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

Average Error: 11.6 → 1.3

Time: 14.8s

Precision: binary64

Cost: 1864

Math

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

↓

\[\begin{array}{l} t_1 := \frac{x \cdot \left(y - z\right)}{t - z}\\ t_2 := \frac{x}{\frac{z - t}{z - y}}\\ \mathbf{if}\;t_1 \leq 0:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+236}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x (- y z)) (- t z))) (t_2 (/ x (/ (- z t) (- z y)))))
   (if (<= t_1 0.0) t_2 (if (<= t_1 2e+236) t_1 t_2))))

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 t_1 = (x * (y - z)) / (t - z);
	double t_2 = x / ((z - t) / (z - y));
	double tmp;
	if (t_1 <= 0.0) {
		tmp = t_2;
	} else if (t_1 <= 2e+236) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * (y - z)) / (t - z)
    t_2 = x / ((z - t) / (z - y))
    if (t_1 <= 0.0d0) then
        tmp = t_2
    else if (t_1 <= 2d+236) then
        tmp = t_1
    else
        tmp = t_2
    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 t_1 = (x * (y - z)) / (t - z);
	double t_2 = x / ((z - t) / (z - y));
	double tmp;
	if (t_1 <= 0.0) {
		tmp = t_2;
	} else if (t_1 <= 2e+236) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t):
	t_1 = (x * (y - z)) / (t - z)
	t_2 = x / ((z - t) / (z - y))
	tmp = 0
	if t_1 <= 0.0:
		tmp = t_2
	elif t_1 <= 2e+236:
		tmp = t_1
	else:
		tmp = t_2
	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)
	t_1 = Float64(Float64(x * Float64(y - z)) / Float64(t - z))
	t_2 = Float64(x / Float64(Float64(z - t) / Float64(z - y)))
	tmp = 0.0
	if (t_1 <= 0.0)
		tmp = t_2;
	elseif (t_1 <= 2e+236)
		tmp = t_1;
	else
		tmp = t_2;
	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)
	t_1 = (x * (y - z)) / (t - z);
	t_2 = x / ((z - t) / (z - y));
	tmp = 0.0;
	if (t_1 <= 0.0)
		tmp = t_2;
	elseif (t_1 <= 2e+236)
		tmp = t_1;
	else
		tmp = t_2;
	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_] := Block[{t$95$1 = N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(N[(z - t), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 0.0], t$95$2, If[LessEqual[t$95$1, 2e+236], t$95$1, t$95$2]]]]

Target

Original	11.6
Target	2.0
Herbie	1.3

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < -0.0 or 2.00000000000000011e236 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 17.7

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

   2. Simplified 8.6

      \[\leadsto \color{blue}{\left(z - y\right) \cdot \frac{x}{z - t}} \]
      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)))): 30 points increase in error, 82 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))): 76 points increase in error, 27 points decrease in error

   3. Taylor expanded in y around 0 17.7

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

   4. Simplified 1.9

      \[\leadsto \color{blue}{x \cdot \frac{z - y}{z - t}} \]
      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))))): 1 points increase in error, 0 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)): 53 points increase in error, 9 points decrease in error
      (-.f64 (/.f64 z (/.f64 (-.f64 z t) x)) (Rewrite<= associate-/r/_binary64 (/.f64 y (/.f64 (-.f64 z t) x)))): 24 points increase in error, 24 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, 49 points decrease in error
      (-.f64 (/.f64 (*.f64 z x) (-.f64 z t)) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 y x) (-.f64 z t)))): 28 points increase in error, 27 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

   5. Applied egg-rr 1.9

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

   if -0.0 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 2.00000000000000011e236

   1. Initial program 0.3

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 1.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq 0:\\ \;\;\;\;\frac{x}{\frac{z - t}{z - y}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq 2 \cdot 10^{+236}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z - t}{z - y}}\\ \end{array} \]

