Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 7.8s

Alternatives: 13

Speedup: 1.0×

• 34.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-def 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 56.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := z \cdot \left(-t\right)\\ \mathbf{if}\;y \leq -0.00032:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-169}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-283}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-169}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.7 \cdot 10^{-128}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-6}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* z (- t))))
   (if (<= y -0.00032)
     t_1
     (if (<= y -3.8e-169)
       t_2
       (if (<= y -7.5e-283)
         x
         (if (<= y 4e-169)
           t_2
           (if (<= y 7.7e-128) x (if (<= y 1.65e-6) (* z x) t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = z * -t;
	double tmp;
	if (y <= -0.00032) {
		tmp = t_1;
	} else if (y <= -3.8e-169) {
		tmp = t_2;
	} else if (y <= -7.5e-283) {
		tmp = x;
	} else if (y <= 4e-169) {
		tmp = t_2;
	} else if (y <= 7.7e-128) {
		tmp = x;
	} else if (y <= 1.65e-6) {
		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) :: t_2
    real(8) :: tmp
    t_1 = y * (t - x)
    t_2 = z * -t
    if (y <= (-0.00032d0)) then
        tmp = t_1
    else if (y <= (-3.8d-169)) then
        tmp = t_2
    else if (y <= (-7.5d-283)) then
        tmp = x
    else if (y <= 4d-169) then
        tmp = t_2
    else if (y <= 7.7d-128) then
        tmp = x
    else if (y <= 1.65d-6) 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 t_2 = z * -t;
	double tmp;
	if (y <= -0.00032) {
		tmp = t_1;
	} else if (y <= -3.8e-169) {
		tmp = t_2;
	} else if (y <= -7.5e-283) {
		tmp = x;
	} else if (y <= 4e-169) {
		tmp = t_2;
	} else if (y <= 7.7e-128) {
		tmp = x;
	} else if (y <= 1.65e-6) {
		tmp = z * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = z * -t
	tmp = 0
	if y <= -0.00032:
		tmp = t_1
	elif y <= -3.8e-169:
		tmp = t_2
	elif y <= -7.5e-283:
		tmp = x
	elif y <= 4e-169:
		tmp = t_2
	elif y <= 7.7e-128:
		tmp = x
	elif y <= 1.65e-6:
		tmp = z * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(z * Float64(-t))
	tmp = 0.0
	if (y <= -0.00032)
		tmp = t_1;
	elseif (y <= -3.8e-169)
		tmp = t_2;
	elseif (y <= -7.5e-283)
		tmp = x;
	elseif (y <= 4e-169)
		tmp = t_2;
	elseif (y <= 7.7e-128)
		tmp = x;
	elseif (y <= 1.65e-6)
		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);
	t_2 = z * -t;
	tmp = 0.0;
	if (y <= -0.00032)
		tmp = t_1;
	elseif (y <= -3.8e-169)
		tmp = t_2;
	elseif (y <= -7.5e-283)
		tmp = x;
	elseif (y <= 4e-169)
		tmp = t_2;
	elseif (y <= 7.7e-128)
		tmp = x;
	elseif (y <= 1.65e-6)
		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]}, Block[{t$95$2 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[y, -0.00032], t$95$1, If[LessEqual[y, -3.8e-169], t$95$2, If[LessEqual[y, -7.5e-283], x, If[LessEqual[y, 4e-169], t$95$2, If[LessEqual[y, 7.7e-128], x, If[LessEqual[y, 1.65e-6], N[(z * x), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.20000000000000026e-4 or 1.65000000000000008e-6 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 79.1%

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

   3. Taylor expanded in y around inf 76.9%

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

   if -3.20000000000000026e-4 < y < -3.8e-169 or -7.5000000000000001e-283 < y < 4.00000000000000008e-169

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 93.9%

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

      1. +-commutative 93.9%

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

      2. mul-1-neg 93.9%

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

      3. unsub-neg 93.9%

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

      4. *-commutative 93.9%

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

   4. Simplified 93.9%

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

   5. Taylor expanded in x around 0 43.3%

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

      1. mul-1-neg 43.3%

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

      2. distribute-rgt-neg-in 43.3%

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

   7. Simplified 43.3%

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

   if -3.8e-169 < y < -7.5000000000000001e-283 or 4.00000000000000008e-169 < y < 7.7e-128

