Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A

Percentage Accurate: 85.2% → 98.4%

Time: 3.4s

Alternatives: 11

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 85.2%

   \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-+.f64 N/A

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

   2. lift--.f64 N/A

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

   3. lift-/.f64 N/A

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

   4. lift--.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. *-commutative N/A

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

   7. +-commutative N/A

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

   8. associate-/l* N/A

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

   9. sub-div N/A

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

   10. *-commutative N/A

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

   11. lower-fma.f64 N/A

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

   12. sub-div N/A

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

   13. lower-/.f64 N/A

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

   14. lift--.f64 N/A

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

   15. lift--.f64 98.4

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

4. Applied rewrites 98.4%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t, x\right)} \]
5. Add Preprocessing

Alternative 2: 81.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t}{a - z}\\ t_2 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+171}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 200:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+131}:\\ \;\;\;\;\left(x + t\right) - \frac{t \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y z) (/ t (- a z)))) (t_2 (/ (* (- y z) t) (- a z))))
   (if (<= t_2 -2e+171)
     t_1
     (if (<= t_2 200.0)
       (+ x (/ (* y t) (- a z)))
       (if (<= t_2 5e+131) (- (+ x t) (/ (* t y) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) * (t / (a - z));
	double t_2 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_2 <= -2e+171) {
		tmp = t_1;
	} else if (t_2 <= 200.0) {
		tmp = x + ((y * t) / (a - z));
	} else if (t_2 <= 5e+131) {
		tmp = (x + t) - ((t * y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y - z) * (t / (a - z))
    t_2 = ((y - z) * t) / (a - z)
    if (t_2 <= (-2d+171)) then
        tmp = t_1
    else if (t_2 <= 200.0d0) then
        tmp = x + ((y * t) / (a - z))
    else if (t_2 <= 5d+131) then
        tmp = (x + t) - ((t * y) / 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 a) {
	double t_1 = (y - z) * (t / (a - z));
	double t_2 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_2 <= -2e+171) {
		tmp = t_1;
	} else if (t_2 <= 200.0) {
		tmp = x + ((y * t) / (a - z));
	} else if (t_2 <= 5e+131) {
		tmp = (x + t) - ((t * y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - z) * (t / (a - z))
	t_2 = ((y - z) * t) / (a - z)
	tmp = 0
	if t_2 <= -2e+171:
		tmp = t_1
	elif t_2 <= 200.0:
		tmp = x + ((y * t) / (a - z))
	elif t_2 <= 5e+131:
		tmp = (x + t) - ((t * y) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) * Float64(t / Float64(a - z)))
	t_2 = Float64(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if (t_2 <= -2e+171)
		tmp = t_1;
	elseif (t_2 <= 200.0)
		tmp = Float64(x + Float64(Float64(y * t) / Float64(a - z)));
	elseif (t_2 <= 5e+131)
		tmp = Float64(Float64(x + t) - Float64(Float64(t * y) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - z) * (t / (a - z));
	t_2 = ((y - z) * t) / (a - z);
	tmp = 0.0;
	if (t_2 <= -2e+171)
		tmp = t_1;
	elseif (t_2 <= 200.0)
		tmp = x + ((y * t) / (a - z));
	elseif (t_2 <= 5e+131)
		tmp = (x + t) - ((t * y) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+171], t$95$1, If[LessEqual[t$95$2, 200.0], N[(x + N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+131], N[(N[(x + t), $MachinePrecision] - N[(N[(t * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -1.99999999999999991e171 or 4.99999999999999995e131 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 55.4%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 83.2

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

   5. Applied rewrites 83.2%

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

   if -1.99999999999999991e171 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 200

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 83.7%

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

   if 200 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 4.99999999999999995e131

   1. Initial program 99.8%

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

   3. Taylor expanded in z around -inf

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

      1. associate-+r+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. fp-cancel-sub-sign-inv N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 57.6

