y around -inf 38.9%

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

      1. associate-/l* 47.7%

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

   7. Simplified 47.7%

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

   if -8.5000000000000002e-147 < z < 4.29999999999999998e117

   1. Initial program 91.6%

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

      1. +-commutative 91.6%

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

      2. fma-def 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in a around inf 81.9%

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

   5. Taylor expanded in t around 0 56.4%

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

      1. mul-1-neg 56.4%

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

      2. unsub-neg 56.4%

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

      3. associate-/l* 60.7%

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

   7. Simplified 60.7%

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

   8. Taylor expanded in y around inf 57.3%

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

      1. associate-/l* 60.9%

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

   10. Simplified 60.9%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+119}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-147}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+117}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 13: 62.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - a \cdot \frac{x - t}{z}\\ \mathbf{if}\;z \leq -8 \cdot 10^{+115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-149}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+148}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* a (/ (- x t) z)))))
   (if (<= z -8e+115)
     t_1
     (if (<= z -2.6e-149)
       (* (- t x) (/ y (- a z)))
       (if (<= z 1.8e+148) (+ x (* (- t x) (/ y a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * ((x - t) / z));
	double tmp;
	if (z <= -8e+115) {
		tmp = t_1;
	} else if (z <= -2.6e-149) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= 1.8e+148) {
		tmp = x + ((t - x) * (y / 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 - (a * ((x - t) / z))
    if (z <= (-8d+115)) then
        tmp = t_1
    else if (z <= (-2.6d-149)) then
        tmp = (t - x) * (y / (a - z))
    else if (z <= 1.8d+148) then
        tmp = x + ((t - x) * (y / 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 - (a * ((x - t) / z));
	double tmp;
	if (z <= -8e+115) {
		tmp = t_1;
	} else if (z <= -2.6e-149) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= 1.8e+148) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (a * ((x - t) / z))
	tmp = 0
	if z <= -8e+115:
		tmp = t_1
	elif z <= -2.6e-149:
		tmp = (t - x) * (y / (a - z))
	elif z <= 1.8e+148:
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(a * Float64(Float64(x - t) / z)))
	tmp = 0.0
	if (z <= -8e+115)
		tmp = t_1;
	elseif (z <= -2.6e-149)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (z <= 1.8e+148)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (a * ((x - t) / z));
	tmp = 0.0;
	if (z <= -8e+115)
		tmp = t_1;
	elseif (z <= -2.6e-149)
		tmp = (t - x) * (y / (a - z));
	elseif (z <= 1.8e+148)
		tmp = x + ((t - x) * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(a * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8e+115], t$95$1, If[LessEqual[z, -2.6e-149], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e+148], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.0000000000000001e115 or 1.80000000000000003e148 < z

   1. Initial program 61.3%

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

   2. Taylor expanded in z around inf 68.0%

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

      1. associate--l+ 68.0%

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

      2. distribute-lft-out-- 68.0%

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

      3. div-sub 68.0%

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

      4. mul-1-neg 68.0%

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

      5. unsub-neg 68.0%

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

      6. distribute-rgt-out-- 68.0%

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

      7. associate-/l* 79.9%

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

   4. Simplified 79.9%

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

   5. Taylor expanded in y around 0 62.1%

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

      1. sub-neg 62.1%

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

      2. associate-*r/ 62.1%

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

      3. associate-*r* 62.1%

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

      4. neg-mul-1 62.1%

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

      5. associate-*r/ 74.0%

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

      6. distribute-lft-neg-out 74.0%

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

      7. remove-double-neg 74.0%

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

   7. Simplified 74.0%

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

   if -8.0000000000000001e115 < z < -2.59999999999999999e-149

   1. Initial program 91.4%

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

   2. Taylor expanded in y around inf 59.9%

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

      1. div-sub 61.6%

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

      2. associate-*r/ 53.6%

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

      3. associate-/l* 61.5%

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

      4. associate-/r/ 60.0%

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

   4. Simplified 60.0%

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

   if -2.59999999999999999e-149 < z < 1.80000000000000003e148

   1. Initial program 90.3%

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

   2. Taylor expanded in z around 0 73.7%

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

      1. associate-/l* 77.5%

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

      2. associate-/r/ 79.1%

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

   4. Simplified 79.1%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+115}:\\ \;\;\;\;t - a \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-149}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+148}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t - a \cdot \frac{x - t}{z}\\ \end{array} \]

