Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 7.7s

Alternatives: 15

Speedup: 1.0×

• 34.8% 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: 53.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;y - z \leq -4 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y - z \leq 10^{-78}:\\ \;\;\;\;x\\ \mathbf{elif}\;y - z \leq 4 \cdot 10^{+222}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y - z \leq 4 \cdot 10^{+248}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y - z \leq 5 \cdot 10^{+279}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= (- y z) -4e-11)
     t_1
     (if (<= (- y z) 1e-78)
       x
       (if (<= (- y z) 4e+222)
         t_1
         (if (<= (- y z) 4e+248)
           (* y (- x))
           (if (<= (- y z) 5e+279) 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) <= -4e-11) {
		tmp = t_1;
	} else if ((y - z) <= 1e-78) {
		tmp = x;
	} else if ((y - z) <= 4e+222) {
		tmp = t_1;
	} else if ((y - z) <= 4e+248) {
		tmp = y * -x;
	} else if ((y - z) <= 5e+279) {
		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) <= (-4d-11)) then
        tmp = t_1
    else if ((y - z) <= 1d-78) then
        tmp = x
    else if ((y - z) <= 4d+222) then
        tmp = t_1
    else if ((y - z) <= 4d+248) then
        tmp = y * -x
    else if ((y - z) <= 5d+279) 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) <= -4e-11) {
		tmp = t_1;
	} else if ((y - z) <= 1e-78) {
		tmp = x;
	} else if ((y - z) <= 4e+222) {
		tmp = t_1;
	} else if ((y - z) <= 4e+248) {
		tmp = y * -x;
	} else if ((y - z) <= 5e+279) {
		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) <= -4e-11:
		tmp = t_1
	elif (y - z) <= 1e-78:
		tmp = x
	elif (y - z) <= 4e+222:
		tmp = t_1
	elif (y - z) <= 4e+248:
		tmp = y * -x
	elif (y - z) <= 5e+279:
		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) <= -4e-11)
		tmp = t_1;
	elseif (Float64(y - z) <= 1e-78)
		tmp = x;
	elseif (Float64(y - z) <= 4e+222)
		tmp = t_1;
	elseif (Float64(y - z) <= 4e+248)
		tmp = Float64(y * Float64(-x));
	elseif (Float64(y - z) <= 5e+279)
		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) <= -4e-11)
		tmp = t_1;
	elseif ((y - z) <= 1e-78)
		tmp = x;
	elseif ((y - z) <= 4e+222)
		tmp = t_1;
	elseif ((y - z) <= 4e+248)
		tmp = y * -x;
	elseif ((y - z) <= 5e+279)
		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], -4e-11], t$95$1, If[LessEqual[N[(y - z), $MachinePrecision], 1e-78], x, If[LessEqual[N[(y - z), $MachinePrecision], 4e+222], t$95$1, If[LessEqual[N[(y - z), $MachinePrecision], 4e+248], N[(y * (-x)), $MachinePrecision], If[LessEqual[N[(y - z), $MachinePrecision], 5e+279], t$95$1, N[(z * x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 y z) < -3.99999999999999976e-11 or 9.99999999999999999e-79 < (-.f64 y z) < 4.0000000000000002e222 or 4.00000000000000018e248 < (-.f64 y z) < 5.0000000000000002e279

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 95.8%

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

      1. +-commutative 95.8%

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

      2. mul-1-neg 95.8%

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

      3. unsub-neg 95.8%

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

      4. sub-neg 95.8%

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

      5. +-commutative 95.8%

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

      6. distribute-neg-in 95.8%

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

      7. metadata-eval 95.8%

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

      8. associate-+l+ 95.8%

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

      9. +-commutative 95.8%

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

      10. sub-neg 95.8%

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

   4. Simplified 95.8%

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

   5. Taylor expanded in t around inf 58.5%

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

   if -3.99999999999999976e-11 < (-.f64 y z) < 9.99999999999999999e-79

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 83.4%

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

      1. mul-1-neg 83.4%

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

      2. *-commutative 83.4%

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

      3. distribute-rgt-neg-in 83.4%

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

      4. +-commutative 83.4%

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

   4. Simplified 83.4%

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

   5. Taylor expanded in y around 0 83.4%

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

   6. Taylor expanded in z around 0 83.3%

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

   if 4.0000000000000002e222 < (-.f64 y z) < 4.00000000000000018e248

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. *-commutative 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

      4. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around inf 74.1%

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

   if 5.0000000000000002e279 < (-.f64 y z)

