Data.Colour.RGB:hslsv from colour-2.3.3, B

Percentage Accurate: 99.4% → 99.8%

Time: 7.3s

Alternatives: 23

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

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 = ((60.0d0 * (x - y)) / (z - t)) + (a * 120.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

Python

def code(x, y, z, t, a):
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t)) + Float64(a * 120.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

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 = ((60.0d0 * (x - y)) / (z - t)) + (a * 120.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

Python

def code(x, y, z, t, a):
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t)) + Float64(a * 120.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(a, 120, \frac{-60}{z - t} \cdot \left(y - x\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (fma a 120.0 (* (/ -60.0 (- z t)) (- y x))))

C

double code(double x, double y, double z, double t, double a) {
	return fma(a, 120.0, ((-60.0 / (z - t)) * (y - x)));
}

Julia

function code(x, y, z, t, a)
	return fma(a, 120.0, Float64(Float64(-60.0 / Float64(z - t)) * Float64(y - x)))
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(a * 120.0 + N[(N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.4%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
2. Step-by-step derivation

   1. lift-+.f64 N/A

      \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{a \cdot 120 + \frac{60 \cdot \left(x - y\right)}{z - t}} \]

   3. lift-/.f64 N/A

      \[\leadsto a \cdot 120 + \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

   4. mult-flip N/A

      \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right) \cdot \frac{1}{z - t}} \]

   5. lift-*.f64 N/A

      \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

   6. *-commutative N/A

      \[\leadsto a \cdot 120 + \color{blue}{\left(\left(x - y\right) \cdot 60\right)} \cdot \frac{1}{z - t} \]

   7. associate-*l* N/A

      \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

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

      \[\leadsto \color{blue}{a \cdot 120 - \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

   9. distribute-lft-neg-in N/A

      \[\leadsto a \cdot 120 - \color{blue}{\left(\mathsf{neg}\left(\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)\right)\right)} \]

   10. distribute-rgt-neg-in N/A

       \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right)} \]

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

       \[\leadsto \color{blue}{a \cdot 120 + \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right)} \]

   12. lift-*.f64 N/A

       \[\leadsto \color{blue}{a \cdot 120} + \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

   13. lift--.f64 N/A

       \[\leadsto a \cdot 120 + \left(\mathsf{neg}\left(\color{blue}{\left(x - y\right)}\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

   14. sub-negate-rev N/A

       \[\leadsto a \cdot 120 + \color{blue}{\left(y - x\right)} \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

   15. distribute-rgt-neg-in N/A

       \[\leadsto a \cdot 120 + \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)\right)\right)} \]

   16. distribute-lft-neg-out N/A

       \[\leadsto a \cdot 120 + \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right)\right)\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

   17. sub-negate-rev N/A

       \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right) \]

   18. lift--.f64 N/A

       \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right) \]

   19. associate-*l* N/A

       \[\leadsto a \cdot 120 + \color{blue}{\left(\left(x - y\right) \cdot 60\right) \cdot \frac{1}{z - t}} \]

   20. *-commutative N/A

       \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

   21. lift-*.f64 N/A

       \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

3. Applied rewrites 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{-60}{z - t} \cdot \left(y - x\right)\right)} \]
4. Add Preprocessing

Alternative 2: 88.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot x}{z - t} + a \cdot 120\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{+160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+55}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y \cdot -60}{z - t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (/ (* 60.0 x) (- z t)) (* a 120.0))))
   (if (<= x -1.2e+160)
     t_1
     (if (<= x 5.5e+55) (fma a 120.0 (/ (* y -60.0) (- z t))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((60.0 * x) / (z - t)) + (a * 120.0);
	double tmp;
	if (x <= -1.2e+160) {
		tmp = t_1;
	} else if (x <= 5.5e+55) {
		tmp = fma(a, 120.0, ((y * -60.0) / (z - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(60.0 * x) / Float64(z - t)) + Float64(a * 120.0))
	tmp = 0.0
	if (x <= -1.2e+160)
		tmp = t_1;
	elseif (x <= 5.5e+55)
		tmp = fma(a, 120.0, Float64(Float64(y * -60.0) / Float64(z - t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.2e+160], t$95$1, If[LessEqual[x, 5.5e+55], N[(a * 120.0 + N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.2000000000000001e160 or 5.5000000000000004e55 < x

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in x around inf

      \[\leadsto \frac{\color{blue}{60 \cdot x}}{z - t} + a \cdot 120 \]
   3. Step-by-step derivation

      1. lower-*.f64 74.7

         \[\leadsto \frac{60 \cdot \color{blue}{x}}{z - t} + a \cdot 120 \]

   4. Applied rewrites 74.7%

      \[\leadsto \frac{\color{blue}{60 \cdot x}}{z - t} + a \cdot 120 \]

   if -1.2000000000000001e160 < x < 5.5000000000000004e55

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{-60 \cdot y}}{z - t} + a \cdot 120 \]
   3. Step-by-step derivation

      1. lower-*.f64 74.4

         \[\leadsto \frac{-60 \cdot \color{blue}{y}}{z - t} + a \cdot 120 \]

   4. Applied rewrites 74.4%

      \[\leadsto \frac{\color{blue}{-60 \cdot y}}{z - t} + a \cdot 120 \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{-60 \cdot y}{z - t} + a \cdot 120} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{a \cdot 120 + \frac{-60 \cdot y}{z - t}} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot 120} + \frac{-60 \cdot y}{z - t} \]

      4. lower-fma.f64 74.5

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{-60 \cdot y}{z - t}\right)} \]

      5. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60 \cdot \color{blue}{y}}{z - t}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{y \cdot \color{blue}{-60}}{z - t}\right) \]

      7. lower-*.f64 74.5

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{y \cdot \color{blue}{-60}}{z - t}\right) \]

   6. Applied rewrites 74.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{y \cdot -60}{z - t}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 84.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{if}\;x \leq -1.75 \cdot 10^{+192}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+102}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{y \cdot -60}{z - t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ 60.0 (- z t)) (- x y))))
   (if (<= x -1.75e+192)
     t_1
     (if (<= x 1.9e+102) (fma a 120.0 (/ (* y -60.0) (- z t))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 / (z - t)) * (x - y);
	double tmp;
	if (x <= -1.75e+192) {
		tmp = t_1;
	} else if (x <= 1.9e+102) {
		tmp = fma(a, 120.0, ((y * -60.0) / (z - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y))
	tmp = 0.0
	if (x <= -1.75e+192)
		tmp = t_1;
	elseif (x <= 1.9e+102)
		tmp = fma(a, 120.0, Float64(Float64(y * -60.0) / Float64(z - t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.75e+192], t$95$1, If[LessEqual[x, 1.9e+102], N[(a * 120.0 + N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.74999999999999991e192 or 1.89999999999999989e102 < x

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z} - t} \]

      4. lower--.f64 51.6

         \[\leadsto 60 \cdot \frac{x - y}{z - \color{blue}{t}} \]

   4. Applied rewrites 51.6%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. associate-/l* N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{\color{blue}{z - t}} \]

      4. associate-*l/ N/A

         \[\leadsto \frac{60}{z - t} \cdot \color{blue}{\left(x - y\right)} \]

      5. metadata-eval N/A

         \[\leadsto \frac{\mathsf{neg}\left(-60\right)}{z - t} \cdot \left(x - y\right) \]

      6. distribute-neg-frac N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-60}{z - t}\right)\right) \cdot \left(\color{blue}{x} - y\right) \]

      7. lift-/.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-60}{z - t}\right)\right) \cdot \left(x - y\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-60}{z - t}\right)\right) \cdot \color{blue}{\left(x - y\right)} \]

      9. lift-/.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-60}{z - t}\right)\right) \cdot \left(x - y\right) \]

      10. distribute-neg-frac N/A

          \[\leadsto \frac{\mathsf{neg}\left(-60\right)}{z - t} \cdot \left(\color{blue}{x} - y\right) \]

      11. metadata-eval N/A

          \[\leadsto \frac{60}{z - t} \cdot \left(x - y\right) \]

      12. lower-/.f64 51.6

          \[\leadsto \frac{60}{z - t} \cdot \left(\color{blue}{x} - y\right) \]

   6. Applied rewrites 51.6%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} \]

   if -1.74999999999999991e192 < x < 1.89999999999999989e102

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{-60 \cdot y}}{z - t} + a \cdot 120 \]
   3. Step-by-step derivation

      1. lower-*.f64 74.4

         \[\leadsto \frac{-60 \cdot \color{blue}{y}}{z - t} + a \cdot 120 \]

   4. Applied rewrites 74.4%

      \[\leadsto \frac{\color{blue}{-60 \cdot y}}{z - t} + a \cdot 120 \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{-60 \cdot y}{z - t} + a \cdot 120} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{a \cdot 120 + \frac{-60 \cdot y}{z - t}} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot 120} + \frac{-60 \cdot y}{z - t} \]

      4. lower-fma.f64 74.5

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{-60 \cdot y}{z - t}\right)} \]

      5. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60 \cdot \color{blue}{y}}{z - t}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{y \cdot \color{blue}{-60}}{z - t}\right) \]

      7. lower-*.f64 74.5

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{y \cdot \color{blue}{-60}}{z - t}\right) \]

