Metrics for ENA, Section 1.4, Exercise 4d

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze15.0ms (0.2%)

Memory

23.9MiB live, 23.9MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	12.8%	87.2%	0%	0%	0%	0
0%	0%	12.8%	87.2%	0%	0%	0%	1
0%	0%	12.8%	87.2%	0%	0%	0%	2
50%	6.4%	6.4%	87.2%	0%	0%	0%	3
57.1%	6.4%	4.8%	87.2%	0%	1.6%	0%	4
69.2%	7.2%	3.2%	87.2%	0%	2.4%	0%	5
75%	7.2%	2.4%	87.2%	0%	3.2%	0%	6
82.6%	7.6%	1.6%	87.2%	0%	3.6%	0%	7
86.4%	7.6%	1.2%	87.2%	0%	4%	0%	8
90.7%	7.8%	0.8%	87.2%	0%	4.2%	0%	9
92.6%	7.8%	0.6%	87.2%	0%	4.4%	0%	10
95%	7.9%	0.4%	87.2%	0%	4.5%	0%	11
96.3%	8%	0.3%	87.2%	0%	4.5%	0%	12

Compiler

Compiled 24 to 18 computations (25% saved)

sample1.4s (16.5%)

Memory

-49.9MiB live, 1 648.1MiB allocated

Samples

401.0ms	4 998×	0	valid
354.0ms	2 640×	1	valid
178.0ms	618×	2	valid
11.0ms	167×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 658.0ms

ival-sub: 169.0ms (25.7% of total)

ival-sqrt: 136.0ms (20.7% of total)

ival-<=: 126.0ms (19.2% of total)

adjust: 98.0ms (14.9% of total)

ival-mult: 87.0ms (13.2% of total)

ival-and: 22.0ms (3.3% of total)

exact: 17.0ms (2.6% of total)

ival-assert: 3.0ms (0.5% of total)

Bogosity

explain110.0ms (1.3%)

Memory

14.6MiB live, 170.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
106	-	-	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
0	-	-	`eps`
0	-	-	`(sqrt.f64 (-.f64 (*.f64 x x) eps))`
0	-	-	`(-.f64 (*.f64 x x) eps)`
0	-	-	`(*.f64 x x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`	cancellation	106	0

Confusion

	Predicted +	Predicted -
+	106	0
-	0	150

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	106	0	0
-	0	0	150

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	150
1	106

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

34.0ms	168×	1	valid
16.0ms	306×	0	valid
6.0ms	38×	2	valid

Compiler

Compiled 60 to 22 computations (63.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

adjust: 18.0ms (48.7% of total)

ival-sub: 7.0ms (18.9% of total)

ival-sqrt: 6.0ms (16.2% of total)

ival-mult: 5.0ms (13.5% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

preprocess29.0ms (0.3%)

Memory

-7.1MiB live, 31.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	46
1	43	44
2	118	41
3	280	41
4	498	41
5	572	41
6	586	41
0	6	8
0	10	8
1	14	8
2	22	8
3	34	8
4	52	8
5	96	8
6	163	8
7	213	8
8	301	8
9	333	8
10	349	8
0	349	8

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Outputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.2%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify9.0ms (0.1%)

Memory

11.2MiB live, 11.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 x x)
cost-diff	0	(-.f64 (*.f64 x x) eps)
cost-diff	0	(sqrt.f64 (-.f64 (*.f64 x x) eps))
cost-diff	0	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	24
0	10	24
1	14	24
2	22	24
3	34	24
4	52	24
5	96	24
6	163	24
7	213	24
8	301	24
9	333	24
10	349	24
0	349	24

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
x
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
eps

Outputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
x
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
eps

localize303.0ms (3.6%)

Memory

-4.1MiB live, 34.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	0.00390625	(-.f64 (*.f64 x x) eps)
accuracy	0.0078125	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	24.156316750143127	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Samples

287.0ms	84×	1	valid
8.0ms	153×	0	valid
3.0ms	19×	2	valid

Compiler

Compiled 26 to 8 computations (69.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-mult: 4.0ms (32.5% of total)

ival-sqrt: 3.0ms (24.4% of total)

ival-sub: 3.0ms (24.4% of total)

adjust: 2.0ms (16.3% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series8.0ms (0.1%)

Memory

12.9MiB live, 12.9MiB allocated

Counts

4 → 49

Calls

Call 1

Inputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)

Outputs
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* (sqrt eps) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(* -1 eps)
(- (pow x 2) eps)
(pow x 2)
(* 1/2 (/ eps x))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(+ (* -1 eps) (pow x 2))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* eps (- (/ (pow x 2) eps) 1))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	eps	@	inf	((- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x))
1.0ms	x	@	inf	((- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x))
1.0ms	x	@	0	((- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x))
1.0ms	eps	@	-inf	((- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x))
1.0ms	eps	@	0	((- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x))

simplify171.0ms (2%)

Memory

13.9MiB live, 159.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	257	1067
1	784	1053
2	2629	1015
3	7085	1012
0	8084	948

Stop Event

1×	iter limit
1×	node limit

Counts

49 → 48

Calls

Call 1

Inputs
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* (sqrt eps) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(* -1 eps)
(- (pow x 2) eps)
(pow x 2)
(* 1/2 (/ eps x))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(+ (* -1 eps) (pow x 2))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* eps (- (/ (pow x 2) eps) 1))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))

Outputs
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps))
(- x (* (sqrt eps) (sqrt -1)))
(fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)) x)
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal 1 binary64)) x (.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal -1/8 binary64))) (.f64 x x) (fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)) x))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (.f64 x x))) (.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))))) (fma.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))))
(* -1 eps)
(neg.f64 eps)
(- (pow x 2) eps)
(fma.f64 x x (neg.f64 eps))
(pow x 2)
(*.f64 x x)
(* 1/2 (/ eps x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) x) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
(/.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal 5/64 binary64) (pow.f64 x #s(literal 6 binary64))) eps) (fma.f64 (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (.f64 (pow.f64 eps #s(literal 3 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64)))))) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) eps) (/.f64 eps (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 1 binary64))) x)
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (.f64 #s(literal -1/8 binary64) eps) (/.f64 eps (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 eps x) x)) x) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) eps) (/.f64 eps (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 eps x) #s(literal -2 binary64))) (neg.f64 x))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(.f64 (neg.f64 x) (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (.f64 #s(literal 1/8 binary64) eps) (/.f64 eps (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 eps x) #s(literal -2 binary64)))))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 eps x) #s(literal -1 binary64)) x)
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) eps) (/.f64 eps (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 eps x) #s(literal -1 binary64))) x)
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(.f64 (neg.f64 x) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (.f64 #s(literal -1/8 binary64) eps) (/.f64 eps (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 7 binary64))) #s(literal 5/128 binary64) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) eps (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(+ x (* -1/2 (/ eps x)))
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal -1/2 binary64) x)) eps x)
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal -1/16 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal -1/2 binary64) x)) eps x)
(+ (* -1 eps) (pow x 2))
(fma.f64 x x (neg.f64 eps))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(*.f64 (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x eps)) eps)
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x eps))) eps)
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (fma.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/8 binary64) (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x eps)))) eps)
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) eps)
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (fma.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/8 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) eps)
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(.f64 (fma.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/8 binary64) (fma.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) eps)
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 x eps)) eps)
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)) x) eps)) eps)
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 x (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 (sqrt.f64 eps) x) x) (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))) eps)) eps)) eps)
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) (neg.f64 eps))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))))) (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))) (neg.f64 eps))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/16 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))) (pow.f64 x #s(literal 6 binary64))) (.f64 #s(literal -1/8 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (*.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))) (neg.f64 eps))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)

rewrite215.0ms (2.5%)

Memory

-28.8MiB live, 189.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	22
0	10	22
1	42	22
2	310	22
3	3602	22
0	8540	22

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

4 → 224

Calls

Call 1

Inputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)

Outputs
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps)) #s(literal 2 binary64)))) (-.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))) (+.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps)) (-.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps)) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(.f64 (/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (-.f64 (fma.f64 x x eps) (.f64 x x))) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
(.f64 (/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)))) (-.f64 (fma.f64 x x (-.f64 (.f64 x x) eps)) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))
(.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (-.f64 (fma.f64 x x eps) (*.f64 x x)))
(.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (.f64 x x) eps))) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))))
(.f64 (neg.f64 (-.f64 (fma.f64 x x eps) (.f64 x x))) (pow.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) #s(literal -1 binary64)))
(.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)))) (pow.f64 (neg.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (.f64 x x) eps)))) #s(literal -1 binary64)))
(.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
(.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (/.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))
(.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal -1 binary64))))
(.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal -1 binary64)))
(.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (.f64 x x) eps))) (/.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (.f64 x x) eps)))))
(.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (.f64 x x) eps))) (.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (pow.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64))))
(.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))) (pow.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (.f64 x x) eps))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
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(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (neg.f64 eps) (.f64 x x)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))))
(neg.f64 (neg.f64 (-.f64 (*.f64 x x) eps)))
(fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (.f64 (fma.f64 x x eps) eps) #s(literal 2 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (fma.f64 x x eps) eps)) (neg.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (pow.f64 (.f64 (fma.f64 x x eps) eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (.f64 (fma.f64 x x eps) eps) (-.f64 (*.f64 (fma.f64 x x eps) eps) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 eps (-.f64 eps (.f64 x x)) (pow.f64 x #s(literal 4 binary64))) (neg.f64 (.f64 eps (/.f64 eps (fma.f64 x x eps)))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 eps) eps (pow.f64 x #s(literal 4 binary64)))) (-.f64 (.f64 x x) eps) (neg.f64 (.f64 eps (/.f64 eps (fma.f64 x x eps)))))
(fma.f64 #s(literal -1 binary64) eps (*.f64 x x))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 (*.f64 x x) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (fma.f64 x x eps) #s(literal -1 binary64)) (neg.f64 (*.f64 eps (/.f64 eps (fma.f64 x x eps)))))
(fma.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 x (fma.f64 x x eps)) (neg.f64 (*.f64 eps (/.f64 eps (fma.f64 x x eps)))))
(fma.f64 eps #s(literal -1 binary64) (*.f64 x x))
(fma.f64 (*.f64 x x) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))))))
(fma.f64 (.f64 x x) (/.f64 (.f64 x x) (fma.f64 x x eps)) (neg.f64 (*.f64 eps (/.f64 eps (fma.f64 x x eps)))))
(fma.f64 x (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x eps)) (neg.f64 (*.f64 eps (/.f64 eps (fma.f64 x x eps)))))
(fma.f64 x x (neg.f64 eps))
(sqrt.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64)))
(-.f64 (fma.f64 x x #s(literal 0 binary64)) eps)
(-.f64 #s(literal 0 binary64) (-.f64 eps (*.f64 x x)))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) (*.f64 eps (/.f64 eps (fma.f64 x x eps))))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64)))))
(-.f64 (*.f64 x x) eps)
(fabs.f64 (-.f64 (*.f64 x x) eps))
(exp.f64 (.f64 (neg.f64 (log.f64 (-.f64 (.f64 x x) eps))) #s(literal -1 binary64)))
(exp.f64 (.f64 (log.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))) #s(literal 2 binary64)))
(exp.f64 (log.f64 (-.f64 (*.f64 x x) eps)))
(+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) (neg.f64 (*.f64 eps (/.f64 eps (fma.f64 x x eps)))))
(+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))))))
(+.f64 (neg.f64 eps) (*.f64 x x))
(+.f64 (*.f64 x x) (neg.f64 eps))
(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval41.0ms (0.5%)

Memory: 29.0MiB live, 101.3MiB allocated
Compiler: Compiled 7 015 to 1 083 computations (84.6% saved)

prune13.0ms (0.2%)

Memory

-4.4MiB live, 33.2MiB allocated

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	257	12	269
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	257	13	270

Accuracy

99.8%

Counts

270 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	61.7%	(fma.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64)) (neg.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64))) x)
	47.0%	(fma.f64 (.f64 x x) (/.f64 x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (.f64 x x) eps)))) (neg.f64 (/.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)) (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (.f64 x x) eps))))))
	61.9%	(fma.f64 x (/.f64 x (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (neg.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
▶	62.0%	(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
▶	61.8%	(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))
✓	62.2%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	58.5%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
	6.7%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
▶	3.5%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
	61.9%	(.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (-.f64 (fma.f64 x x eps) (*.f64 x x)))
	21.1%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal 5/64 binary64) (pow.f64 x #s(literal 6 binary64))) eps) (fma.f64 (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (.f64 (pow.f64 eps #s(literal 3 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64)))))) x))
▶	37.0%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
▶	43.7%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))

Compiler

Compiled 516 to 278 computations (46.1% saved)

simplify156.0ms (1.8%)

Memory

-24.6MiB live, 215.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
cost-diff	0	(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
cost-diff	0	(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
cost-diff	0	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
cost-diff	0	(*.f64 x x)
cost-diff	0	(-.f64 (*.f64 x x) eps)
cost-diff	0	(/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))
cost-diff	0	(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))
cost-diff	0	(/.f64 #s(literal 1/2 binary64) x)
cost-diff	0	(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
cost-diff	0	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
cost-diff	0	(neg.f64 x)
cost-diff	0	#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
cost-diff	0	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 x x eps)
cost-diff	0	(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
cost-diff	7	(-.f64 (fma.f64 x x eps) (*.f64 x x))

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	29	202
0	48	195
1	84	195
2	147	190
3	294	188
4	554	188
5	1697	188
6	4811	188
0	8397	188

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Calls

Call 1

Inputs
(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
(-.f64 (fma.f64 x x eps) (*.f64 x x))
(fma.f64 x x eps)
x
eps
(*.f64 x x)
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
x
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
(neg.f64 x)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
eps
(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))
x
(/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
eps
(sqrt.f64 (-.f64 (*.f64 x x) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
#s(literal 1/8 binary64)
(pow.f64 x #s(literal 3 binary64))
x
#s(literal 3 binary64)
eps
(/.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)

Outputs
(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(-.f64 (fma.f64 x x eps) (*.f64 x x))
eps
(fma.f64 x x eps)
x
eps
(*.f64 x x)
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
x
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
(neg.f64 x)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
eps
(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))
x
(/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
eps
(sqrt.f64 (-.f64 (*.f64 x x) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
#s(literal 1/8 binary64)
(pow.f64 x #s(literal 3 binary64))
x
#s(literal 3 binary64)
eps
(/.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)

localize145.0ms (1.7%)