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 84.9%

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

      1. mul-1-neg 84.9%

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

      2. unsub-neg 84.9%

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

      3. distribute-lft-out-- 84.9%

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

      4. *-rgt-identity 84.9%

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

   4. Simplified 84.9%

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

   5. Taylor expanded in z around inf 61.9%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y - z \leq -4 \cdot 10^{-11}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y - z \leq 10^{-78}:\\ \;\;\;\;x\\ \mathbf{elif}\;y - z \leq 4 \cdot 10^{+222}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y - z \leq 4 \cdot 10^{+248}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y - z \leq 5 \cdot 10^{+279}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 3: 69.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z + 1\right)\\ t_2 := y \cdot \left(t - x\right)\\ t_3 := x - z \cdot t\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-209}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-296}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-192}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ z 1.0))) (t_2 (* y (- t x))) (t_3 (- x (* z t))))
   (if (<= y -1.8e+42)
     t_2
     (if (<= y -1e-209)
       t_3
       (if (<= y 2.7e-296)
         t_1
         (if (<= y 1.6e-192) t_3 (if (<= y 2.1e-10) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z + 1.0);
	double t_2 = y * (t - x);
	double t_3 = x - (z * t);
	double tmp;
	if (y <= -1.8e+42) {
		tmp = t_2;
	} else if (y <= -1e-209) {
		tmp = t_3;
	} else if (y <= 2.7e-296) {
		tmp = t_1;
	} else if (y <= 1.6e-192) {
		tmp = t_3;
	} else if (y <= 2.1e-10) {
		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) :: t_3
    real(8) :: tmp
    t_1 = x * (z + 1.0d0)
    t_2 = y * (t - x)
    t_3 = x - (z * t)
    if (y <= (-1.8d+42)) then
        tmp = t_2
    else if (y <= (-1d-209)) then
        tmp = t_3
    else if (y <= 2.7d-296) then
        tmp = t_1
    else if (y <= 1.6d-192) then
        tmp = t_3
    else if (y <= 2.1d-10) 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 = x * (z + 1.0);
	double t_2 = y * (t - x);
	double t_3 = x - (z * t);
	double tmp;
	if (y <= -1.8e+42) {
		tmp = t_2;
	} else if (y <= -1e-209) {
		tmp = t_3;
	} else if (y <= 2.7e-296) {
		tmp = t_1;
	} else if (y <= 1.6e-192) {
		tmp = t_3;
	} else if (y <= 2.1e-10) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z + 1.0)
	t_2 = y * (t - x)
	t_3 = x - (z * t)
	tmp = 0
	if y <= -1.8e+42:
		tmp = t_2
	elif y <= -1e-209:
		tmp = t_3
	elif y <= 2.7e-296:
		tmp = t_1
	elif y <= 1.6e-192:
		tmp = t_3
	elif y <= 2.1e-10:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z + 1.0))
	t_2 = Float64(y * Float64(t - x))
	t_3 = Float64(x - Float64(z * t))
	tmp = 0.0
	if (y <= -1.8e+42)
		tmp = t_2;
	elseif (y <= -1e-209)
		tmp = t_3;
	elseif (y <= 2.7e-296)
		tmp = t_1;
	elseif (y <= 1.6e-192)
		tmp = t_3;
	elseif (y <= 2.1e-10)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z + 1.0);
	t_2 = y * (t - x);
	t_3 = x - (z * t);
	tmp = 0.0;
	if (y <= -1.8e+42)
		tmp = t_2;
	elseif (y <= -1e-209)
		tmp = t_3;
	elseif (y <= 2.7e-296)
		tmp = t_1;
	elseif (y <= 1.6e-192)
		tmp = t_3;
	elseif (y <= 2.1e-10)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.8e+42], t$95$2, If[LessEqual[y, -1e-209], t$95$3, If[LessEqual[y, 2.7e-296], t$95$1, If[LessEqual[y, 1.6e-192], t$95$3, If[LessEqual[y, 2.1e-10], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8e42 or 2.1e-10 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 93.9%

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

      1. +-commutative 93.9%

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

      2. mul-1-neg 93.9%

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

      3. unsub-neg 93.9%

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

      4. sub-neg 93.9%

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

      5. +-commutative 93.9%

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

      6. distribute-neg-in 93.9%

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

      7. metadata-eval 93.9%

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

      8. associate-+l+ 93.9%

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

      9. +-commutative 93.9%

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

      10. sub-neg 93.9%

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

   4. Simplified 93.9%

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

   5. Taylor expanded in y around inf 86.6%

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

   if -1.8e42 < y < -1e-209 or 2.69999999999999999e-296 < y < 1.6000000000000001e-192

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 81.3%

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

   3. Taylor expanded in y around 0 79.5%

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

      1. mul-1-neg 79.5%

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

      2. *-commutative 79.5%

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

      3. distribute-rgt-neg-in 79.5%

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

   5. Simplified 79.5%

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

   if -1e-209 < y < 2.69999999999999999e-296 or 1.6000000000000001e-192 < y < 2.1e-10