   6. Applied rewrites 74.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{y \cdot -60}{z - t}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 84.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{-56}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, 120 \cdot a\right)\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{-38}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{-60}{z} \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{60}{t} \cdot \left(y - x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.8e-56)
   (fma -60.0 (/ (- x y) t) (* 120.0 a))
   (if (<= t 7.4e-38)
     (fma a 120.0 (* (/ -60.0 z) (- y x)))
     (fma a 120.0 (* (/ 60.0 t) (- y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.8e-56) {
		tmp = fma(-60.0, ((x - y) / t), (120.0 * a));
	} else if (t <= 7.4e-38) {
		tmp = fma(a, 120.0, ((-60.0 / z) * (y - x)));
	} else {
		tmp = fma(a, 120.0, ((60.0 / t) * (y - x)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.8e-56)
		tmp = fma(-60.0, Float64(Float64(x - y) / t), Float64(120.0 * a));
	elseif (t <= 7.4e-38)
		tmp = fma(a, 120.0, Float64(Float64(-60.0 / z) * Float64(y - x)));
	else
		tmp = fma(a, 120.0, Float64(Float64(60.0 / t) * Float64(y - x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.8e-56], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.4e-38], N[(a * 120.0 + N[(N[(-60.0 / z), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0 + N[(N[(60.0 / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.79999999999999982e-56

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \color{blue}{\frac{x - y}{t}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \frac{x - y}{\color{blue}{t}}, 120 \cdot a\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \frac{x - y}{t}, 120 \cdot a\right) \]

      4. lower-*.f64 63.7

         \[\leadsto \mathsf{fma}\left(-60, \frac{x - y}{t}, 120 \cdot a\right) \]

   4. Applied rewrites 63.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-60, \frac{x - y}{t}, 120 \cdot a\right)} \]

   if -5.79999999999999982e-56 < t < 7.4e-38

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{a \cdot 120 + \frac{60 \cdot \left(x - y\right)}{z - t}} \]

      3. lift-/.f64 N/A

         \[\leadsto a \cdot 120 + \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

      4. mult-flip N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right) \cdot \frac{1}{z - t}} \]

      5. lift-*.f64 N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

      6. *-commutative N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(\left(x - y\right) \cdot 60\right)} \cdot \frac{1}{z - t} \]

      7. associate-*l* N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

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

         \[\leadsto \color{blue}{a \cdot 120 - \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

      9. distribute-lft-neg-in N/A

         \[\leadsto a \cdot 120 - \color{blue}{\left(\mathsf{neg}\left(\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)\right)\right)} \]

      10. distribute-rgt-neg-in N/A

          \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right)} \]

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

          \[\leadsto \color{blue}{a \cdot 120 + \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right)} \]

      12. lift-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot 120} + \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      13. lift--.f64 N/A

          \[\leadsto a \cdot 120 + \left(\mathsf{neg}\left(\color{blue}{\left(x - y\right)}\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      14. sub-negate-rev N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(y - x\right)} \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      15. distribute-rgt-neg-in N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)\right)\right)} \]

      16. distribute-lft-neg-out N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right)\right)\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

      17. sub-negate-rev N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right) \]

      18. lift--.f64 N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right) \]

      19. associate-*l* N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(\left(x - y\right) \cdot 60\right) \cdot \frac{1}{z - t}} \]

      20. *-commutative N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

      21. lift-*.f64 N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{-60}{z - t} \cdot \left(y - x\right)\right)} \]

   4. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{-60}{z}} \cdot \left(y - x\right)\right) \]
   5. Step-by-step derivation

      1. lower-/.f64 63.4

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{\color{blue}{z}} \cdot \left(y - x\right)\right) \]

   6. Applied rewrites 63.4%

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{-60}{z}} \cdot \left(y - x\right)\right) \]

   if 7.4e-38 < t

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{a \cdot 120 + \frac{60 \cdot \left(x - y\right)}{z - t}} \]

      3. lift-/.f64 N/A

         \[\leadsto a \cdot 120 + \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

      4. mult-flip N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right) \cdot \frac{1}{z - t}} \]

      5. lift-*.f64 N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

      6. *-commutative N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(\left(x - y\right) \cdot 60\right)} \cdot \frac{1}{z - t} \]

      7. associate-*l* N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

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

         \[\leadsto \color{blue}{a \cdot 120 - \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

      9. distribute-lft-neg-in N/A

         \[\leadsto a \cdot 120 - \color{blue}{\left(\mathsf{neg}\left(\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)\right)\right)} \]

      10. distribute-rgt-neg-in N/A

          \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right)} \]

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

          \[\leadsto \color{blue}{a \cdot 120 + \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right)} \]

      12. lift-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot 120} + \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      13. lift--.f64 N/A

          \[\leadsto a \cdot 120 + \left(\mathsf{neg}\left(\color{blue}{\left(x - y\right)}\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      14. sub-negate-rev N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(y - x\right)} \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      15. distribute-rgt-neg-in N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)\right)\right)} \]

      16. distribute-lft-neg-out N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right)\right)\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

      17. sub-negate-rev N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right) \]

      18. lift--.f64 N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right) \]

      19. associate-*l* N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(\left(x - y\right) \cdot 60\right) \cdot \frac{1}{z - t}} \]

      20. *-commutative N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

      21. lift-*.f64 N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{-60}{z - t} \cdot \left(y - x\right)\right)} \]

   4. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{60}{t}} \cdot \left(y - x\right)\right) \]
   5. Step-by-step derivation

      1. lower-/.f64 63.7

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{60}{\color{blue}{t}} \cdot \left(y - x\right)\right) \]

   6. Applied rewrites 63.7%

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{60}{t}} \cdot \left(y - x\right)\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 84.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-60, \frac{x - y}{t}, 120 \cdot a\right)\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{-38}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{-60}{z} \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma -60.0 (/ (- x y) t) (* 120.0 a))))
   (if (<= t -5.8e-56)
     t_1
     (if (<= t 7.4e-38) (fma a 120.0 (* (/ -60.0 z) (- y x))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(-60.0, ((x - y) / t), (120.0 * a));
	double tmp;
	if (t <= -5.8e-56) {
		tmp = t_1;
	} else if (t <= 7.4e-38) {
		tmp = fma(a, 120.0, ((-60.0 / z) * (y - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(-60.0, Float64(Float64(x - y) / t), Float64(120.0 * a))
	tmp = 0.0
	if (t <= -5.8e-56)
		tmp = t_1;
	elseif (t <= 7.4e-38)
		tmp = fma(a, 120.0, Float64(Float64(-60.0 / z) * Float64(y - x)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.8e-56], t$95$1, If[LessEqual[t, 7.4e-38], N[(a * 120.0 + N[(N[(-60.0 / z), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.79999999999999982e-56 or 7.4e-38 < t

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \color{blue}{\frac{x - y}{t}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \frac{x - y}{\color{blue}{t}}, 120 \cdot a\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \frac{x - y}{t}, 120 \cdot a\right) \]

      4. lower-*.f64 63.7

         \[\leadsto \mathsf{fma}\left(-60, \frac{x - y}{t}, 120 \cdot a\right) \]

   4. Applied rewrites 63.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-60, \frac{x - y}{t}, 120 \cdot a\right)} \]

   if -5.79999999999999982e-56 < t < 7.4e-38

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{a \cdot 120 + \frac{60 \cdot \left(x - y\right)}{z - t}} \]

      3. lift-/.f64 N/A

         \[\leadsto a \cdot 120 + \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

      4. mult-flip N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right) \cdot \frac{1}{z - t}} \]

      5. lift-*.f64 N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

      6. *-commutative N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(\left(x - y\right) \cdot 60\right)} \cdot \frac{1}{z - t} \]

      7. associate-*l* N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

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

         \[\leadsto \color{blue}{a \cdot 120 - \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

      9. distribute-lft-neg-in N/A

         \[\leadsto a \cdot 120 - \color{blue}{\left(\mathsf{neg}\left(\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)\right)\right)} \]

      10. distribute-rgt-neg-in N/A

          \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right)} \]

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

          \[\leadsto \color{blue}{a \cdot 120 + \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right)} \]

      12. lift-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot 120} + \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      13. lift--.f64 N/A

          \[\leadsto a \cdot 120 + \left(\mathsf{neg}\left(\color{blue}{\left(x - y\right)}\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      14. sub-negate-rev N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(y - x\right)} \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      15. distribute-rgt-neg-in N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)\right)\right)} \]

      16. distribute-lft-neg-out N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right)\right)\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

      17. sub-negate-rev N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right) \]

      18. lift--.f64 N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right) \]

      19. associate-*l* N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(\left(x - y\right) \cdot 60\right) \cdot \frac{1}{z - t}} \]

      20. *-commutative N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

      21. lift-*.f64 N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{-60}{z - t} \cdot \left(y - x\right)\right)} \]

   4. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{-60}{z}} \cdot \left(y - x\right)\right) \]
   5. Step-by-step derivation

      1. lower-/.f64 63.4

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{\color{blue}{z}} \cdot \left(y - x\right)\right) \]

   6. Applied rewrites 63.4%

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{-60}{z}} \cdot \left(y - x\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 81.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-60, \frac{x - y}{t}, 120 \cdot a\right)\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{-38}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x - y}{z}, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma -60.0 (/ (- x y) t) (* 120.0 a))))
   (if (<= t -5.8e-56)
     t_1
     (if (<= t 7.4e-38) (fma 60.0 (/ (- x y) z) (* 120.0 a)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(-60.0, ((x - y) / t), (120.0 * a));
	double tmp;
	if (t <= -5.8e-56) {
		tmp = t_1;
	} else if (t <= 7.4e-38) {
		tmp = fma(60.0, ((x - y) / z), (120.0 * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(-60.0, Float64(Float64(x - y) / t), Float64(120.0 * a))
	tmp = 0.0
	if (t <= -5.8e-56)
		tmp = t_1;
	elseif (t <= 7.4e-38)
		tmp = fma(60.0, Float64(Float64(x - y) / z), Float64(120.0 * a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.8e-56], t$95$1, If[LessEqual[t, 7.4e-38], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.79999999999999982e-56 or 7.4e-38 < t

