Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 8.6s

Alternatives: 16

Speedup: 1.0×

• 34.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y - z, t - x, x\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (fma (- y z) (- t x) x))

C

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

Julia

function code(x, y, z, t)
	return fma(Float64(y - z), Float64(t - x), x)
end

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-def 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 51.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;y - z \leq -5 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y - z \leq 10^{-19}:\\ \;\;\;\;x\\ \mathbf{elif}\;y - z \leq 5 \cdot 10^{+174} \lor \neg \left(y - z \leq 2 \cdot 10^{+267}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= (- y z) -5e-26)
     t_1
     (if (<= (- y z) 1e-19)
       x
       (if (or (<= (- y z) 5e+174) (not (<= (- y z) 2e+267))) t_1 (* z x))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if ((y - z) <= -5e-26) {
		tmp = t_1;
	} else if ((y - z) <= 1e-19) {
		tmp = x;
	} else if (((y - z) <= 5e+174) || !((y - z) <= 2e+267)) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * t
    if ((y - z) <= (-5d-26)) then
        tmp = t_1
    else if ((y - z) <= 1d-19) then
        tmp = x
    else if (((y - z) <= 5d+174) .or. (.not. ((y - z) <= 2d+267))) then
        tmp = t_1
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if ((y - z) <= -5e-26) {
		tmp = t_1;
	} else if ((y - z) <= 1e-19) {
		tmp = x;
	} else if (((y - z) <= 5e+174) || !((y - z) <= 2e+267)) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if (y - z) <= -5e-26:
		tmp = t_1
	elif (y - z) <= 1e-19:
		tmp = x
	elif ((y - z) <= 5e+174) or not ((y - z) <= 2e+267):
		tmp = t_1
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (Float64(y - z) <= -5e-26)
		tmp = t_1;
	elseif (Float64(y - z) <= 1e-19)
		tmp = x;
	elseif ((Float64(y - z) <= 5e+174) || !(Float64(y - z) <= 2e+267))
		tmp = t_1;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	tmp = 0.0;
	if ((y - z) <= -5e-26)
		tmp = t_1;
	elseif ((y - z) <= 1e-19)
		tmp = x;
	elseif (((y - z) <= 5e+174) || ~(((y - z) <= 2e+267)))
		tmp = t_1;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[N[(y - z), $MachinePrecision], -5e-26], t$95$1, If[LessEqual[N[(y - z), $MachinePrecision], 1e-19], x, If[Or[LessEqual[N[(y - z), $MachinePrecision], 5e+174], N[Not[LessEqual[N[(y - z), $MachinePrecision], 2e+267]], $MachinePrecision]], t$95$1, N[(z * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 y z) < -5.00000000000000019e-26 or 9.9999999999999998e-20 < (-.f64 y z) < 4.9999999999999997e174 or 1.9999999999999999e267 < (-.f64 y z)