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 71.9%

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

      1. mul-1-neg 71.9%

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

      2. *-commutative 71.9%

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

      3. distribute-rgt-neg-in 71.9%

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

      4. +-commutative 71.9%

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

   4. Simplified 71.9%

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

   5. Taylor expanded in y around 0 71.6%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-209}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-296}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-192}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 4: 76.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x + \left(y - z\right) \cdot t\\ \mathbf{if}\;y \leq -2 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-208}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-296}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+24}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (+ x (* (- y z) t))))
   (if (<= y -2e+42)
     t_1
     (if (<= y -1.2e-208)
       t_2
       (if (<= y 8.6e-296) (* x (+ z 1.0)) (if (<= y 2.25e+24) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = x + ((y - z) * t);
	double tmp;
	if (y <= -2e+42) {
		tmp = t_1;
	} else if (y <= -1.2e-208) {
		tmp = t_2;
	} else if (y <= 8.6e-296) {
		tmp = x * (z + 1.0);
	} else if (y <= 2.25e+24) {
		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 = x + ((y - z) * t)
    if (y <= (-2d+42)) then
        tmp = t_1
    else if (y <= (-1.2d-208)) then
        tmp = t_2
    else if (y <= 8.6d-296) then
        tmp = x * (z + 1.0d0)
    else if (y <= 2.25d+24) 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 = x + ((y - z) * t);
	double tmp;
	if (y <= -2e+42) {
		tmp = t_1;
	} else if (y <= -1.2e-208) {
		tmp = t_2;
	} else if (y <= 8.6e-296) {
		tmp = x * (z + 1.0);
	} else if (y <= 2.25e+24) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = x + ((y - z) * t)
	tmp = 0
	if y <= -2e+42:
		tmp = t_1
	elif y <= -1.2e-208:
		tmp = t_2
	elif y <= 8.6e-296:
		tmp = x * (z + 1.0)
	elif y <= 2.25e+24:
		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(x + Float64(Float64(y - z) * t))
	tmp = 0.0
	if (y <= -2e+42)
		tmp = t_1;
	elseif (y <= -1.2e-208)
		tmp = t_2;
	elseif (y <= 8.6e-296)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (y <= 2.25e+24)
		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 = x + ((y - z) * t);
	tmp = 0.0;
	if (y <= -2e+42)
		tmp = t_1;
	elseif (y <= -1.2e-208)
		tmp = t_2;
	elseif (y <= 8.6e-296)
		tmp = x * (z + 1.0);
	elseif (y <= 2.25e+24)
		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[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e+42], t$95$1, If[LessEqual[y, -1.2e-208], t$95$2, If[LessEqual[y, 8.6e-296], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.25e+24], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.00000000000000009e42 or 2.2500000000000001e24 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 93.5%

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

      1. +-commutative 93.5%

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

      2. mul-1-neg 93.5%

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

      3. unsub-neg 93.5%

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

      4. sub-neg 93.5%

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

      5. +-commutative 93.5%

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

      6. distribute-neg-in 93.5%

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

      7. metadata-eval 93.5%

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

      8. associate-+l+ 93.5%

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

      9. +-commutative 93.5%

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

      10. sub-neg 93.5%

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

   4. Simplified 93.5%

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

   5. Taylor expanded in y around inf 88.9%

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

   if -2.00000000000000009e42 < y < -1.1999999999999999e-208 or 8.59999999999999956e-296 < y < 2.2500000000000001e24