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \color{blue}{\frac{x - y}{t}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \frac{x - y}{\color{blue}{t}}, 120 \cdot a\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \frac{x - y}{t}, 120 \cdot a\right) \]

      4. lower-*.f64 63.7

         \[\leadsto \mathsf{fma}\left(-60, \frac{x - y}{t}, 120 \cdot a\right) \]

   4. Applied rewrites 63.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-60, \frac{x - y}{t}, 120 \cdot a\right)} \]

   if -5.79999999999999982e-56 < t < 7.4e-38

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \color{blue}{\frac{x - y}{z}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x - y}{\color{blue}{z}}, 120 \cdot a\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x - y}{z}, 120 \cdot a\right) \]

      4. lower-*.f64 63.4

         \[\leadsto \mathsf{fma}\left(60, \frac{x - y}{z}, 120 \cdot a\right) \]

   4. Applied rewrites 63.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(60, \frac{x - y}{z}, 120 \cdot a\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 77.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(60, \frac{x}{z}, 120 \cdot a\right)\\ \mathbf{if}\;z \leq -2 \cdot 10^{+136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+37}:\\ \;\;\;\;\mathsf{fma}\left(a, 120, \frac{-60}{z} \cdot y\right)\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-56}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;z \leq 8000000000000:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{x - y}{t}, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma 60.0 (/ x z) (* 120.0 a))))
   (if (<= z -2e+136)
     t_1
     (if (<= z -3.8e+37)
       (fma a 120.0 (* (/ -60.0 z) y))
       (if (<= z -2.05e-56)
         (* (/ 60.0 (- z t)) (- x y))
         (if (<= z 8000000000000.0)
           (fma -60.0 (/ (- x y) t) (* 120.0 a))
           t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(60.0, (x / z), (120.0 * a));
	double tmp;
	if (z <= -2e+136) {
		tmp = t_1;
	} else if (z <= -3.8e+37) {
		tmp = fma(a, 120.0, ((-60.0 / z) * y));
	} else if (z <= -2.05e-56) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else if (z <= 8000000000000.0) {
		tmp = fma(-60.0, ((x - y) / t), (120.0 * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(60.0, Float64(x / z), Float64(120.0 * a))
	tmp = 0.0
	if (z <= -2e+136)
		tmp = t_1;
	elseif (z <= -3.8e+37)
		tmp = fma(a, 120.0, Float64(Float64(-60.0 / z) * y));
	elseif (z <= -2.05e-56)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	elseif (z <= 8000000000000.0)
		tmp = fma(-60.0, Float64(Float64(x - y) / t), Float64(120.0 * a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(x / z), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+136], t$95$1, If[LessEqual[z, -3.8e+37], N[(a * 120.0 + N[(N[(-60.0 / z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.05e-56], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8000000000000.0], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.00000000000000012e136 or 8e12 < z

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \color{blue}{\frac{x - y}{z}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x - y}{\color{blue}{z}}, 120 \cdot a\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x - y}{z}, 120 \cdot a\right) \]

      4. lower-*.f64 63.4

         \[\leadsto \mathsf{fma}\left(60, \frac{x - y}{z}, 120 \cdot a\right) \]

   4. Applied rewrites 63.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(60, \frac{x - y}{z}, 120 \cdot a\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(60, \frac{x}{\color{blue}{z}}, 120 \cdot a\right) \]
   6. Step-by-step derivation

      1. lower-/.f64 54.1

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z}, 120 \cdot a\right) \]

   7. Applied rewrites 54.1%

      \[\leadsto \mathsf{fma}\left(60, \frac{x}{\color{blue}{z}}, 120 \cdot a\right) \]

   if -2.00000000000000012e136 < z < -3.7999999999999999e37

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{a \cdot 120 + \frac{60 \cdot \left(x - y\right)}{z - t}} \]

      3. lift-/.f64 N/A

         \[\leadsto a \cdot 120 + \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

      4. mult-flip N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right) \cdot \frac{1}{z - t}} \]

      5. lift-*.f64 N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

      6. *-commutative N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(\left(x - y\right) \cdot 60\right)} \cdot \frac{1}{z - t} \]

      7. associate-*l* N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

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

         \[\leadsto \color{blue}{a \cdot 120 - \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

      9. distribute-lft-neg-in N/A

         \[\leadsto a \cdot 120 - \color{blue}{\left(\mathsf{neg}\left(\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)\right)\right)} \]

      10. distribute-rgt-neg-in N/A

          \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right)} \]

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

          \[\leadsto \color{blue}{a \cdot 120 + \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right)} \]

      12. lift-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot 120} + \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      13. lift--.f64 N/A

          \[\leadsto a \cdot 120 + \left(\mathsf{neg}\left(\color{blue}{\left(x - y\right)}\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      14. sub-negate-rev N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(y - x\right)} \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      15. distribute-rgt-neg-in N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)\right)\right)} \]

      16. distribute-lft-neg-out N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right)\right)\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

      17. sub-negate-rev N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right) \]

      18. lift--.f64 N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right) \]

      19. associate-*l* N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(\left(x - y\right) \cdot 60\right) \cdot \frac{1}{z - t}} \]

      20. *-commutative N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

      21. lift-*.f64 N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{-60}{z - t} \cdot \left(y - x\right)\right)} \]

   4. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{-60}{z}} \cdot \left(y - x\right)\right) \]
   5. Step-by-step derivation

      1. lower-/.f64 63.4

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{\color{blue}{z}} \cdot \left(y - x\right)\right) \]

   6. Applied rewrites 63.4%

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{-60}{z}} \cdot \left(y - x\right)\right) \]

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{z} \cdot \color{blue}{y}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 53.9%

      \[\leadsto \mathsf{fma}\left(a, 120, \frac{-60}{z} \cdot \color{blue}{y}\right) \]

   if -3.7999999999999999e37 < z < -2.0500000000000001e-56

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z} - t} \]

      4. lower--.f64 51.6

         \[\leadsto 60 \cdot \frac{x - y}{z - \color{blue}{t}} \]

   4. Applied rewrites 51.6%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. associate-/l* N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{\color{blue}{z - t}} \]

      4. associate-*l/ N/A

         \[\leadsto \frac{60}{z - t} \cdot \color{blue}{\left(x - y\right)} \]

      5. metadata-eval N/A

         \[\leadsto \frac{\mathsf{neg}\left(-60\right)}{z - t} \cdot \left(x - y\right) \]

      6. distribute-neg-frac N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-60}{z - t}\right)\right) \cdot \left(\color{blue}{x} - y\right) \]

      7. lift-/.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-60}{z - t}\right)\right) \cdot \left(x - y\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-60}{z - t}\right)\right) \cdot \color{blue}{\left(x - y\right)} \]

      9. lift-/.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-60}{z - t}\right)\right) \cdot \left(x - y\right) \]

      10. distribute-neg-frac N/A

          \[\leadsto \frac{\mathsf{neg}\left(-60\right)}{z - t} \cdot \left(\color{blue}{x} - y\right) \]

      11. metadata-eval N/A

          \[\leadsto \frac{60}{z - t} \cdot \left(x - y\right) \]

      12. lower-/.f64 51.6

          \[\leadsto \frac{60}{z - t} \cdot \left(\color{blue}{x} - y\right) \]

   6. Applied rewrites 51.6%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} \]

   if -2.0500000000000001e-56 < z < 8e12

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \color{blue}{\frac{x - y}{t}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \frac{x - y}{\color{blue}{t}}, 120 \cdot a\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \frac{x - y}{t}, 120 \cdot a\right) \]

      4. lower-*.f64 63.7

         \[\leadsto \mathsf{fma}\left(-60, \frac{x - y}{t}, 120 \cdot a\right) \]

   4. Applied rewrites 63.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-60, \frac{x - y}{t}, 120 \cdot a\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 8: 75.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -24000000:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 10^{-51}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+163}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x}{z}, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -24000000.0)
   (* 120.0 a)
   (if (<= a 1e-51)
     (* (/ 60.0 (- z t)) (- x y))
     (if (<= a 8.2e+163) (fma 60.0 (/ x z) (* 120.0 a)) (* 120.0 a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -24000000.0) {
		tmp = 120.0 * a;
	} else if (a <= 1e-51) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else if (a <= 8.2e+163) {
		tmp = fma(60.0, (x / z), (120.0 * a));
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -24000000.0)
		tmp = Float64(120.0 * a);
	elseif (a <= 1e-51)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	elseif (a <= 8.2e+163)
		tmp = fma(60.0, Float64(x / z), Float64(120.0 * a));
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -24000000.0], N[(120.0 * a), $MachinePrecision], If[LessEqual[a, 1e-51], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.2e+163], N[(60.0 * N[(x / z), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.4e7 or 8.1999999999999998e163 < a

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-*.f64 49.8

         \[\leadsto 120 \cdot \color{blue}{a} \]

   4. Applied rewrites 49.8%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -2.4e7 < a < 1e-51

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z} - t} \]

      4. lower--.f64 51.6

         \[\leadsto 60 \cdot \frac{x - y}{z - \color{blue}{t}} \]