Memory

12.8MiB live, 173.2MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.14877915172363415	(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
accuracy	8.218400380695169	(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
accuracy	9.220789506224468	(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
accuracy	37.322284869743385	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
accuracy	0.00390625	(-.f64 (*.f64 x x) eps)
accuracy	0.0078125	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.33984375	(/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))
accuracy	24.156316750143127	(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))
accuracy	0.0	(/.f64 #s(literal 1/2 binary64) x)
accuracy	0.25390625	(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
accuracy	35.914051382705765	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
accuracy	0.0	(neg.f64 x)
accuracy	24.156316750143127	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
accuracy	62.39680297017749	#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
accuracy	0.0078125	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.03125	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy	0.2890625	(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
accuracy	23.682421391276836	(-.f64 (fma.f64 x x eps) (*.f64 x x))

Samples

86.0ms	84×	1	valid
25.0ms	153×	0	valid
9.0ms	19×	2	valid

Compiler

Compiled 184 to 25 computations (86.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 43.0ms

ival-div: 8.0ms (18.7% of total)

ival-mult: 8.0ms (18.7% of total)

ival-add: 7.0ms (16.3% of total)

adjust: 6.0ms (14% of total)

ival-sub: 6.0ms (14% of total)

ival-sqrt: 3.0ms (7% of total)

ival-pow: 3.0ms (7% of total)

ival-neg: 1.0ms (2.3% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series24.0ms (0.3%)

Memory

21.8MiB live, 21.8MiB allocated

Counts

19 → 98

Calls

Call 1

Inputs
(-.f64 (fma.f64 x x eps) (*.f64 x x))
(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
(fma.f64 x x eps)
(*.f64 x x)
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
(neg.f64 x)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/.f64 #s(literal 1/2 binary64) x)
(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))
(/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))
(-.f64 (*.f64 x x) eps)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))

Outputs
eps
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ eps (pow x 2))
(pow x 2)
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* (sqrt eps) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(* -1 x)
(* 1/2 (/ eps x))
(/ 1/2 x)
(* -1 eps)
(- (pow x 2) eps)
(* 1/8 (/ (pow eps 2) (pow x 3)))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(* 1/8 (/ eps (pow x 3)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/ 1/8 (pow x 3))
(+ x (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(* (pow x 2) (+ 1 (/ eps (pow x 2))))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(* 2 x)
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(+ (* -1 eps) (pow x 2))
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(+ (* -1/2 (/ eps x)) (* 2 x))
(+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(* eps (+ 1 (/ (pow x 2) eps)))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* eps (- (/ (pow x 2) eps) 1))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))
(* -1 (* eps (- (* -1 (/ (pow x 2) eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))

Calls

6 calls:

Time	Variable		Point	Expression
6.0ms	eps	@	-inf	((- (+ (* x x) eps) (* x x)) (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (+ (* x x) eps) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)))
4.0ms	x	@	0	((- (+ (* x x) eps) (* x x)) (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (+ (* x x) eps) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)))
4.0ms	x	@	inf	((- (+ (* x x) eps) (* x x)) (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (+ (* x x) eps) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)))
4.0ms	eps	@	inf	((- (+ (* x x) eps) (* x x)) (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (+ (* x x) eps) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)))
3.0ms	x	@	-inf	((- (+ (* x x) eps) (* x x)) (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (+ (* x x) eps) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)))

simplify232.0ms (2.7%)

Memory

-28.8MiB live, 209.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	464	2160
1	1453	2060
2	5013	2016
0	8335	1898

Stop Event

1×	iter limit
1×	node limit

Counts

98 → 96

Calls

Call 1

Inputs
eps
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ eps (pow x 2))
(pow x 2)
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* (sqrt eps) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(* -1 x)
(* 1/2 (/ eps x))
(/ 1/2 x)
(* -1 eps)
(- (pow x 2) eps)
(* 1/8 (/ (pow eps 2) (pow x 3)))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(* 1/8 (/ eps (pow x 3)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/ 1/8 (pow x 3))
(+ x (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(* (pow x 2) (+ 1 (/ eps (pow x 2))))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(* 2 x)
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(+ (* -1 eps) (pow x 2))
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(+ (* -1/2 (/ eps x)) (* 2 x))
(+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(* eps (+ 1 (/ (pow x 2) eps)))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* eps (- (/ (pow x 2) eps) 1))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))
(* -1 (* eps (- (* -1 (/ (pow x 2) eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))

Outputs
eps
(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) x)
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(fma.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1 binary64)) x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) eps))) x (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))) x #s(literal 1 binary64)) x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ eps (pow x 2))
(fma.f64 x x eps)
(pow x 2)
(*.f64 x x)
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps))
(- x (* (sqrt eps) (sqrt -1)))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) x)
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) x))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (neg.f64 x) (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64))) (.f64 x x) x))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 (.f64 (neg.f64 x) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 x (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) #s(literal 1/16 binary64) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/8 binary64))) (.f64 x x) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(* -1 x)
(neg.f64 x)
(* 1/2 (/ eps x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(* -1 eps)
(neg.f64 eps)
(- (pow x 2) eps)
(fma.f64 x x (neg.f64 eps))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps) eps)
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(/.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3 binary64)))
(* 1/8 (/ eps (pow x 3)))
(*.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps)
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/.f64 (fma.f64 #s(literal 1/8 binary64) eps (.f64 (.f64 x x) #s(literal 1/2 binary64))) (pow.f64 x #s(literal 3 binary64)))
(/ 1/8 (pow x 3))
(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
(+ x (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) x)
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) x))
(+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 (.f64 (neg.f64 x) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) x #s(literal 1 binary64)) x (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/16 binary64) x) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(/.f64 (-.f64 (fma.f64 (/.f64 (.f64 eps eps) x) (/.f64 #s(literal 1/8 binary64) x) (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (.f64 #s(literal 1/2 binary64) eps))) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 6 binary64))))) x)
(* (pow x 2) (+ 1 (/ eps (pow x 2))))
(*.f64 x (fma.f64 (/.f64 (/.f64 eps x) x) x x))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/16 binary64) x) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
(/.f64 (fma.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal 5/64 binary64) (pow.f64 x #s(literal 6 binary64)))) #s(literal 1/2 binary64) (fma.f64 (/.f64 (.f64 eps eps) x) (/.f64 #s(literal 1/8 binary64) x) (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (*.f64 #s(literal 1/2 binary64) eps)))) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(.f64 (fma.f64 (.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 binary64)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 1 binary64))) x)
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(fma.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 eps x) (fma.f64 (.f64 eps eps) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 #s(literal -1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 6 binary64))))) x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 eps x) x)) x) x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(.f64 (fma.f64 (.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 binary64)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 2 binary64))) x)
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(.f64 (+.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 2 binary64)) (fma.f64 (.f64 eps eps) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 6 binary64))))) x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/2 binary64) #s(literal -2 binary64)) (neg.f64 x))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(.f64 (fma.f64 (.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 binary64)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 2 binary64))) x)
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
(.f64 (+.f64 (/.f64 (fma.f64 (/.f64 (.f64 #s(literal 5/64 binary64) (pow.f64 eps #s(literal 4 binary64))) eps) #s(literal -2 binary64) (fma.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/8 binary64)) #s(literal -1/4 binary64) (.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 3 binary64))))) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (*.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 binary64)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 2 binary64)))) x)
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(.f64 (fma.f64 (.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/8 binary64) (-.f64 #s(literal -2 binary64) (*.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64)))) (neg.f64 x))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(.f64 (fma.f64 #s(literal -1 binary64) (.f64 (pow.f64 eps #s(literal 3 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (*.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 binary64)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 2 binary64)))) x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (neg.f64 x))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(.f64 (fma.f64 (.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 binary64)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (neg.f64 x))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(neg.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 eps x) (fma.f64 (.f64 eps eps) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 #s(literal -1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 6 binary64))))) x x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/8 binary64) #s(literal -1/2 binary64)) (neg.f64 x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/16 binary64) x) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 eps (.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal 5/64 binary64) (pow.f64 x #s(literal 6 binary64))))) (fma.f64 (/.f64 #s(literal -1/8 binary64) x) (/.f64 (.f64 eps eps) x) (/.f64 (*.f64 #s(literal -1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 4 binary64))))) (neg.f64 x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 7 binary64))) #s(literal 5/128 binary64) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) eps (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(+ x (* -1/2 (/ eps x)))
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/8 binary64) #s(literal -1/2 binary64)) x) eps x)
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal -1/16 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal -1/2 binary64) x)) eps x)
(+ (* -1 eps) (pow x 2))
(fma.f64 x x (neg.f64 eps))
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
(+ (* -1/2 (/ eps x)) (* 2 x))
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (*.f64 #s(literal 2 binary64) x))
(+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/8 binary64) #s(literal -1/2 binary64)) x) eps (*.f64 #s(literal 2 binary64) x))
(+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal -1/16 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal -1/2 binary64) x)) eps (*.f64 #s(literal 2 binary64) x))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(-.f64 (+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) x) (.f64 (.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (.f64 (neg.f64 x) (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(-.f64 (-.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (.f64 (.f64 (neg.f64 x) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal -1/2 binary64) (neg.f64 x))) (/.f64 (fma.f64 (.f64 (neg.f64 (sqrt.f64 eps)) x) (.f64 (.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (.f64 (neg.f64 x) (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))) (pow.f64 eps #s(literal 3 binary64))))
(* eps (+ 1 (/ (pow x 2) eps)))
(fma.f64 (/.f64 (*.f64 x x) eps) eps eps)
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(fma.f64 (*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) eps x)
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(+.f64 x (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) eps))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(+.f64 x (.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) #s(literal 1/8 binary64)) (/.f64 (pow.f64 x #s(literal 4 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (neg.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) eps))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) eps)
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (fma.f64 (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) #s(literal -1/8 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) eps)
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))) (fma.f64 (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) #s(literal -1/8 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) eps)
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(.f64 (.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps) eps)
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(*.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps)
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(fma.f64 (*.f64 eps (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) x)
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) eps x)
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
(fma.f64 (fma.f64 (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) #s(literal -1/8 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) eps x)
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) x)
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (fma.f64 (.f64 (.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) (sqrt.f64 eps)) (/.f64 #s(literal 1/2 binary64) eps) (neg.f64 x))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (-.f64 (/.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) eps (.f64 (.f64 (neg.f64 x) x) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (pow.f64 eps #s(literal 3 binary64)))))) (neg.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) x) (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (.f64 x x)) #s(literal -1 binary64))))))) (.f64 eps eps)) x)))
(* -1 (* eps (- (* -1 (/ (pow x 2) eps)) 1)))
(.f64 (-.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) eps)) (neg.f64 eps))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(fma.f64 (*.f64 eps (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) x)
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (+.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)) x) eps) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) eps)
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (+.f64 (/.f64 (-.f64 x (/.f64 (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 eps)) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64)) (.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/8 binary64)))) eps)) eps) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) eps)
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (.f64 x x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) (neg.f64 eps))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(.f64 (fma.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64)) (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (.f64 x x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) (neg.f64 eps))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(.f64 (fma.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64)) (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))) (pow.f64 x #s(literal 6 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/16 binary64)) (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (.f64 x x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) (neg.f64 eps))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)
(* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))
(*.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps)
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(-.f64 x (.f64 (.f64 eps (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/2 binary64)) x) (neg.f64 eps))) (neg.f64 eps))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 x (/.f64 (fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 eps)) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64)) (.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64)))) eps)) (neg.f64 eps))) (neg.f64 eps))

rewrite329.0ms (3.9%)

Memory

6.9MiB live, 284.3MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	29	169
0	48	163
1	199	163
2	1628	157
0	8706	157

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

19 → 937

Calls

Call 1

Inputs
(-.f64 (fma.f64 x x eps) (*.f64 x x))
(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
(fma.f64 x x eps)
(*.f64 x x)
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
(neg.f64 x)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/.f64 #s(literal 1/2 binary64) x)
(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))
(/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))
(-.f64 (*.f64 x x) eps)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))