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around 0 58.6%

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

   if -5.00000000000000019e-26 < (-.f64 y z) < 9.9999999999999998e-20

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in z around 0 82.4%

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

   3. Taylor expanded in y around 0 71.9%

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

   if 4.9999999999999997e174 < (-.f64 y z) < 1.9999999999999999e267

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in z around inf 54.1%

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

      1. mul-1-neg 54.1%

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

      2. distribute-lft-neg-out 54.1%

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

      3. *-commutative 54.1%

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

   4. Simplified 54.1%

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

   5. Taylor expanded in t around 0 49.2%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y - z \leq -5 \cdot 10^{-26}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y - z \leq 10^{-19}:\\ \;\;\;\;x\\ \mathbf{elif}\;y - z \leq 5 \cdot 10^{+174} \lor \neg \left(y - z \leq 2 \cdot 10^{+267}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 3: 69.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := z \cdot \left(x - t\right)\\ \mathbf{if}\;y \leq -1.76 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-14}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-26}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-291}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-242}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-121}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-11}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* z (- x t))))
   (if (<= y -1.76e+30)
     t_1
     (if (<= y -3.4e-14)
       (- x (* y x))
       (if (<= y -1.15e-26)
         (* (- y z) t)
         (if (<= y 3.4e-291)
           (- x (* z t))
           (if (<= y 9e-242)
             t_2
             (if (<= y 6.8e-121)
               (+ x (* z x))
               (if (<= y 7.8e-11) t_2 t_1)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = z * (x - t);
	double tmp;
	if (y <= -1.76e+30) {
		tmp = t_1;
	} else if (y <= -3.4e-14) {
		tmp = x - (y * x);
	} else if (y <= -1.15e-26) {
		tmp = (y - z) * t;
	} else if (y <= 3.4e-291) {
		tmp = x - (z * t);
	} else if (y <= 9e-242) {
		tmp = t_2;
	} else if (y <= 6.8e-121) {
		tmp = x + (z * x);
	} else if (y <= 7.8e-11) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (t - x)
    t_2 = z * (x - t)
    if (y <= (-1.76d+30)) then
        tmp = t_1
    else if (y <= (-3.4d-14)) then
        tmp = x - (y * x)
    else if (y <= (-1.15d-26)) then
        tmp = (y - z) * t
    else if (y <= 3.4d-291) then
        tmp = x - (z * t)
    else if (y <= 9d-242) then
        tmp = t_2
    else if (y <= 6.8d-121) then
        tmp = x + (z * x)
    else if (y <= 7.8d-11) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = z * (x - t);
	double tmp;
	if (y <= -1.76e+30) {
		tmp = t_1;
	} else if (y <= -3.4e-14) {
		tmp = x - (y * x);
	} else if (y <= -1.15e-26) {
		tmp = (y - z) * t;
	} else if (y <= 3.4e-291) {
		tmp = x - (z * t);
	} else if (y <= 9e-242) {
		tmp = t_2;
	} else if (y <= 6.8e-121) {
		tmp = x + (z * x);
	} else if (y <= 7.8e-11) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = z * (x - t)
	tmp = 0
	if y <= -1.76e+30:
		tmp = t_1
	elif y <= -3.4e-14:
		tmp = x - (y * x)
	elif y <= -1.15e-26:
		tmp = (y - z) * t
	elif y <= 3.4e-291:
		tmp = x - (z * t)
	elif y <= 9e-242:
		tmp = t_2
	elif y <= 6.8e-121:
		tmp = x + (z * x)
	elif y <= 7.8e-11:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (y <= -1.76e+30)
		tmp = t_1;
	elseif (y <= -3.4e-14)
		tmp = Float64(x - Float64(y * x));
	elseif (y <= -1.15e-26)
		tmp = Float64(Float64(y - z) * t);
	elseif (y <= 3.4e-291)
		tmp = Float64(x - Float64(z * t));
	elseif (y <= 9e-242)
		tmp = t_2;
	elseif (y <= 6.8e-121)
		tmp = Float64(x + Float64(z * x));
	elseif (y <= 7.8e-11)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	t_2 = z * (x - t);
	tmp = 0.0;
	if (y <= -1.76e+30)
		tmp = t_1;
	elseif (y <= -3.4e-14)
		tmp = x - (y * x);
	elseif (y <= -1.15e-26)
		tmp = (y - z) * t;
	elseif (y <= 3.4e-291)
		tmp = x - (z * t);
	elseif (y <= 9e-242)
		tmp = t_2;
	elseif (y <= 6.8e-121)
		tmp = x + (z * x);
	elseif (y <= 7.8e-11)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.76e+30], t$95$1, If[LessEqual[y, -3.4e-14], N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.15e-26], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 3.4e-291], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e-242], t$95$2, If[LessEqual[y, 6.8e-121], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.8e-11], t$95$2, t$95$1]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.7600000000000001e30 or 7.80000000000000021e-11 < y

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around inf 78.8%

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

   if -1.7600000000000001e30 < y < -3.40000000000000003e-14

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in z around 0 73.1%

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

   3. Taylor expanded in t around 0 64.5%

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

      1. mul-1-neg 19.5%

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

      2. distribute-rgt-neg-out 19.5%

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

   5. Simplified 64.5%

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

   if -3.40000000000000003e-14 < y < -1.15000000000000004e-26

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around 0 100.0%

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

   if -1.15000000000000004e-26 < y < 3.40000000000000026e-291

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around 0 94.3%

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

      1. +-commutative 94.3%

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

      2. mul-1-neg 94.3%

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

      3. unsub-neg 94.3%

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

      4. *-commutative 94.3%

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

   4. Simplified 94.3%

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

   5. Taylor expanded in t around inf 76.6%

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

   if 3.40000000000000026e-291 < y < 8.9999999999999997e-242 or 6.80000000000000003e-121 < y < 7.80000000000000021e-11

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around 0 94.3%

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

      1. +-commutative 94.3%

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

      2. mul-1-neg 94.3%

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

      3. unsub-neg 94.3%

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

      4. *-commutative 94.3%

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

   4. Simplified 94.3%

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

   5. Taylor expanded in z around inf 88.8%

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

   if 8.9999999999999997e-242 < y < 6.80000000000000003e-121

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around inf 76.4%

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

      1. sub-neg 76.4%

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

      2. neg-mul-1 76.4%

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

      3. remove-double-neg 76.4%

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

      4. *-commutative 76.4%

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

      5. distribute-lft-in 76.5%

         \[\leadsto \color{blue}{x \cdot 1 + x \cdot z} \]

      6. *-rgt-identity 76.5%

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

   7. Simplified 76.5%

      \[\leadsto \color{blue}{x + x \cdot z} \]
3. Recombined 6 regimes into one program.

