Metrics for ENA, Section 1.4, Exercise 4d

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze13.0ms (0.1%)

Memory

22.9MiB live, 22.9MiB 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 (15.3%)

Memory

-34.8MiB live, 1 542.8MiB allocated

Samples

383.0ms	4 926×	0	valid
347.0ms	2 715×	1	valid
198.0ms	615×	2	valid
19.0ms	206×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 625.0ms

ival-sqrt: 160.0ms (25.6% of total)

ival-sub: 127.0ms (20.3% of total)

ival-mult: 117.0ms (18.7% of total)

ival-<=: 104.0ms (16.6% of total)

adjust: 77.0ms (12.3% of total)

ival-and: 21.0ms (3.4% of total)

exact: 15.0ms (2.4% of total)

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

Bogosity

explain449.0ms (5.1%)

Memory

19.1MiB live, 104.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
107	1	(7.252280441925151e-136 -8.913566977128214e-273)	-	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
0	0	-	-	`eps`
0	0	-	-	`(sqrt.f64 (-.f64 (*.f64 x x) eps))`
0	0	-	-	`(-.f64 (*.f64 x x) eps)`
0	0	-	-	`(*.f64 x x)`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`	cancellation	108	0

Confusion

	Predicted +	Predicted -
+	107	0
-	1	148

Precision

0.9907407407407407

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	107	0	0
-	1	0	148

Precision?

0.9907407407407407

Recall?

1.0

Freqs

test

number	freq
0	148
1	108

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

17.0ms	170×	1	valid
15.0ms	302×	0	valid
6.0ms	40×	2	valid

Compiler

Compiled 84 to 28 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-sub: 6.0ms (28.2% of total)

ival-sqrt: 5.0ms (23.5% of total)

ival-mult: 5.0ms (23.5% of total)

adjust: 4.0ms (18.8% of total)

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

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

preprocess83.0ms (0.9%)

Memory

-33.1MiB live, 40.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	46
1	43	44
2	118	41
3	278	41
4	488	41
5	557	41
6	568	41
0	6	8
0	10	8
1	14	8
2	22	8
3	34	8
4	52	8
5	94	8
6	161	8
7	206	8
8	289	8
9	319	8
10	335	8
0	335	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)

eval2.0ms (0%)

Memory: 2.5MiB live, 2.5MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	61.5%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify10.0ms (0.1%)

Memory

15.9MiB live, 15.9MiB 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	94	24
6	161	24
7	206	24
8	289	24
9	319	24
10	335	24
0	335	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

localize30.0ms (0.3%)

Memory

6.8MiB live, 41.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(-.f64 (*.f64 x x) eps)
accuracy	0.00390625	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	24.648760063051665	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Samples

8.0ms	85×	1	valid
8.0ms	151×	0	valid
8.0ms	20×	2	valid

Compiler

Compiled 50 to 14 computations (72% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-sub: 4.0ms (35.2% of total)

ival-sqrt: 3.0ms (26.4% of total)

adjust: 2.0ms (17.6% of total)

ival-mult: 2.0ms (17.6% of total)

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

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

series8.0ms (0.1%)

Memory

16.6MiB live, 16.6MiB 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))
2.0ms	x	@	inf	((- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x))
2.0ms	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))

simplify225.0ms (2.5%)

Memory

-7.1MiB live, 235.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	257	1067
1	784	1053
2	2592	1015
3	6953	1012
0	8103	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 (neg.f64 x) (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 (- (* 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 (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 #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)

rewrite183.0ms (2.1%)

Memory

-18.5MiB live, 214.7MiB 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	8549	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)))
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(pow.f64 (pow.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64)) #s(literal -1 binary64))
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(/.f64 (fma.f64 (neg.f64 eps) eps (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x eps))
(/.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)))

eval52.0ms (0.6%)

Memory: -1.1MiB live, 85.0MiB allocated
Compiler: Compiled 7 015 to 1 083 computations (84.6% saved)

prune12.0ms (0.1%)

Memory

-4.2MiB live, 32.9MiB allocated

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	259	10	269
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	259	11	270

Accuracy

99.7%

Counts

270 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	60.8%	(fma.f64 (.f64 x x) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (neg.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))))
	61.0%	(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))))
▶	61.0%	(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
▶	61.2%	(-.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1 binary64)))))
✓	61.5%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	57.5%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
	6.8%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
▶	3.4%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
	28.5%	#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))
▶	38.1%	#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))
▶	44.7%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))

Compiler

Compiled 404 to 242 computations (40.1% saved)

simplify177.0ms (2%)

Memory

9.9MiB live, 197.2MiB 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	(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	896	(-.f64 (fma.f64 x x eps) (*.f64 x x))
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	(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1 binary64))
cost-diff	0	(sqrt.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1 binary64)))
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1 binary64))))
cost-diff	0	(-.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1 binary64)))))

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	209
0	54	202
1	88	202
2	146	197
3	262	195
4	415	195
5	1124	195
6	4122	195
0	8318	195

