Metrics for sqrt times

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze1.0ms (0.1%)

Memory

2.1MiB live, 2.1MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	50%	0%	0%	50%	0%	2
50%	25%	25%	0%	0%	50%	0%	3
66.7%	25%	12.5%	0%	0%	62.5%	0%	4
80%	25%	6.2%	0%	0%	68.7%	0%	5
88.9%	25%	3.1%	0%	0%	71.8%	0%	6
94.1%	25%	1.6%	0%	0%	73.4%	0%	7
97%	25%	0.8%	0%	0%	74.2%	0%	8
98.5%	25%	0.4%	0%	0%	74.6%	0%	9
99.2%	25%	0.2%	0%	0%	74.8%	0%	10
99.6%	25%	0.1%	0%	0%	74.9%	0%	11
99.8%	25%	0%	0%	0%	74.9%	0%	12

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample598.0ms (25.2%)

Memory

67.6MiB live, 705.5MiB allocated

Samples

392.0ms	8 243×	0	valid
1.0ms	13×	1	valid
0.0ms	7×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 227.0ms

ival-sqrt: 106.0ms (46.6% of total)

ival-sub: 54.0ms (23.8% of total)

ival-mult: 53.0ms (23.3% of total)

ival-true: 5.0ms (2.2% of total)

exact: 5.0ms (2.2% of total)

ival-assert: 3.0ms (1.3% of total)

adjust: 0.0ms (0% of total)

Bogosity

explain74.0ms (3.1%)

Memory

-14.6MiB live, 104.1MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
-	-	`(sqrt.f64 (-.f64 x #s(literal 1 binary64)))`
-	-	`(sqrt.f64 x)`
-	-	`(-.f64 x #s(literal 1 binary64))`
-	-	`#s(literal 1 binary64)`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

33.0ms	510×	0	valid
0.0ms	2×	1	valid

Compiler

Compiled 65 to 28 computations (56.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-sqrt: 12.0ms (64.1% of total)

ival-mult: 3.0ms (16% of total)

ival-sub: 3.0ms (16% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

preprocess14.0ms (0.6%)

Memory

26.3MiB live, 26.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	22	19
2	38	17
3	59	17
4	77	17
5	97	17
6	116	17
7	131	17
8	132	17
0	6	7
0	10	7
1	16	7
2	17	7
0	17	7

Stop Event

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

Calls

Call 1

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

Outputs
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.2%	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify8.0ms (0.3%)

Memory

-32.4MiB live, 5.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(-.f64 x #s(literal 1 binary64))
cost-diff	0	(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
cost-diff	0	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	10	18
1	16	18
2	17	18
0	17	18

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

Outputs
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
(-.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(sqrt.f64 x)

localize18.0ms (0.8%)

Memory

30.8MiB live, 30.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(-.f64 x #s(literal 1 binary64))
accuracy	0	(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
accuracy	0	(sqrt.f64 x)
accuracy	0.50390625	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Samples

12.0ms	255×	0	valid
0.0ms	1×	1	valid

Compiler

Compiled 38 to 14 computations (63.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-sqrt: 3.0ms (44.8% of total)

ival-mult: 2.0ms (29.8% of total)

ival-sub: 2.0ms (29.8% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series10.0ms (0.4%)

Memory

-27.7MiB live, 10.3MiB allocated

Counts

4 → 48

Calls

Call 1

Inputs
#s(alt (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())

Outputs
#s(alt (* (sqrt x) (sqrt -1)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1))) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1))))))) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5))))))))) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt -1) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* 1/2 (/ x (sqrt -1)))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* x (+ (* -1/8 (/ x (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1)))))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1)))))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))) (taylor inf x) (#s(alt (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5))))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* -1/16 (sqrt (/ 1 (pow x 7)))))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (/ 1 x))) (taylor inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (/ 1 x))) (taylor inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (/ 1 x))) (taylor inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 x) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 x) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 x) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
6.0ms	x	@	-inf	((* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) (sqrt x))
1.0ms	x	@	0	((* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) (sqrt x))
1.0ms	x	@	inf	((* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) (sqrt x))

simplify147.0ms (6.2%)

Memory

32.4MiB live, 152.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	150	492
1	442	431
2	1561	410
3	4077	392
0	8270	368

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 45

Calls

Call 1

Inputs
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
(sqrt -1)
(+ (sqrt -1) (* 1/2 (/ x (sqrt -1))))
(+ (sqrt -1) (* x (+ (* -1/8 (/ x (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(+ (sqrt -1) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
-1
(- x 1)
(- x 1)
(- x 1)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* -1/16 (sqrt (/ 1 (pow x 7))))))))
x
(* x (- 1 (/ 1 x)))
(* x (- 1 (/ 1 x)))
(* x (- 1 (/ 1 x)))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
x
(* -1 (* x (- (/ 1 x) 1)))
(* -1 (* x (- (/ 1 x) 1)))
(* -1 (* x (- (/ 1 x) 1)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))