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.76 \cdot 10^{+30}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-14}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-26}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-291}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-242}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-121}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-11}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 4: 37.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{-17}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-285}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{-268}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{-238}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-132}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+63}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- z))))
   (if (<= y -1.6e-17)
     (* y t)
     (if (<= y -2.9e-285)
       t_1
       (if (<= y 8.4e-268)
         (* z x)
         (if (<= y 6.1e-238)
           t_1
           (if (<= y 1.35e-132)
             x
             (if (<= y 1.6e-19)
               t_1
               (if (<= y 4.7e+63) (* z x) (* y (- x)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * -z;
	double tmp;
	if (y <= -1.6e-17) {
		tmp = y * t;
	} else if (y <= -2.9e-285) {
		tmp = t_1;
	} else if (y <= 8.4e-268) {
		tmp = z * x;
	} else if (y <= 6.1e-238) {
		tmp = t_1;
	} else if (y <= 1.35e-132) {
		tmp = x;
	} else if (y <= 1.6e-19) {
		tmp = t_1;
	} else if (y <= 4.7e+63) {
		tmp = z * x;
	} else {
		tmp = y * -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * -z
    if (y <= (-1.6d-17)) then
        tmp = y * t
    else if (y <= (-2.9d-285)) then
        tmp = t_1
    else if (y <= 8.4d-268) then
        tmp = z * x
    else if (y <= 6.1d-238) then
        tmp = t_1
    else if (y <= 1.35d-132) then
        tmp = x
    else if (y <= 1.6d-19) then
        tmp = t_1
    else if (y <= 4.7d+63) then
        tmp = z * x
    else
        tmp = y * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * -z;
	double tmp;
	if (y <= -1.6e-17) {
		tmp = y * t;
	} else if (y <= -2.9e-285) {
		tmp = t_1;
	} else if (y <= 8.4e-268) {
		tmp = z * x;
	} else if (y <= 6.1e-238) {
		tmp = t_1;
	} else if (y <= 1.35e-132) {
		tmp = x;
	} else if (y <= 1.6e-19) {
		tmp = t_1;
	} else if (y <= 4.7e+63) {
		tmp = z * x;
	} else {
		tmp = y * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * -z
	tmp = 0
	if y <= -1.6e-17:
		tmp = y * t
	elif y <= -2.9e-285:
		tmp = t_1
	elif y <= 8.4e-268:
		tmp = z * x
	elif y <= 6.1e-238:
		tmp = t_1
	elif y <= 1.35e-132:
		tmp = x
	elif y <= 1.6e-19:
		tmp = t_1
	elif y <= 4.7e+63:
		tmp = z * x
	else:
		tmp = y * -x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(-z))
	tmp = 0.0
	if (y <= -1.6e-17)
		tmp = Float64(y * t);
	elseif (y <= -2.9e-285)
		tmp = t_1;
	elseif (y <= 8.4e-268)
		tmp = Float64(z * x);
	elseif (y <= 6.1e-238)
		tmp = t_1;
	elseif (y <= 1.35e-132)
		tmp = x;
	elseif (y <= 1.6e-19)
		tmp = t_1;
	elseif (y <= 4.7e+63)
		tmp = Float64(z * x);
	else
		tmp = Float64(y * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * -z;
	tmp = 0.0;
	if (y <= -1.6e-17)
		tmp = y * t;
	elseif (y <= -2.9e-285)
		tmp = t_1;
	elseif (y <= 8.4e-268)
		tmp = z * x;
	elseif (y <= 6.1e-238)
		tmp = t_1;
	elseif (y <= 1.35e-132)
		tmp = x;
	elseif (y <= 1.6e-19)
		tmp = t_1;
	elseif (y <= 4.7e+63)
		tmp = z * x;
	else
		tmp = y * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * (-z)), $MachinePrecision]}, If[LessEqual[y, -1.6e-17], N[(y * t), $MachinePrecision], If[LessEqual[y, -2.9e-285], t$95$1, If[LessEqual[y, 8.4e-268], N[(z * x), $MachinePrecision], If[LessEqual[y, 6.1e-238], t$95$1, If[LessEqual[y, 1.35e-132], x, If[LessEqual[y, 1.6e-19], t$95$1, If[LessEqual[y, 4.7e+63], N[(z * x), $MachinePrecision], N[(y * (-x)), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.6000000000000001e-17

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around 0 55.2%

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

   3. Taylor expanded in y around inf 50.1%

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

   if -1.6000000000000001e-17 < y < -2.9e-285 or 8.39999999999999991e-268 < y < 6.1000000000000001e-238 or 1.34999999999999995e-132 < y < 1.59999999999999991e-19

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around 0 60.0%

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

   3. Taylor expanded in y around 0 52.4%

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

      1. associate-*r* 52.4%

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

      2. mul-1-neg 52.4%

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

   5. Simplified 52.4%

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

   if -2.9e-285 < y < 8.39999999999999991e-268 or 1.59999999999999991e-19 < y < 4.7000000000000003e63

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in z around inf 58.1%

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

      1. mul-1-neg 58.1%

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

      2. distribute-lft-neg-out 58.1%

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

      3. *-commutative 58.1%

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

   4. Simplified 58.1%

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

   5. Taylor expanded in t around 0 47.3%

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

   if 6.1000000000000001e-238 < y < 1.34999999999999995e-132

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in z around 0 48.7%

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

   3. Taylor expanded in y around 0 48.5%

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

   if 4.7000000000000003e63 < y

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around inf 78.5%

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

   3. Taylor expanded in t around 0 49.6%

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

      1. mul-1-neg 49.6%

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

      2. distribute-rgt-neg-out 49.6%

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

   5. Simplified 49.6%

      \[\leadsto \color{blue}{y \cdot \left(-x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-17}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-285}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{-268}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{-238}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-132}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-19}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+63}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]

