Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1

Percentage Accurate: 96.8% → 96.8%

Time: 9.9s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

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 - y)) * t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - y)) * t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - y)) * t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.7%

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

Alternative 2: 71.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := t \cdot \frac{x}{z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-142}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-179}:\\ \;\;\;\;-\frac{y \cdot t}{z}\\ \mathbf{elif}\;t\_1 \leq 0.4:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{z}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* t (/ x z))))
   (if (<= t_1 -5e-142)
     t_2
     (if (<= t_1 2e-179)
       (- (/ (* y t) z))
       (if (<= t_1 0.4) t_2 (if (<= t_1 2.0) (fma t (/ z y) t) t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = t * (x / z);
	double tmp;
	if (t_1 <= -5e-142) {
		tmp = t_2;
	} else if (t_1 <= 2e-179) {
		tmp = -((y * t) / z);
	} else if (t_1 <= 0.4) {
		tmp = t_2;
	} else if (t_1 <= 2.0) {
		tmp = fma(t, (z / y), t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(t * Float64(x / z))
	tmp = 0.0
	if (t_1 <= -5e-142)
		tmp = t_2;
	elseif (t_1 <= 2e-179)
		tmp = Float64(-Float64(Float64(y * t) / z));
	elseif (t_1 <= 0.4)
		tmp = t_2;
	elseif (t_1 <= 2.0)
		tmp = fma(t, Float64(z / y), t);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-142], t$95$2, If[LessEqual[t$95$1, 2e-179], (-N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), If[LessEqual[t$95$1, 0.4], t$95$2, If[LessEqual[t$95$1, 2.0], N[(t * N[(z / y), $MachinePrecision] + t), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -5.0000000000000002e-142 or 2e-179 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.40000000000000002 or 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 96.7%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 63.4

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

   5. Simplified 63.4%

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

   if -5.0000000000000002e-142 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2e-179

   1. Initial program 91.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 93.9

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

   5. Simplified 93.9%

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

   6. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 79.1

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

   8. Simplified 79.1%

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

   if 0.40000000000000002 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. frac-2neg N/A

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

      4. div-inv N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

      7. neg-sub0 N/A

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

      8. lift--.f64 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. associate--r+ N/A

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

      12. neg-sub0 N/A

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

      13. remove-double-neg N/A

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

      14. lower--.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. lower-/.f64 N/A

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

      17. neg-sub0 N/A

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

      18. lift--.f64 N/A

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

      19. sub-neg N/A

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

      20. +-commutative N/A

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

      21. associate--r+ N/A

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

      22. neg-sub0 N/A

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

      23. remove-double-neg N/A

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

      24. lower--.f64 75.3

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

   4. Applied egg-rr 75.3%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. frac-2neg N/A

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

      4. metadata-eval N/A

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

      5. metadata-eval N/A

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

      6. frac-2neg N/A

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

      7. lift-/.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. associate-*l/ N/A