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

rewrite332.0ms (14%)

Memory

8.7MiB live, 162.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	15
1	34	15
2	161	15
3	1388	15
0	8393	15

Stop Event

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

Counts

4 → 368

Calls

Call 1

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

Outputs
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eval154.0ms (6.5%)

Memory: -42.9MiB live, 99.3MiB allocated
Compiler: Compiled 8 893 to 1 545 computations (82.6% saved)

prune8.0ms (0.4%)

Memory

-10.6MiB live, 27.1MiB allocated

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	409	4	413
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	409	5	414

Accuracy

100.0%

Counts

414 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	54.8%	(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
▶	99.3%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
▶	99.0%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
▶	97.5%	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify19.0ms (0.8%)

Memory

11.5MiB live, 46.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(-.f64 x #s(literal 1 binary64))
cost-diff	0	(*.f64 (-.f64 x #s(literal 1 binary64)) x)
cost-diff	0	(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
cost-diff	0	(/.f64 #s(literal -1/8 binary64) x)
cost-diff	0	(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
cost-diff	0	(-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
cost-diff	0	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
cost-diff	0	(-.f64 x #s(literal 1/2 binary64))
cost-diff	0	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
cost-diff	0	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	75
0	25	75
1	40	75
2	64	75
3	110	75
4	189	75
5	372	75
6	598	75
7	650	75
8	652	75
0	652	75

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
x
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
(-.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
x
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
#s(literal 1/2 binary64)
(/.f64 #s(literal -1/8 binary64) x)
#s(literal -1/8 binary64)
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(-.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)

Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
x
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
(-.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
x
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
#s(literal 1/2 binary64)
(/.f64 #s(literal -1/8 binary64) x)
#s(literal -1/8 binary64)
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(-.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)

localize72.0ms (3%)

Memory

-10.3MiB live, 76.5MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0	(-.f64 x #s(literal 1 binary64))
accuracy	0	(*.f64 (-.f64 x #s(literal 1 binary64)) x)
accuracy	28.920672195040844	(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
accuracy	0	(/.f64 #s(literal -1/8 binary64) x)
accuracy	0	(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
accuracy	0.00390625	(-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
accuracy	0.44094740049863246	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
accuracy	0	(-.f64 x #s(literal 1/2 binary64))
accuracy	0.6633403799356294	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
accuracy	1.574227712570543	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Samples

57.0ms	255×	0	valid
0.0ms	1×	1	valid

Compiler

Compiled 117 to 30 computations (74.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 48.0ms

ival-sqrt: 37.0ms (77.9% of total)

ival-sub: 5.0ms (10.5% of total)

ival-mult: 3.0ms (6.3% of total)

ival-div: 2.0ms (4.2% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series6.0ms (0.2%)