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 88.0%

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

   3. Taylor expanded in x around inf 64.9%

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

   if 7.7e-128 < y < 1.65000000000000008e-6

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 66.5%

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

      1. *-commutative 66.5%

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

      2. mul-1-neg 66.5%

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

      3. unsub-neg 66.5%

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

      4. distribute-lft-out-- 66.5%

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

      5. *-rgt-identity 66.5%

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

   4. Simplified 66.5%

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

   5. Taylor expanded in z around inf 54.9%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00032:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-169}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-283}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-169}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 7.7 \cdot 10^{-128}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-6}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 3: 67.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot x\\ t_2 := y \cdot \left(t - x\right)\\ t_3 := z \cdot \left(x - t\right)\\ \mathbf{if}\;y \leq -11.5:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-105}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-285}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-229}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.14 \cdot 10^{-128}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+76}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* z x))) (t_2 (* y (- t x))) (t_3 (* z (- x t))))
   (if (<= y -11.5)
     t_2
     (if (<= y -4.8e-105)
       t_3
       (if (<= y -6.5e-285)
         t_1
         (if (<= y 1.12e-229)
           t_3
           (if (<= y 1.14e-128) t_1 (if (<= y 1.22e+76) t_3 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (z * x);
	double t_2 = y * (t - x);
	double t_3 = z * (x - t);
	double tmp;
	if (y <= -11.5) {
		tmp = t_2;
	} else if (y <= -4.8e-105) {
		tmp = t_3;
	} else if (y <= -6.5e-285) {
		tmp = t_1;
	} else if (y <= 1.12e-229) {
		tmp = t_3;
	} else if (y <= 1.14e-128) {
		tmp = t_1;
	} else if (y <= 1.22e+76) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (z * x)
    t_2 = y * (t - x)
    t_3 = z * (x - t)
    if (y <= (-11.5d0)) then
        tmp = t_2
    else if (y <= (-4.8d-105)) then
        tmp = t_3
    else if (y <= (-6.5d-285)) then
        tmp = t_1
    else if (y <= 1.12d-229) then
        tmp = t_3
    else if (y <= 1.14d-128) then
        tmp = t_1
    else if (y <= 1.22d+76) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (z * x);
	double t_2 = y * (t - x);
	double t_3 = z * (x - t);
	double tmp;
	if (y <= -11.5) {
		tmp = t_2;
	} else if (y <= -4.8e-105) {
		tmp = t_3;
	} else if (y <= -6.5e-285) {
		tmp = t_1;
	} else if (y <= 1.12e-229) {
		tmp = t_3;
	} else if (y <= 1.14e-128) {
		tmp = t_1;
	} else if (y <= 1.22e+76) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (z * x)
	t_2 = y * (t - x)
	t_3 = z * (x - t)
	tmp = 0
	if y <= -11.5:
		tmp = t_2
	elif y <= -4.8e-105:
		tmp = t_3
	elif y <= -6.5e-285:
		tmp = t_1
	elif y <= 1.12e-229:
		tmp = t_3
	elif y <= 1.14e-128:
		tmp = t_1
	elif y <= 1.22e+76:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(z * x))
	t_2 = Float64(y * Float64(t - x))
	t_3 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (y <= -11.5)
		tmp = t_2;
	elseif (y <= -4.8e-105)
		tmp = t_3;
	elseif (y <= -6.5e-285)
		tmp = t_1;
	elseif (y <= 1.12e-229)
		tmp = t_3;
	elseif (y <= 1.14e-128)
		tmp = t_1;
	elseif (y <= 1.22e+76)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (z * x);
	t_2 = y * (t - x);
	t_3 = z * (x - t);
	tmp = 0.0;
	if (y <= -11.5)
		tmp = t_2;
	elseif (y <= -4.8e-105)
		tmp = t_3;
	elseif (y <= -6.5e-285)
		tmp = t_1;
	elseif (y <= 1.12e-229)
		tmp = t_3;
	elseif (y <= 1.14e-128)
		tmp = t_1;
	elseif (y <= 1.22e+76)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -11.5], t$95$2, If[LessEqual[y, -4.8e-105], t$95$3, If[LessEqual[y, -6.5e-285], t$95$1, If[LessEqual[y, 1.12e-229], t$95$3, If[LessEqual[y, 1.14e-128], t$95$1, If[LessEqual[y, 1.22e+76], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -11.5 or 1.22000000000000002e76 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 86.1%

