Diagrams.Trail:splitAtParam from diagrams-lib-1.3.0.3, A

Percentage Accurate: 89.5% → 98.2%

Time: 12.7s

Alternatives: 9

Speedup: 0.3×

Specification

Math

\[\begin{array}{l} \\ \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))

C

double code(double x, double y, double z, double t) {
	return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
}

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) - x) / ((t * z) - x))) / (x + 1.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
}

Python

def code(x, y, z, t):
	return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 89.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))

C

double code(double x, double y, double z, double t) {
	return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
}

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) - x) / ((t * z) - x))) / (x + 1.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
}

Python

def code(x, y, z, t):
	return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x - \frac{x - y \cdot z}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+230}:\\ \;\;\;\;\frac{y \cdot \left(\frac{z}{x - z \cdot t} + \frac{\frac{x}{t\_1} - x}{y}\right)}{-1 - x}\\ \mathbf{elif}\;t\_2 \leq 10^{+52}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;\frac{y}{\left(x + 1\right) \cdot \frac{t\_1}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x \cdot \left(1 + \frac{1}{x}\right)} + \frac{\frac{y}{x + 1} + \frac{\frac{x}{z}}{-1 - x}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)) (t_2 (/ (- x (/ (- x (* y z)) t_1)) (+ x 1.0))))
   (if (<= t_2 -2e+230)
     (/ (* y (+ (/ z (- x (* z t))) (/ (- (/ x t_1) x) y))) (- -1.0 x))
     (if (<= t_2 1e+52)
       t_2
       (if (<= t_2 INFINITY)
         (/ y (* (+ x 1.0) (/ t_1 z)))
         (+
          (/ x (* x (+ 1.0 (/ 1.0 x))))
          (/ (+ (/ y (+ x 1.0)) (/ (/ x z) (- -1.0 x))) t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x - ((x - (y * z)) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -2e+230) {
		tmp = (y * ((z / (x - (z * t))) + (((x / t_1) - x) / y))) / (-1.0 - x);
	} else if (t_2 <= 1e+52) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = y / ((x + 1.0) * (t_1 / z));
	} else {
		tmp = (x / (x * (1.0 + (1.0 / x)))) + (((y / (x + 1.0)) + ((x / z) / (-1.0 - x))) / t);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x - ((x - (y * z)) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -2e+230) {
		tmp = (y * ((z / (x - (z * t))) + (((x / t_1) - x) / y))) / (-1.0 - x);
	} else if (t_2 <= 1e+52) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = y / ((x + 1.0) * (t_1 / z));
	} else {
		tmp = (x / (x * (1.0 + (1.0 / x)))) + (((y / (x + 1.0)) + ((x / z) / (-1.0 - x))) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = (x - ((x - (y * z)) / t_1)) / (x + 1.0)
	tmp = 0
	if t_2 <= -2e+230:
		tmp = (y * ((z / (x - (z * t))) + (((x / t_1) - x) / y))) / (-1.0 - x)
	elif t_2 <= 1e+52:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = y / ((x + 1.0) * (t_1 / z))
	else:
		tmp = (x / (x * (1.0 + (1.0 / x)))) + (((y / (x + 1.0)) + ((x / z) / (-1.0 - x))) / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(x - Float64(Float64(x - Float64(y * z)) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -2e+230)
		tmp = Float64(Float64(y * Float64(Float64(z / Float64(x - Float64(z * t))) + Float64(Float64(Float64(x / t_1) - x) / y))) / Float64(-1.0 - x));
	elseif (t_2 <= 1e+52)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(y / Float64(Float64(x + 1.0) * Float64(t_1 / z)));
	else
		tmp = Float64(Float64(x / Float64(x * Float64(1.0 + Float64(1.0 / x)))) + Float64(Float64(Float64(y / Float64(x + 1.0)) + Float64(Float64(x / z) / Float64(-1.0 - x))) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = (x - ((x - (y * z)) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -2e+230)
		tmp = (y * ((z / (x - (z * t))) + (((x / t_1) - x) / y))) / (-1.0 - x);
	elseif (t_2 <= 1e+52)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = y / ((x + 1.0) * (t_1 / z));
	else
		tmp = (x / (x * (1.0 + (1.0 / x)))) + (((y / (x + 1.0)) + ((x / z) / (-1.0 - x))) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+230], N[(N[(y * N[(N[(z / N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x / t$95$1), $MachinePrecision] - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+52], t$95$2, If[LessEqual[t$95$2, Infinity], N[(y / N[(N[(x + 1.0), $MachinePrecision] * N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(x * N[(1.0 + N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x / z), $MachinePrecision] / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -2.0000000000000002e230