Outputs
(*.f64 (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (fma.f64 x x (fma.f64 x x eps)) #s(literal -1 binary64)))
(.f64 (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (fma.f64 (.f64 x x) (fma.f64 x x (fma.f64 x x eps)) (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (fma.f64 x x (fma.f64 x x eps)) (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (*.f64 x x) (fma.f64 x x (fma.f64 x x eps)) (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64))) (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) #s(literal -1 binary64))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (-.f64 eps (.f64 x x)) #s(literal 2 binary64)))) (neg.f64 (-.f64 (.f64 x x) (-.f64 eps (*.f64 x x)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 eps (.f64 x x)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 (-.f64 eps (.f64 x x)) #s(literal 2 binary64)) (.f64 (.f64 x x) (-.f64 eps (*.f64 x x)))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))))) (neg.f64 (neg.f64 (fma.f64 x x (fma.f64 x x eps)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))) (neg.f64 (neg.f64 (fma.f64 (*.f64 x x) (fma.f64 x x (fma.f64 x x eps)) (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64))))))
(/.f64 (-.f64 (.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (fma.f64 x x (fma.f64 x x eps))) (.f64 (fma.f64 x x (fma.f64 x x eps)) (pow.f64 x #s(literal 4 binary64)))) (*.f64 (fma.f64 x x (fma.f64 x x eps)) (fma.f64 x x (fma.f64 x x eps))))
(/.f64 (-.f64 (.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (fma.f64 (.f64 x x) (fma.f64 x x (fma.f64 x x eps)) (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)))) (.f64 (fma.f64 (.f64 x x) (fma.f64 x x (fma.f64 x x eps)) (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64))) (pow.f64 x #s(literal 6 binary64)))) (.f64 (fma.f64 (.f64 x x) (fma.f64 x x (fma.f64 x x eps)) (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64))) (fma.f64 (*.f64 x x) (fma.f64 x x (fma.f64 x x eps)) (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (-.f64 eps (.f64 x x)) #s(literal 2 binary64))) (-.f64 (.f64 x x) (-.f64 eps (*.f64 x x))))
(/.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 eps (.f64 x x)) #s(literal 3 binary64))) (+.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 (-.f64 eps (.f64 x x)) #s(literal 2 binary64)) (.f64 (.f64 x x) (-.f64 eps (*.f64 x x))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (-.f64 (fma.f64 x x eps) (*.f64 (neg.f64 x) x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (fma.f64 x x (fma.f64 x x eps))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (+.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (fma.f64 x x eps) (.f64 (neg.f64 x) x))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (fma.f64 (*.f64 x x) (fma.f64 x x (fma.f64 x x eps)) (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (fma.f64 x x eps) (*.f64 (neg.f64 x) x)))
(/.f64 (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x (fma.f64 x x eps)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 x x (fma.f64 x x eps)) (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (*.f64 x x) (fma.f64 x x (fma.f64 x x eps)) (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64))) (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (fma.f64 x x eps)) (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 x x) (fma.f64 x x (fma.f64 x x eps)) (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64))) (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))))
(/.f64 (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (fma.f64 x x eps) (.f64 (neg.f64 x) x)))))
(/.f64 (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (*.f64 x x) (fma.f64 x x (fma.f64 x x eps)) (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64))))
(fma.f64 (/.f64 (fma.f64 x x eps) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))) (/.f64 (-.f64 (.f64 x x) eps) (fma.f64 eps (-.f64 eps (.f64 x x)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (neg.f64 x) x))
(fma.f64 (/.f64 (fma.f64 x x eps) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)))) (/.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps)) (*.f64 (neg.f64 x) x))
(fma.f64 (/.f64 (fma.f64 x x eps) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (/.f64 (-.f64 (.f64 x x) eps) (pow.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))) (.f64 (neg.f64 x) x))
(fma.f64 (/.f64 (fma.f64 x x eps) (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (-.f64 (.f64 x x) eps)) (*.f64 (neg.f64 x) x))
(fma.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps))) (fma.f64 x x eps) (*.f64 (neg.f64 x) x))
(fma.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) (.f64 (neg.f64 x) x))
(fma.f64 (/.f64 (fma.f64 x x eps) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps))) (/.f64 (-.f64 (.f64 x x) eps) (pow.f64 (fma.f64 x x eps) #s(literal -1 binary64))) (*.f64 (neg.f64 x) x))
(fma.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal -1 binary64)) (*.f64 (neg.f64 x) x))
(fma.f64 #s(literal -1 binary64) (*.f64 x x) (fma.f64 x x eps))
(fma.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (fma.f64 eps (-.f64 eps (.f64 x x)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (.f64 (neg.f64 x) x))
(fma.f64 (neg.f64 x) (neg.f64 x) (-.f64 eps (*.f64 x x)))
(fma.f64 (neg.f64 x) x (fma.f64 x x eps))
(fma.f64 x (neg.f64 x) (fma.f64 x x eps))
(fma.f64 x x (-.f64 eps (*.f64 x x)))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) (-.f64 eps (.f64 x x)))) (/.f64 (pow.f64 (-.f64 eps (.f64 x x)) #s(literal 2 binary64)) (-.f64 (.f64 x x) (-.f64 eps (*.f64 x x)))))
(-.f64 (/.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (-.f64 (fma.f64 x x eps) (.f64 (neg.f64 x) x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (fma.f64 x x eps) (.f64 (neg.f64 x) x))))
(-.f64 (/.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (fma.f64 x x (fma.f64 x x eps))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x (fma.f64 x x eps))))
(-.f64 (/.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (fma.f64 (.f64 x x) (fma.f64 x x (fma.f64 x x eps)) (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (.f64 x x) (fma.f64 x x (fma.f64 x x eps)) (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)))))
(-.f64 (fma.f64 x x eps) (*.f64 x x))
(+.f64 (-.f64 eps (.f64 x x)) (.f64 x x))
(+.f64 (*.f64 (neg.f64 x) x) (fma.f64 x x eps))
(+.f64 (.f64 x x) (-.f64 eps (.f64 x x)))
(+.f64 (fma.f64 x x eps) (*.f64 (neg.f64 x) x))
(+.f64 eps (-.f64 (.f64 x x) (.f64 x x)))
(+.f64 eps (fma.f64 x x (*.f64 (neg.f64 x) x)))
(.f64 (/.f64 (fma.f64 x x (fma.f64 x x eps)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (/.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps)) (fma.f64 x x (fma.f64 x x eps))))
(.f64 (/.f64 (fma.f64 (.f64 x x) (fma.f64 x x (fma.f64 x x eps)) (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64))) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (/.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps)) (fma.f64 (.f64 x x) (fma.f64 x x (fma.f64 x x eps)) (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)))))
(.f64 (/.f64 (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (-.f64 (.f64 x x) eps) (.f64 x x))) (/.f64 (pow.f64 (fma.f64 x x (fma.f64 x x eps)) #s(literal -1 binary64)) (pow.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (+.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 (pow.f64 (fma.f64 x x (fma.f64 x x eps)) #s(literal -1 binary64)) (pow.f64 (fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) eps)) #s(literal -1 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (-.f64 (.f64 x x) eps) (.f64 x x))) (/.f64 (pow.f64 (fma.f64 (.f64 x x) (fma.f64 x x (fma.f64 x x eps)) (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal -1 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 (pow.f64 (fma.f64 (.f64 x x) (fma.f64 x x (fma.f64 x x eps)) (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (*.f64 x x) eps)) #s(literal -1 binary64))))
(.f64 (pow.f64 (/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 x x (fma.f64 x x eps)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (*.f64 x x) (fma.f64 x x (fma.f64 x x eps)) (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps)) (-.f64 (-.f64 (.f64 x x) eps) (.f64 x x))) (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64))))
(.f64 (/.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps)) (-.f64 (-.f64 (.f64 x x) eps) (.f64 x x))) (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
(.f64 (/.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps)) (+.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) eps)) #s(literal -1 binary64))))
(.f64 (/.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps)) (+.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) eps)))
(.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (pow.f64 (pow.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (fma.f64 (neg.f64 x) x (fma.f64 x x eps)))
(.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))
(.f64 (neg.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps))) (pow.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #s(literal -1 binary64)))
(.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)))
(pow.f64 (/.f64 (/.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (fma.f64 (neg.f64 x) x (fma.f64 x x eps))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (fma.f64 (neg.f64 x) x (fma.f64 x x eps))) #s(literal -1 binary64))
(/.f64 (neg.f64 (.f64 (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)))) (neg.f64 (fma.f64 x x (fma.f64 x x eps))))
(/.f64 (neg.f64 (.f64 (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)))) (neg.f64 (fma.f64 (*.f64 x x) (fma.f64 x x (fma.f64 x x eps)) (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps)) #s(literal 1 binary64))) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 (fma.f64 x x eps) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #s(literal 2 binary64)))) (neg.f64 (+.f64 (/.f64 (fma.f64 x x eps) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (/.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 (fma.f64 x x eps) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (/.f64 (fma.f64 x x eps) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #s(literal 2 binary64)) (.f64 (/.f64 (fma.f64 x x eps) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (/.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps))))) (neg.f64 (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))))
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(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps))) (sqrt.f64 (-.f64 (.f64 x x) (neg.f64 eps))))
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(fma.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (/.f64 eps (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(fma.f64 (.f64 x x) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal -1/2 binary64)) (neg.f64 (/.f64 eps (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(fma.f64 x (/.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (/.f64 eps (sqrt.f64 (-.f64 (.f64 x x) eps)))))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
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(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 (/.f64 (.f64 eps eps) (fma.f64 x x eps)) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (-.f64 (.f64 x x) eps))))
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(-.f64 (/.f64 (.f64 x x) (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 eps (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(fabs.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(exp.f64 (.f64 (log.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal -1/2 binary64))) #s(literal -1 binary64)))
(exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(+.f64 (/.f64 (.f64 x x) (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (/.f64 eps (sqrt.f64 (-.f64 (*.f64 x x) eps)))))

eval212.0ms (2.5%)

Memory: -5.9MiB live, 235.7MiB allocated
Compiler: Compiled 36 638 to 4 226 computations (88.5% saved)

prune47.0ms (0.6%)

Memory

13.7MiB live, 53.4MiB allocated

Pruning

13 alts after pruning (9 fresh and 4 done)

	Pruned	Kept	Total
New	1 184	7	1 191
Fresh	5	2	7
Picked	2	3	5
Done	0	1	1
Total	1 191	13	1 204

Accuracy

100.0%

Counts

1 204 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	61.8%	(/.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
▶	99.5%	(/.f64 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
✓	61.8%	(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))
▶	58.7%	(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))))
	61.8%	(-.f64 x (.f64 (neg.f64 (-.f64 (.f64 x x) eps)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
✓	62.2%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶	58.5%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
▶	6.7%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
✓	3.5%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
	43.9%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
	43.7%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 #s(literal 1/2 binary64) eps))))
✓	43.7%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
	41.5%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(approx (+ ( (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps))

Compiler

Compiled 363 to 237 computations (34.7% saved)

simplify254.0ms (3%)

Memory

-2.4MiB live, 187.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 x x eps)
cost-diff	0	(neg.f64 x)
cost-diff	0	(/.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
cost-diff	7	(fma.f64 (neg.f64 x) x (fma.f64 x x eps))
cost-diff	0	(*.f64 x x)
cost-diff	0	(-.f64 (*.f64 x x) eps)
cost-diff	0	(/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))))
cost-diff	0	(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))))
cost-diff	0	(/.f64 eps x)
cost-diff	0	(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
cost-diff	0	#s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))
cost-diff	0	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
cost-diff	0	(neg.f64 eps)
cost-diff	0	#s(approx (- (* x x) eps) (neg.f64 eps))
cost-diff	0	(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
cost-diff	0	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
cost-diff	0	(*.f64 x x)
cost-diff	0	(/.f64 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
cost-diff	2	(+.f64 eps (-.f64 (.f64 x x) (.f64 x x)))
cost-diff	6	(-.f64 (.f64 x x) (.f64 x x))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	246
0	49	214
1	87	210
2	137	210
3	339	210
4	1096	210
5	4099	210
6	6909	210
0	8036	210

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Calls

Call 1

Inputs
(/.f64 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(+.f64 eps (-.f64 (.f64 x x) (.f64 x x)))
eps
(-.f64 (.f64 x x) (.f64 x x))
(*.f64 x x)
x
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
x
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
#s(approx (- (* x x) eps) (neg.f64 eps))
(neg.f64 eps)
eps
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
x
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
(/.f64 eps x)
eps
#s(literal -1/2 binary64)
(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))))
x
(/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
eps
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
#s(approx (- (* x x) eps) (neg.f64 eps))
(neg.f64 eps)
(/.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(fma.f64 (neg.f64 x) x (fma.f64 x x eps))
(neg.f64 x)
x
(fma.f64 x x eps)
eps
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)

Outputs
(/.f64 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(+.f64 eps (-.f64 (.f64 x x) (.f64 x x)))
eps
eps
(-.f64 (.f64 x x) (.f64 x x))
#s(literal 0 binary64)
(*.f64 x x)
x
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
x
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
#s(approx (- (* x x) eps) (neg.f64 eps))
(neg.f64 eps)
eps
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)))
x
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x))
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
(fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)
(/.f64 eps x)
eps
#s(literal -1/2 binary64)
(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))))
x
(/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
eps
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
#s(approx (- (* x x) eps) (neg.f64 eps))
(neg.f64 eps)
(/.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(fma.f64 (neg.f64 x) x (fma.f64 x x eps))
eps
(neg.f64 x)
x
(fma.f64 x x eps)
eps
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)

localize167.0ms (2%)

Memory

26.1MiB live, 223.9MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.0234375	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy	0.2890625	(/.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
accuracy	10.211963492675816	(fma.f64 (neg.f64 x) x (fma.f64 x x eps))
accuracy	0.0078125	(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
accuracy	0.31640625	(/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))))
accuracy	10.423983094334586	(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))))
accuracy	11.532091470468826	#s(approx (- (* x x) eps) (neg.f64 eps))
accuracy	0.0	(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
accuracy	0.0	(/.f64 eps x)
accuracy	10.423983094334586	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
accuracy	35.56599767732268	#s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))
accuracy	0.0	(neg.f64 eps)
accuracy	0.0078125	(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
accuracy	10.423983094334586	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
accuracy	11.532091470468826	#s(approx (- (* x x) eps) (neg.f64 eps))
accuracy	0.0	(*.f64 x x)
accuracy	0.0078125	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.0234375	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy	0.2890625	(/.f64 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))

Samples

60.0ms	66×	1	valid
50.0ms	131×	0	valid
14.0ms	45×	1	exit
6.0ms	14×	2	exit

Compiler

Compiled 219 to 24 computations (89% saved)

Precisions

Click to see histograms. Total time spent on operations: 81.0ms

ival-add: 44.0ms (54.4% of total)

adjust: 12.0ms (14.8% of total)

ival-div: 8.0ms (9.9% of total)

ival-mult: 6.0ms (7.4% of total)

ival-sub: 6.0ms (7.4% of total)

ival-sqrt: 3.0ms (3.7% of total)

ival-neg: 2.0ms (2.5% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series55.0ms (0.7%)

Memory

-17.3MiB live, 30.7MiB allocated

Counts

21 → 107

Calls

Call 1

Inputs
(-.f64 (.f64 x x) (.f64 x x))
(+.f64 eps (-.f64 (.f64 x x) (.f64 x x)))
(/.f64 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(*.f64 x x)
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
#s(approx (- (* x x) eps) (neg.f64 eps))
(neg.f64 eps)
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
(/.f64 eps x)
(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))))
(/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))))
(-.f64 (*.f64 x x) eps)
(fma.f64 (neg.f64 x) x (fma.f64 x x eps))
(/.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(neg.f64 x)
(fma.f64 x x eps)
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))

