Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 12.8s

Alternatives: 14

Speedup: 1.0×

• 34.7% 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: 82.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := x + y \cdot \left(t - x\right)\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{+88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-180}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-69}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+51}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))) (t_2 (+ x (* y (- t x)))))
   (if (<= z -6.8e+121)
     t_1
     (if (<= z -5.7e+88)
       t_2
       (if (<= z -2e+39)
         t_1
         (if (<= z 5.5e-180)
           t_2
           (if (<= z 2.7e-69)
             (- x (* t (- z y)))
             (if (<= z 4.2e+51) t_2 t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = x + (y * (t - x));
	double tmp;
	if (z <= -6.8e+121) {
		tmp = t_1;
	} else if (z <= -5.7e+88) {
		tmp = t_2;
	} else if (z <= -2e+39) {
		tmp = t_1;
	} else if (z <= 5.5e-180) {
		tmp = t_2;
	} else if (z <= 2.7e-69) {
		tmp = x - (t * (z - y));
	} else if (z <= 4.2e+51) {
		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 = z * (x - t)
    t_2 = x + (y * (t - x))
    if (z <= (-6.8d+121)) then
        tmp = t_1
    else if (z <= (-5.7d+88)) then
        tmp = t_2
    else if (z <= (-2d+39)) then
        tmp = t_1
    else if (z <= 5.5d-180) then
        tmp = t_2
    else if (z <= 2.7d-69) then
        tmp = x - (t * (z - y))
    else if (z <= 4.2d+51) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = x + (y * (t - x));
	double tmp;
	if (z <= -6.8e+121) {
		tmp = t_1;
	} else if (z <= -5.7e+88) {
		tmp = t_2;
	} else if (z <= -2e+39) {
		tmp = t_1;
	} else if (z <= 5.5e-180) {
		tmp = t_2;
	} else if (z <= 2.7e-69) {
		tmp = x - (t * (z - y));
	} else if (z <= 4.2e+51) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	t_2 = x + (y * (t - x))
	tmp = 0
	if z <= -6.8e+121:
		tmp = t_1
	elif z <= -5.7e+88:
		tmp = t_2
	elif z <= -2e+39:
		tmp = t_1
	elif z <= 5.5e-180:
		tmp = t_2
	elif z <= 2.7e-69:
		tmp = x - (t * (z - y))
	elif z <= 4.2e+51:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	t_2 = Float64(x + Float64(y * Float64(t - x)))
	tmp = 0.0
	if (z <= -6.8e+121)
		tmp = t_1;
	elseif (z <= -5.7e+88)
		tmp = t_2;
	elseif (z <= -2e+39)
		tmp = t_1;
	elseif (z <= 5.5e-180)
		tmp = t_2;
	elseif (z <= 2.7e-69)
		tmp = Float64(x - Float64(t * Float64(z - y)));
	elseif (z <= 4.2e+51)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	t_2 = x + (y * (t - x));
	tmp = 0.0;
	if (z <= -6.8e+121)
		tmp = t_1;
	elseif (z <= -5.7e+88)
		tmp = t_2;
	elseif (z <= -2e+39)
		tmp = t_1;
	elseif (z <= 5.5e-180)
		tmp = t_2;
	elseif (z <= 2.7e-69)
		tmp = x - (t * (z - y));
	elseif (z <= 4.2e+51)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.8e+121], t$95$1, If[LessEqual[z, -5.7e+88], t$95$2, If[LessEqual[z, -2e+39], t$95$1, If[LessEqual[z, 5.5e-180], t$95$2, If[LessEqual[z, 2.7e-69], N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+51], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.80000000000000021e121 or -5.70000000000000021e88 < z < -1.99999999999999988e39 or 4.2000000000000002e51 < z

   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%

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

   5. Taylor expanded in z around inf 91.6%

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

   if -6.80000000000000021e121 < z < -5.70000000000000021e88 or -1.99999999999999988e39 < z < 5.50000000000000011e-180 or 2.6999999999999997e-69 < z < 4.2000000000000002e51