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

   3. Taylor expanded in y around inf 85.4%

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

   if -11.5 < y < -4.8000000000000003e-105 or -6.5e-285 < y < 1.12e-229 or 1.14e-128 < y < 1.22000000000000002e76

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 81.6%

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

      1. +-commutative 81.6%

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

      2. mul-1-neg 81.6%

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

      3. unsub-neg 81.6%

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

      4. *-commutative 81.6%

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

   4. Simplified 81.6%

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

   5. Taylor expanded in z around inf 67.5%

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

   if -4.8000000000000003e-105 < y < -6.5e-285 or 1.12e-229 < y < 1.14e-128

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 93.0%

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

      1. +-commutative 93.0%

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

      2. mul-1-neg 93.0%

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

      3. unsub-neg 93.0%

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

      4. *-commutative 93.0%

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

   4. Simplified 93.0%

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

   5. Taylor expanded in x around inf 71.5%

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

      1. *-commutative 71.5%

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

      2. sub-neg 71.5%

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

      3. neg-mul-1 71.5%

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

      4. remove-double-neg 71.5%

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

      5. distribute-rgt-in 71.5%

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

      6. *-lft-identity 71.5%

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

   7. Simplified 71.5%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -11.5:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-105}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-285}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-229}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 1.14 \cdot 10^{-128}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+76}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 4: 37.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;y \leq -0.0026:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-285}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-127}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+88}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= y -0.0026)
     (* y t)
     (if (<= y -3.6e-169)
       t_1
       (if (<= y -2.6e-285)
         x
         (if (<= y 1.45e-168)
           t_1
           (if (<= y 2.6e-127) x (if (<= y 8.5e+88) (* z x) (* y t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (y <= -0.0026) {
		tmp = y * t;
	} else if (y <= -3.6e-169) {
		tmp = t_1;
	} else if (y <= -2.6e-285) {
		tmp = x;
	} else if (y <= 1.45e-168) {
		tmp = t_1;
	} else if (y <= 2.6e-127) {
		tmp = x;
	} else if (y <= 8.5e+88) {
		tmp = z * 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) :: t_1
    real(8) :: tmp
    t_1 = z * -t
    if (y <= (-0.0026d0)) then
        tmp = y * t
    else if (y <= (-3.6d-169)) then
        tmp = t_1
    else if (y <= (-2.6d-285)) then
        tmp = x
    else if (y <= 1.45d-168) then
        tmp = t_1
    else if (y <= 2.6d-127) then
        tmp = x
    else if (y <= 8.5d+88) then
        tmp = z * 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 t_1 = z * -t;
	double tmp;
	if (y <= -0.0026) {
		tmp = y * t;
	} else if (y <= -3.6e-169) {
		tmp = t_1;
	} else if (y <= -2.6e-285) {
		tmp = x;
	} else if (y <= 1.45e-168) {
		tmp = t_1;
	} else if (y <= 2.6e-127) {
		tmp = x;
	} else if (y <= 8.5e+88) {
		tmp = z * x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if y <= -0.0026:
		tmp = y * t
	elif y <= -3.6e-169:
		tmp = t_1
	elif y <= -2.6e-285:
		tmp = x
	elif y <= 1.45e-168:
		tmp = t_1
	elif y <= 2.6e-127:
		tmp = x
	elif y <= 8.5e+88:
		tmp = z * x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (y <= -0.0026)
		tmp = Float64(y * t);
	elseif (y <= -3.6e-169)
		tmp = t_1;
	elseif (y <= -2.6e-285)
		tmp = x;
	elseif (y <= 1.45e-168)
		tmp = t_1;
	elseif (y <= 2.6e-127)
		tmp = x;
	elseif (y <= 8.5e+88)
		tmp = Float64(z * x);
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (y <= -0.0026)
		tmp = y * t;
	elseif (y <= -3.6e-169)
		tmp = t_1;
	elseif (y <= -2.6e-285)
		tmp = x;
	elseif (y <= 1.45e-168)
		tmp = t_1;
	elseif (y <= 2.6e-127)
		tmp = x;
	elseif (y <= 8.5e+88)
		tmp = z * x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[y, -0.0026], N[(y * t), $MachinePrecision], If[LessEqual[y, -3.6e-169], t$95$1, If[LessEqual[y, -2.6e-285], x, If[LessEqual[y, 1.45e-168], t$95$1, If[LessEqual[y, 2.6e-127], x, If[LessEqual[y, 8.5e+88], N[(z * x), $MachinePrecision], N[(y * t), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -0.0025999999999999999 or 8.5000000000000005e88 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 85.0%