Alternative 14: 69.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{-41} \lor \neg \left(a \leq 6.2 \cdot 10^{-122}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y \cdot \left(t - x\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4e-41) (not (<= a 6.2e-122)))
   (+ x (* (- y z) (/ (- t x) a)))
   (- t (/ (* y (- t x)) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4e-41) || !(a <= 6.2e-122)) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else {
		tmp = t - ((y * (t - x)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-4d-41)) .or. (.not. (a <= 6.2d-122))) then
        tmp = x + ((y - z) * ((t - x) / a))
    else
        tmp = t - ((y * (t - x)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4e-41) || !(a <= 6.2e-122)) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else {
		tmp = t - ((y * (t - x)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4e-41) or not (a <= 6.2e-122):
		tmp = x + ((y - z) * ((t - x) / a))
	else:
		tmp = t - ((y * (t - x)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4e-41) || !(a <= 6.2e-122))
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / a)));
	else
		tmp = Float64(t - Float64(Float64(y * Float64(t - x)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4e-41) || ~((a <= 6.2e-122)))
		tmp = x + ((y - z) * ((t - x) / a));
	else
		tmp = t - ((y * (t - x)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4e-41], N[Not[LessEqual[a, 6.2e-122]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.00000000000000002e-41 or 6.1999999999999997e-122 < a

   1. Initial program 89.8%

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

      1. +-commutative 89.8%

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

      2. fma-def 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in a around inf 75.7%

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

      1. fma-udef 75.7%

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

   6. Applied egg-rr 75.7%

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

   if -4.00000000000000002e-41 < a < 6.1999999999999997e-122

   1. Initial program 70.0%

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

   2. Taylor expanded in z around inf 82.5%

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

      1. associate--l+ 82.5%

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

      2. distribute-lft-out-- 82.5%

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

      3. div-sub 82.5%

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

      4. mul-1-neg 82.5%

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

      5. unsub-neg 82.5%

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

      6. distribute-rgt-out-- 82.5%

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

      7. associate-/l* 81.3%

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

   4. Simplified 81.3%

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

   5. Taylor expanded in y around inf 77.3%

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

      1. *-commutative 77.3%

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

   7. Simplified 77.3%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{-41} \lor \neg \left(a \leq 6.2 \cdot 10^{-122}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y \cdot \left(t - x\right)}{z}\\ \end{array} \]

Alternative 15: 73.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{-41} \lor \neg \left(a \leq 6.6 \cdot 10^{-122}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.1e-41) (not (<= a 6.6e-122)))
   (+ x (* (- y z) (/ (- t x) a)))
   (+ t (/ (- x t) (/ z (- y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.1e-41) || !(a <= 6.6e-122)) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-4.1d-41)) .or. (.not. (a <= 6.6d-122))) then
        tmp = x + ((y - z) * ((t - x) / a))
    else
        tmp = t + ((x - t) / (z / (y - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.1e-41) || !(a <= 6.6e-122)) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.1e-41) or not (a <= 6.6e-122):
		tmp = x + ((y - z) * ((t - x) / a))
	else:
		tmp = t + ((x - t) / (z / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.1e-41) || !(a <= 6.6e-122))
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / a)));
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.1e-41) || ~((a <= 6.6e-122)))
		tmp = x + ((y - z) * ((t - x) / a));
	else
		tmp = t + ((x - t) / (z / (y - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.1e-41], N[Not[LessEqual[a, 6.6e-122]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.10000000000000014e-41 or 6.59999999999999999e-122 < a

   1. Initial program 89.8%

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

      1. +-commutative 89.8%

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

      2. fma-def 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in a around inf 75.7%