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

   5. Applied rewrites 57.6%

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

   6. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 58.7

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

   8. Applied rewrites 58.7%

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

Alternative 3: 81.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t}{a - z}\\ t_2 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+171}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 200:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a - z}, t, x\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+131}:\\ \;\;\;\;\left(x + t\right) - \frac{t \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y z) (/ t (- a z)))) (t_2 (/ (* (- y z) t) (- a z))))
   (if (<= t_2 -2e+171)
     t_1
     (if (<= t_2 200.0)
       (fma (/ y (- a z)) t x)
       (if (<= t_2 5e+131) (- (+ x t) (/ (* t y) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) * (t / (a - z));
	double t_2 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_2 <= -2e+171) {
		tmp = t_1;
	} else if (t_2 <= 200.0) {
		tmp = fma((y / (a - z)), t, x);
	} else if (t_2 <= 5e+131) {
		tmp = (x + t) - ((t * y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) * Float64(t / Float64(a - z)))
	t_2 = Float64(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if (t_2 <= -2e+171)
		tmp = t_1;
	elseif (t_2 <= 200.0)
		tmp = fma(Float64(y / Float64(a - z)), t, x);
	elseif (t_2 <= 5e+131)
		tmp = Float64(Float64(x + t) - Float64(Float64(t * y) / z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+171], t$95$1, If[LessEqual[t$95$2, 200.0], N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision], If[LessEqual[t$95$2, 5e+131], N[(N[(x + t), $MachinePrecision] - N[(N[(t * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -1.99999999999999991e171 or 4.99999999999999995e131 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 55.4%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 83.2

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

   5. Applied rewrites 83.2%

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

   if -1.99999999999999991e171 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 200

   1. Initial program 99.6%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 98.9

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

   4. Applied rewrites 98.9%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 83.2%

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

   if 200 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 4.99999999999999995e131

   1. Initial program 99.8%

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

   3. Taylor expanded in z around -inf

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

      1. associate-+r+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. fp-cancel-sub-sign-inv N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 57.6

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

   5. Applied rewrites 57.6%

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

   6. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 58.7

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

   8. Applied rewrites 58.7%

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

Alternative 4: 55.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+165}:\\ \;\;\;\;t\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+106}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y z) t) (- a z))))
   (if (<= t_1 -1e+165) t (if (<= t_1 5e+106) x t))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_1 <= -1e+165) {
		tmp = t;
	} else if (t_1 <= 5e+106) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y - z) * t) / (a - z)
    if (t_1 <= (-1d+165)) then
        tmp = t
    else if (t_1 <= 5d+106) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_1 <= -1e+165) {
		tmp = t;
	} else if (t_1 <= 5e+106) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y - z) * t) / (a - z)
	tmp = 0
	if t_1 <= -1e+165:
		tmp = t
	elif t_1 <= 5e+106:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if (t_1 <= -1e+165)
		tmp = t;
	elseif (t_1 <= 5e+106)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y - z) * t) / (a - z);
	tmp = 0.0;
	if (t_1 <= -1e+165)
		tmp = t;
	elseif (t_1 <= 5e+106)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+165], t, If[LessEqual[t$95$1, 5e+106], x, t]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -9.99999999999999899e164 or 4.9999999999999998e106 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 57.4%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 82.6

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

   5. Applied rewrites 82.6%

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

   6. Taylor expanded in z around inf

      \[\leadsto t \]
   7. Step-by-step derivation

   8. Applied rewrites 29.7%

      \[\leadsto t \]

   if -9.99999999999999899e164 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 4.9999999999999998e106

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 68.4%

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

Alternative 5: 84.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+137}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+84}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a - z}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + t\right) - \frac{t \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.8e+137)
   (+ x t)
   (if (<= z 5e+84) (fma (/ y (- a z)) t x) (- (+ x t) (/ (* t y) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e+137) {
		tmp = x + t;
	} else if (z <= 5e+84) {
		tmp = fma((y / (a - z)), t, x);
	} else {
		tmp = (x + t) - ((t * y) / z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.8e+137)
		tmp = Float64(x + t);
	elseif (z <= 5e+84)
		tmp = fma(Float64(y / Float64(a - z)), t, x);
	else
		tmp = Float64(Float64(x + t) - Float64(Float64(t * y) / z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.8e+137], N[(x + t), $MachinePrecision], If[LessEqual[z, 5e+84], N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision], N[(N[(x + t), $MachinePrecision] - N[(N[(t * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8e137