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

      10. *-lft-identity N/A

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

      11. clear-num N/A

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

      12. un-div-inv N/A

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

      13. lower-/.f64 N/A

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

      14. lower-/.f64 75.5

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

   6. Applied egg-rr 75.5%

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

   7. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 99.7

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

   9. Simplified 99.7%

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

   10. Taylor expanded in y around inf

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

       1. +-commutative N/A

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

       2. associate-/l* N/A

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

       3. lower-fma.f64 N/A

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

       4. lower-/.f64 99.3

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

   12. Simplified 99.3%

       \[\leadsto \color{blue}{\mathsf{fma}\left(t, \frac{z}{y}, t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -5 \cdot 10^{-142}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2 \cdot 10^{-179}:\\ \;\;\;\;-\frac{y \cdot t}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 0.4:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{z}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+37}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{elif}\;t\_1 \leq 0.4:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 -2e+37)
     (/ (* x t) (- z y))
     (if (<= t_1 0.4)
       (* t (/ (- x y) z))
       (if (<= t_1 2.0) (* t (/ y (- y z))) (* t (/ x (- z y))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -2e+37) {
		tmp = (x * t) / (z - y);
	} else if (t_1 <= 0.4) {
		tmp = t * ((x - y) / z);
	} else if (t_1 <= 2.0) {
		tmp = t * (y / (y - z));
	} else {
		tmp = t * (x / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= (-2d+37)) then
        tmp = (x * t) / (z - y)
    else if (t_1 <= 0.4d0) then
        tmp = t * ((x - y) / z)
    else if (t_1 <= 2.0d0) then
        tmp = t * (y / (y - z))
    else
        tmp = t * (x / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -2e+37) {
		tmp = (x * t) / (z - y);
	} else if (t_1 <= 0.4) {
		tmp = t * ((x - y) / z);
	} else if (t_1 <= 2.0) {
		tmp = t * (y / (y - z));
	} else {
		tmp = t * (x / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= -2e+37:
		tmp = (x * t) / (z - y)
	elif t_1 <= 0.4:
		tmp = t * ((x - y) / z)
	elif t_1 <= 2.0:
		tmp = t * (y / (y - z))
	else:
		tmp = t * (x / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= -2e+37)
		tmp = Float64(Float64(x * t) / Float64(z - y));
	elseif (t_1 <= 0.4)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	elseif (t_1 <= 2.0)
		tmp = Float64(t * Float64(y / Float64(y - z)));
	else
		tmp = Float64(t * Float64(x / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= -2e+37)
		tmp = (x * t) / (z - y);
	elseif (t_1 <= 0.4)
		tmp = t * ((x - y) / z);
	elseif (t_1 <= 2.0)
		tmp = t * (y / (y - z));
	else
		tmp = t * (x / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+37], N[(N[(x * t), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.4], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1.99999999999999991e37

   1. Initial program 93.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-inv N/A

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

      4. lift--.f64 N/A

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

      5. flip3-- N/A

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

      6. clear-num N/A

         \[\leadsto \left(\left(x - y\right) \cdot \color{blue}{\frac{z \cdot z + \left(y \cdot y + z \cdot y\right)}{{z}^{3} - {y}^{3}}}\right) \cdot t \]

      7. associate-*r* N/A

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \left(\frac{z \cdot z + \left(y \cdot y + z \cdot y\right)}{{z}^{3} - {y}^{3}} \cdot t\right)} \]

      8. *-commutative N/A

         \[\leadsto \left(x - y\right) \cdot \color{blue}{\left(t \cdot \frac{z \cdot z + \left(y \cdot y + z \cdot y\right)}{{z}^{3} - {y}^{3}}\right)} \]

      9. clear-num N/A

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

      10. flip3-- N/A

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

      11. lift--.f64 N/A

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

      12. div-inv N/A

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

      13. associate-/l* N/A

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

      14. lower-/.f64 N/A

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

      15. lower-*.f64 96.8

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

   4. Applied egg-rr 96.8%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 96.8

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

   7. Simplified 96.8%

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

   if -1.99999999999999991e37 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.40000000000000002

   1. Initial program 95.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 94.2

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

   5. Simplified 94.2%

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

   if 0.40000000000000002 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. frac-2neg N/A

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

      4. div-inv N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

      7. neg-sub0 N/A

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

      8. lift--.f64 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. associate--r+ N/A

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

      12. neg-sub0 N/A

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

      13. remove-double-neg N/A

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

      14. lower--.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. lower-/.f64 N/A

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

      17. neg-sub0 N/A

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

      18. lift--.f64 N/A

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

      19. sub-neg N/A

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

      20. +-commutative N/A

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

      21. associate--r+ N/A

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

      22. neg-sub0 N/A

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

      23. remove-double-neg N/A

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

      24. lower--.f64 75.3

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

   4. Applied egg-rr 75.3%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. frac-2neg N/A

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

      4. metadata-eval N/A

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

      5. metadata-eval N/A

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

      6. frac-2neg N/A

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

      7. lift-/.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. associate-*l/ N/A