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

      1. fma-udef 75.7%

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

   6. Applied egg-rr 75.7%

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

   if -4.10000000000000014e-41 < a < 6.59999999999999999e-122

   1. Initial program 70.0%

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

   2. Taylor expanded in z around inf 82.5%

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

      1. associate--l+ 82.5%

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

      2. distribute-lft-out-- 82.5%

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

      3. div-sub 82.5%

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

      4. mul-1-neg 82.5%

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

      5. unsub-neg 82.5%

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

      6. distribute-rgt-out-- 82.5%

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

      7. associate-/l* 81.3%

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

   4. Simplified 81.3%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{-41} \lor \neg \left(a \leq 6.6 \cdot 10^{-122}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 16: 37.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+114}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-233}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-262}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+146}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.2e+114)
   t
   (if (<= z -3.5e-28)
     (* x (/ y z))
     (if (<= z -1.75e-233)
       x
       (if (<= z -6.5e-262) (* t (/ y a)) (if (<= z 1.2e+146) x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.2e+114) {
		tmp = t;
	} else if (z <= -3.5e-28) {
		tmp = x * (y / z);
	} else if (z <= -1.75e-233) {
		tmp = x;
	} else if (z <= -6.5e-262) {
		tmp = t * (y / a);
	} else if (z <= 1.2e+146) {
		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 <= (-8.2d+114)) then
        tmp = t
    else if (z <= (-3.5d-28)) then
        tmp = x * (y / z)
    else if (z <= (-1.75d-233)) then
        tmp = x
    else if (z <= (-6.5d-262)) then
        tmp = t * (y / a)
    else if (z <= 1.2d+146) 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 <= -8.2e+114) {
		tmp = t;
	} else if (z <= -3.5e-28) {
		tmp = x * (y / z);
	} else if (z <= -1.75e-233) {
		tmp = x;
	} else if (z <= -6.5e-262) {
		tmp = t * (y / a);
	} else if (z <= 1.2e+146) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.2e+114:
		tmp = t
	elif z <= -3.5e-28:
		tmp = x * (y / z)
	elif z <= -1.75e-233:
		tmp = x
	elif z <= -6.5e-262:
		tmp = t * (y / a)
	elif z <= 1.2e+146:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.2e+114)
		tmp = t;
	elseif (z <= -3.5e-28)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= -1.75e-233)
		tmp = x;
	elseif (z <= -6.5e-262)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 1.2e+146)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.2e+114)
		tmp = t;
	elseif (z <= -3.5e-28)
		tmp = x * (y / z);
	elseif (z <= -1.75e-233)
		tmp = x;
	elseif (z <= -6.5e-262)
		tmp = t * (y / a);
	elseif (z <= 1.2e+146)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.2e+114], t, If[LessEqual[z, -3.5e-28], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.75e-233], x, If[LessEqual[z, -6.5e-262], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e+146], x, t]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.2000000000000001e114 or 1.2000000000000001e146 < z

   1. Initial program 61.9%

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

   2. Taylor expanded in z around inf 58.4%

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

   if -8.2000000000000001e114 < z < -3.5e-28

   1. Initial program 83.4%

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

   2. Taylor expanded in z around inf 54.6%

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

      1. associate--l+ 54.6%

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

      2. distribute-lft-out-- 54.6%

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

      3. div-sub 54.6%

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

      4. mul-1-neg 54.6%

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

      5. unsub-neg 54.6%

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

      6. distribute-rgt-out-- 54.6%

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

      7. associate-/l* 57.8%

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

   4. Simplified 57.8%

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

   5. Taylor expanded in t around 0 31.8%

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

      1. expm1-log1p-u 10.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x \cdot \left(y - a\right)}{z}\right)\right)} \]

      2. expm1-udef 7.6%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x \cdot \left(y - a\right)}{z}\right)} - 1} \]

      3. associate-/l* 10.7%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{x}{\frac{z}{y - a}}}\right)} - 1 \]

   7. Applied egg-rr 10.7%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{\frac{z}{y - a}}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 14.0%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{\frac{z}{y - a}}\right)\right)} \]

