Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3

Average Error: 11.4 → 2.3

Time: 14.9s

Precision: binary64

Cost: 968

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x \leq -4.1973107753517903 \cdot 10^{-190}:\\ \;\;\;\;x \cdot \frac{z - y}{z - t}\\ \mathbf{elif}\;x \leq 1.1178200296667817 \cdot 10^{-55}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - y}{\frac{z}{x} - \frac{t}{x}}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.1973107753517903e-190)
   (* x (/ (- z y) (- z t)))
   (if (<= x 1.1178200296667817e-55)
     (/ (* x (- y z)) (- t z))
     (/ (- z y) (- (/ z x) (/ t x))))))

C

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

↓

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.1973107753517903e-190) {
		tmp = x * ((z - y) / (z - t));
	} else if (x <= 1.1178200296667817e-55) {
		tmp = (x * (y - z)) / (t - z);
	} else {
		tmp = (z - y) / ((z / x) - (t / x));
	}
	return tmp;
}

Fortran

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

↓

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-4.1973107753517903d-190)) then
        tmp = x * ((z - y) / (z - t))
    else if (x <= 1.1178200296667817d-55) then
        tmp = (x * (y - z)) / (t - z)
    else
        tmp = (z - y) / ((z / x) - (t / x))
    end if
    code = tmp
end function

Java

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

↓

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.1973107753517903e-190) {
		tmp = x * ((z - y) / (z - t));
	} else if (x <= 1.1178200296667817e-55) {
		tmp = (x * (y - z)) / (t - z);
	} else {
		tmp = (z - y) / ((z / x) - (t / x));
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t):
	tmp = 0
	if x <= -4.1973107753517903e-190:
		tmp = x * ((z - y) / (z - t))
	elif x <= 1.1178200296667817e-55:
		tmp = (x * (y - z)) / (t - z)
	else:
		tmp = (z - y) / ((z / x) - (t / x))
	return tmp

Julia

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

↓

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.1973107753517903e-190)
		tmp = Float64(x * Float64(Float64(z - y) / Float64(z - t)));
	elseif (x <= 1.1178200296667817e-55)
		tmp = Float64(Float64(x * Float64(y - z)) / Float64(t - z));
	else
		tmp = Float64(Float64(z - y) / Float64(Float64(z / x) - Float64(t / x)));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4.1973107753517903e-190)
		tmp = x * ((z - y) / (z - t));
	elseif (x <= 1.1178200296667817e-55)
		tmp = (x * (y - z)) / (t - z);
	else
		tmp = (z - y) / ((z / x) - (t / x));
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_, t_] := If[LessEqual[x, -4.1973107753517903e-190], N[(x * N[(N[(z - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.1178200296667817e-55], N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(z - y), $MachinePrecision] / N[(N[(z / x), $MachinePrecision] - N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	11.4
Target	2.0
Herbie	2.3

\[\frac{x}{\frac{t - z}{y - z}} \]

Derivation

1. Split input into 3 regimes

2. if x < -4.1973107753517903e-190

   1. Initial program 13.0

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

   2. Simplified 6.8

      \[\leadsto \color{blue}{\left(z - y\right) \cdot \frac{x}{z - t}} \]
      Proof
      (*.f64 (-.f64 z y) (/.f64 x (-.f64 z t))): 0 points increase in error, 0 points decrease in error
      (Rewrite=> *-commutative_binary64 (*.f64 (/.f64 x (-.f64 z t)) (-.f64 z y))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/r/_binary64 (/.f64 x (/.f64 (-.f64 z t) (-.f64 z y)))): 32 points increase in error, 64 points decrease in error
      (/.f64 x (Rewrite<= *-lft-identity_binary64 (*.f64 1 (/.f64 (-.f64 z t) (-.f64 z y))))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (*.f64 (Rewrite<= metadata-eval (/.f64 -1 -1)) (/.f64 (-.f64 z t) (-.f64 z y)))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (Rewrite<= times-frac_binary64 (/.f64 (*.f64 -1 (-.f64 z t)) (*.f64 -1 (-.f64 z y))))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (Rewrite<= neg-mul-1_binary64 (neg.f64 (-.f64 z t))) (*.f64 -1 (-.f64 z y)))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (Rewrite<= sub0-neg_binary64 (-.f64 0 (-.f64 z t))) (*.f64 -1 (-.f64 z y)))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 0 z) t)) (*.f64 -1 (-.f64 z y)))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (+.f64 (Rewrite<= neg-sub0_binary64 (neg.f64 z)) t) (*.f64 -1 (-.f64 z y)))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 t (neg.f64 z))) (*.f64 -1 (-.f64 z y)))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (Rewrite<= sub-neg_binary64 (-.f64 t z)) (*.f64 -1 (-.f64 z y)))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (-.f64 t z) (Rewrite<= neg-mul-1_binary64 (neg.f64 (-.f64 z y))))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (-.f64 t z) (Rewrite<= sub0-neg_binary64 (-.f64 0 (-.f64 z y))))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (-.f64 t z) (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 0 z) y)))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (-.f64 t z) (+.f64 (Rewrite<= neg-sub0_binary64 (neg.f64 z)) y))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (-.f64 t z) (Rewrite<= +-commutative_binary64 (+.f64 y (neg.f64 z))))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (-.f64 t z) (Rewrite<= sub-neg_binary64 (-.f64 y z)))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))): 69 points increase in error, 31 points decrease in error