   1. Initial program 63.8%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 63.8%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 63.8%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around -inf 99.8%

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

      1. mul-1-neg 99.8%

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

      2. distribute-rgt-neg-in 99.8%

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

      3. mul-1-neg 99.8%

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

      4. unsub-neg 99.8%

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

      5. mul-1-neg 99.8%

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

      6. *-commutative 99.8%

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

      7. distribute-neg-frac2 99.8%

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

      8. sub-neg 99.8%

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

      9. *-commutative 99.8%

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

      10. distribute-neg-in 99.8%

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

      11. distribute-rgt-neg-in 99.8%

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

      12. remove-double-neg 99.8%

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

   7. Simplified 99.8%

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

   if -2.0000000000000002e230 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 9.9999999999999999e51

   1. Initial program 98.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   if 9.9999999999999999e51 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < +inf.0

   1. Initial program 52.6%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 52.6%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 52.6%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 52.3%

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

      1. times-frac 99.5%

         \[\leadsto \color{blue}{\frac{y}{1 + x} \cdot \frac{z}{t \cdot z - x}} \]

      2. +-commutative 99.5%

         \[\leadsto \frac{y}{\color{blue}{x + 1}} \cdot \frac{z}{t \cdot z - x} \]

   7. Simplified 99.5%

      \[\leadsto \color{blue}{\frac{y}{x + 1} \cdot \frac{z}{t \cdot z - x}} \]
   8. Step-by-step derivation

      1. *-commutative 99.5%

         \[\leadsto \color{blue}{\frac{z}{t \cdot z - x} \cdot \frac{y}{x + 1}} \]

      2. clear-num 99.4%

         \[\leadsto \color{blue}{\frac{1}{\frac{t \cdot z - x}{z}}} \cdot \frac{y}{x + 1} \]

      3. frac-times 99.9%

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

      4. *-un-lft-identity 99.9%

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

      5. fmm-def 99.9%

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

   9. Applied egg-rr 99.9%

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

       1. *-commutative 99.9%

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

       2. +-commutative 99.9%

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

       3. fmm-def 99.9%

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

   11. Simplified 99.9%

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

   if +inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 0.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 0.0%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around -inf 99.8%

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

      1. +-commutative 99.8%

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

      2. mul-1-neg 99.8%

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

      3. unsub-neg 99.8%

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

      4. +-commutative 99.8%

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

   7. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{x}{x + 1} - \frac{\frac{y}{-1 - x} + \frac{\frac{x}{z}}{x + 1}}{t}} \]