Alternative 5: 70.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := x + y \cdot t\\ t_3 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -4.3 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-75}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-128}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-228}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-290}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1600000000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))) (t_2 (+ x (* y t))) (t_3 (* x (- 1.0 y))))
   (if (<= z -4.3e-13)
     t_1
     (if (<= z -7.5e-75)
       t_3
       (if (<= z -2.8e-128)
         (* (- y z) t)
         (if (<= z -4.2e-228)
           t_2
           (if (<= z -5e-290) t_3 (if (<= z 1600000000.0) t_2 t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = x + (y * t);
	double t_3 = x * (1.0 - y);
	double tmp;
	if (z <= -4.3e-13) {
		tmp = t_1;
	} else if (z <= -7.5e-75) {
		tmp = t_3;
	} else if (z <= -2.8e-128) {
		tmp = (y - z) * t;
	} else if (z <= -4.2e-228) {
		tmp = t_2;
	} else if (z <= -5e-290) {
		tmp = t_3;
	} else if (z <= 1600000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * (x - t)
    t_2 = x + (y * t)
    t_3 = x * (1.0d0 - y)
    if (z <= (-4.3d-13)) then
        tmp = t_1
    else if (z <= (-7.5d-75)) then
        tmp = t_3
    else if (z <= (-2.8d-128)) then
        tmp = (y - z) * t
    else if (z <= (-4.2d-228)) then
        tmp = t_2
    else if (z <= (-5d-290)) then
        tmp = t_3
    else if (z <= 1600000000.0d0) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = x + (y * t);
	double t_3 = x * (1.0 - y);
	double tmp;
	if (z <= -4.3e-13) {
		tmp = t_1;
	} else if (z <= -7.5e-75) {
		tmp = t_3;
	} else if (z <= -2.8e-128) {
		tmp = (y - z) * t;
	} else if (z <= -4.2e-228) {
		tmp = t_2;
	} else if (z <= -5e-290) {
		tmp = t_3;
	} else if (z <= 1600000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	t_2 = x + (y * t)
	t_3 = x * (1.0 - y)
	tmp = 0
	if z <= -4.3e-13:
		tmp = t_1
	elif z <= -7.5e-75:
		tmp = t_3
	elif z <= -2.8e-128:
		tmp = (y - z) * t
	elif z <= -4.2e-228:
		tmp = t_2
	elif z <= -5e-290:
		tmp = t_3
	elif z <= 1600000000.0:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	t_2 = Float64(x + Float64(y * t))
	t_3 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (z <= -4.3e-13)
		tmp = t_1;
	elseif (z <= -7.5e-75)
		tmp = t_3;
	elseif (z <= -2.8e-128)
		tmp = Float64(Float64(y - z) * t);
	elseif (z <= -4.2e-228)
		tmp = t_2;
	elseif (z <= -5e-290)
		tmp = t_3;
	elseif (z <= 1600000000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	t_2 = x + (y * t);
	t_3 = x * (1.0 - y);
	tmp = 0.0;
	if (z <= -4.3e-13)
		tmp = t_1;
	elseif (z <= -7.5e-75)
		tmp = t_3;
	elseif (z <= -2.8e-128)
		tmp = (y - z) * t;
	elseif (z <= -4.2e-228)
		tmp = t_2;
	elseif (z <= -5e-290)
		tmp = t_3;
	elseif (z <= 1600000000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.3e-13], t$95$1, If[LessEqual[z, -7.5e-75], t$95$3, If[LessEqual[z, -2.8e-128], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[z, -4.2e-228], t$95$2, If[LessEqual[z, -5e-290], t$95$3, If[LessEqual[z, 1600000000.0], t$95$2, t$95$1]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.2999999999999999e-13 or 1.6e9 < z

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around 0 82.8%

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

      1. +-commutative 82.8%

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

      2. mul-1-neg 82.8%

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

      3. unsub-neg 82.8%

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

      4. *-commutative 82.8%

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

   4. Simplified 82.8%

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

   5. Taylor expanded in z around inf 82.6%

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

   if -4.2999999999999999e-13 < z < -7.50000000000000017e-75 or -4.19999999999999982e-228 < z < -5.0000000000000001e-290

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in z around 0 96.5%

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

   3. Taylor expanded in t around 0 84.0%

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

      1. *-lft-identity 84.0%

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

      2. associate-*r* 84.0%

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

      3. distribute-rgt-in 84.0%

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

      4. mul-1-neg 84.0%

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

      5. unsub-neg 84.0%

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

   5. Simplified 84.0%

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

   if -7.50000000000000017e-75 < z < -2.7999999999999998e-128

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around 0 78.1%

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

   if -2.7999999999999998e-128 < z < -4.19999999999999982e-228 or -5.0000000000000001e-290 < z < 1.6e9