Stop Event

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

Calls

Call 1

Inputs
(-.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1 binary64)))))
x
(/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1 binary64))))
#s(literal 1 binary64)
(sqrt.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1 binary64)))
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1 binary64))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
eps
#s(literal -1 binary64)
(-.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 (-.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)
#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 x (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1 binary64)))))
x
(/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1 binary64))))
#s(literal 1 binary64)
(sqrt.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1 binary64)))
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1 binary64))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
eps
#s(literal -1 binary64)
(-.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 (-.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)
#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)

localize202.0ms (2.3%)

Memory

15.3MiB live, 298.3MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.10546875	(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
accuracy	8.046401653276337	(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
accuracy	8.781386680619642	(*.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	36.69680409461666	#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	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.01953125	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy	0.29296875	(/.f64 (-.f64 (fma.f64 x x eps) (.f64 x x)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
accuracy	24.365680977429662	(-.f64 (fma.f64 x x eps) (*.f64 x x))
accuracy	0	(/.f64 #s(literal 1/2 binary64) x)
accuracy	0.24609375	(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
accuracy	35.32497013772367	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
accuracy	0	(neg.f64 x)
accuracy	24.648760063051665	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
accuracy	62.42500602950661	#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
accuracy	0.09375	(sqrt.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1 binary64)))
accuracy	0.1328125	(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1 binary64))
accuracy	0.17578125	(/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1 binary64))))
accuracy	24.648760063051665	(-.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1 binary64)))))

Samples

129.0ms	85×	1	valid
39.0ms	151×	0	valid
10.0ms	20×	2	valid

Compiler

Compiled 400 to 62 computations (84.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 74.0ms

ival-mult: 25.0ms (34% of total)

ival-pow: 16.0ms (21.8% of total)

ival-div: 8.0ms (10.9% of total)

adjust: 7.0ms (9.5% of total)

ival-sub: 7.0ms (9.5% of total)

ival-sqrt: 5.0ms (6.8% of total)

ival-add: 4.0ms (5.4% of total)

exact: 1.0ms (1.4% of total)

ival-neg: 1.0ms (1.4% of total)

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

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

series35.0ms (0.4%)