   3. Taylor expanded in y around 0 13.0

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

   4. Simplified 1.8

      \[\leadsto \color{blue}{x \cdot \frac{z - y}{z - t}} \]
      Proof
      (*.f64 x (/.f64 (-.f64 z y) (-.f64 z t))): 0 points increase in error, 0 points decrease in error
      (*.f64 x (Rewrite=> div-sub_binary64 (-.f64 (/.f64 z (-.f64 z t)) (/.f64 y (-.f64 z t))))): 0 points increase in error, 2 points decrease in error
      (Rewrite<= distribute-rgt-out--_binary64 (-.f64 (*.f64 (/.f64 z (-.f64 z t)) x) (*.f64 (/.f64 y (-.f64 z t)) x))): 2 points increase in error, 1 points decrease in error
      (-.f64 (Rewrite<= associate-/r/_binary64 (/.f64 z (/.f64 (-.f64 z t) x))) (*.f64 (/.f64 y (-.f64 z t)) x)): 37 points increase in error, 4 points decrease in error
      (-.f64 (/.f64 z (/.f64 (-.f64 z t) x)) (Rewrite<= associate-/r/_binary64 (/.f64 y (/.f64 (-.f64 z t) x)))): 28 points increase in error, 33 points decrease in error
      (-.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 z x) (-.f64 z t))) (/.f64 y (/.f64 (-.f64 z t) x))): 44 points increase in error, 37 points decrease in error
      (-.f64 (/.f64 (*.f64 z x) (-.f64 z t)) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 y x) (-.f64 z t)))): 25 points increase in error, 28 points decrease in error
      (Rewrite<= unsub-neg_binary64 (+.f64 (/.f64 (*.f64 z x) (-.f64 z t)) (neg.f64 (/.f64 (*.f64 y x) (-.f64 z t))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (*.f64 z x) (-.f64 z t)) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (*.f64 y x) (-.f64 z t))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 (/.f64 (*.f64 y x) (-.f64 z t))) (/.f64 (*.f64 z x) (-.f64 z t)))): 0 points increase in error, 0 points decrease in error

   if -4.1973107753517903e-190 < x < 1.1178200296667817e-55

   1. Initial program 2.8

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

   if 1.1178200296667817e-55 < x

   1. Initial program 19.1

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

   2. Simplified 2.5

      \[\leadsto \color{blue}{\left(z - y\right) \cdot \frac{x}{z - t}} \]
      Proof
      (*.f64 (-.f64 z y) (/.f64 x (-.f64 z t))): 0 points increase in error, 0 points decrease in error
      (Rewrite=> *-commutative_binary64 (*.f64 (/.f64 x (-.f64 z t)) (-.f64 z y))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/r/_binary64 (/.f64 x (/.f64 (-.f64 z t) (-.f64 z y)))): 32 points increase in error, 64 points decrease in error
      (/.f64 x (Rewrite<= *-lft-identity_binary64 (*.f64 1 (/.f64 (-.f64 z t) (-.f64 z y))))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (*.f64 (Rewrite<= metadata-eval (/.f64 -1 -1)) (/.f64 (-.f64 z t) (-.f64 z y)))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (Rewrite<= times-frac_binary64 (/.f64 (*.f64 -1 (-.f64 z t)) (*.f64 -1 (-.f64 z y))))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (Rewrite<= neg-mul-1_binary64 (neg.f64 (-.f64 z t))) (*.f64 -1 (-.f64 z y)))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (Rewrite<= sub0-neg_binary64 (-.f64 0 (-.f64 z t))) (*.f64 -1 (-.f64 z y)))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 0 z) t)) (*.f64 -1 (-.f64 z y)))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (+.f64 (Rewrite<= neg-sub0_binary64 (neg.f64 z)) t) (*.f64 -1 (-.f64 z y)))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 t (neg.f64 z))) (*.f64 -1 (-.f64 z y)))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (Rewrite<= sub-neg_binary64 (-.f64 t z)) (*.f64 -1 (-.f64 z y)))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (-.f64 t z) (Rewrite<= neg-mul-1_binary64 (neg.f64 (-.f64 z y))))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (-.f64 t z) (Rewrite<= sub0-neg_binary64 (-.f64 0 (-.f64 z y))))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (-.f64 t z) (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 0 z) y)))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (-.f64 t z) (+.f64 (Rewrite<= neg-sub0_binary64 (neg.f64 z)) y))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (-.f64 t z) (Rewrite<= +-commutative_binary64 (+.f64 y (neg.f64 z))))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (-.f64 t z) (Rewrite<= sub-neg_binary64 (-.f64 y z)))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))): 69 points increase in error, 31 points decrease in error