Outputs
0
eps
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(pow x 2)
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* (sqrt eps) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(* -1 eps)
(- (pow x 2) eps)
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/ eps x)
(* -1 x)
(+ eps (pow x 2))
(+ x (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (/ eps (pow x 2))))
(* 2 x)
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(+ (* -1 eps) (pow x 2))
(+ (* -1 (pow x 2)) (pow x 2))
(+ eps (+ (* -1 (pow x 2)) (pow x 2)))
(* 1/2 (/ (+ (* -1 (pow x 2)) (pow x 2)) x))
(+ (* 1/2 (/ (+ (* -1 (pow x 2)) (pow x 2)) x)) (* eps (- (* 1/2 (/ 1 x)) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3))))))
(+ (* 1/2 (/ (+ (* -1 (pow x 2)) (pow x 2)) x)) (* eps (- (+ (* -1 (* eps (+ (* -1/4 (/ (- (* 1/2 (/ 1 x)) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3)))) (pow x 2))) (* -1/32 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 5)))))) (* 1/2 (/ 1 x))) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3))))))
(+ (* 1/2 (/ (+ (* -1 (pow x 2)) (pow x 2)) x)) (* eps (- (+ (* 1/2 (/ 1 x)) (* eps (- (* -1 (* eps (+ (* -1/16 (/ (- (* 1/2 (/ 1 x)) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3)))) (pow x 4))) (+ (* -1/64 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 7))) (* 1/4 (/ (+ (* -1/4 (/ (- (* 1/2 (/ 1 x)) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3)))) (pow x 2))) (* -1/32 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 5)))) (pow x 2))))))) (+ (* -1/4 (/ (- (* 1/2 (/ 1 x)) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3)))) (pow x 2))) (* -1/32 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 5))))))) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3))))))
(+ (* -1/2 (/ eps x)) (* 2 x))
(+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* eps (+ 1 (+ (* -1 (/ (pow x 2) eps)) (/ (pow x 2) eps))))
(- (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (sqrt -1)))) (pow eps 2))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (sqrt -1))))) (sqrt -1)))) (* 1/2 (/ (* eps (* (pow x 2) (- (* (sqrt eps) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2))))) (pow (sqrt -1) 2)))) (pow eps 3))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (sqrt -1))) (/ x (pow (sqrt -1) 2)))))
(* eps (+ 1 (/ (pow x 2) eps)))
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (- (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps)) 1)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (+ (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x))))))) (* eps x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x)))))))))) (* -1/2 (* (pow x 2) (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x))))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x))))))) eps)) (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2))))) (* eps x)) eps)))
(* -1 (* eps (- (* -1 (/ (pow x 2) eps)) 1)))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))

Calls

6 calls:

Time	Variable		Point	Expression
43.0ms	x	@	-inf	((- (* x x) (* x x)) (+ eps (- (* x x) (* x x))) (/ (+ eps (- (* x x) (* x x))) (+ (sqrt (- (* x x) eps)) x)) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (/ eps x) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (- (* x x) eps) (+ (* (neg x) x) (+ (* x x) eps)) (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (neg x) (+ (* x x) eps) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)))
3.0ms	eps	@	-inf	((- (* x x) (* x x)) (+ eps (- (* x x) (* x x))) (/ (+ eps (- (* x x) (* x x))) (+ (sqrt (- (* x x) eps)) x)) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (/ eps x) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (- (* x x) eps) (+ (* (neg x) x) (+ (* x x) eps)) (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (neg x) (+ (* x x) eps) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)))
3.0ms	eps	@	inf	((- (* x x) (* x x)) (+ eps (- (* x x) (* x x))) (/ (+ eps (- (* x x) (* x x))) (+ (sqrt (- (* x x) eps)) x)) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (/ eps x) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (- (* x x) eps) (+ (* (neg x) x) (+ (* x x) eps)) (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (neg x) (+ (* x x) eps) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)))
2.0ms	eps	@	0	((- (* x x) (* x x)) (+ eps (- (* x x) (* x x))) (/ (+ eps (- (* x x) (* x x))) (+ (sqrt (- (* x x) eps)) x)) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (/ eps x) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (- (* x x) eps) (+ (* (neg x) x) (+ (* x x) eps)) (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (neg x) (+ (* x x) eps) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)))
1.0ms	x	@	0	((- (* x x) (* x x)) (+ eps (- (* x x) (* x x))) (/ (+ eps (- (* x x) (* x x))) (+ (sqrt (- (* x x) eps)) x)) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (+ (* (/ eps x) -1/2) x) (/ eps x) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (- (* x x) eps) (+ (* (neg x) x) (+ (* x x) eps)) (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (neg x) (+ (* x x) eps) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)))

simplify1.0s (11.9%)

Memory

1.5MiB live, 215.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	559	2788
1	1788	2500
2	6547	2238
0	8501	2103

Stop Event

1×	iter limit
1×	node limit

Counts

107 → 105

Calls

Call 1

Inputs
0
eps
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(pow x 2)
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* (sqrt eps) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(* -1 eps)
(- (pow x 2) eps)
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/ eps x)
(* -1 x)
(+ eps (pow x 2))
(+ x (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (/ eps (pow x 2))))
(* 2 x)
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(+ (* -1 eps) (pow x 2))
(+ (* -1 (pow x 2)) (pow x 2))
(+ eps (+ (* -1 (pow x 2)) (pow x 2)))
(* 1/2 (/ (+ (* -1 (pow x 2)) (pow x 2)) x))
(+ (* 1/2 (/ (+ (* -1 (pow x 2)) (pow x 2)) x)) (* eps (- (* 1/2 (/ 1 x)) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3))))))
(+ (* 1/2 (/ (+ (* -1 (pow x 2)) (pow x 2)) x)) (* eps (- (+ (* -1 (* eps (+ (* -1/4 (/ (- (* 1/2 (/ 1 x)) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3)))) (pow x 2))) (* -1/32 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 5)))))) (* 1/2 (/ 1 x))) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3))))))
(+ (* 1/2 (/ (+ (* -1 (pow x 2)) (pow x 2)) x)) (* eps (- (+ (* 1/2 (/ 1 x)) (* eps (- (* -1 (* eps (+ (* -1/16 (/ (- (* 1/2 (/ 1 x)) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3)))) (pow x 4))) (+ (* -1/64 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 7))) (* 1/4 (/ (+ (* -1/4 (/ (- (* 1/2 (/ 1 x)) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3)))) (pow x 2))) (* -1/32 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 5)))) (pow x 2))))))) (+ (* -1/4 (/ (- (* 1/2 (/ 1 x)) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3)))) (pow x 2))) (* -1/32 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 5))))))) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3))))))
(+ (* -1/2 (/ eps x)) (* 2 x))
(+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* eps (+ 1 (+ (* -1 (/ (pow x 2) eps)) (/ (pow x 2) eps))))
(- (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (sqrt -1)))) (pow eps 2))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (sqrt -1))))) (sqrt -1)))) (* 1/2 (/ (* eps (* (pow x 2) (- (* (sqrt eps) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2))))) (pow (sqrt -1) 2)))) (pow eps 3))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (sqrt -1))) (/ x (pow (sqrt -1) 2)))))
(* eps (+ 1 (/ (pow x 2) eps)))
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (- (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps)) 1)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (+ (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x))))))) (* eps x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x)))))))))) (* -1/2 (* (pow x 2) (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x))))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x))))))) eps)) (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2))))) (* eps x)) eps)))
(* -1 (* eps (- (* -1 (/ (pow x 2) eps)) 1)))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))

Outputs
0
#s(literal 0 binary64)
eps
(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) x)
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(fma.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1 binary64)) x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) eps))) x (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))) x #s(literal 1 binary64)) x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(pow x 2)
(*.f64 x x)
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps))
(- x (* (sqrt eps) (sqrt -1)))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) x)
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) x))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (neg.f64 x) (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64))) (.f64 x x) x))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 (.f64 (neg.f64 x) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 x (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) #s(literal 1/16 binary64) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/8 binary64))) (.f64 x x) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(* -1 eps)
(neg.f64 eps)
(- (pow x 2) eps)
(fma.f64 x x (neg.f64 eps))
(* -1/2 (/ eps x))
(*.f64 (/.f64 eps x) #s(literal -1/2 binary64))
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/.f64 (fma.f64 #s(literal -1/2 binary64) eps (*.f64 x x)) x)
(/ eps x)
(/.f64 eps x)
(* -1 x)
(neg.f64 x)
(+ eps (pow x 2))
(fma.f64 x x eps)
(+ x (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) x)
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) x))
(+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 (.f64 (neg.f64 x) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) x #s(literal 1 binary64)) x (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(* 1/2 (/ eps x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/.f64 (fma.f64 (/.f64 (.f64 eps eps) x) (/.f64 #s(literal 1/8 binary64) x) (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (.f64 #s(literal 1/2 binary64) eps))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(/.f64 (fma.f64 #s(literal -1 binary64) (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 #s(literal -1/8 binary64) x) (/.f64 (.f64 eps eps) x) (.f64 #s(literal -1/2 binary64) eps))) (*.f64 (pow.f64 eps #s(literal 3 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64))))) x)
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/.f64 (fma.f64 (/.f64 (.f64 eps eps) x) (/.f64 #s(literal 1/8 binary64) x) (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (.f64 #s(literal 1/2 binary64) eps))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
(/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal 5/64 binary64) (pow.f64 x #s(literal 6 binary64))) eps) (.f64 (/.f64 (.f64 eps eps) x) (/.f64 #s(literal 1/8 binary64) x))) (/.f64 (*.f64 #s(literal -1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 4 binary64)))) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(.f64 (fma.f64 (.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 binary64)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 1 binary64))) x)
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(fma.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 eps x) (fma.f64 (.f64 eps eps) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 #s(literal -1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 6 binary64))))) x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 eps x) x)) x) x)
(* (pow x 2) (+ 1 (/ eps (pow x 2))))
(*.f64 x (fma.f64 (/.f64 (/.f64 eps x) x) x x))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(.f64 (fma.f64 (.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 binary64)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 2 binary64))) x)
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(.f64 (+.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 2 binary64)) (fma.f64 (.f64 eps eps) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 6 binary64))))) x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 eps x) #s(literal -2 binary64)) (neg.f64 x))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(.f64 (fma.f64 (.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 binary64)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 2 binary64))) x)
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
(.f64 (+.f64 (/.f64 (fma.f64 (/.f64 (.f64 #s(literal 5/64 binary64) (pow.f64 eps #s(literal 4 binary64))) eps) #s(literal -2 binary64) (fma.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/8 binary64)) #s(literal -1/4 binary64) (.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 3 binary64))))) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (*.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 binary64)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 2 binary64)))) x)
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(.f64 (fma.f64 (.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/8 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 eps x) #s(literal -2 binary64))) (neg.f64 x))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/16 binary64) (-.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 eps x) #s(literal -2 binary64)) (.f64 (*.f64 eps eps) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64)))))) (neg.f64 x))
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (neg.f64 x))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(.f64 (fma.f64 (.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 binary64)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (neg.f64 x))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(neg.f64 (fma.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 eps x) (fma.f64 (.f64 eps eps) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 #s(literal -1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 6 binary64))))) x x))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(fma.f64 (*.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/2 binary64)) (neg.f64 x) x)
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(* eps (+ 1 (+ (* -1 (/ (pow x 2) eps)) (/ (pow x 2) eps))))
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(* eps (+ 1 (/ (pow x 2) eps)))
(*.f64 (fma.f64 x (/.f64 x eps) #s(literal 1 binary64)) eps)
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
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(.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) #s(literal 1/2 binary64)) (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) (neg.f64 eps))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))))) (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) #s(literal 1/2 binary64)) (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))) (neg.f64 eps))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/16 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))) (pow.f64 x #s(literal 6 binary64))) (.f64 #s(literal -1/8 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) #s(literal 1/2 binary64)) (*.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))) (neg.f64 eps))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x (/.f64 x eps))) (neg.f64 eps))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(-.f64 x (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
(* -1 (* eps (- (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps)) 1)))
eps
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x)) eps)))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) x)
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (+ (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x))))))) (* eps x)) eps)))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (-.f64 (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) x) (.f64 (neg.f64 x) eps) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 eps)) (.f64 x x)))) eps) x)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x)))))))))) (* -1/2 (* (pow x 2) (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x))))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x))))))) eps)) (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2))))) (* eps x)) eps)))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (-.f64 (/.f64 (/.f64 (fma.f64 (/.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) eps) #s(literal -1 binary64)) #s(literal -1/2 binary64) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) #s(literal -1/2 binary64)) (.f64 x x) (.f64 (.f64 (sqrt.f64 eps) x) (.f64 (neg.f64 x) eps)))) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) #s(literal -1 binary64)))) (neg.f64 eps)) eps) x)))
(* -1 (* eps (- (* -1 (/ (pow x 2) eps)) 1)))
(fma.f64 (/.f64 (*.f64 (neg.f64 x) x) eps) (neg.f64 eps) eps)
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(-.f64 x (.f64 (.f64 eps (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/2 binary64)) x) (neg.f64 eps))) (neg.f64 eps))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 x (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal -1/8 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (sqrt.f64 eps) x) x)))) eps)) (neg.f64 eps))) (neg.f64 eps))

rewrite1.5s (17.5%)

Memory

3.4MiB live, 195.8MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	186
0	49	158
1	216	150
2	1683	150
0	8641	150

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

21 → 917

Calls

Call 1

Inputs
(-.f64 (.f64 x x) (.f64 x x))
(+.f64 eps (-.f64 (.f64 x x) (.f64 x x)))
(/.f64 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(*.f64 x x)
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
#s(approx (- (* x x) eps) (neg.f64 eps))
(neg.f64 eps)
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
#s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
(/.f64 eps x)
(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))))
(/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))))
(-.f64 (*.f64 x x) eps)
(fma.f64 (neg.f64 x) x (fma.f64 x x eps))
(/.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(neg.f64 x)
(fma.f64 x x eps)
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))