Memory

7.3MiB live, 96.3MiB allocated

Counts

20 → 129

Calls

Call 1

Inputs
(-.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1 binary64))))
(sqrt.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1 binary64)))
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1 binary64))
(-.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 (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)
#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
(* -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)))))))))
(* (sqrt (/ 1 eps)) (sqrt -1))
(+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))
(+ (* (sqrt (/ 1 eps)) (sqrt -1)) (* (pow x 2) (+ (* -1/2 (* (sqrt eps) (/ (* (pow x 2) (+ (* 1/4 (/ 1 (* (pow eps 3) (pow (sqrt -1) 2)))) (/ 1 (pow eps 3)))) (sqrt -1)))) (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (sqrt -1)))))))
(+ (* (sqrt (/ 1 eps)) (sqrt -1)) (* (pow x 2) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/2 (* (sqrt eps) (/ (* (pow x 2) (+ (* 1/2 (/ (+ (* 1/4 (/ 1 (* (pow eps 3) (pow (sqrt -1) 2)))) (/ 1 (pow eps 3))) (* eps (pow (sqrt -1) 2)))) (/ 1 (pow eps 4)))) (sqrt -1)))) (* -1/2 (* (sqrt eps) (/ (+ (* 1/4 (/ 1 (* (pow eps 3) (pow (sqrt -1) 2)))) (/ 1 (pow eps 3))) (sqrt -1)))))))))
(/ -1 eps)
(- (* -1 (/ (pow x 2) (pow eps 2))) (/ 1 eps))
(- (* (pow x 2) (- (* -1 (/ (pow x 2) (pow eps 3))) (/ 1 (pow eps 2)))) (/ 1 eps))
(- (* (pow x 2) (- (* (pow x 2) (- (* -1 (/ (pow x 2) (pow eps 4))) (/ 1 (pow eps 3)))) (/ 1 (pow eps 2)))) (/ 1 eps))
(* -1 x)
(* 1/2 (/ eps x))
(/ 1/2 x)
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)
(* 1/8 (/ (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)
(/ (- (* 1/2 (/ (+ (* 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)))))))
(/ 1 x)
(/ (+ 1 (* 1/2 (/ eps (pow x 2)))) x)
(/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) x)
(/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 4))) (+ (* -1/2 (/ (+ (* -1 (pow eps 3)) (* -1/2 (* eps (+ (* -1 (pow eps 2)) (* 1/4 (pow eps 2)))))) (pow x 6))) (* 1/2 (/ eps (pow x 2)))))) x)
(/ 1 (pow x 2))
(/ (+ 1 (/ eps (pow x 2))) (pow x 2))
(/ (- (+ 1 (/ (pow eps 2) (pow x 4))) (* -1 (/ eps (pow x 2)))) (pow x 2))
(/ (- (+ 1 (/ (pow eps 3) (pow x 6))) (+ (* -1 (/ eps (pow x 2))) (* -1 (/ (pow eps 2) (pow x 4))))) (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 (/ (+ (* -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))))
(/ (+ 1/2 (* 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 (- (* 1/8 (/ (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 (/ (+ 1 (* 1/2 (/ eps (pow x 2)))) x))
(* -1 (/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) x))
(* -1 (/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 4))) (+ (* -1/2 (/ (+ (* -1 (pow eps 3)) (* -1/2 (* eps (+ (* -1 (pow eps 2)) (* 1/4 (pow eps 2)))))) (pow x 6))) (* 1/2 (/ eps (pow x 2)))))) x))
(* -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 (/ (- (* -1/8 (/ 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)))))
(+ (* 1/2 (/ eps (pow x 3))) (/ 1 x))
(+ (* eps (+ (* 3/8 (/ eps (pow x 5))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x))
(+ (* eps (+ (* eps (+ (* 5/16 (/ eps (pow x 7))) (* 3/8 (/ 1 (pow x 5))))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x))
(+ (/ 1 (pow x 2)) (/ eps (pow x 4)))
(+ (* eps (+ (/ 1 (pow x 4)) (/ eps (pow x 6)))) (/ 1 (pow x 2)))
(+ (* eps (+ (* eps (+ (/ 1 (pow x 6)) (/ eps (pow x 8)))) (/ 1 (pow x 4)))) (/ 1 (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)))))
(* 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))))))
(+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 7))) (/ (+ (* 1/4 (/ (* eps (pow x 4)) (pow (sqrt -1) 2))) (pow x 6)) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(/ (- (* -1 (/ (pow x 2) eps)) 1) eps)
(/ (- (* -1 (/ (pow x 4) (pow eps 2))) (+ 1 (/ (pow x 2) eps))) eps)
(/ (- (* -1 (/ (pow x 6) (pow eps 3))) (+ 1 (+ (/ (pow x 2) eps) (/ (pow x 4) (pow eps 2))))) 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)))
(- (+ (* -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)))
(* (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)))))
(* -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)))))))
(+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))
(+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(+ (* -1 (/ (+ (* 1/2 (* (sqrt eps) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 eps)) (* (sqrt -1) (+ (* -1/4 (* eps (pow x 4))) (pow x 6)))))) (pow eps 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* -1 (/ (+ 1 (/ (pow x 2) eps)) eps))
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (pow x 4) eps)) (pow x 2)) eps))) eps))
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow x 6) eps) (* -1 (pow x 4))) eps)) (pow x 2)) eps))) 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)))
(* 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
8.0ms	x	@	0	((- x (/ 1 (sqrt (pow (- (* x x) eps) -1)))) (/ 1 (sqrt (pow (- (* x x) eps) -1))) (sqrt (pow (- (* x x) eps) -1)) (pow (- (* x x) eps) -1) (- 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) eps) (* x x)) (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (+ (* x x) eps) (* x x) (- 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)))
7.0ms	x	@	-inf	((- x (/ 1 (sqrt (pow (- (* x x) eps) -1)))) (/ 1 (sqrt (pow (- (* x x) eps) -1))) (sqrt (pow (- (* x x) eps) -1)) (pow (- (* x x) eps) -1) (- 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) eps) (* x x)) (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (+ (* x x) eps) (* x x) (- 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)))
7.0ms	eps	@	inf	((- x (/ 1 (sqrt (pow (- (* x x) eps) -1)))) (/ 1 (sqrt (pow (- (* x x) eps) -1))) (sqrt (pow (- (* x x) eps) -1)) (pow (- (* x x) eps) -1) (- 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) eps) (* x x)) (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (+ (* x x) eps) (* x x) (- 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 (/ 1 (sqrt (pow (- (* x x) eps) -1)))) (/ 1 (sqrt (pow (- (* x x) eps) -1))) (sqrt (pow (- (* x x) eps) -1)) (pow (- (* x x) eps) -1) (- 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) eps) (* x x)) (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (+ (* x x) eps) (* x x) (- 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 (/ 1 (sqrt (pow (- (* x x) eps) -1)))) (/ 1 (sqrt (pow (- (* x x) eps) -1))) (sqrt (pow (- (* x x) eps) -1)) (pow (- (* x x) eps) -1) (- 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) eps) (* x x)) (/ (- (+ (* x x) eps) (* x x)) (+ (sqrt (- (* x x) eps)) x)) (+ (* x x) eps) (* x x) (- 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)))

simplify224.0ms (2.5%)

Memory

-3.5MiB live, 261.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	632	3047
1	1973	2887
2	6703	2841
0	8468	2678

Stop Event

1×	iter limit
1×	node limit

Counts

129 → 127

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

rewrite261.0ms (2.9%)

Memory

-33.7MiB live, 162.8MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	33	175
0	54	175
1	210	166
2	1630	166
0	8315	166

Stop Event

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

Counts

20 → 770

Calls

Call 1

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

eval241.0ms (2.7%)

Memory: -19.0MiB live, 180.9MiB allocated
Compiler: Compiled 26 346 to 3 508 computations (86.7% saved)

prune45.0ms (0.5%)

Memory

13.2MiB live, 51.1MiB allocated

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	865	9	874
Fresh	4	1	5
Picked	3	2	5
Done	0	1	1
Total	872	13	885