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around -inf 98.8%

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

      1. +-commutative 98.8%

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

      2. mul-1-neg 98.8%

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

      3. unsub-neg 98.8%

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

      4. *-commutative 98.8%

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

      5. +-commutative 98.8%

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

   4. Simplified 98.8%

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

   5. Taylor expanded in z around 0 89.4%

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

   6. Taylor expanded in y around 0 72.1%

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

      1. neg-mul-1 72.1%

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

   8. Simplified 72.1%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-13}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-75}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-128}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-228}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-290}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 1600000000:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 6: 70.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -5.6 \cdot 10^{-7}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-290}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-241}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-122}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))) (t_2 (* y (- t x))))
   (if (<= y -5.6e-7)
     t_2
     (if (<= y 5.4e-290)
       (- x (* z t))
       (if (<= y 4.1e-241)
         t_1
         (if (<= y 3.2e-122) (+ x (* z x)) (if (<= y 6e-11) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = y * (t - x);
	double tmp;
	if (y <= -5.6e-7) {
		tmp = t_2;
	} else if (y <= 5.4e-290) {
		tmp = x - (z * t);
	} else if (y <= 4.1e-241) {
		tmp = t_1;
	} else if (y <= 3.2e-122) {
		tmp = x + (z * x);
	} else if (y <= 6e-11) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (x - t)
    t_2 = y * (t - x)
    if (y <= (-5.6d-7)) then
        tmp = t_2
    else if (y <= 5.4d-290) then
        tmp = x - (z * t)
    else if (y <= 4.1d-241) then
        tmp = t_1
    else if (y <= 3.2d-122) then
        tmp = x + (z * x)
    else if (y <= 6d-11) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = y * (t - x);
	double tmp;
	if (y <= -5.6e-7) {
		tmp = t_2;
	} else if (y <= 5.4e-290) {
		tmp = x - (z * t);
	} else if (y <= 4.1e-241) {
		tmp = t_1;
	} else if (y <= 3.2e-122) {
		tmp = x + (z * x);
	} else if (y <= 6e-11) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	t_2 = y * (t - x)
	tmp = 0
	if y <= -5.6e-7:
		tmp = t_2
	elif y <= 5.4e-290:
		tmp = x - (z * t)
	elif y <= 4.1e-241:
		tmp = t_1
	elif y <= 3.2e-122:
		tmp = x + (z * x)
	elif y <= 6e-11:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	t_2 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (y <= -5.6e-7)
		tmp = t_2;
	elseif (y <= 5.4e-290)
		tmp = Float64(x - Float64(z * t));
	elseif (y <= 4.1e-241)
		tmp = t_1;
	elseif (y <= 3.2e-122)
		tmp = Float64(x + Float64(z * x));
	elseif (y <= 6e-11)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	t_2 = y * (t - x);
	tmp = 0.0;
	if (y <= -5.6e-7)
		tmp = t_2;
	elseif (y <= 5.4e-290)
		tmp = x - (z * t);
	elseif (y <= 4.1e-241)
		tmp = t_1;
	elseif (y <= 3.2e-122)
		tmp = x + (z * x);
	elseif (y <= 6e-11)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.6e-7], t$95$2, If[LessEqual[y, 5.4e-290], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e-241], t$95$1, If[LessEqual[y, 3.2e-122], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e-11], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.60000000000000038e-7 or 6e-11 < y

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around inf 75.9%

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

   if -5.60000000000000038e-7 < y < 5.39999999999999997e-290

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around 0 91.0%

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

      1. +-commutative 91.0%

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

      2. mul-1-neg 91.0%

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

      3. unsub-neg 91.0%

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

      4. *-commutative 91.0%

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

   4. Simplified 91.0%

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

   5. Taylor expanded in t around inf 74.9%

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

   if 5.39999999999999997e-290 < y < 4.0999999999999999e-241 or 3.2000000000000002e-122 < y < 6e-11

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around 0 94.3%

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

      1. +-commutative 94.3%

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

      2. mul-1-neg 94.3%

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

      3. unsub-neg 94.3%

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

      4. *-commutative 94.3%

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

   4. Simplified 94.3%

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

   5. Taylor expanded in z around inf 88.8%

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

   if 4.0999999999999999e-241 < y < 3.2000000000000002e-122

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around inf 76.4%

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

      1. sub-neg 76.4%

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

      2. neg-mul-1 76.4%

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

      3. remove-double-neg 76.4%

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

      4. *-commutative 76.4%

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

      5. distribute-lft-in 76.5%

         \[\leadsto \color{blue}{x \cdot 1 + x \cdot z} \]

      6. *-rgt-identity 76.5%

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

   7. Simplified 76.5%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-290}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-241}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-122}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-11}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 7: 38.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+76}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+39}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq -5.5:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3400000000:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5e+76)
   (* z x)
   (if (<= z -2.4e+39)
     (* y t)
     (if (<= z -5.5)
       (* z x)
       (if (<= z -6.4e-75) x (if (<= z 3400000000.0) (* y t) (* z x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5e+76) {
		tmp = z * x;
	} else if (z <= -2.4e+39) {
		tmp = y * t;
	} else if (z <= -5.5) {
		tmp = z * x;
	} else if (z <= -6.4e-75) {
		tmp = x;
	} else if (z <= 3400000000.0) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-5d+76)) then
        tmp = z * x
    else if (z <= (-2.4d+39)) then
        tmp = y * t
    else if (z <= (-5.5d0)) then
        tmp = z * x
    else if (z <= (-6.4d-75)) then
        tmp = x
    else if (z <= 3400000000.0d0) then
        tmp = y * t
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5e+76) {
		tmp = z * x;
	} else if (z <= -2.4e+39) {
		tmp = y * t;
	} else if (z <= -5.5) {
		tmp = z * x;
	} else if (z <= -6.4e-75) {
		tmp = x;
	} else if (z <= 3400000000.0) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5e+76:
		tmp = z * x
	elif z <= -2.4e+39:
		tmp = y * t
	elif z <= -5.5:
		tmp = z * x
	elif z <= -6.4e-75:
		tmp = x
	elif z <= 3400000000.0:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5e+76)
		tmp = Float64(z * x);
	elseif (z <= -2.4e+39)
		tmp = Float64(y * t);
	elseif (z <= -5.5)
		tmp = Float64(z * x);
	elseif (z <= -6.4e-75)
		tmp = x;
	elseif (z <= 3400000000.0)
		tmp = Float64(y * t);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5e+76)
		tmp = z * x;
	elseif (z <= -2.4e+39)
		tmp = y * t;
	elseif (z <= -5.5)
		tmp = z * x;
	elseif (z <= -6.4e-75)
		tmp = x;
	elseif (z <= 3400000000.0)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5e+76], N[(z * x), $MachinePrecision], If[LessEqual[z, -2.4e+39], N[(y * t), $MachinePrecision], If[LessEqual[z, -5.5], N[(z * x), $MachinePrecision], If[LessEqual[z, -6.4e-75], x, If[LessEqual[z, 3400000000.0], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.99999999999999991e76 or -2.4000000000000001e39 < z < -5.5 or 3.4e9 < z

