Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 6.9s

Alternatives: 12

Speedup: 1.0×

• 35.2% 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-define 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. Add Preprocessing
5. Add Preprocessing

Alternative 2: 63.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot t\\ t_2 := x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{if}\;t \leq -2 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-83}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 0.00078:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+54}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+162}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y t))) (t_2 (* x (+ (- z y) 1.0))))
   (if (<= t -2e+41)
     t_1
     (if (<= t 5.2e-83)
       t_2
       (if (<= t 0.00078)
         (* y (- t x))
         (if (<= t 5.5e+54) t_2 (if (<= t 3.2e+162) t_1 (- x (* z t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * t);
	double t_2 = x * ((z - y) + 1.0);
	double tmp;
	if (t <= -2e+41) {
		tmp = t_1;
	} else if (t <= 5.2e-83) {
		tmp = t_2;
	} else if (t <= 0.00078) {
		tmp = y * (t - x);
	} else if (t <= 5.5e+54) {
		tmp = t_2;
	} else if (t <= 3.2e+162) {
		tmp = t_1;
	} else {
		tmp = x - (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y * t)
    t_2 = x * ((z - y) + 1.0d0)
    if (t <= (-2d+41)) then
        tmp = t_1
    else if (t <= 5.2d-83) then
        tmp = t_2
    else if (t <= 0.00078d0) then
        tmp = y * (t - x)
    else if (t <= 5.5d+54) then
        tmp = t_2
    else if (t <= 3.2d+162) then
        tmp = t_1
    else
        tmp = x - (z * 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 * t);
	double t_2 = x * ((z - y) + 1.0);
	double tmp;
	if (t <= -2e+41) {
		tmp = t_1;
	} else if (t <= 5.2e-83) {
		tmp = t_2;
	} else if (t <= 0.00078) {
		tmp = y * (t - x);
	} else if (t <= 5.5e+54) {
		tmp = t_2;
	} else if (t <= 3.2e+162) {
		tmp = t_1;
	} else {
		tmp = x - (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * t)
	t_2 = x * ((z - y) + 1.0)
	tmp = 0
	if t <= -2e+41:
		tmp = t_1
	elif t <= 5.2e-83:
		tmp = t_2
	elif t <= 0.00078:
		tmp = y * (t - x)
	elif t <= 5.5e+54:
		tmp = t_2
	elif t <= 3.2e+162:
		tmp = t_1
	else:
		tmp = x - (z * t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * t))
	t_2 = Float64(x * Float64(Float64(z - y) + 1.0))
	tmp = 0.0
	if (t <= -2e+41)
		tmp = t_1;
	elseif (t <= 5.2e-83)
		tmp = t_2;
	elseif (t <= 0.00078)
		tmp = Float64(y * Float64(t - x));
	elseif (t <= 5.5e+54)
		tmp = t_2;
	elseif (t <= 3.2e+162)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * t);
	t_2 = x * ((z - y) + 1.0);
	tmp = 0.0;
	if (t <= -2e+41)
		tmp = t_1;
	elseif (t <= 5.2e-83)
		tmp = t_2;
	elseif (t <= 0.00078)
		tmp = y * (t - x);
	elseif (t <= 5.5e+54)
		tmp = t_2;
	elseif (t <= 3.2e+162)
		tmp = t_1;
	else
		tmp = x - (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e+41], t$95$1, If[LessEqual[t, 5.2e-83], t$95$2, If[LessEqual[t, 0.00078], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e+54], t$95$2, If[LessEqual[t, 3.2e+162], t$95$1, N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.00000000000000001e41 or 5.50000000000000026e54 < t < 3.2000000000000001e162

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 93.5%

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

   4. Taylor expanded in y around inf 70.8%

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

   if -2.00000000000000001e41 < t < 5.20000000000000018e-83 or 7.79999999999999986e-4 < t < 5.50000000000000026e54

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 87.2%

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

      1. mul-1-neg 87.2%

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

      2. unsub-neg 87.2%

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

   5. Simplified 87.2%

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

   if 5.20000000000000018e-83 < t < 7.79999999999999986e-4

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 67.3%

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

      1. *-commutative 67.3%

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

   5. Simplified 67.3%

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

   6. Taylor expanded in y around inf 61.9%

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

   if 3.2000000000000001e162 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 94.8%