   4. Applied rewrites 51.6%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. associate-/l* N/A

         \[\leadsto \frac{60 \cdot \left(x - y\right)}{\color{blue}{z - t}} \]

      4. associate-*l/ N/A

         \[\leadsto \frac{60}{z - t} \cdot \color{blue}{\left(x - y\right)} \]

      5. metadata-eval N/A

         \[\leadsto \frac{\mathsf{neg}\left(-60\right)}{z - t} \cdot \left(x - y\right) \]

      6. distribute-neg-frac N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-60}{z - t}\right)\right) \cdot \left(\color{blue}{x} - y\right) \]

      7. lift-/.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-60}{z - t}\right)\right) \cdot \left(x - y\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-60}{z - t}\right)\right) \cdot \color{blue}{\left(x - y\right)} \]

      9. lift-/.f64 N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{-60}{z - t}\right)\right) \cdot \left(x - y\right) \]

      10. distribute-neg-frac N/A

          \[\leadsto \frac{\mathsf{neg}\left(-60\right)}{z - t} \cdot \left(\color{blue}{x} - y\right) \]

      11. metadata-eval N/A

          \[\leadsto \frac{60}{z - t} \cdot \left(x - y\right) \]

      12. lower-/.f64 51.6

          \[\leadsto \frac{60}{z - t} \cdot \left(\color{blue}{x} - y\right) \]

   6. Applied rewrites 51.6%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} \]

   if 1e-51 < a < 8.1999999999999998e163

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \color{blue}{\frac{x - y}{z}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x - y}{\color{blue}{z}}, 120 \cdot a\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x - y}{z}, 120 \cdot a\right) \]

      4. lower-*.f64 63.4

         \[\leadsto \mathsf{fma}\left(60, \frac{x - y}{z}, 120 \cdot a\right) \]

   4. Applied rewrites 63.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(60, \frac{x - y}{z}, 120 \cdot a\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(60, \frac{x}{\color{blue}{z}}, 120 \cdot a\right) \]
   6. Step-by-step derivation

      1. lower-/.f64 54.1

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z}, 120 \cdot a\right) \]

   7. Applied rewrites 54.1%

      \[\leadsto \mathsf{fma}\left(60, \frac{x}{\color{blue}{z}}, 120 \cdot a\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 75.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -24000000:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 10^{-51}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+163}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x}{z}, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -24000000.0)
   (* 120.0 a)
   (if (<= a 1e-51)
     (* 60.0 (/ (- x y) (- z t)))
     (if (<= a 8.2e+163) (fma 60.0 (/ x z) (* 120.0 a)) (* 120.0 a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -24000000.0) {
		tmp = 120.0 * a;
	} else if (a <= 1e-51) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (a <= 8.2e+163) {
		tmp = fma(60.0, (x / z), (120.0 * a));
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -24000000.0)
		tmp = Float64(120.0 * a);
	elseif (a <= 1e-51)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (a <= 8.2e+163)
		tmp = fma(60.0, Float64(x / z), Float64(120.0 * a));
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -24000000.0], N[(120.0 * a), $MachinePrecision], If[LessEqual[a, 1e-51], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.2e+163], N[(60.0 * N[(x / z), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.4e7 or 8.1999999999999998e163 < a

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-*.f64 49.8

         \[\leadsto 120 \cdot \color{blue}{a} \]

   4. Applied rewrites 49.8%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -2.4e7 < a < 1e-51

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z} - t} \]

      4. lower--.f64 51.6

         \[\leadsto 60 \cdot \frac{x - y}{z - \color{blue}{t}} \]

   4. Applied rewrites 51.6%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   if 1e-51 < a < 8.1999999999999998e163

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \color{blue}{\frac{x - y}{z}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x - y}{\color{blue}{z}}, 120 \cdot a\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x - y}{z}, 120 \cdot a\right) \]

      4. lower-*.f64 63.4

         \[\leadsto \mathsf{fma}\left(60, \frac{x - y}{z}, 120 \cdot a\right) \]

   4. Applied rewrites 63.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(60, \frac{x - y}{z}, 120 \cdot a\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(60, \frac{x}{\color{blue}{z}}, 120 \cdot a\right) \]
   6. Step-by-step derivation

      1. lower-/.f64 54.1

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z}, 120 \cdot a\right) \]

   7. Applied rewrites 54.1%

      \[\leadsto \mathsf{fma}\left(60, \frac{x}{\color{blue}{z}}, 120 \cdot a\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 67.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, 120, \frac{60}{t} \cdot y\right)\\ \mathbf{if}\;t \leq -4.9 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 30000000000000:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x}{z}, 120 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma a 120.0 (* (/ 60.0 t) y))))
   (if (<= t -4.9e-56)
     t_1
     (if (<= t 30000000000000.0) (fma 60.0 (/ x z) (* 120.0 a)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(a, 120.0, ((60.0 / t) * y));
	double tmp;
	if (t <= -4.9e-56) {
		tmp = t_1;
	} else if (t <= 30000000000000.0) {
		tmp = fma(60.0, (x / z), (120.0 * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(a, 120.0, Float64(Float64(60.0 / t) * y))
	tmp = 0.0
	if (t <= -4.9e-56)
		tmp = t_1;
	elseif (t <= 30000000000000.0)
		tmp = fma(60.0, Float64(x / z), Float64(120.0 * a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a * 120.0 + N[(N[(60.0 / t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.9e-56], t$95$1, If[LessEqual[t, 30000000000000.0], N[(60.0 * N[(x / z), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.9e-56 or 3e13 < t

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{a \cdot 120 + \frac{60 \cdot \left(x - y\right)}{z - t}} \]

      3. lift-/.f64 N/A

         \[\leadsto a \cdot 120 + \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

      4. mult-flip N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right) \cdot \frac{1}{z - t}} \]

      5. lift-*.f64 N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

      6. *-commutative N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(\left(x - y\right) \cdot 60\right)} \cdot \frac{1}{z - t} \]

      7. associate-*l* N/A

         \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

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

         \[\leadsto \color{blue}{a \cdot 120 - \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

      9. distribute-lft-neg-in N/A

         \[\leadsto a \cdot 120 - \color{blue}{\left(\mathsf{neg}\left(\left(x - y\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)\right)\right)} \]

      10. distribute-rgt-neg-in N/A

          \[\leadsto a \cdot 120 - \color{blue}{\left(x - y\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right)} \]

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

          \[\leadsto \color{blue}{a \cdot 120 + \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right)} \]

      12. lift-*.f64 N/A

          \[\leadsto \color{blue}{a \cdot 120} + \left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      13. lift--.f64 N/A

          \[\leadsto a \cdot 120 + \left(\mathsf{neg}\left(\color{blue}{\left(x - y\right)}\right)\right) \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      14. sub-negate-rev N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(y - x\right)} \cdot \left(\mathsf{neg}\left(60 \cdot \frac{1}{z - t}\right)\right) \]

      15. distribute-rgt-neg-in N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)\right)\right)} \]

      16. distribute-lft-neg-out N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(\mathsf{neg}\left(\left(y - x\right)\right)\right) \cdot \left(60 \cdot \frac{1}{z - t}\right)} \]

      17. sub-negate-rev N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right) \]

      18. lift--.f64 N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(x - y\right)} \cdot \left(60 \cdot \frac{1}{z - t}\right) \]

      19. associate-*l* N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(\left(x - y\right) \cdot 60\right) \cdot \frac{1}{z - t}} \]

      20. *-commutative N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

      21. lift-*.f64 N/A

          \[\leadsto a \cdot 120 + \color{blue}{\left(60 \cdot \left(x - y\right)\right)} \cdot \frac{1}{z - t} \]

   3. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{-60}{z - t} \cdot \left(y - x\right)\right)} \]

   4. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{60}{t}} \cdot \left(y - x\right)\right) \]
   5. Step-by-step derivation

      1. lower-/.f64 63.7

         \[\leadsto \mathsf{fma}\left(a, 120, \frac{60}{\color{blue}{t}} \cdot \left(y - x\right)\right) \]

   6. Applied rewrites 63.7%

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{60}{t}} \cdot \left(y - x\right)\right) \]

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(a, 120, \frac{60}{t} \cdot \color{blue}{y}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 54.3%

      \[\leadsto \mathsf{fma}\left(a, 120, \frac{60}{t} \cdot \color{blue}{y}\right) \]

   if -4.9e-56 < t < 3e13

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \color{blue}{\frac{x - y}{z}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x - y}{\color{blue}{z}}, 120 \cdot a\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x - y}{z}, 120 \cdot a\right) \]

      4. lower-*.f64 63.4

         \[\leadsto \mathsf{fma}\left(60, \frac{x - y}{z}, 120 \cdot a\right) \]

   4. Applied rewrites 63.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(60, \frac{x - y}{z}, 120 \cdot a\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(60, \frac{x}{\color{blue}{z}}, 120 \cdot a\right) \]
   6. Step-by-step derivation

      1. lower-/.f64 54.1

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z}, 120 \cdot a\right) \]