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

      10. *-lft-identity N/A

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

      11. clear-num N/A

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

      12. un-div-inv N/A

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

      13. lower-/.f64 N/A

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

      14. lower-/.f64 75.5

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

   6. Applied egg-rr 75.5%

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

   7. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 99.7

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

   9. Simplified 99.7%

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

   if 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 95.0%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 93.6

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

   5. Simplified 93.6%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -2 \cdot 10^{+37}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 0.4:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := t \cdot \frac{x}{z - y}\\ \mathbf{if}\;t\_1 \leq -4000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.4:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* t (/ x (- z y)))))
   (if (<= t_1 -4000000000.0)
     t_2
     (if (<= t_1 0.4)
       (* t (/ (- x y) z))
       (if (<= t_1 2.0) (* t (/ y (- y z))) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = t * (x / (z - y));
	double tmp;
	if (t_1 <= -4000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.4) {
		tmp = t * ((x - y) / z);
	} else if (t_1 <= 2.0) {
		tmp = t * (y / (y - z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = t * (x / (z - y))
    if (t_1 <= (-4000000000.0d0)) then
        tmp = t_2
    else if (t_1 <= 0.4d0) then
        tmp = t * ((x - y) / z)
    else if (t_1 <= 2.0d0) then
        tmp = t * (y / (y - z))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = t * (x / (z - y));
	double tmp;
	if (t_1 <= -4000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.4) {
		tmp = t * ((x - y) / z);
	} else if (t_1 <= 2.0) {
		tmp = t * (y / (y - z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = t * (x / (z - y))
	tmp = 0
	if t_1 <= -4000000000.0:
		tmp = t_2
	elif t_1 <= 0.4:
		tmp = t * ((x - y) / z)
	elif t_1 <= 2.0:
		tmp = t * (y / (y - z))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(t * Float64(x / Float64(z - y)))
	tmp = 0.0
	if (t_1 <= -4000000000.0)
		tmp = t_2;
	elseif (t_1 <= 0.4)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	elseif (t_1 <= 2.0)
		tmp = Float64(t * Float64(y / Float64(y - z)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = t * (x / (z - y));
	tmp = 0.0;
	if (t_1 <= -4000000000.0)
		tmp = t_2;
	elseif (t_1 <= 0.4)
		tmp = t * ((x - y) / z);
	elseif (t_1 <= 2.0)
		tmp = t * (y / (y - z));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4000000000.0], t$95$2, If[LessEqual[t$95$1, 0.4], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -4e9 or 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 94.6%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 93.4

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

   5. Simplified 93.4%

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

   if -4e9 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.40000000000000002

   1. Initial program 95.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 95.0

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

   5. Simplified 95.0%

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

   if 0.40000000000000002 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. frac-2neg N/A

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

      4. div-inv N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

      7. neg-sub0 N/A

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

      8. lift--.f64 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. associate--r+ N/A

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

      12. neg-sub0 N/A

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

      13. remove-double-neg N/A

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

      14. lower--.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. lower-/.f64 N/A

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

      17. neg-sub0 N/A

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

      18. lift--.f64 N/A

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

      19. sub-neg N/A

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

      20. +-commutative N/A

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

      21. associate--r+ N/A

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

      22. neg-sub0 N/A

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

      23. remove-double-neg N/A

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

      24. lower--.f64 75.3

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

   4. Applied egg-rr 75.3%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. frac-2neg N/A

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

      4. metadata-eval N/A

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

      5. metadata-eval N/A

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

      6. frac-2neg N/A

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

      7. lift-/.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. associate-*l/ N/A