Outputs
#s(literal 0 binary64)
(*.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) eps))
(.f64 (/.f64 eps (+.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (/.f64 eps (pow.f64 (fma.f64 (fma.f64 x x eps) (-.f64 (fma.f64 x x eps) (.f64 (neg.f64 x) x)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))))
(*.f64 (/.f64 eps (pow.f64 eps #s(literal 3 binary64))) (/.f64 eps (pow.f64 eps #s(literal -2 binary64))))
(*.f64 (/.f64 eps eps) eps)
(.f64 (/.f64 eps (.f64 eps (neg.f64 eps))) (/.f64 eps (pow.f64 (neg.f64 eps) #s(literal -1 binary64))))
(.f64 (/.f64 eps (.f64 eps eps)) (/.f64 eps (pow.f64 eps #s(literal -1 binary64))))
(.f64 (.f64 eps (neg.f64 eps)) (pow.f64 (neg.f64 eps) #s(literal -1 binary64)))
(.f64 (+.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (fma.f64 (fma.f64 x x eps) (-.f64 (fma.f64 x x eps) (.f64 (neg.f64 x) x)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))
(.f64 (.f64 eps eps) (pow.f64 eps #s(literal -1 binary64)))
(*.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 eps #s(literal -2 binary64)))
(*.f64 eps (/.f64 eps eps))
(pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 eps (*.f64 eps eps)) #s(literal -1 binary64))
(pow.f64 (/.f64 (neg.f64 eps) (*.f64 eps (neg.f64 eps))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (fma.f64 x x eps) (-.f64 (fma.f64 x x eps) (*.f64 (neg.f64 x) x)) (pow.f64 x #s(literal 4 binary64))) (+.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) #s(literal -1 binary64))
(pow.f64 eps #s(literal 1 binary64))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (neg.f64 eps)) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (neg.f64 eps)) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (neg.f64 eps)) (/.f64 (pow.f64 x #s(literal 4 binary64)) (neg.f64 eps)) (fma.f64 (/.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (neg.f64 eps)) (/.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (neg.f64 eps)) (*.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (neg.f64 eps)) (/.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (neg.f64 eps))))))
(/.f64 (-.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 0 binary64) eps) #s(literal 3 binary64))) (fma.f64 eps eps (fma.f64 (/.f64 #s(literal 0 binary64) eps) (/.f64 #s(literal 0 binary64) eps) (*.f64 eps (/.f64 #s(literal 0 binary64) eps)))))
(/.f64 (+.f64 (pow.f64 (fma.f64 (neg.f64 x) x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (fma.f64 (neg.f64 x) x eps) (fma.f64 (neg.f64 x) x eps) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (fma.f64 (neg.f64 x) x eps) (.f64 x x)))))
(/.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (+.f64 eps (.f64 (neg.f64 x) x)) #s(literal 3 binary64))) (+.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 (+.f64 eps (.f64 (neg.f64 x) x)) (+.f64 eps (.f64 (neg.f64 x) x))) (.f64 (.f64 x x) (+.f64 eps (*.f64 (neg.f64 x) x))))))
(/.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 eps (.f64 x x)) #s(literal 3 binary64))) (+.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 (-.f64 eps (.f64 x x)) (-.f64 eps (.f64 x x))) (.f64 (.f64 x x) (-.f64 eps (*.f64 x x))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (+.f64 (fma.f64 x x eps) (*.f64 x x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (-.f64 (fma.f64 x x eps) (*.f64 (neg.f64 x) x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (+.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (+.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (fma.f64 x x eps) (.f64 x x))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 0 binary64))) (neg.f64 (*.f64 eps eps)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps))) (neg.f64 (neg.f64 eps)))
(/.f64 (neg.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64))) (neg.f64 (neg.f64 (*.f64 eps eps))))
(/.f64 (neg.f64 (neg.f64 (*.f64 eps (neg.f64 eps)))) (neg.f64 (neg.f64 (neg.f64 eps))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))) (neg.f64 (neg.f64 (fma.f64 (fma.f64 x x eps) (-.f64 (fma.f64 x x eps) (*.f64 (neg.f64 x) x)) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (neg.f64 (neg.f64 (*.f64 eps eps))) (neg.f64 (neg.f64 eps)))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (neg.f64 eps)) (.f64 (neg.f64 eps) (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)))) (*.f64 eps eps))
(/.f64 (-.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 eps eps)) eps) (.f64 (neg.f64 eps) #s(literal 0 binary64))) (.f64 (neg.f64 eps) eps))
(/.f64 (-.f64 (.f64 (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) eps) (.f64 (+.f64 (fma.f64 x x eps) (.f64 x x)) #s(literal 0 binary64))) (.f64 (+.f64 (fma.f64 x x eps) (*.f64 x x)) eps))
(/.f64 (-.f64 (.f64 (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) eps) (.f64 (-.f64 (fma.f64 x x eps) (.f64 (neg.f64 x) x)) #s(literal 0 binary64))) (.f64 (-.f64 (fma.f64 x x eps) (*.f64 (neg.f64 x) x)) eps))
(/.f64 (-.f64 (.f64 (neg.f64 (.f64 eps eps)) eps) (.f64 (neg.f64 eps) #s(literal 0 binary64))) (.f64 (neg.f64 eps) eps))
(/.f64 (-.f64 (.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) eps) (.f64 (neg.f64 (.f64 eps eps)) #s(literal 0 binary64))) (.f64 (neg.f64 (*.f64 eps eps)) eps))
(/.f64 (-.f64 (.f64 (-.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 0 binary64)) eps) (.f64 (*.f64 eps eps) #s(literal 0 binary64))) (pow.f64 eps #s(literal 3 binary64)))
(/.f64 (-.f64 (.f64 (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) eps) (.f64 (+.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (+.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (fma.f64 x x eps) (.f64 x x)))) #s(literal 0 binary64))) (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))
(/.f64 (-.f64 (.f64 (neg.f64 (.f64 eps (neg.f64 eps))) eps) (.f64 (neg.f64 (neg.f64 eps)) #s(literal 0 binary64))) (.f64 (neg.f64 (neg.f64 eps)) eps))
(/.f64 (-.f64 (.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) eps) (.f64 (neg.f64 (fma.f64 (fma.f64 x x eps) (-.f64 (fma.f64 x x eps) (.f64 (neg.f64 x) x)) (pow.f64 x #s(literal 4 binary64)))) #s(literal 0 binary64))) (.f64 (neg.f64 (fma.f64 (fma.f64 x x eps) (-.f64 (fma.f64 x x eps) (*.f64 (neg.f64 x) x)) (pow.f64 x #s(literal 4 binary64)))) eps))
(/.f64 (-.f64 (.f64 (.f64 eps (neg.f64 eps)) eps) (.f64 (neg.f64 eps) #s(literal 0 binary64))) (.f64 (neg.f64 eps) eps))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) eps) (.f64 (/.f64 eps (.f64 eps eps)) #s(literal 0 binary64))) (.f64 (/.f64 eps (*.f64 eps eps)) eps))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) eps) (.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 0 binary64))) (*.f64 (pow.f64 eps #s(literal -1 binary64)) eps))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) eps) (.f64 (/.f64 (neg.f64 eps) (.f64 eps (neg.f64 eps))) #s(literal 0 binary64))) (.f64 (/.f64 (neg.f64 eps) (*.f64 eps (neg.f64 eps))) eps))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) eps) (.f64 (/.f64 (fma.f64 (fma.f64 x x eps) (-.f64 (fma.f64 x x eps) (.f64 (neg.f64 x) x)) (pow.f64 x #s(literal 4 binary64))) (+.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) #s(literal 0 binary64))) (.f64 (/.f64 (fma.f64 (fma.f64 x x eps) (-.f64 (fma.f64 x x eps) (*.f64 (neg.f64 x) x)) (pow.f64 x #s(literal 4 binary64))) (+.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) eps))
(/.f64 (-.f64 (.f64 (+.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) eps) (.f64 (+.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 (neg.f64 x) x) (fma.f64 x x eps)))) #s(literal 0 binary64))) (+.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))
(/.f64 (-.f64 (.f64 (+.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) eps) (.f64 (fma.f64 (fma.f64 x x eps) (-.f64 (fma.f64 x x eps) (*.f64 (neg.f64 x) x)) (pow.f64 x #s(literal 4 binary64))) #s(literal 0 binary64))) (+.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))
(/.f64 (-.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) eps) (.f64 (*.f64 eps eps) #s(literal 0 binary64))) (pow.f64 eps #s(literal 3 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (neg.f64 eps))
(/.f64 (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (+.f64 (fma.f64 x x eps) (*.f64 x x)))
(/.f64 (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (fma.f64 x x eps) (*.f64 (neg.f64 x) x)))
(/.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 eps))
(/.f64 (-.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 0 binary64)) (*.f64 eps eps))
(/.f64 (-.f64 (pow.f64 (fma.f64 x x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)) (+.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (fma.f64 x x eps) (.f64 x x)))))
(/.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (neg.f64 (*.f64 eps eps)))
(/.f64 (neg.f64 (*.f64 eps (neg.f64 eps))) (neg.f64 (neg.f64 eps)))
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(/.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(/.f64 (neg.f64 (-.f64 (-.f64 (.f64 x x) eps) (.f64 x x))) (neg.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (neg.f64 (+.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x x (-.f64 (-.f64 (.f64 x x) eps) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))))
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(/.f64 (-.f64 (-.f64 (.f64 x x) eps) (.f64 x x)) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (-.f64 (.f64 x x) eps) (*.f64 x x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) eps)) (+.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))))))
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(fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) x)
(fma.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)))) (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(fma.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps))) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(fma.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) #s(literal 1/2 binary64)) (pow.f64 (fma.f64 eps (-.f64 eps (.f64 x x)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64)) x)
(fma.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64)) x)
(fma.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps))) (sqrt.f64 (pow.f64 (fma.f64 x x eps) #s(literal -1 binary64))) x)
(fma.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps))) (pow.f64 (pow.f64 (fma.f64 x x eps) #s(literal -1 binary64)) #s(literal 1/2 binary64)) x)
(fma.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 (pow.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))) x)
(fma.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (pow.f64 (pow.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64)) x)
(-.f64 (/.f64 (.f64 x x) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (/.f64 (-.f64 (.f64 x x) eps) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))))
(-.f64 (/.f64 (-.f64 (.f64 x x) eps) (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (/.f64 (.f64 x x) (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 (fma.f64 eps (-.f64 eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)))) (sqrt.f64 (-.f64 (.f64 x x) eps)))
(.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps))) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (.f64 x x) eps)))
(.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) #s(literal 1/2 binary64)) (pow.f64 (fma.f64 eps (-.f64 eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps))) (sqrt.f64 (pow.f64 (fma.f64 x x eps) #s(literal -1 binary64))))
(.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps))) (pow.f64 (pow.f64 (fma.f64 x x eps) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 (pow.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (pow.f64 (pow.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
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(/.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)))) (neg.f64 (sqrt.f64 (fma.f64 x x eps))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (neg.f64 (sqrt.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)))) (sqrt.f64 (neg.f64 (fma.f64 x x eps))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps))) (sqrt.f64 (-.f64 (.f64 x x) (neg.f64 eps))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps))) (sqrt.f64 (fma.f64 x x eps)))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 eps eps) (.f64 (*.f64 x x) (neg.f64 eps))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (fma.f64 x x eps) (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))))))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(fabs.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))

eval347.0ms (4.1%)

Memory: -5.1MiB live, 233.6MiB allocated
Compiler: Compiled 37 360 to 3 752 computations (90% saved)

prune103.0ms (1.2%)

Memory

-19.4MiB live, 56.4MiB allocated

Pruning

12 alts after pruning (7 fresh and 5 done)

	Pruned	Kept	Total
New	1 163	4	1 167
Fresh	1	3	4
Picked	3	2	5
Done	1	3	4
Total	1 168	12	1 180

Accuracy

100.0%

Counts

1 180 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	45.8%	(/.f64 (.f64 eps eps) (.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps))
▶	99.5%	(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
	99.3%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps))
✓	62.2%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	58.5%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓	6.7%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
✓	3.5%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
▶	4.2%	#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(literal 0 binary64))
▶	43.9%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
▶	43.7%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 #s(literal 1/2 binary64) eps))))
✓	43.7%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
	41.5%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(approx (+ ( (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps))

Compiler

Compiled 321 to 220 computations (31.5% saved)

simplify181.0ms (2.1%)

Memory

24.1MiB live, 146.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
cost-diff	0	(.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) eps)
cost-diff	0	(*.f64 eps eps)
cost-diff	4	(/.f64 (.f64 eps eps) (.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) eps)
cost-diff	0	(/.f64 x (*.f64 #s(literal 1/2 binary64) eps))
cost-diff	0	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 #s(literal 1/2 binary64) eps))))
cost-diff	2	(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) eps)
cost-diff	0	(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
cost-diff	0	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
cost-diff	0	#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(literal 0 binary64))
cost-diff	0	(sqrt.f64 (-.f64 (*.f64 x x) eps))
cost-diff	0	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
cost-diff	0	#s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps)
cost-diff	0	(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	31	190
0	45	186
1	75	178
2	131	173
3	193	155
4	417	155
5	1774	155
6	6753	155
0	8269	155

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Calls

Call 1

Inputs
(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
#s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps)
eps
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
x
#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(literal 0 binary64))
#s(literal 0 binary64)
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
eps
x
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 #s(literal 1/2 binary64) eps))))
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
#s(literal 1 binary64)
(/.f64 x (*.f64 #s(literal 1/2 binary64) eps))
x
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
eps
(/.f64 (.f64 eps eps) (.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps))
(*.f64 eps eps)
eps
(.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) eps)
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
x

Outputs
(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
#s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps)
eps
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
x
#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(literal 0 binary64))
#s(literal 0 binary64)
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
eps
x
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
#s(literal 1 binary64)
(/.f64 x (*.f64 #s(literal 1/2 binary64) eps))
x
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
eps
(/.f64 (.f64 eps eps) (.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps))
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(*.f64 eps eps)
eps
(.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) eps)
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
x

localize85.0ms (1%)

Memory

-4.5MiB live, 156.7MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.03125	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy	0.125	(.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) eps)
accuracy	34.44771662130934	(/.f64 (.f64 eps eps) (.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps))
accuracy	0.0	(/.f64 x (*.f64 #s(literal 1/2 binary64) eps))
accuracy	0.0	(*.f64 #s(literal 1/2 binary64) eps)
accuracy	0.26953125	(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
accuracy	35.914051382705765	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 #s(literal 1/2 binary64) eps))))
accuracy	0.0	(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
accuracy	0.0	(*.f64 #s(literal 1/2 binary64) eps)
accuracy	35.914051382705765	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
accuracy	61.291709367800934	#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(literal 0 binary64))
accuracy	0.00390625	(-.f64 (*.f64 x x) eps)
accuracy	0.0078125	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.03125	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy	0.2890625	(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))

Samples

29.0ms	84×	1	valid
24.0ms	154×	0	valid
7.0ms	18×	2	valid

Compiler

Compiled 172 to 24 computations (86% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-div: 9.0ms (24.9% of total)

ival-mult: 9.0ms (24.9% of total)

ival-add: 5.0ms (13.8% of total)

adjust: 4.0ms (11.1% of total)

ival-sub: 3.0ms (8.3% of total)

ival-sqrt: 3.0ms (8.3% of total)

ival-neg: 1.0ms (2.8% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series16.0ms (0.2%)

Memory

-3.1MiB live, 35.6MiB allocated

Counts

15 → 121

Calls

Call 1

Inputs
(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
#s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps)
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(literal 0 binary64))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(*.f64 #s(literal 1/2 binary64) eps)
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 #s(literal 1/2 binary64) eps))))
(/.f64 x (*.f64 #s(literal 1/2 binary64) eps))
(/.f64 (.f64 eps eps) (.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps))
(*.f64 eps eps)
(.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) eps)
(-.f64 (*.f64 x x) eps)