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 84.9%

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

      1. *-commutative 84.9%

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

   4. Simplified 84.9%

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

   if 5.50000000000000011e-180 < z < 2.6999999999999997e-69

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 100.0%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+121}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{+88}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+39}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-180}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-69}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+51}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 3: 35.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-x\right)\\ t_2 := -z \cdot t\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{+59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-259}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-179}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+237}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- x))) (t_2 (- (* z t))))
   (if (<= z -5.6e+59)
     t_2
     (if (<= z -1.0)
       (* z x)
       (if (<= z -1.15e-259)
         x
         (if (<= z 7.5e-179)
           t_1
           (if (<= z 9.5e-44)
             x
             (if (<= z 4e+101) t_1 (if (<= z 2.8e+237) t_2 (* z x))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double t_2 = -(z * t);
	double tmp;
	if (z <= -5.6e+59) {
		tmp = t_2;
	} else if (z <= -1.0) {
		tmp = z * x;
	} else if (z <= -1.15e-259) {
		tmp = x;
	} else if (z <= 7.5e-179) {
		tmp = t_1;
	} else if (z <= 9.5e-44) {
		tmp = x;
	} else if (z <= 4e+101) {
		tmp = t_1;
	} else if (z <= 2.8e+237) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = y * -x
    t_2 = -(z * t)
    if (z <= (-5.6d+59)) then
        tmp = t_2
    else if (z <= (-1.0d0)) then
        tmp = z * x
    else if (z <= (-1.15d-259)) then
        tmp = x
    else if (z <= 7.5d-179) then
        tmp = t_1
    else if (z <= 9.5d-44) then
        tmp = x
    else if (z <= 4d+101) then
        tmp = t_1
    else if (z <= 2.8d+237) then
        tmp = t_2
    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 * -x;
	double t_2 = -(z * t);
	double tmp;
	if (z <= -5.6e+59) {
		tmp = t_2;
	} else if (z <= -1.0) {
		tmp = z * x;
	} else if (z <= -1.15e-259) {
		tmp = x;
	} else if (z <= 7.5e-179) {
		tmp = t_1;
	} else if (z <= 9.5e-44) {
		tmp = x;
	} else if (z <= 4e+101) {
		tmp = t_1;
	} else if (z <= 2.8e+237) {
		tmp = t_2;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * -x
	t_2 = -(z * t)
	tmp = 0
	if z <= -5.6e+59:
		tmp = t_2
	elif z <= -1.0:
		tmp = z * x
	elif z <= -1.15e-259:
		tmp = x
	elif z <= 7.5e-179:
		tmp = t_1
	elif z <= 9.5e-44:
		tmp = x
	elif z <= 4e+101:
		tmp = t_1
	elif z <= 2.8e+237:
		tmp = t_2
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(-x))
	t_2 = Float64(-Float64(z * t))
	tmp = 0.0
	if (z <= -5.6e+59)
		tmp = t_2;
	elseif (z <= -1.0)
		tmp = Float64(z * x);
	elseif (z <= -1.15e-259)
		tmp = x;
	elseif (z <= 7.5e-179)
		tmp = t_1;
	elseif (z <= 9.5e-44)
		tmp = x;
	elseif (z <= 4e+101)
		tmp = t_1;
	elseif (z <= 2.8e+237)
		tmp = t_2;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * -x;
	t_2 = -(z * t);
	tmp = 0.0;
	if (z <= -5.6e+59)
		tmp = t_2;
	elseif (z <= -1.0)
		tmp = z * x;
	elseif (z <= -1.15e-259)
		tmp = x;
	elseif (z <= 7.5e-179)
		tmp = t_1;
	elseif (z <= 9.5e-44)
		tmp = x;
	elseif (z <= 4e+101)
		tmp = t_1;
	elseif (z <= 2.8e+237)
		tmp = t_2;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * (-x)), $MachinePrecision]}, Block[{t$95$2 = (-N[(z * t), $MachinePrecision])}, If[LessEqual[z, -5.6e+59], t$95$2, If[LessEqual[z, -1.0], N[(z * x), $MachinePrecision], If[LessEqual[z, -1.15e-259], x, If[LessEqual[z, 7.5e-179], t$95$1, If[LessEqual[z, 9.5e-44], x, If[LessEqual[z, 4e+101], t$95$1, If[LessEqual[z, 2.8e+237], t$95$2, N[(z * x), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.5999999999999996e59 or 3.9999999999999999e101 < z < 2.79999999999999983e237

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 87.6%

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

      1. mul-1-neg 87.6%

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

      2. unsub-neg 87.6%

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

   4. Simplified 87.6%

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

   5. Taylor expanded in x around 0 62.4%

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

      1. associate-*r* 62.4%

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

      2. neg-mul-1 62.4%

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

   7. Simplified 62.4%

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

   if -5.5999999999999996e59 < z < -1 or 2.79999999999999983e237 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 73.1%