   8. Taylor expanded in x around inf 100.0%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1} \leq -2 \cdot 10^{+230}:\\ \;\;\;\;\frac{y \cdot \left(\frac{z}{x - z \cdot t} + \frac{\frac{x}{z \cdot t - x} - x}{y}\right)}{-1 - x}\\ \mathbf{elif}\;\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1} \leq 10^{+52}:\\ \;\;\;\;\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1} \leq \infty:\\ \;\;\;\;\frac{y}{\left(x + 1\right) \cdot \frac{z \cdot t - x}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x \cdot \left(1 + \frac{1}{x}\right)} + \frac{\frac{y}{x + 1} + \frac{\frac{x}{z}}{-1 - x}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x - \frac{x - y \cdot z}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_2 \leq 10^{+52}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;\frac{y}{\left(x + 1\right) \cdot \frac{t\_1}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x \cdot \left(1 + \frac{1}{x}\right)} + \frac{\frac{y}{x + 1} + \frac{\frac{x}{z}}{-1 - x}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)) (t_2 (/ (- x (/ (- x (* y z)) t_1)) (+ x 1.0))))
   (if (<= t_2 1e+52)
     t_2
     (if (<= t_2 INFINITY)
       (/ y (* (+ x 1.0) (/ t_1 z)))
       (+
        (/ x (* x (+ 1.0 (/ 1.0 x))))
        (/ (+ (/ y (+ x 1.0)) (/ (/ x z) (- -1.0 x))) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x - ((x - (y * z)) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= 1e+52) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = y / ((x + 1.0) * (t_1 / z));
	} else {
		tmp = (x / (x * (1.0 + (1.0 / x)))) + (((y / (x + 1.0)) + ((x / z) / (-1.0 - x))) / t);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x - ((x - (y * z)) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= 1e+52) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = y / ((x + 1.0) * (t_1 / z));
	} else {
		tmp = (x / (x * (1.0 + (1.0 / x)))) + (((y / (x + 1.0)) + ((x / z) / (-1.0 - x))) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = (x - ((x - (y * z)) / t_1)) / (x + 1.0)
	tmp = 0
	if t_2 <= 1e+52:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = y / ((x + 1.0) * (t_1 / z))
	else:
		tmp = (x / (x * (1.0 + (1.0 / x)))) + (((y / (x + 1.0)) + ((x / z) / (-1.0 - x))) / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(x - Float64(Float64(x - Float64(y * z)) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= 1e+52)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(y / Float64(Float64(x + 1.0) * Float64(t_1 / z)));
	else
		tmp = Float64(Float64(x / Float64(x * Float64(1.0 + Float64(1.0 / x)))) + Float64(Float64(Float64(y / Float64(x + 1.0)) + Float64(Float64(x / z) / Float64(-1.0 - x))) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = (x - ((x - (y * z)) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= 1e+52)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = y / ((x + 1.0) * (t_1 / z));
	else
		tmp = (x / (x * (1.0 + (1.0 / x)))) + (((y / (x + 1.0)) + ((x / z) / (-1.0 - x))) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, 1e+52], t$95$2, If[LessEqual[t$95$2, Infinity], N[(y / N[(N[(x + 1.0), $MachinePrecision] * N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(x * N[(1.0 + N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x / z), $MachinePrecision] / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 9.9999999999999999e51

   1. Initial program 95.5%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   if 9.9999999999999999e51 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < +inf.0

   1. Initial program 52.6%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 52.6%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 52.6%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 52.3%

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

      1. times-frac 99.5%

         \[\leadsto \color{blue}{\frac{y}{1 + x} \cdot \frac{z}{t \cdot z - x}} \]

      2. +-commutative 99.5%

         \[\leadsto \frac{y}{\color{blue}{x + 1}} \cdot \frac{z}{t \cdot z - x} \]

   7. Simplified 99.5%

      \[\leadsto \color{blue}{\frac{y}{x + 1} \cdot \frac{z}{t \cdot z - x}} \]
   8. Step-by-step derivation

      1. *-commutative 99.5%

         \[\leadsto \color{blue}{\frac{z}{t \cdot z - x} \cdot \frac{y}{x + 1}} \]

      2. clear-num 99.4%

         \[\leadsto \color{blue}{\frac{1}{\frac{t \cdot z - x}{z}}} \cdot \frac{y}{x + 1} \]

      3. frac-times 99.9%

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

      4. *-un-lft-identity 99.9%

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

      5. fmm-def 99.9%

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

   9. Applied egg-rr 99.9%

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

       1. *-commutative 99.9%

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

       2. +-commutative 99.9%

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

       3. fmm-def 99.9%

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

   11. Simplified 99.9%

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

   if +inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 0.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 0.0%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around -inf 99.8%

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

      1. +-commutative 99.8%

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

      2. mul-1-neg 99.8%

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

      3. unsub-neg 99.8%

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

      4. +-commutative 99.8%

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

   7. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{x}{x + 1} - \frac{\frac{y}{-1 - x} + \frac{\frac{x}{z}}{x + 1}}{t}} \]