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 76.1%

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

   if -1.1999999999999999e-208 < y < 8.59999999999999956e-296

   1. Initial program 99.9%

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

   2. Taylor expanded in x around -inf 83.8%

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

      1. mul-1-neg 83.8%

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

      2. *-commutative 83.8%

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

      3. distribute-rgt-neg-in 83.8%

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

      4. +-commutative 83.8%

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

   4. Simplified 83.8%

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

   5. Taylor expanded in y around 0 83.8%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-208}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-296}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+24}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 5: 76.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot t\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-209}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-295}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) t))))
   (if (<= y -2.1e+42)
     (* y (- t x))
     (if (<= y -2.05e-209)
       t_1
       (if (<= y 3.1e-295)
         (* x (+ z 1.0))
         (if (<= y 1.9e-13) t_1 (- x (* y (- x t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y - z) * t);
	double tmp;
	if (y <= -2.1e+42) {
		tmp = y * (t - x);
	} else if (y <= -2.05e-209) {
		tmp = t_1;
	} else if (y <= 3.1e-295) {
		tmp = x * (z + 1.0);
	} else if (y <= 1.9e-13) {
		tmp = t_1;
	} else {
		tmp = x - (y * (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) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * t)
    if (y <= (-2.1d+42)) then
        tmp = y * (t - x)
    else if (y <= (-2.05d-209)) then
        tmp = t_1
    else if (y <= 3.1d-295) then
        tmp = x * (z + 1.0d0)
    else if (y <= 1.9d-13) then
        tmp = t_1
    else
        tmp = x - (y * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((y - z) * t);
	double tmp;
	if (y <= -2.1e+42) {
		tmp = y * (t - x);
	} else if (y <= -2.05e-209) {
		tmp = t_1;
	} else if (y <= 3.1e-295) {
		tmp = x * (z + 1.0);
	} else if (y <= 1.9e-13) {
		tmp = t_1;
	} else {
		tmp = x - (y * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y - z) * t)
	tmp = 0
	if y <= -2.1e+42:
		tmp = y * (t - x)
	elif y <= -2.05e-209:
		tmp = t_1
	elif y <= 3.1e-295:
		tmp = x * (z + 1.0)
	elif y <= 1.9e-13:
		tmp = t_1
	else:
		tmp = x - (y * (x - t))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y - z) * t))
	tmp = 0.0
	if (y <= -2.1e+42)
		tmp = Float64(y * Float64(t - x));
	elseif (y <= -2.05e-209)
		tmp = t_1;
	elseif (y <= 3.1e-295)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (y <= 1.9e-13)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(y * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y - z) * t);
	tmp = 0.0;
	if (y <= -2.1e+42)
		tmp = y * (t - x);
	elseif (y <= -2.05e-209)
		tmp = t_1;
	elseif (y <= 3.1e-295)
		tmp = x * (z + 1.0);
	elseif (y <= 1.9e-13)
		tmp = t_1;
	else
		tmp = x - (y * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.1e+42], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.05e-209], t$95$1, If[LessEqual[y, 3.1e-295], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e-13], t$95$1, N[(x - N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.09999999999999995e42

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 98.3%

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

      1. +-commutative 98.3%

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

      2. mul-1-neg 98.3%

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

      3. unsub-neg 98.3%

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

      4. sub-neg 98.3%

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

      5. +-commutative 98.3%

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

      6. distribute-neg-in 98.3%

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

      7. metadata-eval 98.3%

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

      8. associate-+l+ 98.3%

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

      9. +-commutative 98.3%

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

      10. sub-neg 98.3%

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

   4. Simplified 98.3%

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

   5. Taylor expanded in y around inf 85.8%

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

   if -2.09999999999999995e42 < y < -2.04999999999999989e-209 or 3.1000000000000002e-295 < y < 1.9e-13

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 77.1%

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

   if -2.04999999999999989e-209 < y < 3.1000000000000002e-295

   1. Initial program 99.9%

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

   2. Taylor expanded in x around -inf 83.8%

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

      1. mul-1-neg 83.8%

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

      2. *-commutative 83.8%

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

      3. distribute-rgt-neg-in 83.8%

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

      4. +-commutative 83.8%

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

   4. Simplified 83.8%

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

   5. Taylor expanded in y around 0 83.8%

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

   if 1.9e-13 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 88.7%

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

      1. *-commutative 88.7%

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

   4. Simplified 88.7%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-209}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-295}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-13}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \end{array} \]

Alternative 6: 80.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot t\\ t_2 := x + x \cdot \left(z - y\right)\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{+79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+64}:\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{+124}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) t))) (t_2 (+ x (* x (- z y)))))
   (if (<= x -2.8e+79)
     t_2
     (if (<= x 1.1e+19)
       t_1
       (if (<= x 5.6e+64) (- x (* y (- x t))) (if (<= x 6.4e+124) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y - z) * t);
	double t_2 = x + (x * (z - y));
	double tmp;
	if (x <= -2.8e+79) {
		tmp = t_2;
	} else if (x <= 1.1e+19) {
		tmp = t_1;
	} else if (x <= 5.6e+64) {
		tmp = x - (y * (x - t));
	} else if (x <= 6.4e+124) {
		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 = x + ((y - z) * t)
    t_2 = x + (x * (z - y))
    if (x <= (-2.8d+79)) then
        tmp = t_2
    else if (x <= 1.1d+19) then
        tmp = t_1
    else if (x <= 5.6d+64) then
        tmp = x - (y * (x - t))
    else if (x <= 6.4d+124) 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 = x + ((y - z) * t);
	double t_2 = x + (x * (z - y));
	double tmp;
	if (x <= -2.8e+79) {
		tmp = t_2;
	} else if (x <= 1.1e+19) {
		tmp = t_1;
	} else if (x <= 5.6e+64) {
		tmp = x - (y * (x - t));
	} else if (x <= 6.4e+124) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y - z) * t)
	t_2 = x + (x * (z - y))
	tmp = 0
	if x <= -2.8e+79:
		tmp = t_2
	elif x <= 1.1e+19:
		tmp = t_1
	elif x <= 5.6e+64:
		tmp = x - (y * (x - t))
	elif x <= 6.4e+124:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y - z) * t))
	t_2 = Float64(x + Float64(x * Float64(z - y)))
	tmp = 0.0
	if (x <= -2.8e+79)
		tmp = t_2;
	elseif (x <= 1.1e+19)
		tmp = t_1;
	elseif (x <= 5.6e+64)
		tmp = Float64(x - Float64(y * Float64(x - t)));
	elseif (x <= 6.4e+124)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y - z) * t);
	t_2 = x + (x * (z - y));
	tmp = 0.0;
	if (x <= -2.8e+79)
		tmp = t_2;
	elseif (x <= 1.1e+19)
		tmp = t_1;
	elseif (x <= 5.6e+64)
		tmp = x - (y * (x - t));
	elseif (x <= 6.4e+124)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.8e+79], t$95$2, If[LessEqual[x, 1.1e+19], t$95$1, If[LessEqual[x, 5.6e+64], N[(x - N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.4e+124], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.8000000000000001e79 or 6.39999999999999986e124 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 92.2%