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

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

      3. distribute-lft-out-- 73.1%

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

      4. *-rgt-identity 73.1%

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

   4. Simplified 73.1%

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

   5. Taylor expanded in z around inf 57.7%

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

   if -1 < z < -1.15e-259 or 7.4999999999999996e-179 < z < 9.49999999999999924e-44

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 86.4%

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

   3. Taylor expanded in x around inf 45.0%

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

   if -1.15e-259 < z < 7.4999999999999996e-179 or 9.49999999999999924e-44 < z < 3.9999999999999999e101

   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 y around inf 45.5%

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

      1. mul-1-neg 45.5%

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

      2. distribute-rgt-neg-in 45.5%

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

   7. Simplified 45.5%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+59}:\\ \;\;\;\;-z \cdot t\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-259}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-179}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+101}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+237}:\\ \;\;\;\;-z \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 4: 54.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-x\right)\\ t_2 := z \cdot \left(x - t\right)\\ t_3 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;z \leq -130000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-260}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-179}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-42}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- x))) (t_2 (* z (- x t))) (t_3 (* x (+ z 1.0))))
   (if (<= z -130000.0)
     t_2
     (if (<= z -5.6e-260)
       t_3
       (if (<= z 4.7e-179)
         t_1
         (if (<= z 3.9e-42) t_3 (if (<= z 9e+32) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double t_2 = z * (x - t);
	double t_3 = x * (z + 1.0);
	double tmp;
	if (z <= -130000.0) {
		tmp = t_2;
	} else if (z <= -5.6e-260) {
		tmp = t_3;
	} else if (z <= 4.7e-179) {
		tmp = t_1;
	} else if (z <= 3.9e-42) {
		tmp = t_3;
	} else if (z <= 9e+32) {
		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 = y * -x
    t_2 = z * (x - t)
    t_3 = x * (z + 1.0d0)
    if (z <= (-130000.0d0)) then
        tmp = t_2
    else if (z <= (-5.6d-260)) then
        tmp = t_3
    else if (z <= 4.7d-179) then
        tmp = t_1
    else if (z <= 3.9d-42) then
        tmp = t_3
    else if (z <= 9d+32) 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 = y * -x;
	double t_2 = z * (x - t);
	double t_3 = x * (z + 1.0);
	double tmp;
	if (z <= -130000.0) {
		tmp = t_2;
	} else if (z <= -5.6e-260) {
		tmp = t_3;
	} else if (z <= 4.7e-179) {
		tmp = t_1;
	} else if (z <= 3.9e-42) {
		tmp = t_3;
	} else if (z <= 9e+32) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * -x
	t_2 = z * (x - t)
	t_3 = x * (z + 1.0)
	tmp = 0
	if z <= -130000.0:
		tmp = t_2
	elif z <= -5.6e-260:
		tmp = t_3
	elif z <= 4.7e-179:
		tmp = t_1
	elif z <= 3.9e-42:
		tmp = t_3
	elif z <= 9e+32:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(-x))
	t_2 = Float64(z * Float64(x - t))
	t_3 = Float64(x * Float64(z + 1.0))
	tmp = 0.0
	if (z <= -130000.0)
		tmp = t_2;
	elseif (z <= -5.6e-260)
		tmp = t_3;
	elseif (z <= 4.7e-179)
		tmp = t_1;
	elseif (z <= 3.9e-42)
		tmp = t_3;
	elseif (z <= 9e+32)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * -x;
	t_2 = z * (x - t);
	t_3 = x * (z + 1.0);
	tmp = 0.0;
	if (z <= -130000.0)
		tmp = t_2;
	elseif (z <= -5.6e-260)
		tmp = t_3;
	elseif (z <= 4.7e-179)
		tmp = t_1;
	elseif (z <= 3.9e-42)
		tmp = t_3;
	elseif (z <= 9e+32)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * (-x)), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -130000.0], t$95$2, If[LessEqual[z, -5.6e-260], t$95$3, If[LessEqual[z, 4.7e-179], t$95$1, If[LessEqual[z, 3.9e-42], t$95$3, If[LessEqual[z, 9e+32], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3e5 or 9.0000000000000007e32 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 82.8%