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

   4. Taylor expanded in y around 0 58.3%

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

      1. mul-1-neg 58.3%

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

      2. distribute-rgt-neg-out 58.3%

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

   6. Simplified 58.3%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+41}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-83}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;t \leq 0.00078:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+162}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 48.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-x\right)\\ t_2 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;y \leq -9.2 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{+138}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+25}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -3100000:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+109}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- x))) (t_2 (* x (+ z 1.0))))
   (if (<= y -9.2e+188)
     t_1
     (if (<= y -1.15e+138)
       t_2
       (if (<= y -4e+25)
         (* y t)
         (if (<= y -3100000.0)
           (* x (- 1.0 y))
           (if (<= y 5.6e+109) t_2 t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double t_2 = x * (z + 1.0);
	double tmp;
	if (y <= -9.2e+188) {
		tmp = t_1;
	} else if (y <= -1.15e+138) {
		tmp = t_2;
	} else if (y <= -4e+25) {
		tmp = y * t;
	} else if (y <= -3100000.0) {
		tmp = x * (1.0 - y);
	} else if (y <= 5.6e+109) {
		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 * -x
    t_2 = x * (z + 1.0d0)
    if (y <= (-9.2d+188)) then
        tmp = t_1
    else if (y <= (-1.15d+138)) then
        tmp = t_2
    else if (y <= (-4d+25)) then
        tmp = y * t
    else if (y <= (-3100000.0d0)) then
        tmp = x * (1.0d0 - y)
    else if (y <= 5.6d+109) 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 * -x;
	double t_2 = x * (z + 1.0);
	double tmp;
	if (y <= -9.2e+188) {
		tmp = t_1;
	} else if (y <= -1.15e+138) {
		tmp = t_2;
	} else if (y <= -4e+25) {
		tmp = y * t;
	} else if (y <= -3100000.0) {
		tmp = x * (1.0 - y);
	} else if (y <= 5.6e+109) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * -x
	t_2 = x * (z + 1.0)
	tmp = 0
	if y <= -9.2e+188:
		tmp = t_1
	elif y <= -1.15e+138:
		tmp = t_2
	elif y <= -4e+25:
		tmp = y * t
	elif y <= -3100000.0:
		tmp = x * (1.0 - y)
	elif y <= 5.6e+109:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(-x))
	t_2 = Float64(x * Float64(z + 1.0))
	tmp = 0.0
	if (y <= -9.2e+188)
		tmp = t_1;
	elseif (y <= -1.15e+138)
		tmp = t_2;
	elseif (y <= -4e+25)
		tmp = Float64(y * t);
	elseif (y <= -3100000.0)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (y <= 5.6e+109)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * -x;
	t_2 = x * (z + 1.0);
	tmp = 0.0;
	if (y <= -9.2e+188)
		tmp = t_1;
	elseif (y <= -1.15e+138)
		tmp = t_2;
	elseif (y <= -4e+25)
		tmp = y * t;
	elseif (y <= -3100000.0)
		tmp = x * (1.0 - y);
	elseif (y <= 5.6e+109)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * (-x)), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.2e+188], t$95$1, If[LessEqual[y, -1.15e+138], t$95$2, If[LessEqual[y, -4e+25], N[(y * t), $MachinePrecision], If[LessEqual[y, -3100000.0], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.6e+109], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.20000000000000046e188 or 5.6000000000000004e109 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 65.8%

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

      1. mul-1-neg 65.8%

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

      2. unsub-neg 65.8%

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

   5. Simplified 65.8%

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

   6. Taylor expanded in y around inf 61.2%

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

      1. associate-*r* 61.2%

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

      2. neg-mul-1 61.2%

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

      3. *-commutative 61.2%

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

   8. Simplified 61.2%

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

   if -9.20000000000000046e188 < y < -1.15000000000000004e138 or -3.1e6 < y < 5.6000000000000004e109