Memory

12.7MiB live, 12.7MiB allocated

Counts

10 → 120

Calls

Call 1

Inputs
#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) x) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) x) #<representation binary64>) () ())
#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (-.f64 x #s(literal 1/2 binary64)) (patch (-.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) #<representation binary64>) () ())
#s(alt (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) (patch (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -1/8 binary64) x) (patch (/.f64 #s(literal -1/8 binary64) x) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) (patch (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())
#s(alt (.f64 (-.f64 x #s(literal 1 binary64)) x) (patch (.f64 (-.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())
#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (* (sqrt x) (sqrt -1)) (taylor 0 x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) x) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) x) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1))) (taylor 0 x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) x) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) x) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1))))))) (taylor 0 x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) x) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) x) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5))))))))) (taylor 0 x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) x) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) x) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt -1)) (taylor 0 x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1))) (taylor 0 x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1))))))) (taylor 0 x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5))))))))) (taylor 0 x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt -1/2 (taylor 0 x) (#s(alt (-.f64 x #s(literal 1/2 binary64)) (patch (-.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1/2) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1/2 binary64)) (patch (-.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1/2) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1/2 binary64)) (patch (-.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1/2) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1/2 binary64)) (patch (-.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt -1)) (taylor 0 x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1))) (taylor 0 x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1))))))) (taylor 0 x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5))))))))) (taylor 0 x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (/ -1/8 x) (taylor 0 x) (#s(alt (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) (patch (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* -1/2 x) 1/8) x) (taylor 0 x) (#s(alt (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) (patch (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* x (- x 1/2)) 1/8) x) (taylor 0 x) (#s(alt (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) (patch (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* x (- x 1/2)) 1/8) x) (taylor 0 x) (#s(alt (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) (patch (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ 1/8 x) (taylor 0 x) (#s(alt (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1/8 (* 1/2 x)) x) (taylor 0 x) (#s(alt (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1/8 (* 1/2 x)) x) (taylor 0 x) (#s(alt (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1/8 (* 1/2 x)) x) (taylor 0 x) (#s(alt (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ -1/8 x) (taylor 0 x) (#s(alt (/.f64 #s(literal -1/8 binary64) x) (patch (/.f64 #s(literal -1/8 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -1/8 x) (taylor 0 x) (#s(alt (/.f64 #s(literal -1/8 binary64) x) (patch (/.f64 #s(literal -1/8 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -1/8 x) (taylor 0 x) (#s(alt (/.f64 #s(literal -1/8 binary64) x) (patch (/.f64 #s(literal -1/8 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -1/8 x) (taylor 0 x) (#s(alt (/.f64 #s(literal -1/8 binary64) x) (patch (/.f64 #s(literal -1/8 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt -1)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) (patch (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1))) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) (patch (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1))))))) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) (patch (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5))))))))) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) (patch (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (.f64 (-.f64 x #s(literal 1 binary64)) x) (patch (.f64 (-.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- x 1)) (taylor 0 x) (#s(alt (.f64 (-.f64 x #s(literal 1 binary64)) x) (patch (.f64 (-.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- x 1)) (taylor 0 x) (#s(alt (.f64 (-.f64 x #s(literal 1 binary64)) x) (patch (.f64 (-.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- x 1)) (taylor 0 x) (#s(alt (.f64 (-.f64 x #s(literal 1 binary64)) x) (patch (.f64 (-.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) x) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) x) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))) (taylor inf x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) x) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) x) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) x) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))) (taylor inf x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (-.f64 x #s(literal 1/2 binary64)) (patch (-.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 x #s(literal 1/2 binary64)) (patch (-.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 x #s(literal 1/2 binary64)) (patch (-.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 x #s(literal 1/2 binary64)) (patch (-.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))) (taylor inf x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) (patch (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) (patch (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))) (taylor inf x) (#s(alt (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) (patch (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))) (taylor inf x) (#s(alt (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) (patch (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) #<representation binary64>) () ())) ())
#s(alt 1/2 (taylor inf x) (#s(alt (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* 1/8 (/ 1 x))) (taylor inf x) (#s(alt (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* 1/8 (/ 1 x))) (taylor inf x) (#s(alt (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* 1/8 (/ 1 x))) (taylor inf x) (#s(alt (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ -1/8 x) (taylor inf x) (#s(alt (/.f64 #s(literal -1/8 binary64) x) (patch (/.f64 #s(literal -1/8 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -1/8 x) (taylor inf x) (#s(alt (/.f64 #s(literal -1/8 binary64) x) (patch (/.f64 #s(literal -1/8 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -1/8 x) (taylor inf x) (#s(alt (/.f64 #s(literal -1/8 binary64) x) (patch (/.f64 #s(literal -1/8 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -1/8 x) (taylor inf x) (#s(alt (/.f64 #s(literal -1/8 binary64) x) (patch (/.f64 #s(literal -1/8 binary64) x) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) (patch (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) (patch (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))) (taylor inf x) (#s(alt (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) (patch (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) (patch (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 (-.f64 x #s(literal 1 binary64)) x) (patch (.f64 (-.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 x))) (taylor inf x) (#s(alt (.f64 (-.f64 x #s(literal 1 binary64)) x) (patch (.f64 (-.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 x))) (taylor inf x) (#s(alt (.f64 (-.f64 x #s(literal 1 binary64)) x) (patch (.f64 (-.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 x))) (taylor inf x) (#s(alt (.f64 (-.f64 x #s(literal 1 binary64)) x) (patch (.f64 (-.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (/ 1 x))) (taylor inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (/ 1 x))) (taylor inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (/ 1 x))) (taylor inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) x) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) x) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) x) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) x) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x #s(literal 1/2 binary64)) (patch (-.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1/2 binary64)) (patch (-.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1/2 binary64)) (patch (-.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1/2 binary64)) (patch (-.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) (patch (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1))) (taylor -inf x) (#s(alt (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) (patch (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1))) (taylor -inf x) (#s(alt (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) (patch (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1))) (taylor -inf x) (#s(alt (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) (patch (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) #<representation binary64>) () ())) ())
#s(alt 1/2 (taylor -inf x) (#s(alt (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* 1/8 (/ 1 x))) (taylor -inf x) (#s(alt (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* 1/8 (/ 1 x))) (taylor -inf x) (#s(alt (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* 1/8 (/ 1 x))) (taylor -inf x) (#s(alt (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ -1/8 x) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/8 binary64) x) (patch (/.f64 #s(literal -1/8 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -1/8 x) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/8 binary64) x) (patch (/.f64 #s(literal -1/8 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -1/8 x) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/8 binary64) x) (patch (/.f64 #s(literal -1/8 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -1/8 x) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/8 binary64) x) (patch (/.f64 #s(literal -1/8 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) (patch (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (* 1/2 (/ 1 x))))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) (patch (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) (patch (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x))))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) (patch (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 (-.f64 x #s(literal 1 binary64)) x) (patch (.f64 (-.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 x))) (taylor -inf x) (#s(alt (.f64 (-.f64 x #s(literal 1 binary64)) x) (patch (.f64 (-.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 x))) (taylor -inf x) (#s(alt (.f64 (-.f64 x #s(literal 1 binary64)) x) (patch (.f64 (-.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 x))) (taylor -inf x) (#s(alt (.f64 (-.f64 x #s(literal 1 binary64)) x) (patch (.f64 (-.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 x) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 x) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 x) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	((* (sqrt (- x 1)) (sqrt x)) (* (sqrt (- x 1)) (sqrt x)) (- x 1/2) (* (sqrt (- x 1)) (sqrt x)) (- x (- 1/2 (/ -1/8 x))) (- 1/2 (/ -1/8 x)) (/ -1/8 x) (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1))
1.0ms	x	@	-inf	((* (sqrt (- x 1)) (sqrt x)) (* (sqrt (- x 1)) (sqrt x)) (- x 1/2) (* (sqrt (- x 1)) (sqrt x)) (- x (- 1/2 (/ -1/8 x))) (- 1/2 (/ -1/8 x)) (/ -1/8 x) (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1))
1.0ms	x	@	inf	((* (sqrt (- x 1)) (sqrt x)) (* (sqrt (- x 1)) (sqrt x)) (- x 1/2) (* (sqrt (- x 1)) (sqrt x)) (- x (- 1/2 (/ -1/8 x))) (- 1/2 (/ -1/8 x)) (/ -1/8 x) (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1))