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

      10. *-lft-identity N/A

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

      11. clear-num N/A

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

      12. un-div-inv N/A

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

      13. lower-/.f64 N/A

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

      14. lower-/.f64 75.5

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

   6. Applied egg-rr 75.5%

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

   7. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 99.7

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

   9. Simplified 99.7%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -4000000000:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 0.4:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := t \cdot \frac{x}{z - y}\\ \mathbf{if}\;t\_1 \leq -200000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.4:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* t (/ x (- z y)))))
   (if (<= t_1 -200000.0)
     t_2
     (if (<= t_1 0.4)
       (* (- x y) (/ t z))
       (if (<= t_1 2.0) (* t (/ y (- y z))) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = t * (x / (z - y));
	double tmp;
	if (t_1 <= -200000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.4) {
		tmp = (x - y) * (t / z);
	} else if (t_1 <= 2.0) {
		tmp = t * (y / (y - z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = t * (x / (z - y))
    if (t_1 <= (-200000.0d0)) then
        tmp = t_2
    else if (t_1 <= 0.4d0) then
        tmp = (x - y) * (t / z)
    else if (t_1 <= 2.0d0) then
        tmp = t * (y / (y - z))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = t * (x / (z - y));
	double tmp;
	if (t_1 <= -200000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.4) {
		tmp = (x - y) * (t / z);
	} else if (t_1 <= 2.0) {
		tmp = t * (y / (y - z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = t * (x / (z - y))
	tmp = 0
	if t_1 <= -200000.0:
		tmp = t_2
	elif t_1 <= 0.4:
		tmp = (x - y) * (t / z)
	elif t_1 <= 2.0:
		tmp = t * (y / (y - z))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(t * Float64(x / Float64(z - y)))
	tmp = 0.0
	if (t_1 <= -200000.0)
		tmp = t_2;
	elseif (t_1 <= 0.4)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (t_1 <= 2.0)
		tmp = Float64(t * Float64(y / Float64(y - z)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = t * (x / (z - y));
	tmp = 0.0;
	if (t_1 <= -200000.0)
		tmp = t_2;
	elseif (t_1 <= 0.4)
		tmp = (x - y) * (t / z);
	elseif (t_1 <= 2.0)
		tmp = t * (y / (y - z));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -200000.0], t$95$2, If[LessEqual[t$95$1, 0.4], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -2e5 or 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 94.7%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 93.5

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

   5. Simplified 93.5%

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

   if -2e5 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.40000000000000002

   1. Initial program 95.6%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 90.4

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

   5. Simplified 90.4%

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

   if 0.40000000000000002 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. frac-2neg N/A

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

      4. div-inv N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

      7. neg-sub0 N/A

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

      8. lift--.f64 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. associate--r+ N/A

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

      12. neg-sub0 N/A

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

      13. remove-double-neg N/A

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

      14. lower--.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. lower-/.f64 N/A

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

      17. neg-sub0 N/A

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

      18. lift--.f64 N/A

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

      19. sub-neg N/A

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

      20. +-commutative N/A

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

      21. associate--r+ N/A

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

      22. neg-sub0 N/A

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

      23. remove-double-neg N/A

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

      24. lower--.f64 75.3

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

   4. Applied egg-rr 75.3%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. frac-2neg N/A

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

      4. metadata-eval N/A

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

      5. metadata-eval N/A

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

      6. frac-2neg N/A

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

      7. lift-/.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. associate-*l/ N/A