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 66.6%

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

      1. mul-1-neg 66.6%

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

      2. unsub-neg 66.6%

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

   5. Simplified 66.6%

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

   6. Taylor expanded in y around 0 60.4%

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

      1. +-commutative 60.4%

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

   8. Simplified 60.4%

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

   if -1.15000000000000004e138 < y < -4.00000000000000036e25

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 79.0%

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

   4. Taylor expanded in y around inf 68.1%

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

   5. Taylor expanded in x around 0 67.9%

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

      1. *-commutative 67.9%

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

   7. Simplified 67.9%

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

   if -4.00000000000000036e25 < y < -3.1e6

   1. Initial program 99.5%

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

   3. Taylor expanded in x around inf 83.5%

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

      1. mul-1-neg 83.5%

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

      2. unsub-neg 83.5%

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

   5. Simplified 83.5%

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

   6. Taylor expanded in z around 0 83.8%

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

Alternative 4: 80.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+39} \lor \neg \left(t \leq 8 \cdot 10^{-57}\right) \land \left(t \leq 0.026 \lor \neg \left(t \leq 1.7 \cdot 10^{+58}\right)\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4.2e+39)
         (and (not (<= t 8e-57)) (or (<= t 0.026) (not (<= t 1.7e+58)))))
   (+ x (* (- y z) t))
   (* x (+ (- z y) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.2e+39) || (!(t <= 8e-57) && ((t <= 0.026) || !(t <= 1.7e+58)))) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x * ((z - y) + 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 ((t <= (-4.2d+39)) .or. (.not. (t <= 8d-57)) .and. (t <= 0.026d0) .or. (.not. (t <= 1.7d+58))) then
        tmp = x + ((y - z) * t)
    else
        tmp = x * ((z - y) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.2e+39) || (!(t <= 8e-57) && ((t <= 0.026) || !(t <= 1.7e+58)))) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -4.2e+39) or (not (t <= 8e-57) and ((t <= 0.026) or not (t <= 1.7e+58))):
		tmp = x + ((y - z) * t)
	else:
		tmp = x * ((z - y) + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -4.2e+39) || (!(t <= 8e-57) && ((t <= 0.026) || !(t <= 1.7e+58))))
		tmp = Float64(x + Float64(Float64(y - z) * t));
	else
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -4.2e+39) || (~((t <= 8e-57)) && ((t <= 0.026) || ~((t <= 1.7e+58)))))
		tmp = x + ((y - z) * t);
	else
		tmp = x * ((z - y) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -4.2e+39], And[N[Not[LessEqual[t, 8e-57]], $MachinePrecision], Or[LessEqual[t, 0.026], N[Not[LessEqual[t, 1.7e+58]], $MachinePrecision]]]], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.1999999999999997e39 or 7.99999999999999964e-57 < t < 0.0259999999999999988 or 1.7e58 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 89.9%

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

   if -4.1999999999999997e39 < t < 7.99999999999999964e-57 or 0.0259999999999999988 < t < 1.7e58

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 86.8%

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

      1. mul-1-neg 86.8%

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

      2. unsub-neg 86.8%

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

   5. Simplified 86.8%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+39} \lor \neg \left(t \leq 8 \cdot 10^{-57}\right) \land \left(t \leq 0.026 \lor \neg \left(t \leq 1.7 \cdot 10^{+58}\right)\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-201}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 22500:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+44}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -2.6e-33)
     t_1
     (if (<= y 1.15e-201)
       (* x (+ z 1.0))
       (if (<= y 22500.0) (- x (* z t)) (if (<= y 9.5e+44) (* z x) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -2.6e-33) {
		tmp = t_1;
	} else if (y <= 1.15e-201) {
		tmp = x * (z + 1.0);
	} else if (y <= 22500.0) {
		tmp = x - (z * t);
	} else if (y <= 9.5e+44) {
		tmp = z * x;
	} 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 * (t - x)
    if (y <= (-2.6d-33)) then
        tmp = t_1
    else if (y <= 1.15d-201) then
        tmp = x * (z + 1.0d0)
    else if (y <= 22500.0d0) then
        tmp = x - (z * t)
    else if (y <= 9.5d+44) then
        tmp = z * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -2.6e-33) {
		tmp = t_1;
	} else if (y <= 1.15e-201) {
		tmp = x * (z + 1.0);
	} else if (y <= 22500.0) {
		tmp = x - (z * t);
	} else if (y <= 9.5e+44) {
		tmp = z * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -2.6e-33:
		tmp = t_1
	elif y <= 1.15e-201:
		tmp = x * (z + 1.0)
	elif y <= 22500.0:
		tmp = x - (z * t)
	elif y <= 9.5e+44:
		tmp = z * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (y <= -2.6e-33)
		tmp = t_1;
	elseif (y <= 1.15e-201)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (y <= 22500.0)
		tmp = Float64(x - Float64(z * t));
	elseif (y <= 9.5e+44)
		tmp = Float64(z * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	tmp = 0.0;
	if (y <= -2.6e-33)
		tmp = t_1;
	elseif (y <= 1.15e-201)
		tmp = x * (z + 1.0);
	elseif (y <= 22500.0)
		tmp = x - (z * t);
	elseif (y <= 9.5e+44)
		tmp = z * x;
	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]}, If[LessEqual[y, -2.6e-33], t$95$1, If[LessEqual[y, 1.15e-201], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 22500.0], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e+44], N[(z * x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.59999999999999994e-33 or 9.5000000000000004e44 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 81.0%