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

      1. mul-1-neg 82.8%

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

      2. unsub-neg 82.8%

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

   4. Simplified 82.8%

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

   5. Taylor expanded in z around inf 82.7%

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

   if -1.3e5 < z < -5.5999999999999996e-260 or 4.7000000000000003e-179 < z < 3.9000000000000002e-42

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 63.3%

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

      1. mul-1-neg 63.3%

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

      2. *-commutative 63.3%

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

      3. distribute-rgt-neg-in 63.3%

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

      4. +-commutative 63.3%

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

   4. Simplified 63.3%

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

   5. Taylor expanded in y around 0 47.2%

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

   if -5.5999999999999996e-260 < z < 4.7000000000000003e-179 or 3.9000000000000002e-42 < z < 9.0000000000000007e32

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 68.7%

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

      1. mul-1-neg 68.7%

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

      2. unsub-neg 68.7%

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

      3. distribute-lft-out-- 68.6%

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

      4. *-rgt-identity 68.6%

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

   4. Simplified 68.6%

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

   5. Taylor expanded in y around inf 47.3%

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

      1. mul-1-neg 47.3%

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

      2. distribute-rgt-neg-in 47.3%

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

   7. Simplified 47.3%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -130000:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-260}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-179}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-42}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+32}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 5: 38.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-270}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-178}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.0)
   (* z x)
   (if (<= z -1.65e-270)
     x
     (if (<= z 4.1e-178) (* y t) (if (<= z 1.3e-14) x (* z x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.0) {
		tmp = z * x;
	} else if (z <= -1.65e-270) {
		tmp = x;
	} else if (z <= 4.1e-178) {
		tmp = y * t;
	} else if (z <= 1.3e-14) {
		tmp = x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.0d0)) then
        tmp = z * x
    else if (z <= (-1.65d-270)) then
        tmp = x
    else if (z <= 4.1d-178) then
        tmp = y * t
    else if (z <= 1.3d-14) then
        tmp = x
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.0) {
		tmp = z * x;
	} else if (z <= -1.65e-270) {
		tmp = x;
	} else if (z <= 4.1e-178) {
		tmp = y * t;
	} else if (z <= 1.3e-14) {
		tmp = x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.0:
		tmp = z * x
	elif z <= -1.65e-270:
		tmp = x
	elif z <= 4.1e-178:
		tmp = y * t
	elif z <= 1.3e-14:
		tmp = x
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(z * x);
	elseif (z <= -1.65e-270)
		tmp = x;
	elseif (z <= 4.1e-178)
		tmp = Float64(y * t);
	elseif (z <= 1.3e-14)
		tmp = x;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.0)
		tmp = z * x;
	elseif (z <= -1.65e-270)
		tmp = x;
	elseif (z <= 4.1e-178)
		tmp = y * t;
	elseif (z <= 1.3e-14)
		tmp = x;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.0], N[(z * x), $MachinePrecision], If[LessEqual[z, -1.65e-270], x, If[LessEqual[z, 4.1e-178], N[(y * t), $MachinePrecision], If[LessEqual[z, 1.3e-14], x, N[(z * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1 or 1.29999999999999998e-14 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 52.8%

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

      1. mul-1-neg 52.8%

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

      2. unsub-neg 52.8%

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

      3. distribute-lft-out-- 52.8%

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

      4. *-rgt-identity 52.8%

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

   4. Simplified 52.8%

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

   5. Taylor expanded in z around inf 38.3%

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

   if -1 < z < -1.65000000000000009e-270 or 4.0999999999999999e-178 < z < 1.29999999999999998e-14