Accuracy

100.0%

Counts

885 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	60.8%	(/.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
	60.8%	(/.f64 (+.f64 eps (fma.f64 x x (.f64 (neg.f64 x) x))) (+.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))
▶	57.3%	(-.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (pow (- (* x x) eps) -1) (/.f64 #s(literal -1 binary64) eps)))))
✓	61.5%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶	57.5%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
▶	6.8%	(-.f64 x #s(approx (/ 1 (sqrt (pow (- (* x x) eps) -1))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
✓	3.4%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
	44.8%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
	44.6%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 #s(literal 1/2 binary64) eps))))
	42.5%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (/.f64 eps (.f64 x x)) (/.f64 #s(literal 1/8 binary64) x) (/.f64 #s(literal 1/2 binary64) x)) eps))
✓	44.7%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
	42.5%	#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 403 to 274 computations (32% saved)

simplify405.0ms (4.6%)

Memory

26.6MiB live, 347.0MiB 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	896	(fma.f64 (neg.f64 x) x (fma.f64 x x eps))
cost-diff	0	#s(approx (pow (- (* x x) eps) -1) (/.f64 #s(literal -1 binary64) eps))
cost-diff	0	(sqrt.f64 #s(approx (pow (- (* x x) eps) -1) (/.f64 #s(literal -1 binary64) eps)))
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (pow (- (* x x) eps) -1) (/.f64 #s(literal -1 binary64) eps))))
cost-diff	0	(-.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (pow (- (* x x) eps) -1) (/.f64 #s(literal -1 binary64) 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 (/ 1 (sqrt (pow (- (* x x) eps) -1))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))
cost-diff	0	(-.f64 x #s(approx (/ 1 (sqrt (pow (- (* x x) eps) -1))) (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	192	(+.f64 eps (-.f64 (.f64 x x) (.f64 x x)))
cost-diff	832	(-.f64 (.f64 x x) (.f64 x x))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	34	253
0	58	221
1	94	217
2	140	217
3	306	217
4	856	217
5	2745	217
6	7603	217
0	8299	217

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

localize104.0ms (1.2%)

Memory

-25.6MiB live, 253.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.01953125	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy	0.29296875	(/.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
accuracy	24.707869659962316	(fma.f64 (neg.f64 x) x (fma.f64 x x eps))
accuracy	0.09375	(sqrt.f64 #s(approx (pow (- (* x x) eps) -1) (/.f64 #s(literal -1 binary64) eps)))
accuracy	0.17578125	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (pow (- (* x x) eps) -1) (/.f64 #s(literal -1 binary64) eps))))
accuracy	24.648760063051665	(-.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (pow (- (* x x) eps) -1) (/.f64 #s(literal -1 binary64) eps)))))
accuracy	26.562422234001026	#s(approx (pow (- (* x x) eps) -1) (/.f64 #s(literal -1 binary64) eps))
accuracy	0	(/.f64 eps x)
accuracy	0.00390625	(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
accuracy	24.648760063051665	(-.f64 x #s(approx (/ 1 (sqrt (pow (- (* x x) eps) -1))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
accuracy	34.9625025288531	#s(approx (/ 1 (sqrt (pow (- (* x x) eps) -1))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))
accuracy	0	(neg.f64 eps)
accuracy	0.00390625	(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
accuracy	24.648760063051665	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
accuracy	26.211185957872004	#s(approx (- (* x x) eps) (neg.f64 eps))
accuracy	0.00390625	(-.f64 (*.f64 x x) eps)
accuracy	0.00390625	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.01953125	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy	0.29296875	(/.f64 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))

Samples

39.0ms	85×	1	valid
28.0ms	151×	0	valid
11.0ms	20×	2	valid

Compiler

Compiled 475 to 65 computations (86.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 51.0ms

ival-div: 11.0ms (21.7% of total)

adjust: 8.0ms (15.8% of total)

ival-sub: 6.0ms (11.9% of total)

ival-add: 6.0ms (11.9% of total)

ival-sqrt: 5.0ms (9.9% of total)

ival-mult: 5.0ms (9.9% of total)

ival-neg: 5.0ms (9.9% of total)

ival-pow: 4.0ms (7.9% of total)

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

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

exact: 0.0ms (0% of total)

series15.0ms (0.2%)