Outputs
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
eps
(* (sqrt eps) (sqrt -1))
(+ x (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* 1/2 (/ eps x))
(* 2 (/ x eps))
(* (sqrt (pow eps 3)) (sqrt -1))
(+ (* eps x) (* (sqrt (pow eps 3)) (sqrt -1)))
(+ (* x (+ eps (* 1/2 (* (sqrt eps) (/ x (sqrt -1)))))) (* (sqrt (pow eps 3)) (sqrt -1)))
(+ (* x (+ eps (* x (+ (* -1/8 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt eps) (/ 1 (sqrt -1)))))))) (* (sqrt (pow eps 3)) (sqrt -1)))
(* -1 eps)
(- (pow x 2) eps)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(* 2 x)
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
(* 2 (* eps x))
(* x (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 2 eps)))
(* x (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (+ (* -1/8 (/ (pow eps 3) (pow x 4))) (* 2 eps))))
(* x (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (+ (* -1/8 (/ (pow eps 3) (pow x 4))) (+ (* -1/16 (/ (pow eps 4) (pow x 6))) (* 2 eps)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* 1/2 (/ (pow eps 2) x))
(* -1 (/ (+ (* -1/2 (pow eps 2)) (* -1/8 (/ (pow eps 3) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 (pow eps 2)) (+ (* -1/8 (/ (pow eps 3) (pow x 2))) (* -1/16 (/ (pow eps 4) (pow x 4))))) x))
(* -1 (/ (+ (* -1/2 (/ (* eps (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4)))) (pow x 6))) (+ (* -1/2 (pow eps 2)) (+ (* -1/8 (/ (pow eps 3) (pow x 2))) (* -1/16 (/ (pow eps 4) (pow x 4)))))) x))
(* 1/2 (/ (+ (* -1 (pow x 2)) (pow x 2)) x))
(+ (* 1/2 (/ (+ (* -1 (pow x 2)) (pow x 2)) x)) (* eps (- (* 1/2 (/ 1 x)) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3))))))
(+ (* 1/2 (/ (+ (* -1 (pow x 2)) (pow x 2)) x)) (* eps (- (+ (* -1 (* eps (+ (* -1/4 (/ (- (* 1/2 (/ 1 x)) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3)))) (pow x 2))) (* -1/32 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 5)))))) (* 1/2 (/ 1 x))) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3))))))
(+ (* 1/2 (/ (+ (* -1 (pow x 2)) (pow x 2)) x)) (* eps (- (+ (* 1/2 (/ 1 x)) (* eps (- (* -1 (* eps (+ (* -1/16 (/ (- (* 1/2 (/ 1 x)) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3)))) (pow x 4))) (+ (* -1/64 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 7))) (* 1/4 (/ (+ (* -1/4 (/ (- (* 1/2 (/ 1 x)) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3)))) (pow x 2))) (* -1/32 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 5)))) (pow x 2))))))) (+ (* -1/4 (/ (- (* 1/2 (/ 1 x)) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3)))) (pow x 2))) (* -1/32 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 5))))))) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3))))))
(+ (* -1 (pow x 2)) (pow x 2))
(+ eps (+ (* -1 (pow x 2)) (pow x 2)))
(+ (* -1/2 (/ eps x)) (* 2 x))
(+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* 1/2 eps)
(pow eps 2)
(* eps (+ (* -1/2 (/ eps x)) (* 2 x)))
(* eps (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
(* eps (+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
(+ (* -1 eps) (pow x 2))
(- (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (sqrt -1)))) (pow eps 2))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (sqrt -1))))) (sqrt -1)))) (* 1/2 (/ (* eps (* (pow x 2) (- (* (sqrt eps) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2))))) (pow (sqrt -1) 2)))) (pow eps 3))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (sqrt -1))) (/ x (pow (sqrt -1) 2)))))
(* eps (+ 1 (+ (* -1 (/ (pow x 2) eps)) (/ (pow x 2) eps))))
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(* (pow eps 2) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(* (pow eps 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
(* (pow eps 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
(* eps (- (/ (pow x 2) eps) 1))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (+ (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x))))))) (* eps x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x)))))))))) (* -1/2 (* (pow x 2) (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x))))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x))))))) eps)) (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2))))) (* eps x)) eps)))
(* -1 (* eps (- (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps)) 1)))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))
(* -1 (* (sqrt (pow eps 3)) (sqrt -1)))
(* (pow eps 2) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (/ x eps)))
(* (pow eps 2) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ (+ (* -1 x) (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps))))
(* (pow eps 2) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ (+ (* -1 x) (* -1 (/ (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1))))) eps))) eps))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	eps	@	-inf	((/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (- x (sqrt (- (* x x) eps))) (/ (* 1/2 eps) x) (* 1/2 eps) (/ 1 (/ x (* 1/2 eps))) (- x (sqrt (- (* x x) eps))) (/ x (* 1/2 eps)) (/ (* eps eps) (* (+ (sqrt (- (* x x) eps)) x) eps)) (* eps eps) (* (+ (sqrt (- (* x x) eps)) x) eps) (- (* x x) eps))
2.0ms	eps	@	inf	((/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (- x (sqrt (- (* x x) eps))) (/ (* 1/2 eps) x) (* 1/2 eps) (/ 1 (/ x (* 1/2 eps))) (- x (sqrt (- (* x x) eps))) (/ x (* 1/2 eps)) (/ (* eps eps) (* (+ (sqrt (- (* x x) eps)) x) eps)) (* eps eps) (* (+ (sqrt (- (* x x) eps)) x) eps) (- (* x x) eps))
2.0ms	x	@	0	((/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (- x (sqrt (- (* x x) eps))) (/ (* 1/2 eps) x) (* 1/2 eps) (/ 1 (/ x (* 1/2 eps))) (- x (sqrt (- (* x x) eps))) (/ x (* 1/2 eps)) (/ (* eps eps) (* (+ (sqrt (- (* x x) eps)) x) eps)) (* eps eps) (* (+ (sqrt (- (* x x) eps)) x) eps) (- (* x x) eps))
2.0ms	eps	@	0	((/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (- x (sqrt (- (* x x) eps))) (/ (* 1/2 eps) x) (* 1/2 eps) (/ 1 (/ x (* 1/2 eps))) (- x (sqrt (- (* x x) eps))) (/ x (* 1/2 eps)) (/ (* eps eps) (* (+ (sqrt (- (* x x) eps)) x) eps)) (* eps eps) (* (+ (sqrt (- (* x x) eps)) x) eps) (- (* x x) eps))
2.0ms	x	@	-inf	((/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (- x (sqrt (- (* x x) eps))) (/ (* 1/2 eps) x) (* 1/2 eps) (/ 1 (/ x (* 1/2 eps))) (- x (sqrt (- (* x x) eps))) (/ x (* 1/2 eps)) (/ (* eps eps) (* (+ (sqrt (- (* x x) eps)) x) eps)) (* eps eps) (* (+ (sqrt (- (* x x) eps)) x) eps) (- (* x x) eps))

simplify163.0ms (1.9%)

Memory

1.5MiB live, 241.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	613	3269
1	2009	2956
2	7213	2932
0	8062	2766

Stop Event

1×	iter limit
1×	node limit

Counts

121 → 119

Calls

Call 1

Inputs
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
eps
(* (sqrt eps) (sqrt -1))
(+ x (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* 1/2 (/ eps x))
(* 2 (/ x eps))
(* (sqrt (pow eps 3)) (sqrt -1))
(+ (* eps x) (* (sqrt (pow eps 3)) (sqrt -1)))
(+ (* x (+ eps (* 1/2 (* (sqrt eps) (/ x (sqrt -1)))))) (* (sqrt (pow eps 3)) (sqrt -1)))
(+ (* x (+ eps (* x (+ (* -1/8 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt eps) (/ 1 (sqrt -1)))))))) (* (sqrt (pow eps 3)) (sqrt -1)))
(* -1 eps)
(- (pow x 2) eps)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(* 2 x)
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
(* 2 (* eps x))
(* x (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 2 eps)))
(* x (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (+ (* -1/8 (/ (pow eps 3) (pow x 4))) (* 2 eps))))
(* x (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (+ (* -1/8 (/ (pow eps 3) (pow x 4))) (+ (* -1/16 (/ (pow eps 4) (pow x 6))) (* 2 eps)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* 1/2 (/ (pow eps 2) x))
(* -1 (/ (+ (* -1/2 (pow eps 2)) (* -1/8 (/ (pow eps 3) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 (pow eps 2)) (+ (* -1/8 (/ (pow eps 3) (pow x 2))) (* -1/16 (/ (pow eps 4) (pow x 4))))) x))
(* -1 (/ (+ (* -1/2 (/ (* eps (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4)))) (pow x 6))) (+ (* -1/2 (pow eps 2)) (+ (* -1/8 (/ (pow eps 3) (pow x 2))) (* -1/16 (/ (pow eps 4) (pow x 4)))))) x))
(* 1/2 (/ (+ (* -1 (pow x 2)) (pow x 2)) x))
(+ (* 1/2 (/ (+ (* -1 (pow x 2)) (pow x 2)) x)) (* eps (- (* 1/2 (/ 1 x)) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3))))))
(+ (* 1/2 (/ (+ (* -1 (pow x 2)) (pow x 2)) x)) (* eps (- (+ (* -1 (* eps (+ (* -1/4 (/ (- (* 1/2 (/ 1 x)) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3)))) (pow x 2))) (* -1/32 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 5)))))) (* 1/2 (/ 1 x))) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3))))))
(+ (* 1/2 (/ (+ (* -1 (pow x 2)) (pow x 2)) x)) (* eps (- (+ (* 1/2 (/ 1 x)) (* eps (- (* -1 (* eps (+ (* -1/16 (/ (- (* 1/2 (/ 1 x)) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3)))) (pow x 4))) (+ (* -1/64 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 7))) (* 1/4 (/ (+ (* -1/4 (/ (- (* 1/2 (/ 1 x)) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3)))) (pow x 2))) (* -1/32 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 5)))) (pow x 2))))))) (+ (* -1/4 (/ (- (* 1/2 (/ 1 x)) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3)))) (pow x 2))) (* -1/32 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 5))))))) (* -1/8 (/ (+ (* -1 (pow x 2)) (pow x 2)) (pow x 3))))))
(+ (* -1 (pow x 2)) (pow x 2))
(+ eps (+ (* -1 (pow x 2)) (pow x 2)))
(+ (* -1/2 (/ eps x)) (* 2 x))
(+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* 1/2 eps)
(pow eps 2)
(* eps (+ (* -1/2 (/ eps x)) (* 2 x)))
(* eps (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
(* eps (+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
(+ (* -1 eps) (pow x 2))
(- (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (sqrt -1)))) (pow eps 2))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (sqrt -1))))) (sqrt -1)))) (* 1/2 (/ (* eps (* (pow x 2) (- (* (sqrt eps) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2))))) (pow (sqrt -1) 2)))) (pow eps 3))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (+ (* -1 (pow x 2)) (pow x 2)) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (sqrt -1))) (/ x (pow (sqrt -1) 2)))))
(* eps (+ 1 (+ (* -1 (/ (pow x 2) eps)) (/ (pow x 2) eps))))
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(* (pow eps 2) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(* (pow eps 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
(* (pow eps 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
(* eps (- (/ (pow x 2) eps) 1))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (+ (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x))))))) (* eps x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x)))))))))) (* -1/2 (* (pow x 2) (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x))))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x))))))) eps)) (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2))))) (* eps x)) eps)))
(* -1 (* eps (- (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps)) 1)))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))
(* -1 (* (sqrt (pow eps 3)) (sqrt -1)))
(* (pow eps 2) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (/ x eps)))
(* (pow eps 2) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ (+ (* -1 x) (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps))))
(* (pow eps 2) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ (+ (* -1 x) (* -1 (/ (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1))))) eps))) eps))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))