   8. Taylor expanded in x around inf 100.0%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1} \leq 10^{+52}:\\ \;\;\;\;\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1} \leq \infty:\\ \;\;\;\;\frac{y}{\left(x + 1\right) \cdot \frac{z \cdot t - x}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x \cdot \left(1 + \frac{1}{x}\right)} + \frac{\frac{y}{x + 1} + \frac{\frac{x}{z}}{-1 - x}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x - \frac{x - y \cdot z}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_2 \leq 10^{+52}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;\frac{y}{\left(x + 1\right) \cdot \frac{t\_1}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)) (t_2 (/ (- x (/ (- x (* y z)) t_1)) (+ x 1.0))))
   (if (<= t_2 1e+52)
     t_2
     (if (<= t_2 INFINITY)
       (/ y (* (+ x 1.0) (/ t_1 z)))
       (/ (+ x (/ y t)) (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x - ((x - (y * z)) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= 1e+52) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = y / ((x + 1.0) * (t_1 / z));
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x - ((x - (y * z)) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= 1e+52) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = y / ((x + 1.0) * (t_1 / z));
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = (x - ((x - (y * z)) / t_1)) / (x + 1.0)
	tmp = 0
	if t_2 <= 1e+52:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = y / ((x + 1.0) * (t_1 / z))
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(x - Float64(Float64(x - Float64(y * z)) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= 1e+52)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(y / Float64(Float64(x + 1.0) * Float64(t_1 / z)));
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = (x - ((x - (y * z)) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= 1e+52)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = y / ((x + 1.0) * (t_1 / z));
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, 1e+52], t$95$2, If[LessEqual[t$95$2, Infinity], N[(y / N[(N[(x + 1.0), $MachinePrecision] * N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 9.9999999999999999e51

   1. Initial program 95.5%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   if 9.9999999999999999e51 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < +inf.0

   1. Initial program 52.6%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 52.6%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 52.6%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 52.3%

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

      1. times-frac 99.5%

         \[\leadsto \color{blue}{\frac{y}{1 + x} \cdot \frac{z}{t \cdot z - x}} \]

      2. +-commutative 99.5%

         \[\leadsto \frac{y}{\color{blue}{x + 1}} \cdot \frac{z}{t \cdot z - x} \]

   7. Simplified 99.5%

      \[\leadsto \color{blue}{\frac{y}{x + 1} \cdot \frac{z}{t \cdot z - x}} \]
   8. Step-by-step derivation

      1. *-commutative 99.5%

         \[\leadsto \color{blue}{\frac{z}{t \cdot z - x} \cdot \frac{y}{x + 1}} \]

      2. clear-num 99.4%

         \[\leadsto \color{blue}{\frac{1}{\frac{t \cdot z - x}{z}}} \cdot \frac{y}{x + 1} \]

      3. frac-times 99.9%

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

      4. *-un-lft-identity 99.9%

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

      5. fmm-def 99.9%

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

   9. Applied egg-rr 99.9%

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

       1. *-commutative 99.9%

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

       2. +-commutative 99.9%

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

       3. fmm-def 99.9%

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

   11. Simplified 99.9%

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

   if +inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 0.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 0.0%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 99.8%

      \[\leadsto \color{blue}{\frac{x + \frac{y}{t}}{1 + x}} \]
   6. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \frac{\color{blue}{\frac{y}{t} + x}}{1 + x} \]

      2. +-commutative 99.8%

         \[\leadsto \frac{\frac{y}{t} + x}{\color{blue}{x + 1}} \]