   7. Applied rewrites 54.1%

      \[\leadsto \mathsf{fma}\left(60, \frac{x}{\color{blue}{z}}, 120 \cdot a\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 60.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{+46}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-56}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+19}:\\ \;\;\;\;\mathsf{fma}\left(60, \frac{x}{z}, 120 \cdot a\right)\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{+93}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.25e+46)
   (* 120.0 a)
   (if (<= t -5.8e-56)
     (* -60.0 (/ y (- z t)))
     (if (<= t 2.4e+19)
       (fma 60.0 (/ x z) (* 120.0 a))
       (if (<= t 8.4e+93) (* -60.0 (/ (- x y) t)) (* 120.0 a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.25e+46) {
		tmp = 120.0 * a;
	} else if (t <= -5.8e-56) {
		tmp = -60.0 * (y / (z - t));
	} else if (t <= 2.4e+19) {
		tmp = fma(60.0, (x / z), (120.0 * a));
	} else if (t <= 8.4e+93) {
		tmp = -60.0 * ((x - y) / t);
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.25e+46)
		tmp = Float64(120.0 * a);
	elseif (t <= -5.8e-56)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (t <= 2.4e+19)
		tmp = fma(60.0, Float64(x / z), Float64(120.0 * a));
	elseif (t <= 8.4e+93)
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.25e+46], N[(120.0 * a), $MachinePrecision], If[LessEqual[t, -5.8e-56], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e+19], N[(60.0 * N[(x / z), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.4e+93], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.25000000000000005e46 or 8.39999999999999921e93 < t

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-*.f64 49.8

         \[\leadsto 120 \cdot \color{blue}{a} \]

   4. Applied rewrites 49.8%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -2.25000000000000005e46 < t < -5.79999999999999982e-56

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z} - t} \]

      4. lower--.f64 51.6

         \[\leadsto 60 \cdot \frac{x - y}{z - \color{blue}{t}} \]

   4. Applied rewrites 51.6%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   5. Taylor expanded in z around 0

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{\color{blue}{t}} \]

      2. lower-/.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

      3. lower--.f64 29.2

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

   7. Applied rewrites 29.2%

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]

   8. Taylor expanded in x around 0

      \[\leadsto -60 \cdot \color{blue}{\frac{y}{z - t}} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \frac{y}{\color{blue}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto -60 \cdot \frac{y}{z - \color{blue}{t}} \]

      3. lower--.f64 27.0

         \[\leadsto -60 \cdot \frac{y}{z - t} \]

   10. Applied rewrites 27.0%

       \[\leadsto -60 \cdot \color{blue}{\frac{y}{z - t}} \]

   if -5.79999999999999982e-56 < t < 2.4e19

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \color{blue}{\frac{x - y}{z}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x - y}{\color{blue}{z}}, 120 \cdot a\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x - y}{z}, 120 \cdot a\right) \]

      4. lower-*.f64 63.4

         \[\leadsto \mathsf{fma}\left(60, \frac{x - y}{z}, 120 \cdot a\right) \]

   4. Applied rewrites 63.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(60, \frac{x - y}{z}, 120 \cdot a\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(60, \frac{x}{\color{blue}{z}}, 120 \cdot a\right) \]
   6. Step-by-step derivation

      1. lower-/.f64 54.1

         \[\leadsto \mathsf{fma}\left(60, \frac{x}{z}, 120 \cdot a\right) \]

   7. Applied rewrites 54.1%

      \[\leadsto \mathsf{fma}\left(60, \frac{x}{\color{blue}{z}}, 120 \cdot a\right) \]

   if 2.4e19 < t < 8.39999999999999921e93

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z} - t} \]

      4. lower--.f64 51.6

         \[\leadsto 60 \cdot \frac{x - y}{z - \color{blue}{t}} \]

   4. Applied rewrites 51.6%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   5. Taylor expanded in z around 0

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{\color{blue}{t}} \]

      2. lower-/.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

      3. lower--.f64 29.2

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

   7. Applied rewrites 29.2%

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 12: 59.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+192}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-89}:\\ \;\;\;\;\mathsf{fma}\left(-60, \frac{y}{z}, 120 \cdot a\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+102}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot x}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.75e+192)
   (* (/ 60.0 (- z t)) x)
   (if (<= x 1.25e-89)
     (fma -60.0 (/ y z) (* 120.0 a))
     (if (<= x 1.9e+102) (* 120.0 a) (/ (* 60.0 x) (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.75e+192) {
		tmp = (60.0 / (z - t)) * x;
	} else if (x <= 1.25e-89) {
		tmp = fma(-60.0, (y / z), (120.0 * a));
	} else if (x <= 1.9e+102) {
		tmp = 120.0 * a;
	} else {
		tmp = (60.0 * x) / (z - t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.75e+192)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * x);
	elseif (x <= 1.25e-89)
		tmp = fma(-60.0, Float64(y / z), Float64(120.0 * a));
	elseif (x <= 1.9e+102)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(60.0 * x) / Float64(z - t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.75e+192], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 1.25e-89], N[(-60.0 * N[(y / z), $MachinePrecision] + N[(120.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.9e+102], N[(120.0 * a), $MachinePrecision], N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.74999999999999991e192

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x}{\color{blue}{z - t}} \]

      3. lower--.f64 27.4

         \[\leadsto 60 \cdot \frac{x}{z - \color{blue}{t}} \]

   4. Applied rewrites 27.4%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x}{z - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x}{\color{blue}{z - t}} \]

      3. mult-flip N/A

         \[\leadsto 60 \cdot \left(x \cdot \color{blue}{\frac{1}{z - t}}\right) \]

      4. *-commutative N/A

         \[\leadsto 60 \cdot \left(\frac{1}{z - t} \cdot \color{blue}{x}\right) \]

      5. associate-*r* N/A

         \[\leadsto \left(60 \cdot \frac{1}{z - t}\right) \cdot \color{blue}{x} \]

      6. mult-flip-rev N/A

         \[\leadsto \frac{60}{z - t} \cdot x \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{60}{z - t} \cdot \color{blue}{x} \]

      8. lower-/.f64 27.4

         \[\leadsto \frac{60}{z - t} \cdot x \]

   6. Applied rewrites 27.4%

      \[\leadsto \frac{60}{z - t} \cdot \color{blue}{x} \]

   if -1.74999999999999991e192 < x < 1.24999999999999992e-89

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \color{blue}{\frac{x - y}{z}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x - y}{\color{blue}{z}}, 120 \cdot a\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x - y}{z}, 120 \cdot a\right) \]

      4. lower-*.f64 63.4

         \[\leadsto \mathsf{fma}\left(60, \frac{x - y}{z}, 120 \cdot a\right) \]

   4. Applied rewrites 63.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(60, \frac{x - y}{z}, 120 \cdot a\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto -60 \cdot \frac{y}{z} + \color{blue}{120 \cdot a} \]
   6. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \frac{y}{\color{blue}{z}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(-60, \frac{y}{z}, 120 \cdot a\right) \]

      3. lower-*.f64 53.9

         \[\leadsto \mathsf{fma}\left(-60, \frac{y}{z}, 120 \cdot a\right) \]

   7. Applied rewrites 53.9%

      \[\leadsto \mathsf{fma}\left(-60, \color{blue}{\frac{y}{z}}, 120 \cdot a\right) \]

   if 1.24999999999999992e-89 < x < 1.89999999999999989e102

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-*.f64 49.8

         \[\leadsto 120 \cdot \color{blue}{a} \]

   4. Applied rewrites 49.8%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if 1.89999999999999989e102 < x

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x}{\color{blue}{z - t}} \]

      3. lower--.f64 27.4

         \[\leadsto 60 \cdot \frac{x}{z - \color{blue}{t}} \]

   4. Applied rewrites 27.4%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x}{z - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x}{\color{blue}{z - t}} \]

      3. associate-*r/ N/A

         \[\leadsto \frac{60 \cdot x}{\color{blue}{z - t}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{60 \cdot x}{\color{blue}{z - t}} \]

      5. lower-*.f64 27.3

         \[\leadsto \frac{60 \cdot x}{\color{blue}{z} - t} \]

   6. Applied rewrites 27.3%

      \[\leadsto \frac{60 \cdot x}{\color{blue}{z - t}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 13: 59.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+25}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot 60}{t}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+98}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -5e+25)
     (/ (* (- y x) 60.0) t)
     (if (<= t_1 2e+98) (* 120.0 a) (* (/ 60.0 (- z t)) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -5e+25) {
		tmp = ((y - x) * 60.0) / t;
	} else if (t_1 <= 2e+98) {
		tmp = 120.0 * a;
	} else {
		tmp = (60.0 / (z - t)) * 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) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-5d+25)) then
        tmp = ((y - x) * 60.0d0) / t
    else if (t_1 <= 2d+98) then
        tmp = 120.0d0 * a
    else
        tmp = (60.0d0 / (z - t)) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -5e+25) {
		tmp = ((y - x) * 60.0) / t;
	} else if (t_1 <= 2e+98) {
		tmp = 120.0 * a;
	} else {
		tmp = (60.0 / (z - t)) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -5e+25:
		tmp = ((y - x) * 60.0) / t
	elif t_1 <= 2e+98:
		tmp = 120.0 * a
	else:
		tmp = (60.0 / (z - t)) * x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -5e+25)
		tmp = Float64(Float64(Float64(y - x) * 60.0) / t);
	elseif (t_1 <= 2e+98)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(60.0 / Float64(z - t)) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -5e+25)
		tmp = ((y - x) * 60.0) / t;
	elseif (t_1 <= 2e+98)
		tmp = 120.0 * a;
	else
		tmp = (60.0 / (z - t)) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+25], N[(N[(N[(y - x), $MachinePrecision] * 60.0), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t$95$1, 2e+98], N[(120.0 * a), $MachinePrecision], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5.00000000000000024e25

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z} - t} \]