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 80.2%

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

   3. Taylor expanded in x around inf 42.5%

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

   if -1.65000000000000009e-270 < z < 4.0999999999999999e-178

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 70.5%

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

   3. Taylor expanded in y around 0 70.5%

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

      1. associate-+r+ 70.5%

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

      2. mul-1-neg 70.5%

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

      3. *-commutative 70.5%

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

      4. sub-neg 70.5%

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

      5. associate-+l- 70.5%

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

   5. Applied egg-rr 70.5%

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

   6. Taylor expanded in y around inf 39.6%

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

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-270}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-178}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 6: 71.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -4:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-42}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{+32}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -4.0)
     t_1
     (if (<= z 2.8e-42) (+ x (* y t)) (if (<= z 5.9e+32) (* y (- x)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -4.0) {
		tmp = t_1;
	} else if (z <= 2.8e-42) {
		tmp = x + (y * t);
	} else if (z <= 5.9e+32) {
		tmp = y * -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 = z * (x - t)
    if (z <= (-4.0d0)) then
        tmp = t_1
    else if (z <= 2.8d-42) then
        tmp = x + (y * t)
    else if (z <= 5.9d+32) then
        tmp = y * -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 = z * (x - t);
	double tmp;
	if (z <= -4.0) {
		tmp = t_1;
	} else if (z <= 2.8e-42) {
		tmp = x + (y * t);
	} else if (z <= 5.9e+32) {
		tmp = y * -x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -4.0:
		tmp = t_1
	elif z <= 2.8e-42:
		tmp = x + (y * t)
	elif z <= 5.9e+32:
		tmp = y * -x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -4.0)
		tmp = t_1;
	elseif (z <= 2.8e-42)
		tmp = Float64(x + Float64(y * t));
	elseif (z <= 5.9e+32)
		tmp = Float64(y * Float64(-x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -4.0)
		tmp = t_1;
	elseif (z <= 2.8e-42)
		tmp = x + (y * t);
	elseif (z <= 5.9e+32)
		tmp = y * -x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.0], t$95$1, If[LessEqual[z, 2.8e-42], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.9e+32], N[(y * (-x)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4 or 5.89999999999999965e32 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 83.2%

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

      1. mul-1-neg 83.2%

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

      2. unsub-neg 83.2%

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

   4. Simplified 83.2%

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

   5. Taylor expanded in z around inf 81.5%

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

   if -4 < z < 2.79999999999999998e-42

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 80.2%

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

   3. Taylor expanded in y around inf 69.0%

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

      1. *-commutative 69.0%

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

   5. Simplified 69.0%

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

   if 2.79999999999999998e-42 < z < 5.89999999999999965e32

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 72.0%

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

      1. mul-1-neg 72.0%

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

      2. unsub-neg 72.0%

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

      3. distribute-lft-out-- 71.9%

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

      4. *-rgt-identity 71.9%

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

   4. Simplified 71.9%

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

   5. Taylor expanded in y around inf 59.1%

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

      1. mul-1-neg 59.1%

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

      2. distribute-rgt-neg-in 59.1%

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

   7. Simplified 59.1%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-42}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{+32}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 7: 76.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+36} \lor \neg \left(z \leq 4.3 \cdot 10^{+52}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6e+36) (not (<= z 4.3e+52)))
   (* z (- x t))
   (- x (* t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6e+36) || !(z <= 4.3e+52)) {
		tmp = z * (x - t);
	} else {
		tmp = x - (t * (z - 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 ((z <= (-6d+36)) .or. (.not. (z <= 4.3d+52))) then
        tmp = z * (x - t)
    else
        tmp = x - (t * (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6e+36) || !(z <= 4.3e+52)) {
		tmp = z * (x - t);
	} else {
		tmp = x - (t * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6e+36) or not (z <= 4.3e+52):
		tmp = z * (x - t)
	else:
		tmp = x - (t * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6e+36) || !(z <= 4.3e+52))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x - Float64(t * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6e+36) || ~((z <= 4.3e+52)))
		tmp = z * (x - t);
	else
		tmp = x - (t * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6e+36], N[Not[LessEqual[z, 4.3e+52]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6e36 or 4.3e52 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 86.2%

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

      1. mul-1-neg 86.2%

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

      2. unsub-neg 86.2%

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

   4. Simplified 86.2%

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

   5. Taylor expanded in z around inf 86.2%

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

   if -6e36 < z < 4.3e52

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 73.0%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+36} \lor \neg \left(z \leq 4.3 \cdot 10^{+52}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \end{array} \]

Alternative 8: 80.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-46} \lor \neg \left(t \leq 2 \cdot 10^{+74}\right):\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -6.5e-46) (not (<= t 2e+74)))
   (- x (* t (- z y)))
   (+ x (* x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.5e-46) || !(t <= 2e+74)) {
		tmp = x - (t * (z - y));
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-6.5d-46)) .or. (.not. (t <= 2d+74))) then
        tmp = x - (t * (z - y))
    else
        tmp = x + (x * (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.5e-46) || !(t <= 2e+74)) {
		tmp = x - (t * (z - y));
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -6.5e-46) or not (t <= 2e+74):
		tmp = x - (t * (z - y))
	else:
		tmp = x + (x * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -6.5e-46) || !(t <= 2e+74))
		tmp = Float64(x - Float64(t * Float64(z - y)));
	else
		tmp = Float64(x + Float64(x * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -6.5e-46) || ~((t <= 2e+74)))
		tmp = x - (t * (z - y));
	else
		tmp = x + (x * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -6.5e-46], N[Not[LessEqual[t, 2e+74]], $MachinePrecision]], N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.49999999999999966e-46 or 1.9999999999999999e74 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 92.0%