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

      10. *-lft-identity N/A

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

      11. clear-num N/A

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

      12. un-div-inv N/A

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

      13. lower-/.f64 N/A

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

      14. lower-/.f64 75.5

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

   6. Applied egg-rr 75.5%

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

   7. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 99.7

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

   9. Simplified 99.7%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -200000:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 0.4:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq 0.4:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 0.4)
     (* (- x y) (/ t z))
     (if (<= t_1 2.0) (* t (/ y (- y z))) (* t (/ x z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 0.4) {
		tmp = (x - y) * (t / z);
	} else if (t_1 <= 2.0) {
		tmp = t * (y / (y - z));
	} else {
		tmp = t * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= 0.4d0) then
        tmp = (x - y) * (t / z)
    else if (t_1 <= 2.0d0) then
        tmp = t * (y / (y - z))
    else
        tmp = t * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 0.4) {
		tmp = (x - y) * (t / z);
	} else if (t_1 <= 2.0) {
		tmp = t * (y / (y - z));
	} else {
		tmp = t * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= 0.4:
		tmp = (x - y) * (t / z)
	elif t_1 <= 2.0:
		tmp = t * (y / (y - z))
	else:
		tmp = t * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= 0.4)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (t_1 <= 2.0)
		tmp = Float64(t * Float64(y / Float64(y - z)));
	else
		tmp = Float64(t * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= 0.4)
		tmp = (x - y) * (t / z);
	elseif (t_1 <= 2.0)
		tmp = t * (y / (y - z));
	else
		tmp = t * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 0.4], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 0.40000000000000002

   1. Initial program 95.3%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 81.5

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

   5. Simplified 81.5%

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

   if 0.40000000000000002 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. frac-2neg N/A

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

      4. div-inv N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

      7. neg-sub0 N/A

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

      8. lift--.f64 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. associate--r+ N/A

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

      12. neg-sub0 N/A

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

      13. remove-double-neg N/A

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

      14. lower--.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. lower-/.f64 N/A

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

      17. neg-sub0 N/A

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

      18. lift--.f64 N/A

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

      19. sub-neg N/A

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

      20. +-commutative N/A

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

      21. associate--r+ N/A

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

      22. neg-sub0 N/A

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

      23. remove-double-neg N/A

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

      24. lower--.f64 75.3

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

   4. Applied egg-rr 75.3%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. frac-2neg N/A

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

      4. metadata-eval N/A

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

      5. metadata-eval N/A

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

      6. frac-2neg N/A

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

      7. lift-/.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. associate-*l/ N/A

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

      10. *-lft-identity N/A

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

      11. clear-num N/A

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

      12. un-div-inv N/A

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

      13. lower-/.f64 N/A

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

      14. lower-/.f64 75.5

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

   6. Applied egg-rr 75.5%

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

   7. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 99.7

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

   9. Simplified 99.7%

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

   if 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 95.0%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 62.9

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

   5. Simplified 62.9%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 0.4:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := t \cdot \frac{x}{z}\\ \mathbf{if}\;t\_1 \leq 0.4:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{z}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* t (/ x z))))
   (if (<= t_1 0.4) t_2 (if (<= t_1 2.0) (fma t (/ z y) t) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = t * (x / z);
	double tmp;
	if (t_1 <= 0.4) {
		tmp = t_2;
	} else if (t_1 <= 2.0) {
		tmp = fma(t, (z / y), t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(t * Float64(x / z))
	tmp = 0.0
	if (t_1 <= 0.4)
		tmp = t_2;
	elseif (t_1 <= 2.0)
		tmp = fma(t, Float64(z / y), t);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 0.4], t$95$2, If[LessEqual[t$95$1, 2.0], N[(t * N[(z / y), $MachinePrecision] + t), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 0.40000000000000002 or 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 95.2%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 62.3

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

   5. Simplified 62.3%

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

   if 0.40000000000000002 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. frac-2neg N/A

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

      4. div-inv N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

      7. neg-sub0 N/A

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

      8. lift--.f64 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. associate--r+ N/A

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

      12. neg-sub0 N/A

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

      13. remove-double-neg N/A

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

      14. lower--.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. lower-/.f64 N/A