   3. Applied egg-rr 2.5

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

   4. Applied egg-rr 2.5

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

4. Final simplification 2.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.1973107753517903 \cdot 10^{-190}:\\ \;\;\;\;x \cdot \frac{z - y}{z - t}\\ \mathbf{elif}\;x \leq 1.1178200296667817 \cdot 10^{-55}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - y}{\frac{z}{x} - \frac{t}{x}}\\ \end{array} \]

Alternatives

Alternative 1
Error	17.1
Cost	1108

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := x \cdot \frac{z}{z - t}\\ \mathbf{if}\;z \leq -7.491996048659915 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.214491713364968 \cdot 10^{-53}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 4.6733346313597 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 5.47993459742859 \cdot 10^{+206}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.0618081743834937 \cdot 10^{+238}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	17.1
Cost	1108

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := x \cdot \frac{z}{z - t}\\ \mathbf{if}\;z \leq -7.491996048659915 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.214491713364968 \cdot 10^{-53}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 4.6733346313597 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{1}{t - z}\right)\\ \mathbf{elif}\;z \leq 5.47993459742859 \cdot 10^{+206}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.0618081743834937 \cdot 10^{+238}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	16.7
Cost	976

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := \frac{x}{1 - \frac{t}{z}}\\ \mathbf{if}\;z \leq -7.491996048659915 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.454240722299659 \cdot 10^{-9}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;z \leq 5.47993459742859 \cdot 10^{+206}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.0618081743834937 \cdot 10^{+238}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	17.1
Cost	976

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := \frac{x}{1 - \frac{t}{z}}\\ \mathbf{if}\;z \leq -7.491996048659915 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.3380306908700142 \cdot 10^{-8}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 5.47993459742859 \cdot 10^{+206}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.0618081743834937 \cdot 10^{+238}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	17.1
Cost	976

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := x \cdot \frac{z}{z - t}\\ \mathbf{if}\;z \leq -7.491996048659915 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.3380306908700142 \cdot 10^{-8}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 5.47993459742859 \cdot 10^{+206}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.0618081743834937 \cdot 10^{+238}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	25.1
Cost	912

\[\begin{array}{l} \mathbf{if}\;z \leq -3.125213746493561 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2974597172546479 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 5.244963563282159 \cdot 10^{+39}:\\ \;\;\;\;\frac{x \cdot y}{-z}\\ \mathbf{elif}\;z \leq 3.474988459422974 \cdot 10^{+44}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7
Error	25.0
Cost	848

\[\begin{array}{l} t_1 := \frac{x}{\frac{t}{y}}\\ \mathbf{if}\;z \leq -3.125213746493561 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.454240722299659 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.857919292764227 \cdot 10^{+40}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;z \leq 3.474988459422974 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Error	7.6
Cost	840

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -4.0451285688024204 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.3730933356021433 \cdot 10^{+193}:\\ \;\;\;\;\frac{z - y}{\frac{z - t}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	2.6
Cost	840

\[\begin{array}{l} t_1 := x \cdot \frac{z - y}{z - t}\\ \mathbf{if}\;z \leq -7.094959112860982 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.2884049415290345 \cdot 10^{-93}:\\ \;\;\;\;\frac{z - y}{\frac{z - t}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	2.3
Cost	840

\[\begin{array}{l} \mathbf{if}\;x \leq -4.1973107753517903 \cdot 10^{-190}:\\ \;\;\;\;x \cdot \frac{z - y}{z - t}\\ \mathbf{elif}\;x \leq 1.1178200296667817 \cdot 10^{-55}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - y}{\frac{z - t}{x}}\\ \end{array} \]

Alternative 11
Error	18.9
Cost	712

\[\begin{array}{l} t_1 := \frac{x}{1 - \frac{t}{z}}\\ \mathbf{if}\;z \leq -2.630761689642421 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.454240722299659 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	16.3
Cost	712

\[\begin{array}{l} t_1 := \frac{x}{1 - \frac{t}{z}}\\ \mathbf{if}\;z \leq -7.481657709096917 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.454240722299659 \cdot 10^{-9}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	37.9
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -5.816615239103457 \cdot 10^{-148}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.9972430696100977 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14
Error	37.8
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -6.536874314719281 \cdot 10^{-133}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.9972430696100977 \cdot 10^{+29}:\\ \;\;\;\;\frac{x \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15
Error	26.0
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -3.125213746493561 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.474988459422974 \cdot 10^{+44}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16
Error	25.0
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -3.125213746493561 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.474988459422974 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17
Error	39.4
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022300 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (/ x (/ (- t z) (- y z)))

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