      4. lower--.f64 51.6

         \[\leadsto 60 \cdot \frac{x - y}{z - \color{blue}{t}} \]

   4. Applied rewrites 51.6%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   5. Taylor expanded in z around 0

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{\color{blue}{t}} \]

      2. lower-/.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

      3. lower--.f64 29.2

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

   7. Applied rewrites 29.2%

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{\color{blue}{t}} \]

      2. lift--.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

      3. lift-/.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

      4. associate-*r/ N/A

         \[\leadsto \frac{-60 \cdot \left(x - y\right)}{t} \]

      5. metadata-eval N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(60\right)\right) \cdot \left(x - y\right)}{t} \]

      6. distribute-lft-neg-out N/A

         \[\leadsto \frac{\mathsf{neg}\left(60 \cdot \left(x - y\right)\right)}{t} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{\mathsf{neg}\left(60 \cdot \left(x - y\right)\right)}{t} \]

      8. *-commutative N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(x - y\right) \cdot 60\right)}{t} \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot 60}{t} \]

      10. lower-*.f64 N/A

          \[\leadsto \frac{\left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot 60}{t} \]

      11. sub-negate-rev N/A

          \[\leadsto \frac{\left(y - x\right) \cdot 60}{t} \]

      12. lift--.f64 29.1

          \[\leadsto \frac{\left(y - x\right) \cdot 60}{t} \]

   9. Applied rewrites 29.1%

      \[\leadsto \frac{\left(y - x\right) \cdot 60}{t} \]

   if -5.00000000000000024e25 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2e98

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-*.f64 49.8

         \[\leadsto 120 \cdot \color{blue}{a} \]

   4. Applied rewrites 49.8%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if 2e98 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x}{\color{blue}{z - t}} \]

      3. lower--.f64 27.4

         \[\leadsto 60 \cdot \frac{x}{z - \color{blue}{t}} \]

   4. Applied rewrites 27.4%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x}{z - t}} \]

      2. lift-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x}{\color{blue}{z - t}} \]

      3. mult-flip N/A

         \[\leadsto 60 \cdot \left(x \cdot \color{blue}{\frac{1}{z - t}}\right) \]

      4. *-commutative N/A

         \[\leadsto 60 \cdot \left(\frac{1}{z - t} \cdot \color{blue}{x}\right) \]

      5. associate-*r* N/A

         \[\leadsto \left(60 \cdot \frac{1}{z - t}\right) \cdot \color{blue}{x} \]

      6. mult-flip-rev N/A

         \[\leadsto \frac{60}{z - t} \cdot x \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{60}{z - t} \cdot \color{blue}{x} \]

      8. lower-/.f64 27.4

         \[\leadsto \frac{60}{z - t} \cdot x \]

   6. Applied rewrites 27.4%

      \[\leadsto \frac{60}{z - t} \cdot \color{blue}{x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 59.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+25}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot 60}{t}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+98}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -5e+25)
     (/ (* (- y x) 60.0) t)
     (if (<= t_1 2e+98) (* 120.0 a) (* 60.0 (/ x (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -5e+25) {
		tmp = ((y - x) * 60.0) / t;
	} else if (t_1 <= 2e+98) {
		tmp = 120.0 * a;
	} else {
		tmp = 60.0 * (x / (z - 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 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-5d+25)) then
        tmp = ((y - x) * 60.0d0) / t
    else if (t_1 <= 2d+98) then
        tmp = 120.0d0 * a
    else
        tmp = 60.0d0 * (x / (z - 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 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -5e+25) {
		tmp = ((y - x) * 60.0) / t;
	} else if (t_1 <= 2e+98) {
		tmp = 120.0 * a;
	} else {
		tmp = 60.0 * (x / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -5e+25:
		tmp = ((y - x) * 60.0) / t
	elif t_1 <= 2e+98:
		tmp = 120.0 * a
	else:
		tmp = 60.0 * (x / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -5e+25)
		tmp = Float64(Float64(Float64(y - x) * 60.0) / t);
	elseif (t_1 <= 2e+98)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -5e+25)
		tmp = ((y - x) * 60.0) / t;
	elseif (t_1 <= 2e+98)
		tmp = 120.0 * a;
	else
		tmp = 60.0 * (x / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+25], N[(N[(N[(y - x), $MachinePrecision] * 60.0), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t$95$1, 2e+98], N[(120.0 * a), $MachinePrecision], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5.00000000000000024e25

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z} - t} \]

      4. lower--.f64 51.6

         \[\leadsto 60 \cdot \frac{x - y}{z - \color{blue}{t}} \]

   4. Applied rewrites 51.6%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   5. Taylor expanded in z around 0

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{\color{blue}{t}} \]

      2. lower-/.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

      3. lower--.f64 29.2

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

   7. Applied rewrites 29.2%

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{\color{blue}{t}} \]

      2. lift--.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

      3. lift-/.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

      4. associate-*r/ N/A

         \[\leadsto \frac{-60 \cdot \left(x - y\right)}{t} \]

      5. metadata-eval N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(60\right)\right) \cdot \left(x - y\right)}{t} \]

      6. distribute-lft-neg-out N/A

         \[\leadsto \frac{\mathsf{neg}\left(60 \cdot \left(x - y\right)\right)}{t} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{\mathsf{neg}\left(60 \cdot \left(x - y\right)\right)}{t} \]

      8. *-commutative N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(x - y\right) \cdot 60\right)}{t} \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot 60}{t} \]

      10. lower-*.f64 N/A

          \[\leadsto \frac{\left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot 60}{t} \]

      11. sub-negate-rev N/A

          \[\leadsto \frac{\left(y - x\right) \cdot 60}{t} \]

      12. lift--.f64 29.1

          \[\leadsto \frac{\left(y - x\right) \cdot 60}{t} \]

   9. Applied rewrites 29.1%

      \[\leadsto \frac{\left(y - x\right) \cdot 60}{t} \]

   if -5.00000000000000024e25 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2e98

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-*.f64 49.8

         \[\leadsto 120 \cdot \color{blue}{a} \]

   4. Applied rewrites 49.8%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if 2e98 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x}{\color{blue}{z - t}} \]

      3. lower--.f64 27.4

         \[\leadsto 60 \cdot \frac{x}{z - \color{blue}{t}} \]

   4. Applied rewrites 27.4%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 58.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - x\right) \cdot 60}{t}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+98}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y x) 60.0) t)) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -5e+25) t_1 (if (<= t_2 2e+98) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - x) * 60.0) / t;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e+25) {
		tmp = t_1;
	} else if (t_2 <= 2e+98) {
		tmp = 120.0 * a;
	} 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 - x) * 60.0d0) / t
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-5d+25)) then
        tmp = t_1
    else if (t_2 <= 2d+98) then
        tmp = 120.0d0 * a
    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 - x) * 60.0) / t;
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e+25) {
		tmp = t_1;
	} else if (t_2 <= 2e+98) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y - x) * 60.0) / t
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -5e+25:
		tmp = t_1
	elif t_2 <= 2e+98:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - x) * 60.0) / t)
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -5e+25)
		tmp = t_1;
	elseif (t_2 <= 2e+98)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y - x) * 60.0) / t;
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -5e+25)
		tmp = t_1;
	elseif (t_2 <= 2e+98)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - x), $MachinePrecision] * 60.0), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+25], t$95$1, If[LessEqual[t$95$2, 2e+98], N[(120.0 * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5.00000000000000024e25 or 2e98 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z} - t} \]

      4. lower--.f64 51.6

         \[\leadsto 60 \cdot \frac{x - y}{z - \color{blue}{t}} \]

   4. Applied rewrites 51.6%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   5. Taylor expanded in z around 0

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{\color{blue}{t}} \]

      2. lower-/.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

      3. lower--.f64 29.2

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

   7. Applied rewrites 29.2%

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{\color{blue}{t}} \]

      2. lift--.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

      3. lift-/.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

      4. associate-*r/ N/A

         \[\leadsto \frac{-60 \cdot \left(x - y\right)}{t} \]

      5. metadata-eval N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(60\right)\right) \cdot \left(x - y\right)}{t} \]

      6. distribute-lft-neg-out N/A

         \[\leadsto \frac{\mathsf{neg}\left(60 \cdot \left(x - y\right)\right)}{t} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{\mathsf{neg}\left(60 \cdot \left(x - y\right)\right)}{t} \]

      8. *-commutative N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(x - y\right) \cdot 60\right)}{t} \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot 60}{t} \]

      10. lower-*.f64 N/A

          \[\leadsto \frac{\left(\mathsf{neg}\left(\left(x - y\right)\right)\right) \cdot 60}{t} \]

      11. sub-negate-rev N/A

          \[\leadsto \frac{\left(y - x\right) \cdot 60}{t} \]

      12. lift--.f64 29.1

          \[\leadsto \frac{\left(y - x\right) \cdot 60}{t} \]

   9. Applied rewrites 29.1%

      \[\leadsto \frac{\left(y - x\right) \cdot 60}{t} \]

   if -5.00000000000000024e25 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2e98

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-*.f64 49.8

         \[\leadsto 120 \cdot \color{blue}{a} \]