   7. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{\frac{y}{t} + x}{x + 1}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1} \leq 10^{+52}:\\ \;\;\;\;\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1} \leq \infty:\\ \;\;\;\;\frac{y}{\left(x + 1\right) \cdot \frac{z \cdot t - x}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-47} \lor \neg \left(t \leq 3.4 \cdot 10^{-199}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y \cdot \frac{z}{x}}{-1 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.6e-47) (not (<= t 3.4e-199)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (+ 1.0 (/ (* y (/ z x)) (- -1.0 x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.6e-47) || !(t <= 3.4e-199)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + ((y * (z / x)) / (-1.0 - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.6d-47)) .or. (.not. (t <= 3.4d-199))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 + ((y * (z / x)) / ((-1.0d0) - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.6e-47) || !(t <= 3.4e-199)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + ((y * (z / x)) / (-1.0 - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.6e-47) or not (t <= 3.4e-199):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 + ((y * (z / x)) / (-1.0 - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.6e-47) || !(t <= 3.4e-199))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 + Float64(Float64(y * Float64(z / x)) / Float64(-1.0 - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.6e-47) || ~((t <= 3.4e-199)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 + ((y * (z / x)) / (-1.0 - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.6e-47], N[Not[LessEqual[t, 3.4e-199]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision] / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.6e-47 or 3.40000000000000006e-199 < t

   1. Initial program 87.2%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 87.2%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 87.2%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 88.9%

      \[\leadsto \color{blue}{\frac{x + \frac{y}{t}}{1 + x}} \]
   6. Step-by-step derivation

      1. +-commutative 88.9%

         \[\leadsto \frac{\color{blue}{\frac{y}{t} + x}}{1 + x} \]

      2. +-commutative 88.9%

         \[\leadsto \frac{\frac{y}{t} + x}{\color{blue}{x + 1}} \]

   7. Simplified 88.9%

      \[\leadsto \color{blue}{\frac{\frac{y}{t} + x}{x + 1}} \]

   if -1.6e-47 < t < 3.40000000000000006e-199

   1. Initial program 89.1%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 89.1%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 89.1%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 89.0%

         \[\leadsto \color{blue}{\frac{1}{\frac{x + 1}{x + \frac{y \cdot z - x}{z \cdot t - x}}}} \]

      2. inv-pow 89.0%

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

   6. Applied egg-rr 89.0%

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

      1. unpow-1 89.0%

         \[\leadsto \color{blue}{\frac{1}{\frac{x + 1}{x + \frac{y \cdot z - x}{z \cdot t - x}}}} \]

      2. *-commutative 89.0%

         \[\leadsto \frac{1}{\frac{x + 1}{x + \frac{y \cdot z - x}{\color{blue}{t \cdot z} - x}}} \]

   8. Simplified 89.0%

      \[\leadsto \color{blue}{\frac{1}{\frac{x + 1}{x + \frac{y \cdot z - x}{t \cdot z - x}}}} \]

   9. Taylor expanded in t around 0 74.9%

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

       1. associate-+r+ 74.9%

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

       2. mul-1-neg 74.9%

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

       3. associate-*r/ 83.3%

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

       4. unsub-neg 83.3%

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

       5. +-commutative 83.3%

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

       6. +-commutative 83.3%

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

   11. Simplified 83.3%

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

       1. div-sub 83.3%

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

       2. pow1 83.3%

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

       3. pow1 83.3%

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

       4. pow-div 83.3%

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

       5. metadata-eval 83.3%

          \[\leadsto {\left(x + 1\right)}^{\color{blue}{0}} - \frac{y \cdot \frac{z}{x}}{x + 1} \]

       6. metadata-eval 83.3%

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

   13. Applied egg-rr 83.3%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-47} \lor \neg \left(t \leq 3.4 \cdot 10^{-199}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y \cdot \frac{z}{x}}{-1 - x}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-14}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{+23}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -5.5e-14) 1.0 (if (<= x 2.35e+23) (/ (+ x (/ y t)) (+ x 1.0)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.5e-14) {
		tmp = 1.0;
	} else if (x <= 2.35e+23) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 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 (x <= (-5.5d-14)) then
        tmp = 1.0d0
    else if (x <= 2.35d+23) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.5e-14) {
		tmp = 1.0;
	} else if (x <= 2.35e+23) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -5.5e-14:
		tmp = 1.0
	elif x <= 2.35e+23:
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -5.5e-14)
		tmp = 1.0;
	elseif (x <= 2.35e+23)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -5.5e-14)
		tmp = 1.0;
	elseif (x <= 2.35e+23)
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -5.5e-14], 1.0, If[LessEqual[x, 2.35e+23], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -5.49999999999999991e-14 or 2.3499999999999999e23 < x