Memory

28.1MiB live, 28.1MiB allocated

Counts

23 → 144

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 (/ 1 (sqrt (pow (- (* x x) eps) -1))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
#s(approx (/ 1 (sqrt (pow (- (* x x) eps) -1))) (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 #s(literal 1 binary64) (sqrt.f64 #s(approx (pow (- (* x x) eps) -1) (/.f64 #s(literal -1 binary64) eps)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (pow (- (* x x) eps) -1) (/.f64 #s(literal -1 binary64) eps))))
(sqrt.f64 #s(approx (pow (- (* x x) eps) -1) (/.f64 #s(literal -1 binary64) eps)))
#s(approx (pow (- (* x x) eps) -1) (/.f64 #s(literal -1 binary64) 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))
(-.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)
(* (sqrt (/ 1 eps)) (sqrt -1))
(+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))
(+ (* (sqrt (/ 1 eps)) (sqrt -1)) (* (pow x 2) (+ (* -1/2 (* (sqrt eps) (/ (* (pow x 2) (+ (* 1/4 (/ 1 (* (pow eps 3) (pow (sqrt -1) 2)))) (/ 1 (pow eps 3)))) (sqrt -1)))) (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (sqrt -1)))))))
(+ (* (sqrt (/ 1 eps)) (sqrt -1)) (* (pow x 2) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/2 (* (sqrt eps) (/ (* (pow x 2) (+ (* 1/2 (/ (+ (* 1/4 (/ 1 (* (pow eps 3) (pow (sqrt -1) 2)))) (/ 1 (pow eps 3))) (* eps (pow (sqrt -1) 2)))) (/ 1 (pow eps 4)))) (sqrt -1)))) (* -1/2 (* (sqrt eps) (/ (+ (* 1/4 (/ 1 (* (pow eps 3) (pow (sqrt -1) 2)))) (/ 1 (pow eps 3))) (sqrt -1)))))))))
(/ -1 eps)
(- (* -1 (/ (pow x 2) (pow eps 2))) (/ 1 eps))
(- (* (pow x 2) (- (* -1 (/ (pow x 2) (pow eps 3))) (/ 1 (pow eps 2)))) (/ 1 eps))
(- (* (pow x 2) (- (* (pow x 2) (- (* -1 (/ (pow x 2) (pow eps 4))) (/ 1 (pow eps 3)))) (/ 1 (pow eps 2)))) (/ 1 eps))
(* -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)))))
(/ 1 x)
(/ (+ 1 (* 1/2 (/ eps (pow x 2)))) x)
(/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) x)
(/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 4))) (+ (* -1/2 (/ (+ (* -1 (pow eps 3)) (* -1/2 (* eps (+ (* -1 (pow eps 2)) (* 1/4 (pow eps 2)))))) (pow x 6))) (* 1/2 (/ eps (pow x 2)))))) x)
(/ 1 (pow x 2))
(/ (+ 1 (/ eps (pow x 2))) (pow x 2))
(/ (- (+ 1 (/ (pow eps 2) (pow x 4))) (* -1 (/ eps (pow x 2)))) (pow x 2))
(/ (- (+ 1 (/ (pow eps 3) (pow x 6))) (+ (* -1 (/ eps (pow x 2))) (* -1 (/ (pow eps 2) (pow x 4))))) (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 x)
(* -1 (/ (+ 1 (* 1/2 (/ eps (pow x 2)))) x))
(* -1 (/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) x))
(* -1 (/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 4))) (+ (* -1/2 (/ (+ (* -1 (pow eps 3)) (* -1/2 (* eps (+ (* -1 (pow eps 2)) (* 1/4 (pow eps 2)))))) (pow x 6))) (* 1/2 (/ eps (pow x 2)))))) x))
(* -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))
(+ (* 1/2 (/ eps (pow x 3))) (/ 1 x))
(+ (* eps (+ (* 3/8 (/ eps (pow x 5))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x))
(+ (* eps (+ (* eps (+ (* 5/16 (/ eps (pow x 7))) (* 3/8 (/ 1 (pow x 5))))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x))
(+ (/ 1 (pow x 2)) (/ eps (pow x 4)))
(+ (* eps (+ (/ 1 (pow x 4)) (/ eps (pow x 6)))) (/ 1 (pow x 2)))
(+ (* eps (+ (* eps (+ (/ 1 (pow x 6)) (/ eps (pow x 8)))) (/ 1 (pow x 4)))) (/ 1 (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))))
(+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 7))) (/ (+ (* 1/4 (/ (* eps (pow x 4)) (pow (sqrt -1) 2))) (pow x 6)) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(/ (- (* -1 (/ (pow x 2) eps)) 1) eps)
(/ (- (* -1 (/ (pow x 4) (pow eps 2))) (+ 1 (/ (pow x 2) eps))) eps)
(/ (- (* -1 (/ (pow x 6) (pow eps 3))) (+ 1 (+ (/ (pow x 2) eps) (/ (pow x 4) (pow eps 2))))) eps)
(* 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)))))
(+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))
(+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(+ (* -1 (/ (+ (* 1/2 (* (sqrt eps) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 eps)) (* (sqrt -1) (+ (* -1/4 (* eps (pow x 4))) (pow x 6)))))) (pow eps 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* -1 (/ (+ 1 (/ (pow x 2) eps)) eps))
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (pow x 4) eps)) (pow x 2)) eps))) eps))
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow x 6) eps) (* -1 (pow x 4))) eps)) (pow x 2)) eps))) eps))
(* -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
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 (/ 1 (sqrt (pow (- (* x x) eps) -1)))) (/ 1 (sqrt (pow (- (* x x) eps) -1))) (+ (* (/ eps x) -1/2) x) (/ eps x) (- x (/ 1 (sqrt (pow (- (* x x) eps) -1)))) (/ 1 (sqrt (pow (- (* x x) eps) -1))) (sqrt (pow (- (* x x) eps) -1)) (pow (- (* x x) eps) -1) (+ (* (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)) (- (* 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 (/ 1 (sqrt (pow (- (* x x) eps) -1)))) (/ 1 (sqrt (pow (- (* x x) eps) -1))) (+ (* (/ eps x) -1/2) x) (/ eps x) (- x (/ 1 (sqrt (pow (- (* x x) eps) -1)))) (/ 1 (sqrt (pow (- (* x x) eps) -1))) (sqrt (pow (- (* x x) eps) -1)) (pow (- (* x x) eps) -1) (+ (* (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)) (- (* 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 (/ 1 (sqrt (pow (- (* x x) eps) -1)))) (/ 1 (sqrt (pow (- (* x x) eps) -1))) (+ (* (/ eps x) -1/2) x) (/ eps x) (- x (/ 1 (sqrt (pow (- (* x x) eps) -1)))) (/ 1 (sqrt (pow (- (* x x) eps) -1))) (sqrt (pow (- (* x x) eps) -1)) (pow (- (* x x) eps) -1) (+ (* (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)) (- (* x x) eps))
2.0ms	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 (/ 1 (sqrt (pow (- (* x x) eps) -1)))) (/ 1 (sqrt (pow (- (* x x) eps) -1))) (+ (* (/ eps x) -1/2) x) (/ eps x) (- x (/ 1 (sqrt (pow (- (* x x) eps) -1)))) (/ 1 (sqrt (pow (- (* x x) eps) -1))) (sqrt (pow (- (* x x) eps) -1)) (pow (- (* x x) eps) -1) (+ (* (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)) (- (* x x) eps))
2.0ms	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 (/ 1 (sqrt (pow (- (* x x) eps) -1)))) (/ 1 (sqrt (pow (- (* x x) eps) -1))) (+ (* (/ eps x) -1/2) x) (/ eps x) (- x (/ 1 (sqrt (pow (- (* x x) eps) -1)))) (/ 1 (sqrt (pow (- (* x x) eps) -1))) (sqrt (pow (- (* x x) eps) -1)) (pow (- (* x x) eps) -1) (+ (* (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)) (- (* x x) eps))