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

      1. *-commutative 81.0%

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

   5. Simplified 81.0%

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

   6. Taylor expanded in y around inf 79.0%

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

   if -2.59999999999999994e-33 < y < 1.14999999999999993e-201

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 73.1%

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

      1. mul-1-neg 73.1%

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

      2. unsub-neg 73.1%

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

   5. Simplified 73.1%

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

   6. Taylor expanded in y around 0 73.1%

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

      1. +-commutative 73.1%

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

   8. Simplified 73.1%

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

   if 1.14999999999999993e-201 < y < 22500

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 82.6%

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

   4. Taylor expanded in y around 0 75.9%

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

      1. mul-1-neg 75.9%

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

      2. distribute-rgt-neg-out 75.9%

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

   6. Simplified 75.9%

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

   if 22500 < y < 9.5000000000000004e44

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 61.4%

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

      1. mul-1-neg 61.4%

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

      2. unsub-neg 61.4%

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

   5. Simplified 61.4%

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

   6. Taylor expanded in z around inf 51.7%

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

      1. *-commutative 51.7%

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

   8. Simplified 51.7%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-33}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-201}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 22500:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+44}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 47.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-x\right)\\ t_2 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;y \leq -4.3 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{+141}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.28 \cdot 10^{-26}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+109}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- x))) (t_2 (* x (+ z 1.0))))
   (if (<= y -4.3e+188)
     t_1
     (if (<= y -4.8e+141)
       t_2
       (if (<= y -1.28e-26) (* y t) (if (<= y 4.5e+109) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double t_2 = x * (z + 1.0);
	double tmp;
	if (y <= -4.3e+188) {
		tmp = t_1;
	} else if (y <= -4.8e+141) {
		tmp = t_2;
	} else if (y <= -1.28e-26) {
		tmp = y * t;
	} else if (y <= 4.5e+109) {
		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 * -x
    t_2 = x * (z + 1.0d0)
    if (y <= (-4.3d+188)) then
        tmp = t_1
    else if (y <= (-4.8d+141)) then
        tmp = t_2
    else if (y <= (-1.28d-26)) then
        tmp = y * t
    else if (y <= 4.5d+109) 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 * -x;
	double t_2 = x * (z + 1.0);
	double tmp;
	if (y <= -4.3e+188) {
		tmp = t_1;
	} else if (y <= -4.8e+141) {
		tmp = t_2;
	} else if (y <= -1.28e-26) {
		tmp = y * t;
	} else if (y <= 4.5e+109) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * -x
	t_2 = x * (z + 1.0)
	tmp = 0
	if y <= -4.3e+188:
		tmp = t_1
	elif y <= -4.8e+141:
		tmp = t_2
	elif y <= -1.28e-26:
		tmp = y * t
	elif y <= 4.5e+109:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(-x))
	t_2 = Float64(x * Float64(z + 1.0))
	tmp = 0.0
	if (y <= -4.3e+188)
		tmp = t_1;
	elseif (y <= -4.8e+141)
		tmp = t_2;
	elseif (y <= -1.28e-26)
		tmp = Float64(y * t);
	elseif (y <= 4.5e+109)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * -x;
	t_2 = x * (z + 1.0);
	tmp = 0.0;
	if (y <= -4.3e+188)
		tmp = t_1;
	elseif (y <= -4.8e+141)
		tmp = t_2;
	elseif (y <= -1.28e-26)
		tmp = y * t;
	elseif (y <= 4.5e+109)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * (-x)), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.3e+188], t$95$1, If[LessEqual[y, -4.8e+141], t$95$2, If[LessEqual[y, -1.28e-26], N[(y * t), $MachinePrecision], If[LessEqual[y, 4.5e+109], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.29999999999999985e188 or 4.4999999999999996e109 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 65.8%