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in z around inf 88.0%

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

      1. mul-1-neg 88.0%

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

      2. distribute-lft-neg-out 88.0%

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

      3. *-commutative 88.0%

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

   4. Simplified 88.0%

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

   5. Taylor expanded in t around 0 44.9%

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

   if -4.99999999999999991e76 < z < -2.4000000000000001e39 or -6.39999999999999953e-75 < z < 3.4e9

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around 0 52.0%

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

   3. Taylor expanded in y around inf 43.5%

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

   if -5.5 < z < -6.39999999999999953e-75

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in z around 0 84.4%

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

   3. Taylor expanded in y around 0 34.9%

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

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+76}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+39}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq -5.5:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3400000000:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 8: 39.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+75}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+34}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq -175:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-75}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 750000000:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.6e+75)
   (* z x)
   (if (<= z -3.1e+34)
     (* y t)
     (if (<= z -175.0)
       (* z x)
       (if (<= z -8.8e-75)
         (* y (- x))
         (if (<= z 750000000.0) (* y t) (* z x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e+75) {
		tmp = z * x;
	} else if (z <= -3.1e+34) {
		tmp = y * t;
	} else if (z <= -175.0) {
		tmp = z * x;
	} else if (z <= -8.8e-75) {
		tmp = y * -x;
	} else if (z <= 750000000.0) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.6d+75)) then
        tmp = z * x
    else if (z <= (-3.1d+34)) then
        tmp = y * t
    else if (z <= (-175.0d0)) then
        tmp = z * x
    else if (z <= (-8.8d-75)) then
        tmp = y * -x
    else if (z <= 750000000.0d0) then
        tmp = y * t
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e+75) {
		tmp = z * x;
	} else if (z <= -3.1e+34) {
		tmp = y * t;
	} else if (z <= -175.0) {
		tmp = z * x;
	} else if (z <= -8.8e-75) {
		tmp = y * -x;
	} else if (z <= 750000000.0) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.6e+75:
		tmp = z * x
	elif z <= -3.1e+34:
		tmp = y * t
	elif z <= -175.0:
		tmp = z * x
	elif z <= -8.8e-75:
		tmp = y * -x
	elif z <= 750000000.0:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.6e+75)
		tmp = Float64(z * x);
	elseif (z <= -3.1e+34)
		tmp = Float64(y * t);
	elseif (z <= -175.0)
		tmp = Float64(z * x);
	elseif (z <= -8.8e-75)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 750000000.0)
		tmp = Float64(y * t);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.6e+75)
		tmp = z * x;
	elseif (z <= -3.1e+34)
		tmp = y * t;
	elseif (z <= -175.0)
		tmp = z * x;
	elseif (z <= -8.8e-75)
		tmp = y * -x;
	elseif (z <= 750000000.0)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.6e+75], N[(z * x), $MachinePrecision], If[LessEqual[z, -3.1e+34], N[(y * t), $MachinePrecision], If[LessEqual[z, -175.0], N[(z * x), $MachinePrecision], If[LessEqual[z, -8.8e-75], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 750000000.0], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.59999999999999992e75 or -3.09999999999999977e34 < z < -175 or 7.5e8 < z

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in z around inf 88.0%

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

      1. mul-1-neg 88.0%

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

      2. distribute-lft-neg-out 88.0%

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

      3. *-commutative 88.0%

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

   4. Simplified 88.0%

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

   5. Taylor expanded in t around 0 44.9%

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

   if -1.59999999999999992e75 < z < -3.09999999999999977e34 or -8.80000000000000022e-75 < z < 7.5e8