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

   if -6.49999999999999966e-46 < t < 1.9999999999999999e74

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 80.9%

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

      1. mul-1-neg 80.9%

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

      2. unsub-neg 80.9%

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

      3. distribute-lft-out-- 80.9%

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

      4. *-rgt-identity 80.9%

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

   4. Simplified 80.9%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-46} \lor \neg \left(t \leq 2 \cdot 10^{+74}\right):\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \]

Alternative 9: 80.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{-45} \lor \neg \left(t \leq 3.35 \cdot 10^{+75}\right):\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z + 1\right) - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.85e-45) (not (<= t 3.35e+75)))
   (- x (* t (- z y)))
   (* x (- (+ z 1.0) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.85e-45) || !(t <= 3.35e+75)) {
		tmp = x - (t * (z - y));
	} else {
		tmp = x * ((z + 1.0) - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.85d-45)) .or. (.not. (t <= 3.35d+75))) then
        tmp = x - (t * (z - y))
    else
        tmp = x * ((z + 1.0d0) - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.85e-45) || !(t <= 3.35e+75)) {
		tmp = x - (t * (z - y));
	} else {
		tmp = x * ((z + 1.0) - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.85e-45) or not (t <= 3.35e+75):
		tmp = x - (t * (z - y))
	else:
		tmp = x * ((z + 1.0) - y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.85e-45) || !(t <= 3.35e+75))
		tmp = Float64(x - Float64(t * Float64(z - y)));
	else
		tmp = Float64(x * Float64(Float64(z + 1.0) - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.85e-45) || ~((t <= 3.35e+75)))
		tmp = x - (t * (z - y));
	else
		tmp = x * ((z + 1.0) - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.85e-45], N[Not[LessEqual[t, 3.35e+75]], $MachinePrecision]], N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z + 1.0), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.85e-45 or 3.35e75 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 92.0%

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

   if -1.85e-45 < t < 3.35e75

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 80.9%

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

      1. mul-1-neg 80.9%

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

      2. *-commutative 80.9%

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

      3. distribute-rgt-neg-in 80.9%

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

      4. +-commutative 80.9%

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

   4. Simplified 80.9%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{-45} \lor \neg \left(t \leq 3.35 \cdot 10^{+75}\right):\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z + 1\right) - y\right)\\ \end{array} \]

Alternative 10: 37.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -1950000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+111}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- x))))
   (if (<= y -1950000.0)
     t_1
     (if (<= y 6.5e-45) x (if (<= y 4.7e+111) (* y t) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double tmp;
	if (y <= -1950000.0) {
		tmp = t_1;
	} else if (y <= 6.5e-45) {
		tmp = x;
	} else if (y <= 4.7e+111) {
		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 <= (-1950000.0d0)) then
        tmp = t_1
    else if (y <= 6.5d-45) then
        tmp = x
    else if (y <= 4.7d+111) 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 <= -1950000.0) {
		tmp = t_1;
	} else if (y <= 6.5e-45) {
		tmp = x;
	} else if (y <= 4.7e+111) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * -x
	tmp = 0
	if y <= -1950000.0:
		tmp = t_1
	elif y <= 6.5e-45:
		tmp = x
	elif y <= 4.7e+111:
		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 <= -1950000.0)
		tmp = t_1;
	elseif (y <= 6.5e-45)
		tmp = x;
	elseif (y <= 4.7e+111)
		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 <= -1950000.0)
		tmp = t_1;
	elseif (y <= 6.5e-45)
		tmp = x;
	elseif (y <= 4.7e+111)
		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, -1950000.0], t$95$1, If[LessEqual[y, 6.5e-45], x, If[LessEqual[y, 4.7e+111], N[(y * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.95e6 or 4.70000000000000008e111 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 60.2%