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

   3. Taylor expanded in y around inf 83.4%

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

   4. Taylor expanded in t around inf 55.3%

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

   if -0.0025999999999999999 < y < -3.60000000000000001e-169 or -2.6000000000000002e-285 < y < 1.4499999999999999e-168

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 93.9%

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

      1. +-commutative 93.9%

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

      2. mul-1-neg 93.9%

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

      3. unsub-neg 93.9%

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

      4. *-commutative 93.9%

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

   4. Simplified 93.9%

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

   5. Taylor expanded in x around 0 43.3%

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

      1. mul-1-neg 43.3%

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

      2. distribute-rgt-neg-in 43.3%

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

   7. Simplified 43.3%

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

   if -3.60000000000000001e-169 < y < -2.6000000000000002e-285 or 1.4499999999999999e-168 < y < 2.59999999999999991e-127

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 88.0%

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

   3. Taylor expanded in x around inf 64.9%

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

   if 2.59999999999999991e-127 < y < 8.5000000000000005e88

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 72.9%

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

      1. *-commutative 72.9%

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

      2. mul-1-neg 72.9%

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

      3. unsub-neg 72.9%

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

      4. distribute-lft-out-- 72.9%

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

      5. *-rgt-identity 72.9%

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

   4. Simplified 72.9%

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

   5. Taylor expanded in z around inf 47.7%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0026:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-169}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-285}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-168}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-127}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+88}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 5: 35.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+18}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-284}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-187}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-128}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+92}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.05e+18)
   (* y t)
   (if (<= y -5e-284)
     x
     (if (<= y 1.7e-187)
       (* z x)
       (if (<= y 1.2e-128) x (if (<= y 1.8e+92) (* z x) (* y t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.05e+18) {
		tmp = y * t;
	} else if (y <= -5e-284) {
		tmp = x;
	} else if (y <= 1.7e-187) {
		tmp = z * x;
	} else if (y <= 1.2e-128) {
		tmp = x;
	} else if (y <= 1.8e+92) {
		tmp = z * 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 <= (-1.05d+18)) then
        tmp = y * t
    else if (y <= (-5d-284)) then
        tmp = x
    else if (y <= 1.7d-187) then
        tmp = z * x
    else if (y <= 1.2d-128) then
        tmp = x
    else if (y <= 1.8d+92) then
        tmp = z * 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 <= -1.05e+18) {
		tmp = y * t;
	} else if (y <= -5e-284) {
		tmp = x;
	} else if (y <= 1.7e-187) {
		tmp = z * x;
	} else if (y <= 1.2e-128) {
		tmp = x;
	} else if (y <= 1.8e+92) {
		tmp = z * x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.05e+18:
		tmp = y * t
	elif y <= -5e-284:
		tmp = x
	elif y <= 1.7e-187:
		tmp = z * x
	elif y <= 1.2e-128:
		tmp = x
	elif y <= 1.8e+92:
		tmp = z * x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.05e+18)
		tmp = Float64(y * t);
	elseif (y <= -5e-284)
		tmp = x;
	elseif (y <= 1.7e-187)
		tmp = Float64(z * x);
	elseif (y <= 1.2e-128)
		tmp = x;
	elseif (y <= 1.8e+92)
		tmp = Float64(z * x);
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.05e+18)
		tmp = y * t;
	elseif (y <= -5e-284)
		tmp = x;
	elseif (y <= 1.7e-187)
		tmp = z * x;
	elseif (y <= 1.2e-128)
		tmp = x;
	elseif (y <= 1.8e+92)
		tmp = z * x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.05e+18], N[(y * t), $MachinePrecision], If[LessEqual[y, -5e-284], x, If[LessEqual[y, 1.7e-187], N[(z * x), $MachinePrecision], If[LessEqual[y, 1.2e-128], x, If[LessEqual[y, 1.8e+92], N[(z * x), $MachinePrecision], N[(y * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.05e18 or 1.8e92 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 85.4%