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

      1. mul-1-neg 92.2%

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

      2. unsub-neg 92.2%

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

      3. distribute-lft-out-- 92.2%

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

      4. *-rgt-identity 92.2%

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

   4. Simplified 92.2%

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

   if -2.8000000000000001e79 < x < 1.1e19 or 5.60000000000000047e64 < x < 6.39999999999999986e124

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 80.0%

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

   if 1.1e19 < x < 5.60000000000000047e64

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 100.0%

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

      1. *-commutative 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+79}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+19}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+64}:\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{+124}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \]

Alternative 7: 62.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.85 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+19} \lor \neg \left(x \leq 7.8 \cdot 10^{+66}\right) \land x \leq 2.4 \cdot 10^{+131}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.85e+19)
   (* x (+ z 1.0))
   (if (or (<= x 5.4e+19) (and (not (<= x 7.8e+66)) (<= x 2.4e+131)))
     (* (- y z) t)
     (* x (- 1.0 y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.85e+19) {
		tmp = x * (z + 1.0);
	} else if ((x <= 5.4e+19) || (!(x <= 7.8e+66) && (x <= 2.4e+131))) {
		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 (x <= (-2.85d+19)) then
        tmp = x * (z + 1.0d0)
    else if ((x <= 5.4d+19) .or. (.not. (x <= 7.8d+66)) .and. (x <= 2.4d+131)) 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 (x <= -2.85e+19) {
		tmp = x * (z + 1.0);
	} else if ((x <= 5.4e+19) || (!(x <= 7.8e+66) && (x <= 2.4e+131))) {
		tmp = (y - z) * t;
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.85e+19:
		tmp = x * (z + 1.0)
	elif (x <= 5.4e+19) or (not (x <= 7.8e+66) and (x <= 2.4e+131)):
		tmp = (y - z) * t
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.85e+19)
		tmp = Float64(x * Float64(z + 1.0));
	elseif ((x <= 5.4e+19) || (!(x <= 7.8e+66) && (x <= 2.4e+131)))
		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 (x <= -2.85e+19)
		tmp = x * (z + 1.0);
	elseif ((x <= 5.4e+19) || (~((x <= 7.8e+66)) && (x <= 2.4e+131)))
		tmp = (y - z) * t;
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.85e+19], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 5.4e+19], And[N[Not[LessEqual[x, 7.8e+66]], $MachinePrecision], LessEqual[x, 2.4e+131]]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.85e19

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 82.5%

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

      1. mul-1-neg 82.5%

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

      2. *-commutative 82.5%

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

      3. distribute-rgt-neg-in 82.5%

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

      4. +-commutative 82.5%

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

   4. Simplified 82.5%

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

   5. Taylor expanded in y around 0 58.1%

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

   if -2.85e19 < x < 5.4e19 or 7.8000000000000007e66 < x < 2.3999999999999999e131

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 97.8%

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

      1. +-commutative 97.8%

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

      2. mul-1-neg 97.8%

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

      3. unsub-neg 97.8%

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

      4. sub-neg 97.8%

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

      5. +-commutative 97.8%

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

      6. distribute-neg-in 97.8%

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

      7. metadata-eval 97.8%

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

      8. associate-+l+ 97.8%

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

      9. +-commutative 97.8%

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

      10. sub-neg 97.8%

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

   4. Simplified 97.8%

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

   5. Taylor expanded in t around inf 69.2%

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

   if 5.4e19 < x < 7.8000000000000007e66 or 2.3999999999999999e131 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 92.2%

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

      1. mul-1-neg 92.2%

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

      2. unsub-neg 92.2%

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

      3. distribute-lft-out-- 92.1%

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

      4. *-rgt-identity 92.1%

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

   4. Simplified 92.1%

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

   5. Taylor expanded in y around inf 68.7%

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

   6. Taylor expanded in x around 0 68.7%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.85 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+19} \lor \neg \left(x \leq 7.8 \cdot 10^{+66}\right) \land x \leq 2.4 \cdot 10^{+131}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]