Outputs
(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) x)
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(fma.f64 (fma.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1 binary64)) x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) eps))) x (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))) x #s(literal 1 binary64)) x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
eps
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))
(+ x (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) x)
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (fma.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) x))
(+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 x x) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal -1/8 binary64) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) x #s(literal 1 binary64)) x (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(fma.f64 (fma.f64 (.f64 (/.f64 (.f64 x x) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal -1/8 binary64) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 x (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) #s(literal 1/16 binary64) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/8 binary64))) (.f64 x x) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps))
(- x (* (sqrt eps) (sqrt -1)))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) x)
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) x))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x x) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (.f64 #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) (.f64 x x) x))
(* 1/2 (/ eps x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(* 2 (/ x eps))
(*.f64 (/.f64 x eps) #s(literal 2 binary64))
(* (sqrt (pow eps 3)) (sqrt -1))
(*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64)))
(+ (* eps x) (* (sqrt (pow eps 3)) (sqrt -1)))
(fma.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64)) (*.f64 eps x))
(+ (* x (+ eps (* 1/2 (* (sqrt eps) (/ x (sqrt -1)))))) (* (sqrt (pow eps 3)) (sqrt -1)))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 eps) eps) x (.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64))))
(+ (* x (+ eps (* x (+ (* -1/8 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt eps) (/ 1 (sqrt -1)))))))) (* (sqrt (pow eps 3)) (sqrt -1)))
(fma.f64 (fma.f64 (fma.f64 (.f64 (/.f64 (.f64 x x) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal -1/8 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)))) x eps) x (.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64))))
(* -1 eps)
(neg.f64 eps)
(- (pow x 2) eps)
(fma.f64 x x (neg.f64 eps))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/16 binary64) x) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(/.f64 (-.f64 (-.f64 (.f64 #s(literal 1/2 binary64) eps) (fma.f64 (/.f64 #s(literal -1/8 binary64) x) (.f64 eps (/.f64 eps x)) (/.f64 (.f64 #s(literal -1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 4 binary64))))) (.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 6 binary64))))) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(.f64 (fma.f64 (.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 binary64)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 2 binary64))) x)
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(.f64 (+.f64 (fma.f64 (.f64 eps eps) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 2 binary64))) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(.f64 (fma.f64 (.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 binary64)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 1 binary64))) x)
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(fma.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 eps x) (fma.f64 (.f64 eps eps) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 #s(literal -1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 6 binary64))))) x x)
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/16 binary64) x) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
(/.f64 (fma.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal 5/64 binary64) (pow.f64 x #s(literal 6 binary64)))) #s(literal 1/2 binary64) (-.f64 (.f64 #s(literal 1/2 binary64) eps) (fma.f64 (/.f64 #s(literal -1/8 binary64) x) (.f64 eps (/.f64 eps x)) (/.f64 (.f64 #s(literal -1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 4 binary64)))))) x)
(* 2 (* eps x))
(.f64 (.f64 #s(literal 2 binary64) eps) x)
(* x (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (* 2 eps)))
(.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (.f64 eps (/.f64 eps x)) (*.f64 #s(literal 2 binary64) eps)) x)
(* x (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (+ (* -1/8 (/ (pow eps 3) (pow x 4))) (* 2 eps))))
(.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (.f64 eps (/.f64 eps x)) (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64) (*.f64 #s(literal 2 binary64) eps))) x)
(* x (+ (* -1/2 (/ (pow eps 2) (pow x 2))) (+ (* -1/8 (/ (pow eps 3) (pow x 4))) (+ (* -1/16 (/ (pow eps 4) (pow x 6))) (* 2 eps)))))
(.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1/16 binary64) (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64) (*.f64 #s(literal 2 binary64) eps)))) x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 eps x) x)) x) x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(*.f64 (neg.f64 x) (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/2 binary64) #s(literal -2 binary64)))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
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(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (fma.f64 (.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64))))) #s(literal 1/16 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) eps)
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(*.f64 (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x eps)) eps)
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x eps))) eps)
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (fma.f64 (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) #s(literal 1/8 binary64) (-.f64 (/.f64 x eps) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) eps)
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(-.f64 (+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) x) (.f64 (.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (/.f64 (.f64 x x) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(-.f64 (+.f64 (-.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (.f64 (.f64 (/.f64 (.f64 x x) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal -1/2 binary64))) x) (/.f64 (fma.f64 (.f64 (neg.f64 (sqrt.f64 eps)) x) (.f64 (.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (/.f64 (.f64 x x) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 (/.f64 (.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) eps) eps) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal -1/2 binary64))) (pow.f64 eps #s(literal 3 binary64))))
(* (pow eps 2) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 x eps)) (.f64 eps eps))
(* (pow eps 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 x eps))) (.f64 eps eps))
(* (pow eps 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
(.f64 (.f64 (fma.f64 (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) #s(literal -1/8 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 x eps)))) eps) eps)
(* eps (- (/ (pow x 2) eps) 1))
(*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x)) eps)))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (fma.f64 (.f64 #s(literal 0 binary64) (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)) (.f64 (/.f64 (neg.f64 x) eps) eps))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (+ (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x))))))) (* eps x)) eps)))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (/.f64 (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 eps)) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (fma.f64 (.f64 #s(literal 0 binary64) (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)) (.f64 (neg.f64 x) eps)) (fma.f64 (.f64 #s(literal 0 binary64) (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)) (*.f64 (neg.f64 x) eps)))) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x)))))))))) (* -1/2 (* (pow x 2) (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x))))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2)))) (* eps x))))))) eps)) (* (sqrt eps) (* (sqrt -1) (+ (* -1 (pow x 2)) (pow x 2))))) (* eps x)) eps)))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (/.f64 (-.f64 (fma.f64 (.f64 #s(literal 0 binary64) (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)) (.f64 (neg.f64 x) eps)) (/.f64 (fma.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (.f64 x x)) #s(literal -1 binary64)) #s(literal -1/2 binary64) (.f64 (.f64 (.f64 (sqrt.f64 eps) x) (.f64 (fma.f64 (.f64 #s(literal 0 binary64) (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)) (.f64 (neg.f64 x) eps)) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1 binary64)))) x) (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (fma.f64 (.f64 #s(literal 0 binary64) (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)) (.f64 (neg.f64 x) eps))) (fma.f64 (.f64 (.f64 (sqrt.f64 eps) x) (fma.f64 (.f64 #s(literal 0 binary64) (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)) (.f64 (neg.f64 x) eps))) (sqrt.f64 #s(literal -1 binary64)) (.f64 (.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (.f64 x x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/2 binary64)))))) eps)) eps)))
(* -1 (* eps (- (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps)) 1)))
eps
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (neg.f64 x) eps)) (neg.f64 eps))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/2 binary64)) x) (neg.f64 eps))) (neg.f64 eps))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 x (/.f64 (fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 eps)) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64)) (.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64)))) eps)) (neg.f64 eps))) (neg.f64 eps))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (fma.f64 (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) (neg.f64 eps))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (fma.f64 (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) (neg.f64 eps))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))) (pow.f64 x #s(literal 6 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/16 binary64)) (fma.f64 (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) (neg.f64 eps))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (neg.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 x eps))) (neg.f64 eps))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (fma.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)) x) (neg.f64 eps))) (neg.f64 eps))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (fma.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 x (/.f64 (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 eps)) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64)) (.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/8 binary64)))) eps)) (neg.f64 eps))) (neg.f64 eps))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) x)
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (sqrt.f64 eps) x) x)) (sqrt.f64 #s(literal -1 binary64)) (.f64 (neg.f64 x) eps)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (/.f64 (fma.f64 (neg.f64 x) eps (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) eps) (.f64 (.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64))) (.f64 x x)))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) x) (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (*.f64 x x)) #s(literal -1 binary64))))) (neg.f64 eps))) eps)))
(* -1 (* (sqrt (pow eps 3)) (sqrt -1)))
(*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* (pow eps 2) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (/ x eps)))
(.f64 (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x eps)) (.f64 eps eps))
(* (pow eps 2) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ (+ (* -1 x) (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps))))
(.f64 (neg.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (.f64 x x)) #s(literal 1/2 binary64) (neg.f64 x)) eps))) (*.f64 eps eps))
(* (pow eps 2) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ (+ (* -1 x) (* -1 (/ (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1))))) eps))) eps))))
(.f64 (neg.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 (neg.f64 x) (/.f64 (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 eps)) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64)) (.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/8 binary64)))) eps)) eps))) (.f64 eps eps))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x (/.f64 x eps))) (neg.f64 eps))

rewrite163.0ms (1.9%)

Memory

7.9MiB live, 203.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	150
0	45	146
1	159	136
2	1123	121
0	8642	119

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

15 → 579

Calls

Call 1

Inputs
(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
#s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps)
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(literal 0 binary64))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(*.f64 #s(literal 1/2 binary64) eps)
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 #s(literal 1/2 binary64) eps))))
(/.f64 x (*.f64 #s(literal 1/2 binary64) eps))
(/.f64 (.f64 eps eps) (.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps))
(*.f64 eps eps)
(.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) eps)
(-.f64 (*.f64 x x) eps)

Outputs
(.f64 (pow.f64 (/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(approx (+ ( (neg x) x) (+ (* x x) eps)) eps)) #s(literal -1/2 binary64)))
(.f64 (/.f64 (neg.f64 #s(approx (+ ( (neg x) x) (+ (* x x) eps)) eps)) (fma.f64 x #s(literal 0 binary64) eps)) (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal -1 binary64))))
(.f64 (/.f64 (neg.f64 #s(approx (+ ( (neg x) x) (+ (* x x) eps)) eps)) (fma.f64 x #s(literal 0 binary64) eps)) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
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(fma.f64 (/.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (/.f64 (neg.f64 x) (pow.f64 (fma.f64 eps (-.f64 eps (.f64 x x)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))) (neg.f64 (/.f64 (.f64 eps eps) (fma.f64 x x eps))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (/.f64 x (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (/.f64 (.f64 eps eps) (fma.f64 x x eps))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (/.f64 x (pow.f64 (fma.f64 eps (-.f64 eps (.f64 x x)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))) (neg.f64 (/.f64 (.f64 eps eps) (fma.f64 x x eps))))
(fma.f64 (/.f64 (.f64 x x) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (/.f64 (.f64 x x) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (/.f64 (.f64 eps eps) (fma.f64 x x eps))))
(fma.f64 (/.f64 (.f64 x x) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (/.f64 (.f64 x x) (pow.f64 (fma.f64 eps (-.f64 eps (.f64 x x)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))) (neg.f64 (/.f64 (.f64 eps eps) (fma.f64 x x eps))))
(fma.f64 (/.f64 (.f64 (neg.f64 x) x) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (/.f64 (.f64 (neg.f64 x) x) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (/.f64 (.f64 eps eps) (fma.f64 x x eps))))
(fma.f64 (/.f64 (.f64 (neg.f64 x) x) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (/.f64 (.f64 (neg.f64 x) x) (pow.f64 (fma.f64 eps (-.f64 eps (.f64 x x)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))) (neg.f64 (/.f64 (.f64 eps eps) (fma.f64 x x eps))))
(fma.f64 (/.f64 (neg.f64 x) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (/.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (/.f64 (.f64 eps eps) (fma.f64 x x eps))))
(fma.f64 (/.f64 (neg.f64 x) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (/.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (pow.f64 (fma.f64 eps (-.f64 eps (.f64 x x)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))) (neg.f64 (/.f64 (.f64 eps eps) (fma.f64 x x eps))))
(fma.f64 (/.f64 x (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (/.f64 (neg.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64))) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (/.f64 (.f64 eps eps) (fma.f64 x x eps))))
(fma.f64 (/.f64 x (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (/.f64 (.f64 eps eps) (fma.f64 x x eps))))
(fma.f64 (/.f64 x (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (/.f64 (neg.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64))) (pow.f64 (fma.f64 eps (-.f64 eps (.f64 x x)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))) (neg.f64 (/.f64 (.f64 eps eps) (fma.f64 x x eps))))
(fma.f64 (/.f64 x (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 eps (-.f64 eps (.f64 x x)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))) (neg.f64 (/.f64 (.f64 eps eps) (fma.f64 x x eps))))
(fma.f64 (/.f64 (neg.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64))) #s(literal 1 binary64)) (/.f64 x (fma.f64 x x eps)) (neg.f64 (/.f64 (*.f64 eps eps) (fma.f64 x x eps))))
(fma.f64 (/.f64 (neg.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps))) (/.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal -1 binary64))) (neg.f64 (/.f64 (*.f64 eps eps) (fma.f64 x x eps))))
(fma.f64 (/.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) #s(literal 1 binary64)) (/.f64 (neg.f64 x) (fma.f64 x x eps)) (neg.f64 (/.f64 (*.f64 eps eps) (fma.f64 x x eps))))
(fma.f64 (/.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps))) (/.f64 (neg.f64 x) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal -1 binary64))) (neg.f64 (/.f64 (*.f64 eps eps) (fma.f64 x x eps))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (/.f64 x (fma.f64 x x eps)) (neg.f64 (/.f64 (*.f64 eps eps) (fma.f64 x x eps))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps))) (/.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal -1 binary64))) (neg.f64 (/.f64 (*.f64 eps eps) (fma.f64 x x eps))))
(fma.f64 (/.f64 (.f64 x x) #s(literal 1 binary64)) (/.f64 (.f64 x x) (fma.f64 x x eps)) (neg.f64 (/.f64 (*.f64 eps eps) (fma.f64 x x eps))))
(fma.f64 (/.f64 (.f64 (neg.f64 x) x) #s(literal 1 binary64)) (/.f64 (.f64 (neg.f64 x) x) (fma.f64 x x eps)) (neg.f64 (/.f64 (*.f64 eps eps) (fma.f64 x x eps))))
(fma.f64 (/.f64 (.f64 (neg.f64 x) x) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps))) (/.f64 (.f64 (neg.f64 x) x) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal -1 binary64))) (neg.f64 (/.f64 (*.f64 eps eps) (fma.f64 x x eps))))
(fma.f64 (/.f64 (neg.f64 x) #s(literal 1 binary64)) (/.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (fma.f64 x x eps)) (neg.f64 (/.f64 (*.f64 eps eps) (fma.f64 x x eps))))
(fma.f64 (/.f64 (neg.f64 x) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps))) (/.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal -1 binary64))) (neg.f64 (/.f64 (*.f64 eps eps) (fma.f64 x x eps))))
(fma.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps))) (/.f64 (neg.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64))) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal -1 binary64))) (neg.f64 (/.f64 (*.f64 eps eps) (fma.f64 x x eps))))
(fma.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal -1 binary64))) (neg.f64 (/.f64 (*.f64 eps eps) (fma.f64 x x eps))))
(fma.f64 (/.f64 (.f64 x x) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps))) (fma.f64 eps (.f64 (neg.f64 x) x) (pow.f64 x #s(literal 4 binary64))) (neg.f64 (/.f64 (.f64 eps eps) (fma.f64 x x eps))))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (*.f64 (neg.f64 eps) #s(literal 1 binary64)))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (*.f64 #s(literal 1 binary64) (neg.f64 eps)))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (neg.f64 eps))
(fma.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (.f64 eps (-.f64 eps (.f64 x x))) (.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 x #s(literal 4 binary64))))
(fma.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 x #s(literal 4 binary64)) (.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (.f64 eps (-.f64 eps (*.f64 x x)))))
(fma.f64 (neg.f64 eps) #s(literal 1 binary64) (*.f64 x x))
(fma.f64 (.f64 eps (-.f64 eps (.f64 x x))) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (.f64 (.f64 eps (-.f64 eps (.f64 x x))) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (fma.f64 x x eps) #s(literal -1 binary64)) (neg.f64 (/.f64 (*.f64 eps eps) (fma.f64 x x eps))))
(fma.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))))))
(fma.f64 #s(literal -1 binary64) eps (*.f64 x x))
(fma.f64 #s(literal -1 binary64) (.f64 (neg.f64 x) x) (.f64 (neg.f64 eps) #s(literal 1 binary64)))
(fma.f64 #s(literal -1 binary64) (.f64 (neg.f64 x) x) (.f64 #s(literal 1 binary64) (neg.f64 eps)))
(fma.f64 #s(literal -1 binary64) (*.f64 (neg.f64 x) x) (neg.f64 eps))
(fma.f64 #s(literal 1 binary64) (neg.f64 eps) (*.f64 x x))
(fma.f64 #s(literal 1 binary64) (.f64 x x) (.f64 (neg.f64 eps) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (.f64 x x) (.f64 #s(literal 1 binary64) (neg.f64 eps)))
(fma.f64 #s(literal 1 binary64) (*.f64 x x) (neg.f64 eps))
(fma.f64 (.f64 x x) #s(literal 1 binary64) (.f64 (neg.f64 eps) #s(literal 1 binary64)))
(fma.f64 (.f64 x x) #s(literal 1 binary64) (.f64 #s(literal 1 binary64) (neg.f64 eps)))
(fma.f64 (*.f64 x x) #s(literal 1 binary64) (neg.f64 eps))
(fma.f64 (neg.f64 x) (neg.f64 x) (*.f64 (neg.f64 eps) #s(literal 1 binary64)))
(fma.f64 (neg.f64 x) (neg.f64 x) (*.f64 #s(literal 1 binary64) (neg.f64 eps)))
(fma.f64 (neg.f64 x) (neg.f64 x) (neg.f64 eps))
(fma.f64 x (/.f64 (neg.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64))) (fma.f64 x x eps)) (neg.f64 (/.f64 (*.f64 eps eps) (fma.f64 x x eps))))
(fma.f64 x (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x eps)) (neg.f64 (/.f64 (*.f64 eps eps) (fma.f64 x x eps))))
(fma.f64 x x (*.f64 (neg.f64 eps) #s(literal 1 binary64)))
(fma.f64 x x (*.f64 #s(literal 1 binary64) (neg.f64 eps)))
(fma.f64 x x (neg.f64 eps))
(sqrt.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64)))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) (/.f64 (*.f64 eps eps) (fma.f64 x x eps)))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))))
(-.f64 (*.f64 x x) eps)
(fabs.f64 (-.f64 (*.f64 x x) eps))
(exp.f64 (.f64 (log.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (-.f64 (.f64 x x) eps)) #s(literal 1 binary64)))
(exp.f64 (log.f64 (-.f64 (*.f64 x x) eps)))
(+.f64 (.f64 (.f64 eps (-.f64 eps (.f64 x x))) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))) (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))))
(+.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))) (.f64 (.f64 eps (-.f64 eps (.f64 x x))) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))))
(+.f64 (.f64 (neg.f64 eps) #s(literal 1 binary64)) (.f64 x x))
(+.f64 (.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (.f64 eps (-.f64 eps (.f64 x x)))) (.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 x #s(literal 4 binary64))))
(+.f64 (.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 x #s(literal 4 binary64))) (.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (.f64 eps (-.f64 eps (.f64 x x)))))
(+.f64 (.f64 #s(literal 1 binary64) (neg.f64 eps)) (.f64 x x))
(+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) (neg.f64 (/.f64 (*.f64 eps eps) (fma.f64 x x eps))))
(+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))))))
(+.f64 (neg.f64 eps) (*.f64 x x))
(+.f64 (.f64 x x) (.f64 (neg.f64 eps) #s(literal 1 binary64)))
(+.f64 (.f64 x x) (.f64 #s(literal 1 binary64) (neg.f64 eps)))
(+.f64 (*.f64 x x) (neg.f64 eps))