simplify259.0ms (2.9%)

Memory

-14.5MiB live, 216.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	736	3770
1	2338	3403
0	8081	3211

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 142

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

rewrite368.0ms (4.1%)

Memory

-13.4MiB live, 187.1MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	34	215
0	58	185
1	244	169
2	1737	169
0	8286	169

Stop Event

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

Counts

23 → 914

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

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

eval294.0ms (3.3%)

Memory: 34.7MiB live, 196.3MiB allocated
Compiler: Compiled 33 354 to 3 698 computations (88.9% saved)

prune58.0ms (0.7%)

Memory

-28.1MiB live, 54.0MiB allocated

Pruning

13 alts after pruning (7 fresh and 6 done)

	Pruned	Kept	Total
New	1 050	3	1 053
Fresh	1	4	5
Picked	2	3	5
Done	0	3	3
Total	1 053	13	1 066

Accuracy

100.0%

Counts

1 066 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
▶	99.4%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps))
✓	57.3%	(-.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (pow (- (* x x) eps) -1) (/.f64 #s(literal -1 binary64) eps)))))
✓	61.5%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	57.5%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓	6.8%	(-.f64 x #s(approx (/ 1 (sqrt (pow (- (* x x) eps) -1))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
✓	3.4%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
▶	4.3%	#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (/.f64 #s(literal 0 binary64) x))
▶	44.8%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
▶	44.6%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 #s(literal 1/2 binary64) eps))))
	42.5%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (/.f64 eps (.f64 x x)) (/.f64 #s(literal 1/8 binary64) x) (/.f64 #s(literal 1/2 binary64) x)) eps))
✓	44.7%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
	42.5%	#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 251 computations (30.9% saved)

simplify1.7s (19.5%)

Memory

-12.0MiB live, 187.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
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	(/.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps)
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.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	704	(/.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)) (/.f64 #s(literal 0 binary64) x))
cost-diff	704	(/.f64 #s(literal 0 binary64) x)
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	192
0	45	184
1	70	178
2	108	173
3	168	155
4	286	155
5	659	155
6	3756	155
0	8795	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)) (/.f64 #s(literal 0 binary64) x))
(/.f64 #s(literal 0 binary64) x)
#s(literal 0 binary64)
x
#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 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps))
#s(literal 1 binary64)
(/.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
eps

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

localize543.0ms (6.1%)

Memory

11.2MiB live, 138.3MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.01953125	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy	0.1171875	(/.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps)
accuracy	0.2578125	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps))
accuracy	0	(/.f64 x (*.f64 #s(literal 1/2 binary64) eps))
accuracy	0	(*.f64 #s(literal 1/2 binary64) eps)
accuracy	0.27734375	(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
accuracy	35.32497013772367	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 #s(literal 1/2 binary64) eps))))
accuracy	0	(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
accuracy	0	(*.f64 #s(literal 1/2 binary64) eps)
accuracy	35.32497013772367	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
accuracy	0	(/.f64 #s(literal 0 binary64) x)
accuracy	61.256689081678815	#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (/.f64 #s(literal 0 binary64) x))
accuracy	0.00390625	(-.f64 (*.f64 x x) eps)
accuracy	0.00390625	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.01953125	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy	0.29296875	(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))

Samples

496.0ms	153×	0	valid
23.0ms	86×	1	valid
7.0ms	17×	2	valid

Compiler

Compiled 364 to 55 computations (84.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 470.0ms

ival-add: 421.0ms (89.6% of total)

ival-div: 32.0ms (6.8% of total)

ival-mult: 5.0ms (1.1% of total)

adjust: 4.0ms (0.9% of total)

ival-sub: 3.0ms (0.6% of total)

ival-sqrt: 3.0ms (0.6% of total)

ival-neg: 1.0ms (0.2% of total)