Alternative 8: 38.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{+102}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+186}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- x))))
   (if (<= y -4.1e+102)
     (* y t)
     (if (<= y -4.8e-11)
       t_1
       (if (<= y 1.1e-44) x (if (<= y 1.2e+186) (* y t) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double tmp;
	if (y <= -4.1e+102) {
		tmp = y * t;
	} else if (y <= -4.8e-11) {
		tmp = t_1;
	} else if (y <= 1.1e-44) {
		tmp = x;
	} else if (y <= 1.2e+186) {
		tmp = y * t;
	} 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) :: tmp
    t_1 = y * -x
    if (y <= (-4.1d+102)) then
        tmp = y * t
    else if (y <= (-4.8d-11)) then
        tmp = t_1
    else if (y <= 1.1d-44) then
        tmp = x
    else if (y <= 1.2d+186) then
        tmp = y * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double tmp;
	if (y <= -4.1e+102) {
		tmp = y * t;
	} else if (y <= -4.8e-11) {
		tmp = t_1;
	} else if (y <= 1.1e-44) {
		tmp = x;
	} else if (y <= 1.2e+186) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * -x
	tmp = 0
	if y <= -4.1e+102:
		tmp = y * t
	elif y <= -4.8e-11:
		tmp = t_1
	elif y <= 1.1e-44:
		tmp = x
	elif y <= 1.2e+186:
		tmp = y * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(-x))
	tmp = 0.0
	if (y <= -4.1e+102)
		tmp = Float64(y * t);
	elseif (y <= -4.8e-11)
		tmp = t_1;
	elseif (y <= 1.1e-44)
		tmp = x;
	elseif (y <= 1.2e+186)
		tmp = Float64(y * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * -x;
	tmp = 0.0;
	if (y <= -4.1e+102)
		tmp = y * t;
	elseif (y <= -4.8e-11)
		tmp = t_1;
	elseif (y <= 1.1e-44)
		tmp = x;
	elseif (y <= 1.2e+186)
		tmp = y * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[y, -4.1e+102], N[(y * t), $MachinePrecision], If[LessEqual[y, -4.8e-11], t$95$1, If[LessEqual[y, 1.1e-44], x, If[LessEqual[y, 1.2e+186], N[(y * t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.1e102 or 1.10000000000000006e-44 < y < 1.19999999999999998e186

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 80.8%

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

      1. *-commutative 80.8%

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

   4. Simplified 80.8%

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

   5. Taylor expanded in x around 0 52.7%

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

   if -4.1e102 < y < -4.8000000000000002e-11 or 1.19999999999999998e186 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 71.9%

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

      1. mul-1-neg 71.9%

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

      2. *-commutative 71.9%

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

      3. distribute-rgt-neg-in 71.9%

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

      4. +-commutative 71.9%

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

   4. Simplified 71.9%

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

   5. Taylor expanded in y around inf 63.6%

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

   if -4.8000000000000002e-11 < y < 1.10000000000000006e-44

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 66.1%

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

      1. mul-1-neg 66.1%

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

      2. *-commutative 66.1%

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

      3. distribute-rgt-neg-in 66.1%

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

      4. +-commutative 66.1%

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

   4. Simplified 66.1%

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

   5. Taylor expanded in y around 0 66.1%

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

   6. Taylor expanded in z around 0 39.2%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+102}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+186}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]

Alternative 9: 83.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-13}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.9e+42)
   (* y (- t x))
   (if (<= y 1.9e-13) (+ x (* z (- x t))) (- x (* y (- x t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.9e+42) {
		tmp = y * (t - x);
	} else if (y <= 1.9e-13) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x - (y * (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 <= (-1.9d+42)) then
        tmp = y * (t - x)
    else if (y <= 1.9d-13) then
        tmp = x + (z * (x - t))
    else
        tmp = x - (y * (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 <= -1.9e+42) {
		tmp = y * (t - x);
	} else if (y <= 1.9e-13) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x - (y * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.9e+42:
		tmp = y * (t - x)
	elif y <= 1.9e-13:
		tmp = x + (z * (x - t))
	else:
		tmp = x - (y * (x - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.9e+42)
		tmp = Float64(y * Float64(t - x));
	elseif (y <= 1.9e-13)
		tmp = Float64(x + Float64(z * Float64(x - t)));
	else
		tmp = Float64(x - Float64(y * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.9e+42)
		tmp = y * (t - x);
	elseif (y <= 1.9e-13)
		tmp = x + (z * (x - t));
	else
		tmp = x - (y * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.9e+42], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e-13], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8999999999999999e42