Alternatives

Alternative 1
Error	30.5
Cost	1440

\[\begin{array}{l} t_1 := \frac{x}{\frac{-z}{y}}\\ \mathbf{if}\;z \leq -1.444573770107639 \cdot 10^{+123}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.9521444701257276 \cdot 10^{+52}:\\ \;\;\;\;\left(-x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-194}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-127}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 1.5327601938558055 \cdot 10^{-62}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;z \leq 1.3908103872552967 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 2.0554629335003806 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5367376465664603 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Error	30.5
Cost	1440

\[\begin{array}{l} \mathbf{if}\;z \leq -1.444573770107639 \cdot 10^{+123}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.9521444701257276 \cdot 10^{+52}:\\ \;\;\;\;\left(-x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-194}:\\ \;\;\;\;\frac{x}{\frac{-z}{y}}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-127}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 1.5327601938558055 \cdot 10^{-62}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;z \leq 1.3908103872552967 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 2.0554629335003806 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5367376465664603 \cdot 10^{+108}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Error	30.5
Cost	1440

\[\begin{array}{l} \mathbf{if}\;z \leq -1.444573770107639 \cdot 10^{+123}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.9521444701257276 \cdot 10^{+52}:\\ \;\;\;\;\frac{x}{\frac{-t}{z}}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-194}:\\ \;\;\;\;\frac{x}{\frac{-z}{y}}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-127}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 1.5327601938558055 \cdot 10^{-62}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;z \leq 1.3908103872552967 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 2.0554629335003806 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5367376465664603 \cdot 10^{+108}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4
Error	26.9
Cost	848

\[\begin{array}{l} \mathbf{if}\;z \leq -4.0674535046907884 \cdot 10^{+88}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-127}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 1.5327601938558055 \cdot 10^{-62}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;z \leq 1.3908103872552967 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5
Error	21.0
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -4.0674535046907884 \cdot 10^{+88}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.602982147237021 \cdot 10^{-6}:\\ \;\;\;\;\frac{y}{\frac{t - z}{x}}\\ \mathbf{elif}\;z \leq 8.054027251846453 \cdot 10^{+127}:\\ \;\;\;\;\frac{z - y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Error	18.0
Cost	844

\[\begin{array}{l} t_1 := \frac{x}{\frac{z}{z - y}}\\ \mathbf{if}\;z \leq -4.0674535046907884 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1623034528130565 \cdot 10^{-76}:\\ \;\;\;\;\frac{y}{\frac{t - z}{x}}\\ \mathbf{elif}\;z \leq 1.4090742240948801 \cdot 10^{+48}:\\ \;\;\;\;\frac{x \cdot z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	17.4
Cost	844

\[\begin{array}{l} t_1 := \frac{x}{\frac{z}{z - y}}\\ \mathbf{if}\;z \leq -4.0674535046907884 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-216}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;z \leq 27993543104662556:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	16.9
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -3.9521444701257276 \cdot 10^{+52}:\\ \;\;\;\;\frac{x}{\frac{z - t}{z}}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-194}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;z \leq 1.3908103872552967 \cdot 10^{-23}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{z - y}}\\ \end{array} \]

Alternative 9
Error	16.9
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -3.9521444701257276 \cdot 10^{+52}:\\ \;\;\;\;\frac{x}{\frac{z - t}{z}}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-194}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;z \leq 1.3908103872552967 \cdot 10^{-23}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \end{array} \]

Alternative 10
Error	21.2
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -4.0674535046907884 \cdot 10^{+88}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.360348313404459 \cdot 10^{+125}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11
Error	18.1
Cost	712

\[\begin{array}{l} t_1 := \frac{x}{\frac{z}{z - y}}\\ \mathbf{if}\;z \leq -4.0674535046907884 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.602982147237021 \cdot 10^{-6}:\\ \;\;\;\;\frac{y}{\frac{t - z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	17.5
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -9.747379997370709 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;y \leq 2.796344046120048 \cdot 10^{+42}:\\ \;\;\;\;\frac{x}{\frac{z - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t - z}{x}}\\ \end{array} \]

Alternative 13
Error	38.0
Cost	584

\[\begin{array}{l} t_1 := z \cdot \frac{x}{t}\\ \mathbf{if}\;t \leq -5.866002847400402 \cdot 10^{+150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.109292116290614 \cdot 10^{+195}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	38.0
Cost	584

\[\begin{array}{l} \mathbf{if}\;t \leq -5.866002847400402 \cdot 10^{+150}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 5.109292116290614 \cdot 10^{+195}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \end{array} \]

Alternative 15
Error	26.6
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -4.0674535046907884 \cdot 10^{+88}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3908103872552967 \cdot 10^{-23}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16
Error	25.6
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -4.0674535046907884 \cdot 10^{+88}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3908103872552967 \cdot 10^{-23}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17
Error	26.5
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -4.0674535046907884 \cdot 10^{+88}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3908103872552967 \cdot 10^{-23}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18
Error	2.0
Cost	576

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

Alternative 19
Error	2.1
Cost	576

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

Alternative 20
Error	40.0
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022318 
(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)))