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

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

exact: 0.0ms (0% of total)

series13.0ms (0.1%)

Memory

17.2MiB live, 17.2MiB allocated

Counts

15 → 119

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

simplify305.0ms (3.4%)

Memory

-3.3MiB live, 148.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	605	3150
1	1935	2860
2	6822	2639
0	8777	2478

Stop Event

1×	iter limit
1×	node limit

Counts

119 → 117

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

rewrite146.0ms (1.6%)

Memory

20.3MiB live, 211.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	150
0	45	142
1	162	134
2	1105	125
0	8701	123

Stop Event

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

Counts

15 → 523

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

eval139.0ms (1.6%)

Memory: -13.5MiB live, 228.0MiB allocated
Compiler: Compiled 25 792 to 2 784 computations (89.2% saved)

prune39.0ms (0.4%)

Memory

-10.7MiB live, 66.8MiB allocated

Pruning

15 alts after pruning (6 fresh and 9 done)

	Pruned	Kept	Total
New	852	6	858
Fresh	2	0	2
Picked	2	3	5
Done	0	6	6
Total	856	15	871

Accuracy

100.0%

Counts

871 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	(/.f64 #s(approx (+ (* (neg x) x) (+ (* x x) eps)) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
	45.4%	(/.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))
	45.4%	(/.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))))
✓	99.4%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) eps))
	44.7%	(/.f64 #s(literal 1 binary64) #s(approx (/ (+ (sqrt (- (* x x) eps)) x) eps) (.f64 (-.f64 (/.f64 #s(literal 2 binary64) eps) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) x)))
✓	57.3%	(-.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (pow (- (* x x) eps) -1) (/.f64 #s(literal -1 binary64) eps)))))
✓	61.5%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	57.5%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓	6.8%	(-.f64 x #s(approx (/ 1 (sqrt (pow (- (* x x) eps) -1))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
✓	3.4%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
	4.3%	#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(approx (/ 0 x) #s(literal 0 binary64)))
✓	44.8%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
	44.5%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 2 binary64) eps) x)))
	44.6%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
✓	44.7%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))

Compiler

Compiled 836 to 329 computations (60.6% saved)

regimes27.0ms (0.3%)

Memory

8.6MiB live, 46.6MiB allocated

Counts

29 → 1

Calls

Call 1

Inputs
#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(approx (/ 0 x) #s(literal 0 binary64)))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (/.f64 #s(literal 0 binary64) 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 #s(approx (/ 1 (sqrt (pow (- (* x x) eps) -1))) (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)))
#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 #s(literal 1 binary64) (sqrt.f64 #s(approx (pow (- (* x x) eps) -1) (/.f64 #s(literal -1 binary64) eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) 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 #s(literal 1 binary64) #s(approx (/ (+ (sqrt (- (* x x) eps)) x) eps) (.f64 (-.f64 (/.f64 #s(literal 2 binary64) eps) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) x)))
(/.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 (+.f64 eps (-.f64 (.f64 x x) (.f64 x x))) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 (+.f64 eps (fma.f64 x x (.f64 (neg.f64 x) x))) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (/.f64 eps (.f64 x x)) (/.f64 #s(literal 1/8 binary64) x) (/.f64 #s(literal 1/2 binary64) x)) eps))
(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))))
(-.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal -1 binary64)))))
#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))
(fma.f64 (.f64 x x) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal -1 binary64)) (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 #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:

9.0ms	eps
8.0ms	x
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)

regimes16.0ms (0.2%)

Memory

-18.0MiB live, 25.6MiB allocated

Counts

13 → 2

Calls

Call 1

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

7.0ms	x
4.0ms	eps
4.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Accuracy	Segments	Branch
90.9%	2	`x`
80.0%	2	`eps`
98.6%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 10 to 10 computations (0% saved)

regimes5.0ms (0.1%)

Memory

9.3MiB live, 9.3MiB allocated

Counts

12 → 2

Calls

Call 1

Inputs
#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(approx (/ 0 x) #s(literal 0 binary64)))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (/.f64 #s(literal 0 binary64) 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 #s(approx (/ 1 (sqrt (pow (- (* x x) eps) -1))) (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)))
#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
98.4%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes3.0ms (0%)

Memory

7.3MiB live, 7.3MiB allocated

Counts

8 → 2

Calls

Call 1

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

3.0ms

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

Results

Accuracy	Segments	Branch
97.0%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes3.0ms (0%)

Memory

5.8MiB live, 5.8MiB allocated

Counts

5 → 2

Calls

Call 1

Inputs
#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(approx (/ 0 x) #s(literal 0 binary64)))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (/.f64 #s(literal 0 binary64) 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
96.9%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes7.0ms (0.1%)

Memory

12.3MiB live, 12.3MiB allocated

Counts

4 → 2

Calls

Call 1

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
57.5%	1	`eps`
57.5%	1	`x`
59.1%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 10 to 10 computations (0% saved)

regimes7.0ms (0.1%)

Memory

-27.8MiB live, 10.7MiB allocated

Accuracy

Total -0.8b remaining (-1.3%)

Threshold costs -0.8b (-1.3%)

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

3 calls:

3.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
2.0ms	eps
2.0ms	x

Results

Accuracy	Segments	Branch
4.3%	1	`x`
4.3%	1	`eps`
4.3%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 10 to 10 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-4.35961798186635e-154	0.0

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	-4.35961798186635e-154	0.0

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	-4.35961798186635e-154	0.0

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	-4.35961798186635e-154	0.0

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	-4.35961798186635e-154	0.0

Compiler

Compiled 11 to 11 computations (0% saved)

simplify26.0ms (0.3%)

Memory

3.5MiB live, 41.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	245
1	59	245
2	68	245
3	73	245
4	75	245

Stop Event

1×

saturated

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 -3019169939857233/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 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 -3019169939857233/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 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 -3019169939857233/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 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 -3019169939857233/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 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)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3019169939857233/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 binary64)) (-.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(approx (/ 0 x) #s(literal 0 binary64))))
#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(approx (/ 0 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 -3019169939857233/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 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 -3019169939857233/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 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 -3019169939857233/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 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 -3019169939857233/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 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)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3019169939857233/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 binary64)) (-.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(approx (/ 0 x) #s(literal 0 binary64))))
#s(approx (/ (+ (* (neg x) x) (+ (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) #s(approx (/ 0 x) #s(literal 0 binary64)))

soundness684.0ms (7.7%)

Memory

25.8MiB live, 480.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	736	3770
1	2338	3403
0	8081	3211
0	605	3150
1	1935	2860
2	6822	2639
0	8777	2478
0	6	22
0	10	22
1	42	22
2	310	22
3	3602	22
0	8549	22
0	33	175
0	54	175
1	210	166
2	1630	166
0	8315	166
0	257	1067
1	784	1053
2	2592	1015
3	6953	1012
0	8103	948

Stop Event

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

Compiler

Compiled 560 to 231 computations (58.8% saved)

preprocess64.0ms (0.7%)

Memory: 8.5MiB live, 88.2MiB allocated
Compiler: Compiled 526 to 122 computations (76.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	18	46
1	43	44
2	118	41
3	278	41
4	488	41
5	557	41
6	568	41
0	6	8
0	10	8
1	14	8
2	22	8
3	34	8
4	52	8
5	94	8
6	161	8
7	206	8
8	289	8
9	319	8
10	335	8
0	335	8

Iter	Nodes	Cost
0	6	24
0	10	24
1	14	24
2	22	24
3	34	24
4	52	24
5	94	24
6	161	24
7	206	24
8	289	24
9	319	24
10	335	24
0	335	24

Iter	Nodes	Cost
0	18	46
1	43	44
2	118	41
3	278	41
4	488	41
5	557	41
6	568	41
0	6	8
0	10	8
1	14	8
2	22	8
3	34	8
4	52	8
5	94	8
6	161	8
7	206	8
8	289	8
9	319	8
10	335	8
0	335	8

Iter	Nodes	Cost
0	6	24
0	10	24
1	14	24
2	22	24
3	34	24
4	52	24
5	94	24
6	161	24
7	206	24
8	289	24
9	319	24
10	335	24
0	335	24

start0.0ms (0%)

analyze13.0ms (0.1%)

sample1.4s (15.3%)

explain449.0ms (5.1%)

preprocess83.0ms (0.9%)

eval2.0ms (0%)

prune0.0ms (0%)

simplify10.0ms (0.1%)

localize30.0ms (0.3%)

series8.0ms (0.1%)

simplify225.0ms (2.5%)

rewrite183.0ms (2.1%)

eval52.0ms (0.6%)

prune12.0ms (0.1%)

simplify177.0ms (2%)

localize202.0ms (2.3%)

series35.0ms (0.4%)

simplify224.0ms (2.5%)

rewrite261.0ms (2.9%)

eval241.0ms (2.7%)

prune45.0ms (0.5%)

simplify405.0ms (4.6%)

localize104.0ms (1.2%)

series15.0ms (0.2%)

simplify259.0ms (2.9%)

rewrite368.0ms (4.1%)

eval294.0ms (3.3%)

prune58.0ms (0.7%)

simplify1.7s (19.5%)

localize543.0ms (6.1%)

series13.0ms (0.1%)

simplify305.0ms (3.4%)

rewrite146.0ms (1.6%)

eval139.0ms (1.6%)

prune39.0ms (0.4%)

regimes27.0ms (0.3%)

regimes16.0ms (0.2%)

regimes5.0ms (0.1%)

regimes3.0ms (0%)

regimes3.0ms (0%)

regimes7.0ms (0.1%)

regimes7.0ms (0.1%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify26.0ms (0.3%)

soundness684.0ms (7.7%)

preprocess64.0ms (0.7%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	18	46
1	43	44
2	118	41
3	278	41
4	488	41
5	557	41
6	568	41
0	6	8
0	10	8
1	14	8
2	22	8
3	34	8
4	52	8
5	94	8
6	161	8
7	206	8
8	289	8
9	319	8
10	335	8
0	335	8

Iter	Nodes	Cost
0	6	24
0	10	24
1	14	24
2	22	24
3	34	24
4	52	24
5	94	24
6	161	24
7	206	24
8	289	24
9	319	24
10	335	24
0	335	24