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around 0 52.0%

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

   3. Taylor expanded in y around inf 43.5%

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

   if -175 < z < -8.80000000000000022e-75

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around inf 50.1%

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

   3. Taylor expanded in t around 0 36.3%

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

      1. mul-1-neg 36.3%

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

      2. distribute-rgt-neg-out 36.3%

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

   5. Simplified 36.3%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+75}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+34}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq -175:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-75}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 750000000:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 9: 68.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := z \cdot \left(x - t\right)\\ \mathbf{if}\;y \leq -1.02 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-238}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-124}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-11}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* z (- x t))))
   (if (<= y -1.02e+27)
     t_1
     (if (<= y 4.5e-238)
       t_2
       (if (<= y 3.5e-124) (+ x (* z x)) (if (<= y 7.8e-11) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = z * (x - t);
	double tmp;
	if (y <= -1.02e+27) {
		tmp = t_1;
	} else if (y <= 4.5e-238) {
		tmp = t_2;
	} else if (y <= 3.5e-124) {
		tmp = x + (z * x);
	} else if (y <= 7.8e-11) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (t - x)
    t_2 = z * (x - t)
    if (y <= (-1.02d+27)) then
        tmp = t_1
    else if (y <= 4.5d-238) then
        tmp = t_2
    else if (y <= 3.5d-124) then
        tmp = x + (z * x)
    else if (y <= 7.8d-11) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = z * (x - t);
	double tmp;
	if (y <= -1.02e+27) {
		tmp = t_1;
	} else if (y <= 4.5e-238) {
		tmp = t_2;
	} else if (y <= 3.5e-124) {
		tmp = x + (z * x);
	} else if (y <= 7.8e-11) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = z * (x - t)
	tmp = 0
	if y <= -1.02e+27:
		tmp = t_1
	elif y <= 4.5e-238:
		tmp = t_2
	elif y <= 3.5e-124:
		tmp = x + (z * x)
	elif y <= 7.8e-11:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (y <= -1.02e+27)
		tmp = t_1;
	elseif (y <= 4.5e-238)
		tmp = t_2;
	elseif (y <= 3.5e-124)
		tmp = Float64(x + Float64(z * x));
	elseif (y <= 7.8e-11)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	t_2 = z * (x - t);
	tmp = 0.0;
	if (y <= -1.02e+27)
		tmp = t_1;
	elseif (y <= 4.5e-238)
		tmp = t_2;
	elseif (y <= 3.5e-124)
		tmp = x + (z * x);
	elseif (y <= 7.8e-11)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.02e+27], t$95$1, If[LessEqual[y, 4.5e-238], t$95$2, If[LessEqual[y, 3.5e-124], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.8e-11], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.0199999999999999e27 or 7.80000000000000021e-11 < y

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around inf 79.0%

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

   if -1.0199999999999999e27 < y < 4.49999999999999996e-238 or 3.4999999999999999e-124 < y < 7.80000000000000021e-11

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around 0 89.8%

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

      1. +-commutative 89.8%

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

      2. mul-1-neg 89.8%

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

      3. unsub-neg 89.8%

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

      4. *-commutative 89.8%

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

   4. Simplified 89.8%

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

   5. Taylor expanded in z around inf 67.2%

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

   if 4.49999999999999996e-238 < y < 3.4999999999999999e-124

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around inf 78.7%

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

      1. sub-neg 78.7%

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

      2. neg-mul-1 78.7%

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

      3. remove-double-neg 78.7%

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

      4. *-commutative 78.7%

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

      5. distribute-lft-in 78.7%

         \[\leadsto \color{blue}{x \cdot 1 + x \cdot z} \]

      6. *-rgt-identity 78.7%

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

   7. Simplified 78.7%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+27}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-238}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-124}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-11}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 10: 83.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-12} \lor \neg \left(z \leq 20000000\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.8e-12) (not (<= z 20000000.0)))
   (* z (- x t))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.8e-12) || !(z <= 20000000.0)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.8d-12)) .or. (.not. (z <= 20000000.0d0))) then
        tmp = z * (x - t)
    else
        tmp = x + (y * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.8e-12) || !(z <= 20000000.0)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.8e-12) or not (z <= 20000000.0):
		tmp = z * (x - t)
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.8e-12) || !(z <= 20000000.0))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x + Float64(y * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.8e-12) || ~((z <= 20000000.0)))
		tmp = z * (x - t);
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.8e-12], N[Not[LessEqual[z, 20000000.0]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.79999999999999996e-12 or 2e7 < z

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around 0 83.4%

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

      1. +-commutative 83.4%

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

      2. mul-1-neg 83.4%

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

      3. unsub-neg 83.4%

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

      4. *-commutative 83.4%

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

   4. Simplified 83.4%

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

   5. Taylor expanded in z around inf 83.2%

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

   if -3.79999999999999996e-12 < z < 2e7

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in z around 0 91.1%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-12} \lor \neg \left(z \leq 20000000\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 11: 84.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-17} \lor \neg \left(y \leq 3.1 \cdot 10^{-11}\right):\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -9.5e-17) (not (<= y 3.1e-11)))
   (+ x (* y (- t x)))
   (+ x (* z (- x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9.5e-17) || !(y <= 3.1e-11)) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + (z * (x - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-9.5d-17)) .or. (.not. (y <= 3.1d-11))) then
        tmp = x + (y * (t - x))
    else
        tmp = x + (z * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9.5e-17) || !(y <= 3.1e-11)) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + (z * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -9.5e-17) or not (y <= 3.1e-11):
		tmp = x + (y * (t - x))
	else:
		tmp = x + (z * (x - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -9.5e-17) || !(y <= 3.1e-11))
		tmp = Float64(x + Float64(y * Float64(t - x)));
	else
		tmp = Float64(x + Float64(z * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -9.5e-17) || ~((y <= 3.1e-11)))
		tmp = x + (y * (t - x));
	else
		tmp = x + (z * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -9.5e-17], N[Not[LessEqual[y, 3.1e-11]], $MachinePrecision]], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.50000000000000029e-17 or 3.10000000000000028e-11 < y