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 98.3%

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

      1. +-commutative 98.3%

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

      2. mul-1-neg 98.3%

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

      3. unsub-neg 98.3%

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

      4. sub-neg 98.3%

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

      5. +-commutative 98.3%

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

      6. distribute-neg-in 98.3%

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

      7. metadata-eval 98.3%

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

      8. associate-+l+ 98.3%

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

      9. +-commutative 98.3%

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

      10. sub-neg 98.3%

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

   4. Simplified 98.3%

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

   5. Taylor expanded in y around inf 85.8%

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

   if -1.8999999999999999e42 < y < 1.9e-13

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 91.6%

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

      1. mul-1-neg 91.6%

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

      2. unsub-neg 91.6%

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

   4. Simplified 91.6%

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

   if 1.9e-13 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 88.7%

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

      1. *-commutative 88.7%

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

   4. Simplified 88.7%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-13}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \end{array} \]

Alternative 10: 36.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+90}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-121}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.2e+90)
   (* y t)
   (if (<= y -1.15e-121) (* z x) (if (<= y 1.1e-44) x (* y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.2e+90) {
		tmp = y * t;
	} else if (y <= -1.15e-121) {
		tmp = z * x;
	} else if (y <= 1.1e-44) {
		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 <= (-2.2d+90)) then
        tmp = y * t
    else if (y <= (-1.15d-121)) then
        tmp = z * x
    else if (y <= 1.1d-44) 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 <= -2.2e+90) {
		tmp = y * t;
	} else if (y <= -1.15e-121) {
		tmp = z * x;
	} else if (y <= 1.1e-44) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.2e+90:
		tmp = y * t
	elif y <= -1.15e-121:
		tmp = z * x
	elif y <= 1.1e-44:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.2e+90)
		tmp = Float64(y * t);
	elseif (y <= -1.15e-121)
		tmp = Float64(z * x);
	elseif (y <= 1.1e-44)
		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 <= -2.2e+90)
		tmp = y * t;
	elseif (y <= -1.15e-121)
		tmp = z * x;
	elseif (y <= 1.1e-44)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.2e+90], N[(y * t), $MachinePrecision], If[LessEqual[y, -1.15e-121], N[(z * x), $MachinePrecision], If[LessEqual[y, 1.1e-44], x, N[(y * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.1999999999999999e90 or 1.10000000000000006e-44 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 85.6%

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

      1. *-commutative 85.6%

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

   4. Simplified 85.6%

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

   5. Taylor expanded in x around 0 50.0%

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

   if -2.1999999999999999e90 < y < -1.15000000000000006e-121

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 68.9%

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

      1. mul-1-neg 68.9%

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

      2. unsub-neg 68.9%

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

      3. distribute-lft-out-- 68.9%

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

      4. *-rgt-identity 68.9%

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

   4. Simplified 68.9%

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

   5. Taylor expanded in z around inf 33.9%

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

   if -1.15000000000000006e-121 < y < 1.10000000000000006e-44

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 66.8%

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

      1. mul-1-neg 66.8%

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

      2. *-commutative 66.8%

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

      3. distribute-rgt-neg-in 66.8%

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

      4. +-commutative 66.8%

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

   4. Simplified 66.8%

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

   5. Taylor expanded in y around 0 66.8%

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

   6. Taylor expanded in z around 0 42.2%

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

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+90}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-121}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 11: 62.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.82 \cdot 10^{+19} \lor \neg \left(x \leq 1.6 \cdot 10^{+132}\right):\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.82e+19) (not (<= x 1.6e+132)))
   (* x (+ z 1.0))
   (* (- y z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.82e+19) || !(x <= 1.6e+132)) {
		tmp = x * (z + 1.0);
	} else {
		tmp = (y - z) * 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 ((x <= (-1.82d+19)) .or. (.not. (x <= 1.6d+132))) then
        tmp = x * (z + 1.0d0)
    else
        tmp = (y - z) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.82e+19) || !(x <= 1.6e+132)) {
		tmp = x * (z + 1.0);
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.82e+19) or not (x <= 1.6e+132):
		tmp = x * (z + 1.0)
	else:
		tmp = (y - z) * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.82e+19) || !(x <= 1.6e+132))
		tmp = Float64(x * Float64(z + 1.0));
	else
		tmp = Float64(Float64(y - z) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.82e+19) || ~((x <= 1.6e+132)))
		tmp = x * (z + 1.0);
	else
		tmp = (y - z) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.82e+19], N[Not[LessEqual[x, 1.6e+132]], $MachinePrecision]], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.82e19 or 1.5999999999999999e132 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 86.9%