      2. expm1-log1p 38.1%

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

      3. associate-/r/ 35.0%

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

      4. *-commutative 35.0%

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

      5. associate-*r/ 31.8%

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

      6. *-commutative 31.8%

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

      7. associate-*r/ 38.1%

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

   9. Simplified 38.1%

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

   10. Taylor expanded in y around inf 31.7%

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

   if -3.5e-28 < z < -1.74999999999999995e-233 or -6.5000000000000003e-262 < z < 1.2000000000000001e146

   1. Initial program 92.1%

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

   2. Taylor expanded in a around inf 37.0%

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

   if -1.74999999999999995e-233 < z < -6.5000000000000003e-262

   1. Initial program 89.5%

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

   2. Taylor expanded in x around 0 68.0%

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

      1. associate-/l* 77.6%

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

   4. Simplified 77.6%

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

   5. Taylor expanded in z around 0 77.6%

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

   6. Taylor expanded in t around 0 68.0%

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

      1. associate-*r/ 77.8%

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

   8. Simplified 77.8%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+114}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-233}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-262}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+146}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 17: 36.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+45}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-149}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-233}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-262}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+146}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3e+45)
   t
   (if (<= z -9.2e-149)
     (* y (/ t a))
     (if (<= z -1.75e-233)
       x
       (if (<= z -8.8e-262) (* t (/ y a)) (if (<= z 1.2e+146) x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3e+45) {
		tmp = t;
	} else if (z <= -9.2e-149) {
		tmp = y * (t / a);
	} else if (z <= -1.75e-233) {
		tmp = x;
	} else if (z <= -8.8e-262) {
		tmp = t * (y / a);
	} else if (z <= 1.2e+146) {
		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 <= (-3d+45)) then
        tmp = t
    else if (z <= (-9.2d-149)) then
        tmp = y * (t / a)
    else if (z <= (-1.75d-233)) then
        tmp = x
    else if (z <= (-8.8d-262)) then
        tmp = t * (y / a)
    else if (z <= 1.2d+146) 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 <= -3e+45) {
		tmp = t;
	} else if (z <= -9.2e-149) {
		tmp = y * (t / a);
	} else if (z <= -1.75e-233) {
		tmp = x;
	} else if (z <= -8.8e-262) {
		tmp = t * (y / a);
	} else if (z <= 1.2e+146) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3e+45:
		tmp = t
	elif z <= -9.2e-149:
		tmp = y * (t / a)
	elif z <= -1.75e-233:
		tmp = x
	elif z <= -8.8e-262:
		tmp = t * (y / a)
	elif z <= 1.2e+146:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3e+45)
		tmp = t;
	elseif (z <= -9.2e-149)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= -1.75e-233)
		tmp = x;
	elseif (z <= -8.8e-262)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 1.2e+146)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3e+45)
		tmp = t;
	elseif (z <= -9.2e-149)
		tmp = y * (t / a);
	elseif (z <= -1.75e-233)
		tmp = x;
	elseif (z <= -8.8e-262)
		tmp = t * (y / a);
	elseif (z <= 1.2e+146)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3e+45], t, If[LessEqual[z, -9.2e-149], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.75e-233], x, If[LessEqual[z, -8.8e-262], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e+146], x, t]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.00000000000000011e45 or 1.2000000000000001e146 < z

   1. Initial program 63.9%

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

   2. Taylor expanded in z around inf 51.0%

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

   if -3.00000000000000011e45 < z < -9.1999999999999999e-149

   1. Initial program 97.4%

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

   2. Taylor expanded in x around 0 50.7%

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

      1. associate-/l* 55.2%

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

   4. Simplified 55.2%

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

   5. Taylor expanded in z around 0 27.1%

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

      1. associate-/r/ 29.3%

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

   7. Applied egg-rr 29.3%

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

   if -9.1999999999999999e-149 < z < -1.74999999999999995e-233 or -8.79999999999999954e-262 < z < 1.2000000000000001e146