   4. Applied rewrites 49.8%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 58.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-60}{t} \cdot \left(x - y\right)\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+98}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ -60.0 t) (- x y))) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -5e+25) t_1 (if (<= t_2 2e+98) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (-60.0 / t) * (x - y);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e+25) {
		tmp = t_1;
	} else if (t_2 <= 2e+98) {
		tmp = 120.0 * a;
	} 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 = ((-60.0d0) / t) * (x - y)
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-5d+25)) then
        tmp = t_1
    else if (t_2 <= 2d+98) then
        tmp = 120.0d0 * a
    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 = (-60.0 / t) * (x - y);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e+25) {
		tmp = t_1;
	} else if (t_2 <= 2e+98) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (-60.0 / t) * (x - y)
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -5e+25:
		tmp = t_1
	elif t_2 <= 2e+98:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-60.0 / t) * Float64(x - y))
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -5e+25)
		tmp = t_1;
	elseif (t_2 <= 2e+98)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (-60.0 / t) * (x - y);
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -5e+25)
		tmp = t_1;
	elseif (t_2 <= 2e+98)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(-60.0 / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+25], t$95$1, If[LessEqual[t$95$2, 2e+98], N[(120.0 * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5.00000000000000024e25 or 2e98 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z} - t} \]

      4. lower--.f64 51.6

         \[\leadsto 60 \cdot \frac{x - y}{z - \color{blue}{t}} \]

   4. Applied rewrites 51.6%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   5. Taylor expanded in z around 0

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{\color{blue}{t}} \]

      2. lower-/.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

      3. lower--.f64 29.2

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

   7. Applied rewrites 29.2%

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{\color{blue}{t}} \]

      2. *-commutative N/A

         \[\leadsto \frac{x - y}{t} \cdot -60 \]

      3. lift--.f64 N/A

         \[\leadsto \frac{x - y}{t} \cdot -60 \]

      4. lift-/.f64 N/A

         \[\leadsto \frac{x - y}{t} \cdot -60 \]

      5. mult-flip N/A

         \[\leadsto \left(\left(x - y\right) \cdot \frac{1}{t}\right) \cdot -60 \]

      6. associate-*l* N/A

         \[\leadsto \left(x - y\right) \cdot \left(\frac{1}{t} \cdot \color{blue}{-60}\right) \]

      7. *-commutative N/A

         \[\leadsto \left(\frac{1}{t} \cdot -60\right) \cdot \left(x - \color{blue}{y}\right) \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{t} \cdot -60\right) \cdot \left(x - \color{blue}{y}\right) \]

      9. associate-*l/ N/A

         \[\leadsto \frac{1 \cdot -60}{t} \cdot \left(x - y\right) \]

      10. metadata-eval N/A

          \[\leadsto \frac{-60}{t} \cdot \left(x - y\right) \]

      11. lower-/.f64 N/A

          \[\leadsto \frac{-60}{t} \cdot \left(x - y\right) \]

      12. lift--.f64 29.2

          \[\leadsto \frac{-60}{t} \cdot \left(x - y\right) \]

   9. Applied rewrites 29.2%

      \[\leadsto \frac{-60}{t} \cdot \left(x - \color{blue}{y}\right) \]

   if -5.00000000000000024e25 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2e98

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-*.f64 49.8

         \[\leadsto 120 \cdot \color{blue}{a} \]

   4. Applied rewrites 49.8%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 58.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{x - y}{t}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+98}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ (- x y) t))) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -5e+25) t_1 (if (<= t_2 2e+98) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * ((x - y) / t);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e+25) {
		tmp = t_1;
	} else if (t_2 <= 2e+98) {
		tmp = 120.0 * a;
	} 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 = (-60.0d0) * ((x - y) / t)
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-5d+25)) then
        tmp = t_1
    else if (t_2 <= 2d+98) then
        tmp = 120.0d0 * a
    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 = -60.0 * ((x - y) / t);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e+25) {
		tmp = t_1;
	} else if (t_2 <= 2e+98) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * ((x - y) / t)
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -5e+25:
		tmp = t_1
	elif t_2 <= 2e+98:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(Float64(x - y) / t))
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -5e+25)
		tmp = t_1;
	elseif (t_2 <= 2e+98)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * ((x - y) / t);
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -5e+25)
		tmp = t_1;
	elseif (t_2 <= 2e+98)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+25], t$95$1, If[LessEqual[t$95$2, 2e+98], N[(120.0 * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5.00000000000000024e25 or 2e98 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z} - t} \]

      4. lower--.f64 51.6

         \[\leadsto 60 \cdot \frac{x - y}{z - \color{blue}{t}} \]

   4. Applied rewrites 51.6%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   5. Taylor expanded in z around 0

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{\color{blue}{t}} \]

      2. lower-/.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

      3. lower--.f64 29.2

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

   7. Applied rewrites 29.2%

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]

   if -5.00000000000000024e25 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2e98

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-*.f64 49.8

         \[\leadsto 120 \cdot \color{blue}{a} \]

   4. Applied rewrites 49.8%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 57.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-78}:\\ \;\;\;\;120 \cdot a\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-52}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;120 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.4e-78)
   (* 120.0 a)
   (if (<= a 4.2e-52) (* -60.0 (/ y (- z t))) (* 120.0 a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.4e-78) {
		tmp = 120.0 * a;
	} else if (a <= 4.2e-52) {
		tmp = -60.0 * (y / (z - t));
	} else {
		tmp = 120.0 * a;
	}
	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 <= (-2.4d-78)) then
        tmp = 120.0d0 * a
    else if (a <= 4.2d-52) then
        tmp = (-60.0d0) * (y / (z - t))
    else
        tmp = 120.0d0 * a
    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 <= -2.4e-78) {
		tmp = 120.0 * a;
	} else if (a <= 4.2e-52) {
		tmp = -60.0 * (y / (z - t));
	} else {
		tmp = 120.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.4e-78:
		tmp = 120.0 * a
	elif a <= 4.2e-52:
		tmp = -60.0 * (y / (z - t))
	else:
		tmp = 120.0 * a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.4e-78)
		tmp = Float64(120.0 * a);
	elseif (a <= 4.2e-52)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	else
		tmp = Float64(120.0 * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.4e-78)
		tmp = 120.0 * a;
	elseif (a <= 4.2e-52)
		tmp = -60.0 * (y / (z - t));
	else
		tmp = 120.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.4e-78], N[(120.0 * a), $MachinePrecision], If[LessEqual[a, 4.2e-52], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(120.0 * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.4e-78 or 4.1999999999999997e-52 < a

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-*.f64 49.8

         \[\leadsto 120 \cdot \color{blue}{a} \]

   4. Applied rewrites 49.8%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -2.4e-78 < a < 4.1999999999999997e-52

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z} - t} \]

      4. lower--.f64 51.6

         \[\leadsto 60 \cdot \frac{x - y}{z - \color{blue}{t}} \]

   4. Applied rewrites 51.6%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   5. Taylor expanded in z around 0

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{\color{blue}{t}} \]

      2. lower-/.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

      3. lower--.f64 29.2

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

   7. Applied rewrites 29.2%

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]

   8. Taylor expanded in x around 0

      \[\leadsto -60 \cdot \color{blue}{\frac{y}{z - t}} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \frac{y}{\color{blue}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto -60 \cdot \frac{y}{z - \color{blue}{t}} \]

      3. lower--.f64 27.0

         \[\leadsto -60 \cdot \frac{y}{z - t} \]

   10. Applied rewrites 27.0%

       \[\leadsto -60 \cdot \color{blue}{\frac{y}{z - t}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 19: 54.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x}{z}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+156}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+114}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ x z))) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -5e+156) t_1 (if (<= t_2 1e+114) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (x / z);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e+156) {
		tmp = t_1;
	} else if (t_2 <= 1e+114) {
		tmp = 120.0 * a;
	} 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 = 60.0d0 * (x / z)
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-5d+156)) then
        tmp = t_1
    else if (t_2 <= 1d+114) then
        tmp = 120.0d0 * a
    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 = 60.0 * (x / z);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e+156) {
		tmp = t_1;
	} else if (t_2 <= 1e+114) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * (x / z)
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -5e+156:
		tmp = t_1
	elif t_2 <= 1e+114:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(x / z))
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -5e+156)
		tmp = t_1;
	elseif (t_2 <= 1e+114)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * (x / z);
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -5e+156)
		tmp = t_1;
	elseif (t_2 <= 1e+114)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+156], t$95$1, If[LessEqual[t$95$2, 1e+114], N[(120.0 * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -4.99999999999999992e156 or 1e114 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z} + 120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \color{blue}{\frac{x - y}{z}}, 120 \cdot a\right) \]

      2. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x - y}{\color{blue}{z}}, 120 \cdot a\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(60, \frac{x - y}{z}, 120 \cdot a\right) \]

      4. lower-*.f64 63.4

         \[\leadsto \mathsf{fma}\left(60, \frac{x - y}{z}, 120 \cdot a\right) \]

   4. Applied rewrites 63.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(60, \frac{x - y}{z}, 120 \cdot a\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto 60 \cdot \color{blue}{\frac{x}{z}} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \frac{x}{\color{blue}{z}} \]

      2. lower-/.f64 16.1

         \[\leadsto 60 \cdot \frac{x}{z} \]

   7. Applied rewrites 16.1%

      \[\leadsto 60 \cdot \color{blue}{\frac{x}{z}} \]

   if -4.99999999999999992e156 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 1e114

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-*.f64 49.8

         \[\leadsto 120 \cdot \color{blue}{a} \]