eval108.0ms (1.3%)

Memory: 7.0MiB live, 200.6MiB allocated
Compiler: Compiled 27 951 to 3 019 computations (89.2% saved)

prune28.0ms (0.3%)

Memory

-21.6MiB live, 60.9MiB allocated

Pruning

16 alts after pruning (8 fresh and 8 done)

	Pruned	Kept	Total
New	922	8	930
Fresh	2	0	2
Picked	2	3	5
Done	0	5	5
Total	926	16	942

Accuracy

100.0%

Counts

942 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	11.7%	(/.f64 (.f64 eps eps) (.f64 #s(approx (+ (sqrt (- (* x x) eps)) x) (*.f64 #s(literal 2 binary64) x)) eps))
✓	99.5%	(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
	61.6%	(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
	44.4%	(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)) x))
	44.4%	(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) #s(approx (+ (sqrt (- (* x x) eps)) x) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (*.f64 #s(literal 2 binary64) x))))
	99.3%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(approx (+ ( (neg x) x) (+ (* x x) eps)) eps)))
✓	62.2%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	58.5%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓	6.7%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
✓	3.5%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
	99.3%	(.f64 (neg.f64 #s(approx (+ ( (neg x) x) (+ (* x x) eps)) eps)) (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
✓	4.2%	#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(literal 0 binary64))
✓	43.9%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
	43.7%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 2 binary64) eps) x)))
	43.7%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
✓	43.7%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))

Compiler

Compiled 931 to 337 computations (63.8% saved)

regimes28.0ms (0.3%)

Memory

-1.6MiB live, 36.2MiB allocated

Counts

32 → 1

Calls

Call 1

Inputs
#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(literal 0 binary64))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
(/.f64 (.f64 eps eps) (.f64 #s(approx (+ (sqrt (- (* x x) eps)) x) (*.f64 #s(literal 2 binary64) x)) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 2 binary64) eps) x)))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 #s(literal 1/2 binary64) eps))))
(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)) x))
(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) #s(approx (+ (sqrt (- (* x x) eps)) x) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (*.f64 #s(literal 2 binary64) x))))
(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))))
(.f64 (neg.f64 #s(approx (+ ( (neg x) x) (+ (* x x) eps)) eps)) (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))
(/.f64 (.f64 eps eps) (.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(approx (+ ( (neg x) x) (+ (* x x) eps)) eps)))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(approx (+ ( (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps))
(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
(/.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(-.f64 x (.f64 (neg.f64 (-.f64 (.f64 x x) eps)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(/.f64 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(fma.f64 x (/.f64 x (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (neg.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
(.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (-.f64 (fma.f64 x x eps) (*.f64 x x)))
(fma.f64 (.f64 x x) (/.f64 x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (.f64 x x) eps)))) (neg.f64 (/.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)) (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (.f64 x x) eps))))))
(fma.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64)) (neg.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64))) x)
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal 5/64 binary64) (pow.f64 x #s(literal 6 binary64))) eps) (fma.f64 (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (.f64 (pow.f64 eps #s(literal 3 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64)))))) x))

Outputs
(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))

Calls

3 calls:

10.0ms	x
8.0ms	eps
8.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	1	`eps`
99.5%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 10 to 10 computations (0% saved)

regimes13.0ms (0.2%)

Memory

19.3MiB live, 19.3MiB allocated

Counts

13 → 2

Calls

Call 1

Inputs
#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(literal 0 binary64))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
(/.f64 (.f64 eps eps) (.f64 #s(approx (+ (sqrt (- (* x x) eps)) x) (*.f64 #s(literal 2 binary64) x)) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 2 binary64) eps) x)))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 #s(literal 1/2 binary64) eps))))
(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)) x))

Outputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)) x))

Calls

3 calls:

4.0ms	eps
4.0ms	x
4.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Accuracy	Segments	Branch
89.5%	2	`x`
83.2%	2	`eps`
99.2%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 10 to 10 computations (0% saved)

regimes4.0ms (0.1%)

Memory

6.9MiB live, 6.9MiB allocated

Counts

12 → 2

Calls

Call 1

Inputs
#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(literal 0 binary64))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x))
(/.f64 (.f64 eps eps) (.f64 #s(approx (+ (sqrt (- (* x x) eps)) x) (*.f64 #s(literal 2 binary64) x)) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 2 binary64) eps) x)))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 #s(literal 1/2 binary64) eps))))

Outputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))

Calls

1 calls:

4.0ms

(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Accuracy	Segments	Branch
98.8%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes3.0ms (0%)

Memory

4.4MiB live, 4.4MiB allocated

Counts

6 → 2

Calls

Call 1

Inputs
#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(literal 0 binary64))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))

Outputs
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))

Calls

1 calls:

2.0ms

(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Accuracy	Segments	Branch
97.8%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes2.0ms (0%)

Memory

3.7MiB live, 3.7MiB allocated

Counts

4 → 2

Calls

Call 1

Inputs
#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(literal 0 binary64))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))

Outputs
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))

Calls

1 calls:

2.0ms

(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Accuracy	Segments	Branch
97.6%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes6.0ms (0.1%)

Memory

-29.2MiB live, 9.3MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(literal 0 binary64))

(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))

(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))

Outputs
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))

Calls

3 calls:

2.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
2.0ms	x
2.0ms	eps

Results

Accuracy	Segments	Branch
58.5%	1	`eps`
58.5%	1	`x`
58.5%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 10 to 10 computations (0% saved)

regimes4.0ms (0.1%)

Memory

8.5MiB live, 8.5MiB allocated

Accuracy

Total -0.8b remaining (-1.2%)

Threshold costs -0.8b (-1.2%)

Counts

2 → 1

Calls

Call 1

Inputs
#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(literal 0 binary64))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))

Outputs
#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(literal 0 binary64))

Calls

3 calls:

1.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
1.0ms	x
1.0ms	eps

Results

Accuracy	Segments	Branch
4.2%	1	`eps`
4.2%	1	`x`
4.2%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 10 to 10 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-9.860844315011082e-148	-3.641767935156351e-156

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-9.860844315011082e-148	-3.641767935156351e-156

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-9.860844315011082e-148	-3.641767935156351e-156

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-9.860844315011082e-148	-3.641767935156351e-156

Compiler

Compiled 11 to 11 computations (0% saved)

simplify50.0ms (0.6%)

Memory

-7.8MiB live, 30.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	44	205
1	65	199
2	93	199
3	146	178
4	238	178
5	436	178
6	1104	178
7	2989	178
8	6539	178

Stop Event

1×	node limit

Calls

Call 1

Inputs
(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3599131035634557/7198262071269114212496861612297570974191515389283066612961208916178940129074380592510465097766225371439873457013633432197133225688790879502413624289384262168215552 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3599131035634557/7198262071269114212496861612297570974191515389283066612961208916178940129074380592510465097766225371439873457013633432197133225688790879502413624289384262168215552 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3599131035634557/7198262071269114212496861612297570974191515389283066612961208916178940129074380592510465097766225371439873457013633432197133225688790879502413624289384262168215552 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3599131035634557/7198262071269114212496861612297570974191515389283066612961208916178940129074380592510465097766225371439873457013633432197133225688790879502413624289384262168215552 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(literal 0 binary64))

Outputs
(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3599131035634557/7198262071269114212496861612297570974191515389283066612961208916178940129074380592510465097766225371439873457013633432197133225688790879502413624289384262168215552 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3599131035634557/7198262071269114212496861612297570974191515389283066612961208916178940129074380592510465097766225371439873457013633432197133225688790879502413624289384262168215552 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3599131035634557/7198262071269114212496861612297570974191515389283066612961208916178940129074380592510465097766225371439873457013633432197133225688790879502413624289384262168215552 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3599131035634557/7198262071269114212496861612297570974191515389283066612961208916178940129074380592510465097766225371439873457013633432197133225688790879502413624289384262168215552 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(literal 0 binary64))

soundness692.0ms (8.2%)

Memory

42.0MiB live, 418.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	22
0	10	22
1	42	22
2	310	22
3	3602	22
0	8540	22
0	257	1067
1	784	1053
2	2629	1015
3	7085	1012
0	8084	948
0	559	2788
1	1788	2500
2	6547	2238
0	8501	2103
0	613	3269
1	2009	2956
2	7213	2932
0	8062	2766
0	29	169
0	48	163
1	199	163
2	1628	157
0	8706	157

Stop Event

1×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit

Compiler

Compiled 431 to 178 computations (58.7% saved)

preprocess47.0ms (0.6%)

Memory: -2.7MiB live, 69.9MiB allocated
Compiler: Compiled 446 to 114 computations (74.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	18	46
1	43	44
2	118	41
3	280	41
4	498	41
5	572	41
6	586	41
0	6	8
0	10	8
1	14	8
2	22	8
3	34	8
4	52	8
5	96	8
6	163	8
7	213	8
8	301	8
9	333	8
10	349	8
0	349	8

Iter	Nodes	Cost
0	6	24
0	10	24
1	14	24
2	22	24
3	34	24
4	52	24
5	96	24
6	163	24
7	213	24
8	301	24
9	333	24
10	349	24
0	349	24

Iter	Nodes	Cost
0	18	46
1	43	44
2	118	41
3	280	41
4	498	41
5	572	41
6	586	41
0	6	8
0	10	8
1	14	8
2	22	8
3	34	8
4	52	8
5	96	8
6	163	8
7	213	8
8	301	8
9	333	8
10	349	8
0	349	8

Iter	Nodes	Cost
0	6	24
0	10	24
1	14	24
2	22	24
3	34	24
4	52	24
5	96	24
6	163	24
7	213	24
8	301	24
9	333	24
10	349	24
0	349	24

start0.0ms (0%)

analyze15.0ms (0.2%)

sample1.4s (16.5%)

explain110.0ms (1.3%)

preprocess29.0ms (0.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify9.0ms (0.1%)

localize303.0ms (3.6%)

series8.0ms (0.1%)

simplify171.0ms (2%)

rewrite215.0ms (2.5%)

eval41.0ms (0.5%)

prune13.0ms (0.2%)

simplify156.0ms (1.8%)

localize145.0ms (1.7%)

series24.0ms (0.3%)

simplify232.0ms (2.7%)

rewrite329.0ms (3.9%)

eval212.0ms (2.5%)

prune47.0ms (0.6%)

simplify254.0ms (3%)

localize167.0ms (2%)

series55.0ms (0.7%)

simplify1.0s (11.9%)

rewrite1.5s (17.5%)

eval347.0ms (4.1%)

prune103.0ms (1.2%)

simplify181.0ms (2.1%)

localize85.0ms (1%)

series16.0ms (0.2%)

simplify163.0ms (1.9%)

rewrite163.0ms (1.9%)

eval108.0ms (1.3%)

prune28.0ms (0.3%)

regimes28.0ms (0.3%)

regimes13.0ms (0.2%)

regimes4.0ms (0.1%)

regimes3.0ms (0%)

regimes2.0ms (0%)

regimes6.0ms (0.1%)

regimes4.0ms (0.1%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify50.0ms (0.6%)

soundness692.0ms (8.2%)

preprocess47.0ms (0.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	18	46
1	43	44
2	118	41
3	280	41
4	498	41
5	572	41
6	586	41
0	6	8
0	10	8
1	14	8
2	22	8
3	34	8
4	52	8
5	96	8
6	163	8
7	213	8
8	301	8
9	333	8
10	349	8
0	349	8

Iter	Nodes	Cost
0	6	24
0	10	24
1	14	24
2	22	24
3	34	24
4	52	24
5	96	24
6	163	24
7	213	24
8	301	24
9	333	24
10	349	24
0	349	24