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

   3. Taylor expanded in y around inf 85.4%

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

   4. Taylor expanded in t around inf 57.4%

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

   if -1.05e18 < y < -4.99999999999999973e-284 or 1.7000000000000001e-187 < y < 1.1999999999999999e-128

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 77.4%

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

   3. Taylor expanded in x around inf 41.6%

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

   if -4.99999999999999973e-284 < y < 1.7000000000000001e-187 or 1.1999999999999999e-128 < y < 1.8e92

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 68.5%

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

      1. *-commutative 68.5%

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

      2. mul-1-neg 68.5%

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

      3. unsub-neg 68.5%

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

      4. distribute-lft-out-- 68.5%

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

      5. *-rgt-identity 68.5%

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

   4. Simplified 68.5%

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

   5. Taylor expanded in z around inf 44.2%

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

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+18}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-284}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-187}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-128}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+92}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 6: 65.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := z \cdot \left(x - t\right)\\ \mathbf{if}\;y \leq -12:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-170}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-283}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+77}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* z (- x t))))
   (if (<= y -12.0)
     t_1
     (if (<= y -9.5e-170)
       t_2
       (if (<= y -1.95e-283) x (if (<= y 2.05e+77) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = z * (x - t);
	double tmp;
	if (y <= -12.0) {
		tmp = t_1;
	} else if (y <= -9.5e-170) {
		tmp = t_2;
	} else if (y <= -1.95e-283) {
		tmp = x;
	} else if (y <= 2.05e+77) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (t - x)
    t_2 = z * (x - t)
    if (y <= (-12.0d0)) then
        tmp = t_1
    else if (y <= (-9.5d-170)) then
        tmp = t_2
    else if (y <= (-1.95d-283)) then
        tmp = x
    else if (y <= 2.05d+77) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = z * (x - t);
	double tmp;
	if (y <= -12.0) {
		tmp = t_1;
	} else if (y <= -9.5e-170) {
		tmp = t_2;
	} else if (y <= -1.95e-283) {
		tmp = x;
	} else if (y <= 2.05e+77) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = z * (x - t)
	tmp = 0
	if y <= -12.0:
		tmp = t_1
	elif y <= -9.5e-170:
		tmp = t_2
	elif y <= -1.95e-283:
		tmp = x
	elif y <= 2.05e+77:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (y <= -12.0)
		tmp = t_1;
	elseif (y <= -9.5e-170)
		tmp = t_2;
	elseif (y <= -1.95e-283)
		tmp = x;
	elseif (y <= 2.05e+77)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	t_2 = z * (x - t);
	tmp = 0.0;
	if (y <= -12.0)
		tmp = t_1;
	elseif (y <= -9.5e-170)
		tmp = t_2;
	elseif (y <= -1.95e-283)
		tmp = x;
	elseif (y <= 2.05e+77)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -12.0], t$95$1, If[LessEqual[y, -9.5e-170], t$95$2, If[LessEqual[y, -1.95e-283], x, If[LessEqual[y, 2.05e+77], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -12 or 2.05e77 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 86.1%