   4. Applied rewrites 49.8%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 20: 54.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{y}{t}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+186}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+160}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ y t))) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -4e+186) t_1 (if (<= t_2 2e+160) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (y / t);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -4e+186) {
		tmp = t_1;
	} else if (t_2 <= 2e+160) {
		tmp = 120.0 * a;
	} 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 = 60.0d0 * (y / t)
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-4d+186)) then
        tmp = t_1
    else if (t_2 <= 2d+160) then
        tmp = 120.0d0 * a
    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 = 60.0 * (y / t);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -4e+186) {
		tmp = t_1;
	} else if (t_2 <= 2e+160) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * (y / t)
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -4e+186:
		tmp = t_1
	elif t_2 <= 2e+160:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(y / t))
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -4e+186)
		tmp = t_1;
	elseif (t_2 <= 2e+160)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * (y / t);
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -4e+186)
		tmp = t_1;
	elseif (t_2 <= 2e+160)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+186], t$95$1, If[LessEqual[t$95$2, 2e+160], N[(120.0 * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -3.99999999999999992e186 or 2.00000000000000001e160 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x - y}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z - t}} \]

      3. lower--.f64 N/A

         \[\leadsto 60 \cdot \frac{x - y}{\color{blue}{z} - t} \]

      4. lower--.f64 51.6

         \[\leadsto 60 \cdot \frac{x - y}{z - \color{blue}{t}} \]

   4. Applied rewrites 51.6%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   5. Taylor expanded in z around 0

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{\color{blue}{t}} \]

      2. lower-/.f64 N/A

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

      3. lower--.f64 29.2

         \[\leadsto -60 \cdot \frac{x - y}{t} \]

   7. Applied rewrites 29.2%

      \[\leadsto -60 \cdot \color{blue}{\frac{x - y}{t}} \]

   8. Taylor expanded in x around 0

      \[\leadsto 60 \cdot \frac{y}{\color{blue}{t}} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \frac{y}{t} \]

      2. lower-/.f64 16.1

         \[\leadsto 60 \cdot \frac{y}{t} \]

   10. Applied rewrites 16.1%

       \[\leadsto 60 \cdot \frac{y}{\color{blue}{t}} \]

   if -3.99999999999999992e186 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2.00000000000000001e160

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-*.f64 49.8

         \[\leadsto 120 \cdot \color{blue}{a} \]

   4. Applied rewrites 49.8%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 21: 53.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+156}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+193}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{t} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -5e+156)
     (* -60.0 (/ x t))
     (if (<= t_1 2e+193) (* 120.0 a) (* (/ -60.0 t) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -5e+156) {
		tmp = -60.0 * (x / t);
	} else if (t_1 <= 2e+193) {
		tmp = 120.0 * a;
	} else {
		tmp = (-60.0 / t) * 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) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-5d+156)) then
        tmp = (-60.0d0) * (x / t)
    else if (t_1 <= 2d+193) then
        tmp = 120.0d0 * a
    else
        tmp = ((-60.0d0) / t) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -5e+156) {
		tmp = -60.0 * (x / t);
	} else if (t_1 <= 2e+193) {
		tmp = 120.0 * a;
	} else {
		tmp = (-60.0 / t) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -5e+156:
		tmp = -60.0 * (x / t)
	elif t_1 <= 2e+193:
		tmp = 120.0 * a
	else:
		tmp = (-60.0 / t) * x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -5e+156)
		tmp = Float64(-60.0 * Float64(x / t));
	elseif (t_1 <= 2e+193)
		tmp = Float64(120.0 * a);
	else
		tmp = Float64(Float64(-60.0 / t) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -5e+156)
		tmp = -60.0 * (x / t);
	elseif (t_1 <= 2e+193)
		tmp = 120.0 * a;
	else
		tmp = (-60.0 / t) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+156], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+193], N[(120.0 * a), $MachinePrecision], N[(N[(-60.0 / t), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -4.99999999999999992e156

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x}{\color{blue}{z - t}} \]

      3. lower--.f64 27.4

         \[\leadsto 60 \cdot \frac{x}{z - \color{blue}{t}} \]

   4. Applied rewrites 27.4%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]

   5. Taylor expanded in z around 0

      \[\leadsto -60 \cdot \color{blue}{\frac{x}{t}} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \frac{x}{\color{blue}{t}} \]

      2. lower-/.f64 16.6

         \[\leadsto -60 \cdot \frac{x}{t} \]

   7. Applied rewrites 16.6%

      \[\leadsto -60 \cdot \color{blue}{\frac{x}{t}} \]

   if -4.99999999999999992e156 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2.00000000000000013e193

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-*.f64 49.8

         \[\leadsto 120 \cdot \color{blue}{a} \]

   4. Applied rewrites 49.8%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if 2.00000000000000013e193 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x}{\color{blue}{z - t}} \]

      3. lower--.f64 27.4

         \[\leadsto 60 \cdot \frac{x}{z - \color{blue}{t}} \]

   4. Applied rewrites 27.4%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]

   5. Taylor expanded in z around 0

      \[\leadsto -60 \cdot \color{blue}{\frac{x}{t}} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \frac{x}{\color{blue}{t}} \]

      2. lower-/.f64 16.6

         \[\leadsto -60 \cdot \frac{x}{t} \]

   7. Applied rewrites 16.6%

      \[\leadsto -60 \cdot \color{blue}{\frac{x}{t}} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto -60 \cdot \frac{x}{\color{blue}{t}} \]

      2. *-commutative N/A

         \[\leadsto \frac{x}{t} \cdot -60 \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{x}{t} \cdot -60 \]

      4. mult-flip N/A

         \[\leadsto \left(x \cdot \frac{1}{t}\right) \cdot -60 \]

      5. associate-*l* N/A

         \[\leadsto x \cdot \left(\frac{1}{t} \cdot \color{blue}{-60}\right) \]

      6. *-commutative N/A

         \[\leadsto \left(\frac{1}{t} \cdot -60\right) \cdot x \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\frac{1}{t} \cdot -60\right) \cdot x \]

      8. associate-*l/ N/A

         \[\leadsto \frac{1 \cdot -60}{t} \cdot x \]

      9. metadata-eval N/A

         \[\leadsto \frac{-60}{t} \cdot x \]

      10. lower-/.f64 16.6

          \[\leadsto \frac{-60}{t} \cdot x \]

   9. Applied rewrites 16.6%

      \[\leadsto \frac{-60}{t} \cdot x \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 22: 53.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{x}{t}\\ t_2 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+156}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+193}:\\ \;\;\;\;120 \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ x t))) (t_2 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_2 -5e+156) t_1 (if (<= t_2 2e+193) (* 120.0 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (x / t);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e+156) {
		tmp = t_1;
	} else if (t_2 <= 2e+193) {
		tmp = 120.0 * a;
	} 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 = (-60.0d0) * (x / t)
    t_2 = (60.0d0 * (x - y)) / (z - t)
    if (t_2 <= (-5d+156)) then
        tmp = t_1
    else if (t_2 <= 2d+193) then
        tmp = 120.0d0 * a
    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 = -60.0 * (x / t);
	double t_2 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_2 <= -5e+156) {
		tmp = t_1;
	} else if (t_2 <= 2e+193) {
		tmp = 120.0 * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (x / t)
	t_2 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_2 <= -5e+156:
		tmp = t_1
	elif t_2 <= 2e+193:
		tmp = 120.0 * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(x / t))
	t_2 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_2 <= -5e+156)
		tmp = t_1;
	elseif (t_2 <= 2e+193)
		tmp = Float64(120.0 * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * (x / t);
	t_2 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_2 <= -5e+156)
		tmp = t_1;
	elseif (t_2 <= 2e+193)
		tmp = 120.0 * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+156], t$95$1, If[LessEqual[t$95$2, 2e+193], N[(120.0 * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -4.99999999999999992e156 or 2.00000000000000013e193 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto 60 \cdot \color{blue}{\frac{x}{z - t}} \]

      2. lower-/.f64 N/A

         \[\leadsto 60 \cdot \frac{x}{\color{blue}{z - t}} \]

      3. lower--.f64 27.4

         \[\leadsto 60 \cdot \frac{x}{z - \color{blue}{t}} \]

   4. Applied rewrites 27.4%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]

   5. Taylor expanded in z around 0

      \[\leadsto -60 \cdot \color{blue}{\frac{x}{t}} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -60 \cdot \frac{x}{\color{blue}{t}} \]

      2. lower-/.f64 16.6

         \[\leadsto -60 \cdot \frac{x}{t} \]

   7. Applied rewrites 16.6%

      \[\leadsto -60 \cdot \color{blue}{\frac{x}{t}} \]

   if -4.99999999999999992e156 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 2.00000000000000013e193

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{120 \cdot a} \]
   3. Step-by-step derivation

      1. lower-*.f64 49.8

         \[\leadsto 120 \cdot \color{blue}{a} \]

   4. Applied rewrites 49.8%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 49.8% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ 120 \cdot a \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (* 120.0 a))

C

double code(double x, double y, double z, double t, double a) {
	return 120.0 * a;
}

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 = 120.0d0 * a
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 120.0 * a;
}

Python

def code(x, y, z, t, a):
	return 120.0 * a

Julia

function code(x, y, z, t, a)
	return Float64(120.0 * a)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 120.0 * a;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(120.0 * a), $MachinePrecision]

Derivation

1. Initial program 99.4%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

2. Taylor expanded in z around inf

   \[\leadsto \color{blue}{120 \cdot a} \]
3. Step-by-step derivation

   1. lower-*.f64 49.8

      \[\leadsto 120 \cdot \color{blue}{a} \]

4. Applied rewrites 49.8%

   \[\leadsto \color{blue}{120 \cdot a} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025149 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64
  (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))