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in z around 0 79.7%

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

   if -9.50000000000000029e-17 < y < 3.10000000000000028e-11

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around 0 94.8%

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

      1. +-commutative 94.8%

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

      2. mul-1-neg 94.8%

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

      3. unsub-neg 94.8%

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

      4. *-commutative 94.8%

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

   4. Simplified 94.8%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-17} \lor \neg \left(y \leq 3.1 \cdot 10^{-11}\right):\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 12: 61.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{-103} \lor \neg \left(t \leq 2.05 \cdot 10^{+15}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4.3e-103) (not (<= t 2.05e+15)))
   (* (- y z) t)
   (* x (- 1.0 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.3e-103) || !(t <= 2.05e+15)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-4.3d-103)) .or. (.not. (t <= 2.05d+15))) then
        tmp = (y - z) * t
    else
        tmp = x * (1.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.3e-103) || !(t <= 2.05e+15)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -4.3e-103) or not (t <= 2.05e+15):
		tmp = (y - z) * t
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -4.3e-103) || !(t <= 2.05e+15))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = Float64(x * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -4.3e-103) || ~((t <= 2.05e+15)))
		tmp = (y - z) * t;
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -4.3e-103], N[Not[LessEqual[t, 2.05e+15]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.30000000000000023e-103 or 2.05e15 < t

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around 0 67.9%

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

   if -4.30000000000000023e-103 < t < 2.05e15

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in z around 0 58.3%

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

   3. Taylor expanded in t around 0 54.2%

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

      1. *-lft-identity 54.2%

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

      2. associate-*r* 54.2%

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

      3. distribute-rgt-in 54.2%

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

      4. mul-1-neg 54.2%

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

      5. unsub-neg 54.2%

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

   5. Simplified 54.2%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{-103} \lor \neg \left(t \leq 2.05 \cdot 10^{+15}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]

Alternative 13: 68.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+24} \lor \neg \left(y \leq 7.8 \cdot 10^{-11}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -8.5e+24) (not (<= y 7.8e-11))) (* y (- t x)) (* z (- x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8.5e+24) || !(y <= 7.8e-11)) {
		tmp = y * (t - x);
	} else {
		tmp = z * (x - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-8.5d+24)) .or. (.not. (y <= 7.8d-11))) then
        tmp = y * (t - x)
    else
        tmp = z * (x - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8.5e+24) || !(y <= 7.8e-11)) {
		tmp = y * (t - x);
	} else {
		tmp = z * (x - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -8.5e+24) or not (y <= 7.8e-11):
		tmp = y * (t - x)
	else:
		tmp = z * (x - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -8.5e+24) || !(y <= 7.8e-11))
		tmp = Float64(y * Float64(t - x));
	else
		tmp = Float64(z * Float64(x - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -8.5e+24) || ~((y <= 7.8e-11)))
		tmp = y * (t - x);
	else
		tmp = z * (x - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -8.5e+24], N[Not[LessEqual[y, 7.8e-11]], $MachinePrecision]], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.49999999999999959e24 or 7.80000000000000021e-11 < y

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around inf 79.0%

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

   if -8.49999999999999959e24 < y < 7.80000000000000021e-11

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around 0 91.4%

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

      1. +-commutative 91.4%

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

      2. mul-1-neg 91.4%

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

      3. unsub-neg 91.4%

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

      4. *-commutative 91.4%

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

   4. Simplified 91.4%

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

   5. Taylor expanded in z around inf 65.0%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+24} \lor \neg \left(y \leq 7.8 \cdot 10^{-11}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 14: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \left(y - z\right) \cdot \left(t - x\right) \]

2. Final simplification 100.0%

   \[\leadsto x + \left(y - z\right) \cdot \left(t - x\right) \]

Alternative 15: 36.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-55}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-111}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.7e-55) (* y t) (if (<= y 2.4e-111) x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.7e-55) {
		tmp = y * t;
	} else if (y <= 2.4e-111) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.7d-55)) then
        tmp = y * t
    else if (y <= 2.4d-111) then
        tmp = x
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.7e-55) {
		tmp = y * t;
	} else if (y <= 2.4e-111) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.7e-55:
		tmp = y * t
	elif y <= 2.4e-111:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.7e-55)
		tmp = Float64(y * t);
	elseif (y <= 2.4e-111)
		tmp = x;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.7e-55)
		tmp = y * t;
	elseif (y <= 2.4e-111)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.7e-55], N[(y * t), $MachinePrecision], If[LessEqual[y, 2.4e-111], x, N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.70000000000000004e-55 or 2.4000000000000001e-111 < y

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around 0 54.2%

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

   3. Taylor expanded in y around inf 38.3%

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

   if -2.70000000000000004e-55 < y < 2.4000000000000001e-111

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in z around 0 37.5%

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

   3. Taylor expanded in y around 0 35.3%

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

4. Final simplification 37.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-55}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-111}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 16: 18.1% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 100.0%

   \[x + \left(y - z\right) \cdot \left(t - x\right) \]

2. Taylor expanded in z around 0 56.5%

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

3. Taylor expanded in y around 0 17.2%

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

4. Final simplification 17.2%

   \[\leadsto x \]

Developer target: 96.3% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023171 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

  :herbie-target
  (+ x (+ (* t (- y z)) (* (- x) (- y z))))

  (+ x (* (- y z) (- t x))))