   1. Initial program 66.5%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 85.8%

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

   if -1.8e137 < z < 5.0000000000000001e84

   1. Initial program 93.7%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 97.7

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

   4. Applied rewrites 97.7%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 84.4%

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

   if 5.0000000000000001e84 < z

   1. Initial program 68.2%

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

   3. Taylor expanded in z around -inf

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

      1. associate-+r+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. fp-cancel-sub-sign-inv N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 78.3

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

   5. Applied rewrites 78.3%

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

   6. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 82.7

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

   8. Applied rewrites 82.7%

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

Alternative 6: 84.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+137}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+86}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a - z}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.8e+137)
   (+ x t)
   (if (<= z 2.6e+86) (fma (/ y (- a z)) t x) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e+137) {
		tmp = x + t;
	} else if (z <= 2.6e+86) {
		tmp = fma((y / (a - z)), t, x);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.8e+137)
		tmp = Float64(x + t);
	elseif (z <= 2.6e+86)
		tmp = fma(Float64(y / Float64(a - z)), t, x);
	else
		tmp = Float64(x + t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.8e+137], N[(x + t), $MachinePrecision], If[LessEqual[z, 2.6e+86], N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8e137 or 2.5999999999999998e86 < z

   1. Initial program 67.3%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 84.1%

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

   if -1.8e137 < z < 2.5999999999999998e86

   1. Initial program 93.6%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. sub-div N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-div N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift--.f64 97.7

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

   4. Applied rewrites 97.7%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 84.3%

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

Alternative 7: 77.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+130}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 750000000:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y - z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.15e+130)
   (+ x t)
   (if (<= z 750000000.0) (fma t (/ (- y z) a) x) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.15e+130) {
		tmp = x + t;
	} else if (z <= 750000000.0) {
		tmp = fma(t, ((y - z) / a), x);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.15e+130)
		tmp = Float64(x + t);
	elseif (z <= 750000000.0)
		tmp = fma(t, Float64(Float64(y - z) / a), x);
	else
		tmp = Float64(x + t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.15e+130], N[(x + t), $MachinePrecision], If[LessEqual[z, 750000000.0], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.14999999999999992e130 or 7.5e8 < z

   1. Initial program 71.4%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 80.5%

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

   if -2.14999999999999992e130 < z < 7.5e8

   1. Initial program 94.3%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

         \[\leadsto t \cdot \frac{y - z}{a} + x \]

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 75.0

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

   5. Applied rewrites 75.0%

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

Alternative 8: 77.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+23}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 750000000:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.1e+23)
   (+ x t)
   (if (<= z 750000000.0) (fma t (/ y a) x) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.1e+23) {
		tmp = x + t;
	} else if (z <= 750000000.0) {
		tmp = fma(t, (y / a), x);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.1e+23)
		tmp = Float64(x + t);
	elseif (z <= 750000000.0)
		tmp = fma(t, Float64(y / a), x);
	else
		tmp = Float64(x + t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.1e+23], N[(x + t), $MachinePrecision], If[LessEqual[z, 750000000.0], N[(t * N[(y / a), $MachinePrecision] + x), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.10000000000000004e23 or 7.5e8 < z

   1. Initial program 73.7%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 78.0%

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

   if -1.10000000000000004e23 < z < 7.5e8

   1. Initial program 95.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

         \[\leadsto t \cdot \frac{y}{a} + x \]