   1. Initial program 88.3%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 88.3%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 88.3%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 89.0%

      \[\leadsto \color{blue}{1} \]

   if -5.49999999999999991e-14 < x < 2.3499999999999999e23

   1. Initial program 87.3%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 87.3%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 87.3%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 74.6%

      \[\leadsto \color{blue}{\frac{x + \frac{y}{t}}{1 + x}} \]
   6. Step-by-step derivation

      1. +-commutative 74.6%

         \[\leadsto \frac{\color{blue}{\frac{y}{t} + x}}{1 + x} \]

      2. +-commutative 74.6%

         \[\leadsto \frac{\frac{y}{t} + x}{\color{blue}{x + 1}} \]

   7. Simplified 74.6%

      \[\leadsto \color{blue}{\frac{\frac{y}{t} + x}{x + 1}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-14}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{+23}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-15}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-38}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.3e-15)
   1.0
   (if (<= x 5.8e-38) (* y (/ z (- (* z t) x))) (/ x (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.3e-15) {
		tmp = 1.0;
	} else if (x <= 5.8e-38) {
		tmp = y * (z / ((z * t) - x));
	} else {
		tmp = x / (x + 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 (x <= (-1.3d-15)) then
        tmp = 1.0d0
    else if (x <= 5.8d-38) then
        tmp = y * (z / ((z * t) - x))
    else
        tmp = x / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.3e-15) {
		tmp = 1.0;
	} else if (x <= 5.8e-38) {
		tmp = y * (z / ((z * t) - x));
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.3e-15:
		tmp = 1.0
	elif x <= 5.8e-38:
		tmp = y * (z / ((z * t) - x))
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.3e-15)
		tmp = 1.0;
	elseif (x <= 5.8e-38)
		tmp = Float64(y * Float64(z / Float64(Float64(z * t) - x)));
	else
		tmp = Float64(x / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.3e-15)
		tmp = 1.0;
	elseif (x <= 5.8e-38)
		tmp = y * (z / ((z * t) - x));
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.3e-15], 1.0, If[LessEqual[x, 5.8e-38], N[(y * N[(z / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.30000000000000002e-15

   1. Initial program 87.8%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 87.8%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 87.8%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 89.1%

      \[\leadsto \color{blue}{1} \]

   if -1.30000000000000002e-15 < x < 5.79999999999999988e-38

   1. Initial program 86.7%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 86.7%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 86.7%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 47.9%

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

      1. times-frac 54.2%

         \[\leadsto \color{blue}{\frac{y}{1 + x} \cdot \frac{z}{t \cdot z - x}} \]

      2. +-commutative 54.2%

         \[\leadsto \frac{y}{\color{blue}{x + 1}} \cdot \frac{z}{t \cdot z - x} \]

   7. Simplified 54.2%

      \[\leadsto \color{blue}{\frac{y}{x + 1} \cdot \frac{z}{t \cdot z - x}} \]

   8. Taylor expanded in x around 0 54.2%

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

   if 5.79999999999999988e-38 < x

   1. Initial program 89.4%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 89.4%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 89.4%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 84.5%

      \[\leadsto \color{blue}{\frac{x}{1 + x}} \]
   6. Step-by-step derivation

      1. +-commutative 84.5%

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

   7. Simplified 84.5%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-15}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-38}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-15}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-39}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.4e-15) 1.0 (if (<= x 2.7e-39) (/ y t) (/ x (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.4e-15) {
		tmp = 1.0;
	} else if (x <= 2.7e-39) {
		tmp = y / t;
	} else {
		tmp = x / (x + 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 (x <= (-2.4d-15)) then
        tmp = 1.0d0
    else if (x <= 2.7d-39) then
        tmp = y / t
    else
        tmp = x / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.4e-15) {
		tmp = 1.0;
	} else if (x <= 2.7e-39) {
		tmp = y / t;
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.4e-15:
		tmp = 1.0
	elif x <= 2.7e-39:
		tmp = y / t
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.4e-15)
		tmp = 1.0;
	elseif (x <= 2.7e-39)
		tmp = Float64(y / t);
	else
		tmp = Float64(x / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.4e-15)
		tmp = 1.0;
	elseif (x <= 2.7e-39)
		tmp = y / t;
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.4e-15], 1.0, If[LessEqual[x, 2.7e-39], N[(y / t), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.39999999999999995e-15