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

      1. mul-1-neg 65.8%

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

      2. unsub-neg 65.8%

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

   5. Simplified 65.8%

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

   6. Taylor expanded in y around inf 61.2%

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

      1. associate-*r* 61.2%

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

      2. neg-mul-1 61.2%

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

      3. *-commutative 61.2%

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

   8. Simplified 61.2%

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

   if -4.29999999999999985e188 < y < -4.79999999999999995e141 or -1.27999999999999996e-26 < y < 4.4999999999999996e109

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 67.4%

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

      1. mul-1-neg 67.4%

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

      2. unsub-neg 67.4%

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

   5. Simplified 67.4%

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

   6. Taylor expanded in y around 0 61.4%

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

      1. +-commutative 61.4%

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

   8. Simplified 61.4%

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

   if -4.79999999999999995e141 < y < -1.27999999999999996e-26

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 69.4%

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

   4. Taylor expanded in y around inf 56.6%

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

   5. Taylor expanded in x around 0 54.2%

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

      1. *-commutative 54.2%

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

   7. Simplified 54.2%

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

Alternative 7: 32.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{+120}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-33}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+110}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- x))))
   (if (<= y -4.1e+188)
     t_1
     (if (<= y -9.2e+120)
       (* z x)
       (if (<= y -1.6e-33) (* y t) (if (<= y 1.1e+110) (* z x) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double tmp;
	if (y <= -4.1e+188) {
		tmp = t_1;
	} else if (y <= -9.2e+120) {
		tmp = z * x;
	} else if (y <= -1.6e-33) {
		tmp = y * t;
	} else if (y <= 1.1e+110) {
		tmp = z * x;
	} 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+188)) then
        tmp = t_1
    else if (y <= (-9.2d+120)) then
        tmp = z * x
    else if (y <= (-1.6d-33)) then
        tmp = y * t
    else if (y <= 1.1d+110) then
        tmp = z * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double tmp;
	if (y <= -4.1e+188) {
		tmp = t_1;
	} else if (y <= -9.2e+120) {
		tmp = z * x;
	} else if (y <= -1.6e-33) {
		tmp = y * t;
	} else if (y <= 1.1e+110) {
		tmp = z * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * -x
	tmp = 0
	if y <= -4.1e+188:
		tmp = t_1
	elif y <= -9.2e+120:
		tmp = z * x
	elif y <= -1.6e-33:
		tmp = y * t
	elif y <= 1.1e+110:
		tmp = z * x
	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+188)
		tmp = t_1;
	elseif (y <= -9.2e+120)
		tmp = Float64(z * x);
	elseif (y <= -1.6e-33)
		tmp = Float64(y * t);
	elseif (y <= 1.1e+110)
		tmp = Float64(z * x);
	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+188)
		tmp = t_1;
	elseif (y <= -9.2e+120)
		tmp = z * x;
	elseif (y <= -1.6e-33)
		tmp = y * t;
	elseif (y <= 1.1e+110)
		tmp = z * x;
	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+188], t$95$1, If[LessEqual[y, -9.2e+120], N[(z * x), $MachinePrecision], If[LessEqual[y, -1.6e-33], N[(y * t), $MachinePrecision], If[LessEqual[y, 1.1e+110], N[(z * x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.1e188 or 1.09999999999999996e110 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 65.8%

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

      1. mul-1-neg 65.8%

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

      2. unsub-neg 65.8%

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

   5. Simplified 65.8%

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

   6. Taylor expanded in y around inf 61.2%

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

      1. associate-*r* 61.2%

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

      2. neg-mul-1 61.2%

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

      3. *-commutative 61.2%

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

   8. Simplified 61.2%

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

   if -4.1e188 < y < -9.1999999999999997e120 or -1.59999999999999988e-33 < y < 1.09999999999999996e110

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 67.6%

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

      1. mul-1-neg 67.6%

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

      2. unsub-neg 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in z around inf 40.3%