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

      1. mul-1-neg 60.2%

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

      2. unsub-neg 60.2%

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

      3. distribute-lft-out-- 60.2%

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

      4. *-rgt-identity 60.2%

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

   4. Simplified 60.2%

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

   5. Taylor expanded in y around inf 53.2%

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

      1. mul-1-neg 53.2%

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

      2. distribute-rgt-neg-in 53.2%

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

   7. Simplified 53.2%

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

   if -1.95e6 < y < 6.4999999999999995e-45

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 77.8%

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

   3. Taylor expanded in x around inf 35.7%

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

   if 6.4999999999999995e-45 < y < 4.70000000000000008e111

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 62.4%

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

   3. Taylor expanded in y around 0 62.4%

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

      1. associate-+r+ 62.4%

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

      2. mul-1-neg 62.4%

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

      3. *-commutative 62.4%

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

      4. sub-neg 62.4%

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

      5. associate-+l- 62.4%

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

   5. Applied egg-rr 62.4%

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

   6. Taylor expanded in y around inf 37.7%

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

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1950000:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+111}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]

Alternative 11: 49.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+41} \lor \neg \left(y \leq 9.5 \cdot 10^{+30}\right):\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.2e+41) (not (<= y 9.5e+30))) (* y (- x)) (* x (+ z 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.2e+41) || !(y <= 9.5e+30)) {
		tmp = y * -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 <= (-6.2d+41)) .or. (.not. (y <= 9.5d+30))) then
        tmp = y * -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 <= -6.2e+41) || !(y <= 9.5e+30)) {
		tmp = y * -x;
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.2e+41) or not (y <= 9.5e+30):
		tmp = y * -x
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.2e+41) || !(y <= 9.5e+30))
		tmp = Float64(y * Float64(-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 <= -6.2e+41) || ~((y <= 9.5e+30)))
		tmp = y * -x;
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.2e+41], N[Not[LessEqual[y, 9.5e+30]], $MachinePrecision]], N[(y * (-x)), $MachinePrecision], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.2e41 or 9.5000000000000003e30 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 56.4%

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

      1. mul-1-neg 56.4%

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

      2. unsub-neg 56.4%

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

      3. distribute-lft-out-- 56.4%

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

      4. *-rgt-identity 56.4%

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

   4. Simplified 56.4%

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

   5. Taylor expanded in y around inf 51.6%

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

      1. mul-1-neg 51.6%

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

      2. distribute-rgt-neg-in 51.6%

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

   7. Simplified 51.6%

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

   if -6.2e41 < y < 9.5000000000000003e30

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 59.6%

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

      1. mul-1-neg 59.6%

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

      2. *-commutative 59.6%

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

      3. distribute-rgt-neg-in 59.6%

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

      4. +-commutative 59.6%

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

   4. Simplified 59.6%

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

   5. Taylor expanded in y around 0 58.0%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+41} \lor \neg \left(y \leq 9.5 \cdot 10^{+30}\right):\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]

Alternative 12: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 13: 38.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-23}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.3e-23) (* y t) (if (<= y 9e-45) x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.3e-23) {
		tmp = y * t;
	} else if (y <= 9e-45) {
		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 <= (-1.3d-23)) then
        tmp = y * t
    else if (y <= 9d-45) 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 <= -1.3e-23) {
		tmp = y * t;
	} else if (y <= 9e-45) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.3e-23:
		tmp = y * t
	elif y <= 9e-45:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.3e-23)
		tmp = Float64(y * t);
	elseif (y <= 9e-45)
		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 <= -1.3e-23)
		tmp = y * t;
	elseif (y <= 9e-45)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.3e-23], N[(y * t), $MachinePrecision], If[LessEqual[y, 9e-45], x, N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3e-23 or 8.9999999999999997e-45 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 54.4%

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

   3. Taylor expanded in y around 0 48.4%

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

      1. associate-+r+ 48.4%

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

      2. mul-1-neg 48.4%

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

      3. *-commutative 48.4%

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

      4. sub-neg 48.4%

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

      5. associate-+l- 48.4%

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

   5. Applied egg-rr 48.4%

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

   6. Taylor expanded in y around inf 36.5%

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

   if -1.3e-23 < y < 8.9999999999999997e-45

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 77.2%

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

   3. Taylor expanded in x around inf 36.5%

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

4. Final simplification 36.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-23}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 14: 18.1% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in t around inf 65.4%

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

3. Taylor expanded in x around inf 19.5%

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

4. Final simplification 19.5%

   \[\leadsto x \]

Developer target: 96.4% 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 2023287 
(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))))