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

   3. Taylor expanded in y around inf 85.4%

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

   if -12 < y < -9.5000000000000001e-170 or -1.9500000000000001e-283 < y < 2.05e77

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 84.7%

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

      1. +-commutative 84.7%

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

      2. mul-1-neg 84.7%

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

      3. unsub-neg 84.7%

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

      4. *-commutative 84.7%

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

   4. Simplified 84.7%

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

   5. Taylor expanded in z around inf 64.3%

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

   if -9.5000000000000001e-170 < y < -1.9500000000000001e-283

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 91.9%

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

   3. Taylor expanded in x around inf 63.8%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -12:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-170}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-283}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+77}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 7: 83.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -10.5:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-10}:\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+80}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y (- t x)))))
   (if (<= y -10.5)
     t_1
     (if (<= y 7e-10)
       (- x (* z (- t x)))
       (if (<= y 3.8e+80) (+ x (* x (- z y))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (t - x));
	double tmp;
	if (y <= -10.5) {
		tmp = t_1;
	} else if (y <= 7e-10) {
		tmp = x - (z * (t - x));
	} else if (y <= 3.8e+80) {
		tmp = x + (x * (z - y));
	} 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 = x + (y * (t - x))
    if (y <= (-10.5d0)) then
        tmp = t_1
    else if (y <= 7d-10) then
        tmp = x - (z * (t - x))
    else if (y <= 3.8d+80) then
        tmp = x + (x * (z - y))
    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 = x + (y * (t - x));
	double tmp;
	if (y <= -10.5) {
		tmp = t_1;
	} else if (y <= 7e-10) {
		tmp = x - (z * (t - x));
	} else if (y <= 3.8e+80) {
		tmp = x + (x * (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * (t - x))
	tmp = 0
	if y <= -10.5:
		tmp = t_1
	elif y <= 7e-10:
		tmp = x - (z * (t - x))
	elif y <= 3.8e+80:
		tmp = x + (x * (z - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * Float64(t - x)))
	tmp = 0.0
	if (y <= -10.5)
		tmp = t_1;
	elseif (y <= 7e-10)
		tmp = Float64(x - Float64(z * Float64(t - x)));
	elseif (y <= 3.8e+80)
		tmp = Float64(x + Float64(x * Float64(z - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * (t - x));
	tmp = 0.0;
	if (y <= -10.5)
		tmp = t_1;
	elseif (y <= 7e-10)
		tmp = x - (z * (t - x));
	elseif (y <= 3.8e+80)
		tmp = x + (x * (z - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -10.5], t$95$1, If[LessEqual[y, 7e-10], N[(x - N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e+80], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -10.5 or 3.79999999999999997e80 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 86.1%

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

   if -10.5 < y < 6.99999999999999961e-10

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 90.8%

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

      1. +-commutative 90.8%

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

      2. mul-1-neg 90.8%

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

      3. unsub-neg 90.8%

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

      4. *-commutative 90.8%

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

   4. Simplified 90.8%

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

   if 6.99999999999999961e-10 < y < 3.79999999999999997e80

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 79.0%

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

      1. *-commutative 79.0%

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

      2. mul-1-neg 79.0%

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

      3. unsub-neg 79.0%

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

      4. distribute-lft-out-- 79.0%

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

      5. *-rgt-identity 79.0%

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

   4. Simplified 79.0%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -10.5:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-10}:\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+80}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 8: 77.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -75000000000000 \lor \neg \left(z \leq 5.6 \cdot 10^{+42}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -75000000000000.0) (not (<= z 5.6e+42)))
   (* z (- x t))
   (+ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -75000000000000.0) || !(z <= 5.6e+42)) {
		tmp = z * (x - t);
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-75000000000000.0d0)) .or. (.not. (z <= 5.6d+42))) then
        tmp = z * (x - t)
    else
        tmp = x + ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -75000000000000.0) || !(z <= 5.6e+42)) {
		tmp = z * (x - t);
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -75000000000000.0) or not (z <= 5.6e+42):
		tmp = z * (x - t)
	else:
		tmp = x + ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -75000000000000.0) || !(z <= 5.6e+42))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x + Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -75000000000000.0) || ~((z <= 5.6e+42)))
		tmp = z * (x - t);
	else
		tmp = x + ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -75000000000000.0], N[Not[LessEqual[z, 5.6e+42]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.5e13 or 5.5999999999999999e42 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 80.2%

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

      1. +-commutative 80.2%

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

      2. mul-1-neg 80.2%

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

      3. unsub-neg 80.2%

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

      4. *-commutative 80.2%

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

   4. Simplified 80.2%

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

   5. Taylor expanded in z around inf 80.2%

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

   if -7.5e13 < z < 5.5999999999999999e42

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 79.7%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -75000000000000 \lor \neg \left(z \leq 5.6 \cdot 10^{+42}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]