   1. Initial program 90.4%

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

   2. Taylor expanded in a around inf 41.2%

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

   if -1.74999999999999995e-233 < z < -8.79999999999999954e-262

   1. Initial program 89.5%

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

   2. Taylor expanded in x around 0 68.0%

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

      1. associate-/l* 77.6%

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

   4. Simplified 77.6%

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

   5. Taylor expanded in z around 0 77.6%

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

   6. Taylor expanded in t around 0 68.0%

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

      1. associate-*r/ 77.8%

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

   8. Simplified 77.8%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+45}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-149}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-233}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-262}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+146}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 18: 59.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-38} \lor \neg \left(t \leq 3.2 \cdot 10^{-51}\right):\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.1e-38) (not (<= t 3.2e-51)))
   (* (- y z) (/ t (- a z)))
   (- x (/ x (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.1e-38) || !(t <= 3.2e-51)) {
		tmp = (y - z) * (t / (a - z));
	} else {
		tmp = x - (x / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.1d-38)) .or. (.not. (t <= 3.2d-51))) then
        tmp = (y - z) * (t / (a - z))
    else
        tmp = x - (x / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.1e-38) || !(t <= 3.2e-51)) {
		tmp = (y - z) * (t / (a - z));
	} else {
		tmp = x - (x / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.1e-38) or not (t <= 3.2e-51):
		tmp = (y - z) * (t / (a - z))
	else:
		tmp = x - (x / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.1e-38) || !(t <= 3.2e-51))
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	else
		tmp = Float64(x - Float64(x / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.1e-38) || ~((t <= 3.2e-51)))
		tmp = (y - z) * (t / (a - z));
	else
		tmp = x - (x / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.1e-38], N[Not[LessEqual[t, 3.2e-51]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.10000000000000013e-38 or 3.2e-51 < t

   1. Initial program 89.5%

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

   2. Taylor expanded in x around 0 56.0%

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

      1. associate-/l* 75.5%

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

      2. associate-/r/ 74.2%

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

   4. Simplified 74.2%

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

   if -2.10000000000000013e-38 < t < 3.2e-51

   1. Initial program 73.1%

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

      1. +-commutative 73.1%

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

      2. fma-def 73.2%

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

   3. Simplified 73.2%

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

   4. Taylor expanded in a around inf 62.8%

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

   5. Taylor expanded in t around 0 54.4%

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

      1. mul-1-neg 54.4%

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

      2. unsub-neg 54.4%

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

      3. associate-/l* 58.4%

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

   7. Simplified 58.4%

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

   8. Taylor expanded in y around inf 56.3%

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

      1. associate-/l* 58.9%

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

   10. Simplified 58.9%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-38} \lor \neg \left(t \leq 3.2 \cdot 10^{-51}\right):\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 19: 64.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -480000000:\\ \;\;\;\;t - \frac{y \cdot \left(t - x\right)}{z}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+146}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t - a \cdot \frac{x - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -480000000.0)
   (- t (/ (* y (- t x)) z))
   (if (<= z 1.2e+146) (+ x (* (- t x) (/ y a))) (- t (* a (/ (- x t) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -480000000.0) {
		tmp = t - ((y * (t - x)) / z);
	} else if (z <= 1.2e+146) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t - (a * ((x - t) / 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 <= (-480000000.0d0)) then
        tmp = t - ((y * (t - x)) / z)
    else if (z <= 1.2d+146) then
        tmp = x + ((t - x) * (y / a))
    else
        tmp = t - (a * ((x - t) / 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 <= -480000000.0) {
		tmp = t - ((y * (t - x)) / z);
	} else if (z <= 1.2e+146) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t - (a * ((x - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -480000000.0:
		tmp = t - ((y * (t - x)) / z)
	elif z <= 1.2e+146:
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t - (a * ((x - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -480000000.0)
		tmp = Float64(t - Float64(Float64(y * Float64(t - x)) / z));
	elseif (z <= 1.2e+146)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = Float64(t - Float64(a * Float64(Float64(x - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -480000000.0)
		tmp = t - ((y * (t - x)) / z);
	elseif (z <= 1.2e+146)
		tmp = x + ((t - x) * (y / a));
	else
		tmp = t - (a * ((x - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -480000000.0], N[(t - N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e+146], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(a * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8e8