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

      1. mul-1-neg 86.9%

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

      2. *-commutative 86.9%

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

      3. distribute-rgt-neg-in 86.9%

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

      4. +-commutative 86.9%

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

   4. Simplified 86.9%

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

   5. Taylor expanded in y around 0 59.7%

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

   if -1.82e19 < x < 1.5999999999999999e132

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 98.0%

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

      1. +-commutative 98.0%

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

      2. mul-1-neg 98.0%

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

      3. unsub-neg 98.0%

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

      4. sub-neg 98.0%

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

      5. +-commutative 98.0%

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

      6. distribute-neg-in 98.0%

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

      7. metadata-eval 98.0%

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

      8. associate-+l+ 98.0%

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

      9. +-commutative 98.0%

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

      10. sub-neg 98.0%

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

   4. Simplified 98.0%

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

   5. Taylor expanded in t around inf 64.8%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.82 \cdot 10^{+19} \lor \neg \left(x \leq 1.6 \cdot 10^{+132}\right):\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]

Alternative 12: 68.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+42} \lor \neg \left(y \leq 5.3 \cdot 10^{-11}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.8e+42) (not (<= y 5.3e-11))) (* y (- t x)) (* x (+ z 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.8e+42) || !(y <= 5.3e-11)) {
		tmp = y * (t - x);
	} else {
		tmp = x * (z + 1.0);
	}
	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 <= (-1.8d+42)) .or. (.not. (y <= 5.3d-11))) then
        tmp = y * (t - x)
    else
        tmp = x * (z + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.8e+42) || !(y <= 5.3e-11)) {
		tmp = y * (t - x);
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.8e+42) or not (y <= 5.3e-11):
		tmp = y * (t - x)
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.8e+42) || !(y <= 5.3e-11))
		tmp = Float64(y * Float64(t - x));
	else
		tmp = Float64(x * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.8e+42) || ~((y <= 5.3e-11)))
		tmp = y * (t - x);
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.8e+42], N[Not[LessEqual[y, 5.3e-11]], $MachinePrecision]], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8e42 or 5.2999999999999998e-11 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 93.9%

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

      1. +-commutative 93.9%

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

      2. mul-1-neg 93.9%

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

      3. unsub-neg 93.9%

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

      4. sub-neg 93.9%

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

      5. +-commutative 93.9%

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

      6. distribute-neg-in 93.9%

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

      7. metadata-eval 93.9%

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

      8. associate-+l+ 93.9%

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

      9. +-commutative 93.9%

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

      10. sub-neg 93.9%

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

   4. Simplified 93.9%

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

   5. Taylor expanded in y around inf 86.6%

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

   if -1.8e42 < y < 5.2999999999999998e-11

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 64.1%

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

      1. mul-1-neg 64.1%

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

      2. *-commutative 64.1%

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

      3. distribute-rgt-neg-in 64.1%

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

      4. +-commutative 64.1%

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

   4. Simplified 64.1%

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

   5. Taylor expanded in y around 0 63.9%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+42} \lor \neg \left(y \leq 5.3 \cdot 10^{-11}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]

Alternative 13: 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 14: 38.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-18}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.8e-18) (* y t) (if (<= y 9.8e-49) x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.8e-18) {
		tmp = y * t;
	} else if (y <= 9.8e-49) {
		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 <= (-5.8d-18)) then
        tmp = y * t
    else if (y <= 9.8d-49) 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 <= -5.8e-18) {
		tmp = y * t;
	} else if (y <= 9.8e-49) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.8e-18:
		tmp = y * t
	elif y <= 9.8e-49:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.8e-18)
		tmp = Float64(y * t);
	elseif (y <= 9.8e-49)
		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 <= -5.8e-18)
		tmp = y * t;
	elseif (y <= 9.8e-49)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.8e-18], N[(y * t), $MachinePrecision], If[LessEqual[y, 9.8e-49], x, N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.8e-18 or 9.8000000000000005e-49 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 83.1%

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

      1. *-commutative 83.1%

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

   4. Simplified 83.1%

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

   5. Taylor expanded in x around 0 46.1%

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

   if -5.8e-18 < y < 9.8000000000000005e-49

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 66.1%

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

      1. mul-1-neg 66.1%

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

      2. *-commutative 66.1%

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

      3. distribute-rgt-neg-in 66.1%

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

      4. +-commutative 66.1%

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

   4. Simplified 66.1%

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

   5. Taylor expanded in y around 0 66.1%

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

   6. Taylor expanded in z around 0 39.2%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-18}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 15: 18.4% 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 x around -inf 58.6%

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

   1. mul-1-neg 58.6%

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

   2. *-commutative 58.6%

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

   3. distribute-rgt-neg-in 58.6%

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

   4. +-commutative 58.6%

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

4. Simplified 58.6%

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

5. Taylor expanded in y around 0 38.6%

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

6. Taylor expanded in z around 0 19.2%

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

7. Final simplification 19.2%

   \[\leadsto x \]

Developer target: 96.5% 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 2023293 
(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))))