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

      1. *-commutative 40.3%

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

   8. Simplified 40.3%

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

   if -9.1999999999999997e120 < y < -1.59999999999999988e-33

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 73.9%

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

   4. Taylor expanded in y around inf 60.7%

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

   5. Taylor expanded in x around 0 55.6%

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

      1. *-commutative 55.6%

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

   7. Simplified 55.6%

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

Alternative 8: 67.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-33} \lor \neg \left(y \leq 1.65 \cdot 10^{+44}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.6e-33) (not (<= y 1.65e+44))) (* y (- t x)) (* x (+ z 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.6e-33) || !(y <= 1.65e+44)) {
		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 <= (-2.6d-33)) .or. (.not. (y <= 1.65d+44))) 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 <= -2.6e-33) || !(y <= 1.65e+44)) {
		tmp = y * (t - x);
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.6e-33) or not (y <= 1.65e+44):
		tmp = y * (t - x)
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.6e-33) || !(y <= 1.65e+44))
		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 <= -2.6e-33) || ~((y <= 1.65e+44)))
		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, -2.6e-33], N[Not[LessEqual[y, 1.65e+44]], $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 < -2.59999999999999994e-33 or 1.65000000000000007e44 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 81.0%

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

      1. *-commutative 81.0%

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

   5. Simplified 81.0%

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

   6. Taylor expanded in y around inf 79.0%

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

   if -2.59999999999999994e-33 < y < 1.65000000000000007e44

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 68.5%

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

      1. mul-1-neg 68.5%

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

      2. unsub-neg 68.5%

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

   5. Simplified 68.5%

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

   6. Taylor expanded in y around 0 66.7%

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

      1. +-commutative 66.7%

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

   8. Simplified 66.7%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-33} \lor \neg \left(y \leq 1.65 \cdot 10^{+44}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 34.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+30} \lor \neg \left(t \leq 2.25 \cdot 10^{-57}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4.8e+30) (not (<= t 2.25e-57))) (* y t) (* z x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.8e+30) || !(t <= 2.25e-57)) {
		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 ((t <= (-4.8d+30)) .or. (.not. (t <= 2.25d-57))) 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 ((t <= -4.8e+30) || !(t <= 2.25e-57)) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -4.8e+30) or not (t <= 2.25e-57):
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -4.8e+30) || !(t <= 2.25e-57))
		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 ((t <= -4.8e+30) || ~((t <= 2.25e-57)))
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -4.8e+30], N[Not[LessEqual[t, 2.25e-57]], $MachinePrecision]], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.7999999999999999e30 or 2.24999999999999986e-57 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 81.5%

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

   4. Taylor expanded in y around inf 52.8%

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

   5. Taylor expanded in x around 0 43.5%

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

      1. *-commutative 43.5%

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

   7. Simplified 43.5%

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

   if -4.7999999999999999e30 < t < 2.24999999999999986e-57

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 86.5%

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

      1. mul-1-neg 86.5%

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

      2. unsub-neg 86.5%

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

   5. Simplified 86.5%

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

   6. Taylor expanded in z around inf 42.7%

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

      1. *-commutative 42.7%

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

   8. Simplified 42.7%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+30} \lor \neg \left(t \leq 2.25 \cdot 10^{-57}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 37.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.05 \cdot 10^{-27} \lor \neg \left(y \leq 17500\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.05e-27) (not (<= y 17500.0))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.05e-27) || !(y <= 17500.0)) {
		tmp = y * t;
	} else {
		tmp = 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 ((y <= (-3.05d-27)) .or. (.not. (y <= 17500.0d0))) then
        tmp = y * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.05e-27) || !(y <= 17500.0)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.05e-27) or not (y <= 17500.0):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.05e-27) || !(y <= 17500.0))
		tmp = Float64(y * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.05e-27) || ~((y <= 17500.0)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.05e-27], N[Not[LessEqual[y, 17500.0]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.05e-27 or 17500 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 49.0%

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

   4. Taylor expanded in y around inf 40.5%

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

   5. Taylor expanded in x around 0 39.9%

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

      1. *-commutative 39.9%

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

   7. Simplified 39.9%

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

   if -3.05e-27 < y < 17500

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 67.0%

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

   4. Taylor expanded in x around inf 32.5%

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

4. Final simplification 36.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.05 \cdot 10^{-27} \lor \neg \left(y \leq 17500\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 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. Add Preprocessing
3. Add Preprocessing

Alternative 12: 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. Add Preprocessing

3. Taylor expanded in t around inf 56.4%

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

4. Taylor expanded in x around inf 15.1%

   \[\leadsto \color{blue}{x} \]
5. Add Preprocessing

Developer target: 96.1% 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 2024096 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

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

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