   1. Initial program 71.2%

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

   2. Taylor expanded in z around inf 66.3%

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

      1. associate--l+ 66.3%

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

      2. distribute-lft-out-- 66.3%

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

      3. div-sub 66.3%

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

      4. mul-1-neg 66.3%

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

      5. unsub-neg 66.3%

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

      6. distribute-rgt-out-- 66.3%

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

      7. associate-/l* 69.4%

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

   4. Simplified 69.4%

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

   5. Taylor expanded in y around inf 60.9%

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

      1. *-commutative 60.9%

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

   7. Simplified 60.9%

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

   if -4.8e8 < z < 1.2000000000000001e146

   1. Initial program 91.7%

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

   2. Taylor expanded in z around 0 68.6%

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

      1. associate-/l* 73.8%

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

      2. associate-/r/ 74.5%

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

   4. Simplified 74.5%

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

   if 1.2000000000000001e146 < z

   1. Initial program 58.3%

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

   2. Taylor expanded in z around inf 64.1%

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

      1. associate--l+ 64.1%

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

      2. distribute-lft-out-- 64.1%

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

      3. div-sub 64.1%

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

      4. mul-1-neg 64.1%

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

      5. unsub-neg 64.1%

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

      6. distribute-rgt-out-- 64.2%

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

      7. associate-/l* 86.5%

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

   4. Simplified 86.5%

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

   5. Taylor expanded in y around 0 57.6%

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

      1. sub-neg 57.6%

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

      2. associate-*r/ 57.6%

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

      3. associate-*r* 57.6%

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

      4. neg-mul-1 57.6%

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

      5. associate-*r/ 80.2%

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

      6. distribute-lft-neg-out 80.2%

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

      7. remove-double-neg 80.2%

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

   7. Simplified 80.2%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -480000000:\\ \;\;\;\;t - \frac{y \cdot \left(t - x\right)}{z}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+146}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t - a \cdot \frac{x - t}{z}\\ \end{array} \]

Alternative 20: 45.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.6 \cdot 10^{+76}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-70}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{-z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9.6e+76)
   (* t (/ (- y z) a))
   (if (<= t 3e-70) (- x (/ x (/ a y))) (/ t (/ (- z) (- y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.6e+76) {
		tmp = t * ((y - z) / a);
	} else if (t <= 3e-70) {
		tmp = x - (x / (a / y));
	} else {
		tmp = t / (-z / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-9.6d+76)) then
        tmp = t * ((y - z) / a)
    else if (t <= 3d-70) then
        tmp = x - (x / (a / y))
    else
        tmp = t / (-z / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.6e+76) {
		tmp = t * ((y - z) / a);
	} else if (t <= 3e-70) {
		tmp = x - (x / (a / y));
	} else {
		tmp = t / (-z / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9.6e+76:
		tmp = t * ((y - z) / a)
	elif t <= 3e-70:
		tmp = x - (x / (a / y))
	else:
		tmp = t / (-z / (y - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9.6e+76)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (t <= 3e-70)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	else
		tmp = Float64(t / Float64(Float64(-z) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9.6e+76)
		tmp = t * ((y - z) / a);
	elseif (t <= 3e-70)
		tmp = x - (x / (a / y));
	else
		tmp = t / (-z / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9.6e+76], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e-70], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[((-z) / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.5999999999999999e76

   1. Initial program 90.4%

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

      1. +-commutative 90.4%

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

      2. fma-def 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in a around inf 66.6%