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

      17. neg-sub0 N/A

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

      18. lift--.f64 N/A

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

      19. sub-neg N/A

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

      20. +-commutative N/A

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

      21. associate--r+ N/A

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

      22. neg-sub0 N/A

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

      23. remove-double-neg N/A

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

      24. lower--.f64 75.3

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

   4. Applied egg-rr 75.3%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. frac-2neg N/A

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

      4. metadata-eval N/A

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

      5. metadata-eval N/A

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

      6. frac-2neg N/A

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

      7. lift-/.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. associate-*l/ N/A

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

      10. *-lft-identity N/A

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

      11. clear-num N/A

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

      12. un-div-inv N/A

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

      13. lower-/.f64 N/A

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

      14. lower-/.f64 75.5

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

   6. Applied egg-rr 75.5%

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

   7. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 99.7

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

   9. Simplified 99.7%

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

   10. Taylor expanded in y around inf

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

       1. +-commutative N/A

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

       2. associate-/l* N/A

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

       3. lower-fma.f64 N/A

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

       4. lower-/.f64 99.3

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

   12. Simplified 99.3%

       \[\leadsto \color{blue}{\mathsf{fma}\left(t, \frac{z}{y}, t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 0.4:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{z}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 70.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := t \cdot \frac{x}{z}\\ \mathbf{if}\;t\_1 \leq 0.4:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* t (/ x z))))
   (if (<= t_1 0.4) t_2 (if (<= t_1 2.0) t t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = t * (x / z);
	double tmp;
	if (t_1 <= 0.4) {
		tmp = t_2;
	} else if (t_1 <= 2.0) {
		tmp = t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = t * (x / z)
    if (t_1 <= 0.4d0) then
        tmp = t_2
    else if (t_1 <= 2.0d0) then
        tmp = t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = t * (x / z);
	double tmp;
	if (t_1 <= 0.4) {
		tmp = t_2;
	} else if (t_1 <= 2.0) {
		tmp = t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = t * (x / z)
	tmp = 0
	if t_1 <= 0.4:
		tmp = t_2
	elif t_1 <= 2.0:
		tmp = t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(t * Float64(x / z))
	tmp = 0.0
	if (t_1 <= 0.4)
		tmp = t_2;
	elseif (t_1 <= 2.0)
		tmp = t;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = t * (x / z);
	tmp = 0.0;
	if (t_1 <= 0.4)
		tmp = t_2;
	elseif (t_1 <= 2.0)
		tmp = t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 0.4], t$95$2, If[LessEqual[t$95$1, 2.0], t, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 0.40000000000000002 or 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 95.2%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 62.3

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

   5. Simplified 62.3%

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

   if 0.40000000000000002 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \cdot t \]
   4. Step-by-step derivation

   5. Simplified 98.4%

      \[\leadsto \color{blue}{1} \cdot t \]
   6. Step-by-step derivation

      1. *-lft-identity 98.4

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

   7. Applied egg-rr 98.4%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 0.4:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := x \cdot \frac{t}{z}\\ \mathbf{if}\;t\_1 \leq 0.4:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* x (/ t z))))
   (if (<= t_1 0.4) t_2 (if (<= t_1 2.0) t t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = x * (t / z);
	double tmp;
	if (t_1 <= 0.4) {
		tmp = t_2;
	} else if (t_1 <= 2.0) {
		tmp = t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = x * (t / z)
    if (t_1 <= 0.4d0) then
        tmp = t_2
    else if (t_1 <= 2.0d0) then
        tmp = t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = x * (t / z);
	double tmp;
	if (t_1 <= 0.4) {
		tmp = t_2;
	} else if (t_1 <= 2.0) {
		tmp = t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = x * (t / z)
	tmp = 0
	if t_1 <= 0.4:
		tmp = t_2
	elif t_1 <= 2.0:
		tmp = t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (t_1 <= 0.4)
		tmp = t_2;
	elseif (t_1 <= 2.0)
		tmp = t;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = x * (t / z);
	tmp = 0.0;
	if (t_1 <= 0.4)
		tmp = t_2;
	elseif (t_1 <= 2.0)
		tmp = t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 0.4], t$95$2, If[LessEqual[t$95$1, 2.0], t, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 0.40000000000000002 or 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 95.2%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 62.3