   1. Initial program 87.8%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 87.8%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 87.8%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 89.1%

      \[\leadsto \color{blue}{1} \]

   if -2.39999999999999995e-15 < x < 2.7000000000000001e-39

   1. Initial program 86.7%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 86.7%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 86.7%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 53.9%

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

   if 2.7000000000000001e-39 < x

   1. Initial program 89.4%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 89.4%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 89.4%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 84.5%

      \[\leadsto \color{blue}{\frac{x}{1 + x}} \]
   6. Step-by-step derivation

      1. +-commutative 84.5%

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

   7. Simplified 84.5%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 68.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-15}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-50}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.55e-15) 1.0 (if (<= x 1.7e-50) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.55e-15) {
		tmp = 1.0;
	} else if (x <= 1.7e-50) {
		tmp = y / t;
	} else {
		tmp = 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 (x <= (-1.55d-15)) then
        tmp = 1.0d0
    else if (x <= 1.7d-50) then
        tmp = y / t
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.55e-15) {
		tmp = 1.0;
	} else if (x <= 1.7e-50) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.55e-15:
		tmp = 1.0
	elif x <= 1.7e-50:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.55e-15)
		tmp = 1.0;
	elseif (x <= 1.7e-50)
		tmp = Float64(y / t);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.55e-15)
		tmp = 1.0;
	elseif (x <= 1.7e-50)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.55e-15], 1.0, If[LessEqual[x, 1.7e-50], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.5499999999999999e-15 or 1.70000000000000007e-50 < x

   1. Initial program 88.9%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 88.9%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 88.9%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 83.1%

      \[\leadsto \color{blue}{1} \]

   if -1.5499999999999999e-15 < x < 1.70000000000000007e-50

   1. Initial program 86.4%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 86.4%

         \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

   3. Simplified 86.4%

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 54.7%

      \[\leadsto \color{blue}{\frac{y}{t}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 54.7% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 1.0)

C

double code(double x, double y, double z, double t) {
	return 1.0;
}

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 = 1.0d0
end function

Java

public static double code(double x, double y, double z, double t) {
	return 1.0;
}

Python

def code(x, y, z, t):
	return 1.0

Julia

function code(x, y, z, t)
	return 1.0
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_, t_] := 1.0

Derivation

1. Initial program 87.8%

   \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
2. Step-by-step derivation

   1. *-commutative 87.8%

      \[\leadsto \frac{x + \frac{y \cdot z - x}{\color{blue}{z \cdot t} - x}}{x + 1} \]

3. Simplified 87.8%

   \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 51.5%

   \[\leadsto \color{blue}{1} \]
6. Add Preprocessing

Developer Target 1: 99.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1.0)))

C

double code(double x, double y, double z, double t) {
	return (x + ((y / (t - (x / z))) - (x / ((t * z) - x)))) / (x + 1.0);
}

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 / (t - (x / z))) - (x / ((t * z) - x)))) / (x + 1.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x + ((y / (t - (x / z))) - (x / ((t * z) - x)))) / (x + 1.0);
}

Python

def code(x, y, z, t):
	return (x + ((y / (t - (x / z))) - (x / ((t * z) - x)))) / (x + 1.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(x + Float64(Float64(y / Float64(t - Float64(x / z))) - Float64(x / Float64(Float64(t * z) - x)))) / Float64(x + 1.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x + ((y / (t - (x / z))) - (x / ((t * z) - x)))) / (x + 1.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x + N[(N[(y / N[(t - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024182 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1)))

  (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))