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

   5. Taylor expanded in t around inf 53.2%

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

      1. div-sub 53.3%

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

   7. Simplified 53.3%

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

   if -9.5999999999999999e76 < t < 3.0000000000000001e-70

   1. Initial program 74.8%

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

      1. +-commutative 74.8%

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

      2. fma-def 75.0%

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

   3. Simplified 75.0%

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

   4. Taylor expanded in a around inf 61.4%

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

   5. Taylor expanded in t around 0 52.2%

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

      1. mul-1-neg 52.2%

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

      2. unsub-neg 52.2%

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

      3. associate-/l* 57.1%

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

   7. Simplified 57.1%

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

   8. Taylor expanded in y around inf 54.7%

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

      1. associate-/l* 57.7%

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

   10. Simplified 57.7%

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

   if 3.0000000000000001e-70 < t

   1. Initial program 90.1%

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

   2. Taylor expanded in x around 0 54.5%

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

      1. associate-/l* 79.7%

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

   4. Simplified 79.7%

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

   5. Taylor expanded in a around 0 55.2%

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

      1. neg-mul-1 55.2%

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

      2. distribute-neg-frac 55.2%

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

   7. Simplified 55.2%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.6 \cdot 10^{+76}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-70}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{-z}{y - z}}\\ \end{array} \]

Alternative 21: 36.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+45}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-261}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+146}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.2e+45)
   t
   (if (<= z -2.1e-261) (* t (/ y a)) (if (<= z 3.9e+146) x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.2e+45) {
		tmp = t;
	} else if (z <= -2.1e-261) {
		tmp = t * (y / a);
	} else if (z <= 3.9e+146) {
		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+45)) then
        tmp = t
    else if (z <= (-2.1d-261)) then
        tmp = t * (y / a)
    else if (z <= 3.9d+146) 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+45) {
		tmp = t;
	} else if (z <= -2.1e-261) {
		tmp = t * (y / a);
	} else if (z <= 3.9e+146) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.2e+45:
		tmp = t
	elif z <= -2.1e-261:
		tmp = t * (y / a)
	elif z <= 3.9e+146:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.2e+45)
		tmp = t;
	elseif (z <= -2.1e-261)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 3.9e+146)
		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+45)
		tmp = t;
	elseif (z <= -2.1e-261)
		tmp = t * (y / a);
	elseif (z <= 3.9e+146)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.2e+45], t, If[LessEqual[z, -2.1e-261], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.9e+146], x, t]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.2e45 or 3.9e146 < z

   1. Initial program 63.9%

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

   2. Taylor expanded in z around inf 51.0%

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

   if -7.2e45 < z < -2.09999999999999996e-261

   1. Initial program 97.1%

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

   2. Taylor expanded in x around 0 48.5%

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

      1. associate-/l* 52.3%

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

   4. Simplified 52.3%

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

   5. Taylor expanded in z around 0 33.9%

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

   6. Taylor expanded in t around 0 30.2%

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

      1. associate-*r/ 34.0%

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

   8. Simplified 34.0%

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

   if -2.09999999999999996e-261 < z < 3.9e146

   1. Initial program 88.6%

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

   2. Taylor expanded in a around inf 38.9%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+45}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-261}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+146}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 22: 38.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+33}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+146}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.2e+33) t (if (<= z 1.3e+146) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.2e+33) {
		tmp = t;
	} else if (z <= 1.3e+146) {
		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+33)) then
        tmp = t
    else if (z <= 1.3d+146) 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+33) {
		tmp = t;
	} else if (z <= 1.3e+146) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.2e+33:
		tmp = t
	elif z <= 1.3e+146:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.2e+33)
		tmp = t;
	elseif (z <= 1.3e+146)
		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+33)
		tmp = t;
	elseif (z <= 1.3e+146)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.2e+33], t, If[LessEqual[z, 1.3e+146], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -7.2000000000000005e33 or 1.30000000000000007e146 < z

   1. Initial program 65.2%

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

   2. Taylor expanded in z around inf 50.5%

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

   if -7.2000000000000005e33 < z < 1.30000000000000007e146

   1. Initial program 91.9%

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

   2. Taylor expanded in a around inf 34.1%

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

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+33}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+146}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 23: 25.4% 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 82.8%

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

2. Taylor expanded in z around inf 22.9%

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

3. Final simplification 22.9%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023322 
(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)))))