Alternative 9: 83.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00029 \lor \neg \left(z \leq 9.8 \cdot 10^{+95}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.00029) (not (<= z 9.8e+95)))
   (* z (- x t))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.00029) || !(z <= 9.8e+95)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-0.00029d0)) .or. (.not. (z <= 9.8d+95))) then
        tmp = z * (x - t)
    else
        tmp = x + (y * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.00029) || !(z <= 9.8e+95)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -0.00029) or not (z <= 9.8e+95):
		tmp = z * (x - t)
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -0.00029) || !(z <= 9.8e+95))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x + Float64(y * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -0.00029) || ~((z <= 9.8e+95)))
		tmp = z * (x - t);
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -0.00029], N[Not[LessEqual[z, 9.8e+95]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.9e-4 or 9.7999999999999998e95 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 83.9%

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

      1. +-commutative 83.9%

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

      2. mul-1-neg 83.9%

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

      3. unsub-neg 83.9%

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

      4. *-commutative 83.9%

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

   4. Simplified 83.9%

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

   5. Taylor expanded in z around inf 83.5%

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

   if -2.9e-4 < z < 9.7999999999999998e95

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 87.3%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00029 \lor \neg \left(z \leq 9.8 \cdot 10^{+95}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 10: 72.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-5} \lor \neg \left(z \leq 0.0136\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.8e-5) (not (<= z 0.0136))) (* z (- x t)) (+ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.8e-5) || !(z <= 0.0136)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (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 ((z <= (-5.8d-5)) .or. (.not. (z <= 0.0136d0))) then
        tmp = z * (x - t)
    else
        tmp = x + (y * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.8e-5) || !(z <= 0.0136)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.8e-5) or not (z <= 0.0136):
		tmp = z * (x - t)
	else:
		tmp = x + (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.8e-5) || !(z <= 0.0136))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x + Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.8e-5) || ~((z <= 0.0136)))
		tmp = z * (x - t);
	else
		tmp = x + (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.8e-5], N[Not[LessEqual[z, 0.0136]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.8e-5 or 0.0135999999999999992 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 79.6%

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

      1. +-commutative 79.6%

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

      2. mul-1-neg 79.6%

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

      3. unsub-neg 79.6%

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

      4. *-commutative 79.6%

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

   4. Simplified 79.6%

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

   5. Taylor expanded in z around inf 78.6%

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

   if -5.8e-5 < z < 0.0135999999999999992

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 79.6%

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

   3. Taylor expanded in z around 0 71.9%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-5} \lor \neg \left(z \leq 0.0136\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]

Alternative 11: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x - ((t - x) * (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 - ((t - x) * (z - y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(x - N[(N[(t - x), $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%

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

Alternative 12: 36.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+18}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.05e+18) (* y t) (if (<= y 2.35e-91) x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.05e+18) {
		tmp = y * t;
	} else if (y <= 2.35e-91) {
		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 <= (-1.05d+18)) then
        tmp = y * t
    else if (y <= 2.35d-91) 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 <= -1.05e+18) {
		tmp = y * t;
	} else if (y <= 2.35e-91) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.05e+18:
		tmp = y * t
	elif y <= 2.35e-91:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.05e+18)
		tmp = Float64(y * t);
	elseif (y <= 2.35e-91)
		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 <= -1.05e+18)
		tmp = y * t;
	elseif (y <= 2.35e-91)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.05e+18], N[(y * t), $MachinePrecision], If[LessEqual[y, 2.35e-91], x, N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e18 or 2.35000000000000003e-91 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 73.0%

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

   3. Taylor expanded in y around inf 70.8%

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

   4. Taylor expanded in t around inf 44.7%

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

   if -1.05e18 < y < 2.35000000000000003e-91

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 73.3%

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

   3. Taylor expanded in x around inf 35.7%

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

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+18}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 13: 17.9% 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 64.7%

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

3. Taylor expanded in x around inf 18.5%

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

4. Final simplification 18.5%

   \[\leadsto x \]

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 2023207 
(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))))