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 76.1

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

   5. Applied rewrites 76.1%

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

Alternative 9: 61.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-76}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-222}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 86000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.8e-76)
   (+ x t)
   (if (<= z -5.2e-222) (* t (/ y a)) (if (<= z 86000000.0) x (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.8e-76) {
		tmp = x + t;
	} else if (z <= -5.2e-222) {
		tmp = t * (y / a);
	} else if (z <= 86000000.0) {
		tmp = x;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.8d-76)) then
        tmp = x + t
    else if (z <= (-5.2d-222)) then
        tmp = t * (y / a)
    else if (z <= 86000000.0d0) then
        tmp = x
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.8e-76) {
		tmp = x + t;
	} else if (z <= -5.2e-222) {
		tmp = t * (y / a);
	} else if (z <= 86000000.0) {
		tmp = x;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.8e-76:
		tmp = x + t
	elif z <= -5.2e-222:
		tmp = t * (y / a)
	elif z <= 86000000.0:
		tmp = x
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.8e-76)
		tmp = Float64(x + t);
	elseif (z <= -5.2e-222)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 86000000.0)
		tmp = x;
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.8e-76)
		tmp = x + t;
	elseif (z <= -5.2e-222)
		tmp = t * (y / a);
	elseif (z <= 86000000.0)
		tmp = x;
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.8e-76], N[(x + t), $MachinePrecision], If[LessEqual[z, -5.2e-222], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 86000000.0], x, N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8000000000000001e-76 or 8.6e7 < z

   1. Initial program 76.8%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 74.8%

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

   if -2.8000000000000001e-76 < z < -5.1999999999999997e-222

   1. Initial program 95.0%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 40.2

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

   5. Applied rewrites 40.2%

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

   6. Taylor expanded in z around 0

      \[\leadsto t \cdot \frac{y}{a} \]
   7. Step-by-step derivation

   8. Applied rewrites 30.6%

      \[\leadsto t \cdot \frac{y}{a} \]

   if -5.1999999999999997e-222 < z < 8.6e7

   1. Initial program 95.9%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 50.7%

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

Alternative 10: 63.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{+82}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+184}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.5e+82) x (if (<= a 2e+184) (+ x t) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.5e+82) {
		tmp = x;
	} else if (a <= 2e+184) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-8.5d+82)) then
        tmp = x
    else if (a <= 2d+184) then
        tmp = x + t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.5e+82) {
		tmp = x;
	} else if (a <= 2e+184) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.5e+82:
		tmp = x
	elif a <= 2e+184:
		tmp = x + t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.5e+82)
		tmp = x;
	elseif (a <= 2e+184)
		tmp = Float64(x + t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8.5e+82)
		tmp = x;
	elseif (a <= 2e+184)
		tmp = x + t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.5e+82], x, If[LessEqual[a, 2e+184], N[(x + t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -8.4999999999999995e82 or 2.00000000000000003e184 < a

   1. Initial program 80.5%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 65.1%

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

   if -8.4999999999999995e82 < a < 2.00000000000000003e184

   1. Initial program 87.0%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 63.3%

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

Alternative 11: 50.2% accurate, 26.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.2%

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

3. Taylor expanded in x around inf

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

5. Applied rewrites 50.2%

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

Developer Target 1: 99.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{a - z} \cdot t\\ \mathbf{if}\;t < -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y z) (- a z)) t))))
   (if (< t -1.0682974490174067e-39)
     t_1
     (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - z) / (a - z)) * t)
    if (t < (-1.0682974490174067d-39)) then
        tmp = t_1
    else if (t < 3.9110949887586375d-141) then
        tmp = x + (((y - z) * t) / (a - 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 a) {
	double t_1 = x + (((y - z) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) / (a - z)) * t)
	tmp = 0
	if t < -1.0682974490174067e-39:
		tmp = t_1
	elif t < 3.9110949887586375e-141:
		tmp = x + (((y - z) * t) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) / Float64(a - z)) * t))
	tmp = 0.0
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * t) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) / (a - z)) * t);
	tmp = 0.0;
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = x + (((y - z) * t) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.0682974490174067e-39], t$95$1, If[Less[t, 3.9110949887586375e-141], N[(x + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2025091 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -10682974490174067/10000000000000000000000000000000000000000000000000000000) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 312887599100691/80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t)))))

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