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

   5. Simplified 62.3%

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

      1. associate-*l/ N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 60.1

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

   7. Applied egg-rr 60.1%

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

   if 0.40000000000000002 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \cdot t \]
   4. Step-by-step derivation

   5. Simplified 98.4%

      \[\leadsto \color{blue}{1} \cdot t \]
   6. Step-by-step derivation

      1. *-lft-identity 98.4

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

   7. Applied egg-rr 98.4%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 0.4:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 69.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-97}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z)))))
   (if (<= y -1.65e-59) t_1 (if (<= y 3.1e-97) (* t (/ x z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double tmp;
	if (y <= -1.65e-59) {
		tmp = t_1;
	} else if (y <= 3.1e-97) {
		tmp = t * (x / z);
	} 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 = t * (y / (y - z))
    if (y <= (-1.65d-59)) then
        tmp = t_1
    else if (y <= 3.1d-97) then
        tmp = t * (x / z)
    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 = t * (y / (y - z));
	double tmp;
	if (y <= -1.65e-59) {
		tmp = t_1;
	} else if (y <= 3.1e-97) {
		tmp = t * (x / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / (y - z))
	tmp = 0
	if y <= -1.65e-59:
		tmp = t_1
	elif y <= 3.1e-97:
		tmp = t * (x / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y / Float64(y - z)))
	tmp = 0.0
	if (y <= -1.65e-59)
		tmp = t_1;
	elseif (y <= 3.1e-97)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y / (y - z));
	tmp = 0.0;
	if (y <= -1.65e-59)
		tmp = t_1;
	elseif (y <= 3.1e-97)
		tmp = t * (x / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.65e-59], t$95$1, If[LessEqual[y, 3.1e-97], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.64999999999999991e-59 or 3.10000000000000002e-97 < y

   1. Initial program 99.2%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. frac-2neg N/A

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

      4. div-inv N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

      7. neg-sub0 N/A

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

      8. lift--.f64 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. associate--r+ N/A

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

      12. neg-sub0 N/A

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

      13. remove-double-neg N/A

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

      14. lower--.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. lower-/.f64 N/A

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

      17. neg-sub0 N/A

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

      18. lift--.f64 N/A

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

      19. sub-neg N/A

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

      20. +-commutative N/A

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

      21. associate--r+ N/A

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

      22. neg-sub0 N/A

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

      23. remove-double-neg N/A

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

      24. lower--.f64 79.0

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

   4. Applied egg-rr 79.0%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. frac-2neg N/A

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

      4. metadata-eval N/A

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

      5. metadata-eval N/A

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

      6. frac-2neg N/A

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

      7. lift-/.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. associate-*l/ N/A

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

      10. *-lft-identity N/A

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

      11. clear-num N/A

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

      12. un-div-inv N/A

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

      13. lower-/.f64 N/A

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

      14. lower-/.f64 78.3

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

   6. Applied egg-rr 78.3%

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

   7. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 76.7

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

   9. Simplified 76.7%

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

   if -1.64999999999999991e-59 < y < 3.10000000000000002e-97

   1. Initial program 93.6%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 73.3

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

   5. Simplified 73.3%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-59}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-97}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 35.2% accurate, 23.0× speedup

Math

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

FPCore

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

C

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

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 = t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.7%

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

3. Taylor expanded in y around inf

   \[\leadsto \color{blue}{1} \cdot t \]
4. Step-by-step derivation

5. Simplified 34.0%

   \[\leadsto \color{blue}{1} \cdot t \]
6. Step-by-step derivation

   1. *-lft-identity 34.0

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

7. Applied egg-rr 34.0%

   \[\leadsto \color{blue}{t} \]
8. Add Preprocessing

Developer Target 1: 96.7% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024212 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

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

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