Time

Variable

Point

Expression

1.0ms

((* (sqrt (- x 1)) (sqrt x)) (* (sqrt (- x 1)) (sqrt x)) (- x 1/2) (* (sqrt (- x 1)) (sqrt x)) (- x (- 1/2 (/ -1/8 x))) (- 1/2 (/ -1/8 x)) (/ -1/8 x) (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1))

1.0ms

-inf

((* (sqrt (- x 1)) (sqrt x)) (* (sqrt (- x 1)) (sqrt x)) (- x 1/2) (* (sqrt (- x 1)) (sqrt x)) (- x (- 1/2 (/ -1/8 x))) (- 1/2 (/ -1/8 x)) (/ -1/8 x) (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1))

1.0ms

inf

((* (sqrt (- x 1)) (sqrt x)) (* (sqrt (- x 1)) (sqrt x)) (- x 1/2) (* (sqrt (- x 1)) (sqrt x)) (- x (- 1/2 (/ -1/8 x))) (- 1/2 (/ -1/8 x)) (/ -1/8 x) (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1))

simplify139.0ms (5.9%)

Memory

12.6MiB live, 170.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	128	976
1	352	919
2	1176	852
3	4746	812
0	8128	785

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 110

Calls

Call 1

Inputs
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
-1/2
(- x 1/2)
(- x 1/2)
(- x 1/2)
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
(/ -1/8 x)
(/ (- (* -1/2 x) 1/8) x)
(/ (- (* x (- x 1/2)) 1/8) x)
(/ (- (* x (- x 1/2)) 1/8) x)
(/ 1/8 x)
(/ (+ 1/8 (* 1/2 x)) x)
(/ (+ 1/8 (* 1/2 x)) x)
(/ (+ 1/8 (* 1/2 x)) x)
(/ -1/8 x)
(/ -1/8 x)
(/ -1/8 x)
(/ -1/8 x)
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
(* -1 x)
(* x (- x 1))
(* x (- x 1))
(* x (- x 1))
-1
(- x 1)
(- x 1)
(- x 1)
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (- 1 (* 1/2 (/ 1 x))))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
1/2
(+ 1/2 (* 1/8 (/ 1 x)))
(+ 1/2 (* 1/8 (/ 1 x)))
(+ 1/2 (* 1/8 (/ 1 x)))
(/ -1/8 x)
(/ -1/8 x)
(/ -1/8 x)
(/ -1/8 x)
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (- 1 (/ 1 x)))
x
(* x (- 1 (/ 1 x)))
(* x (- 1 (/ 1 x)))
(* x (- 1 (/ 1 x)))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
x
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
x
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
1/2
(+ 1/2 (* 1/8 (/ 1 x)))
(+ 1/2 (* 1/8 (/ 1 x)))
(+ 1/2 (* 1/8 (/ 1 x)))
(/ -1/8 x)
(/ -1/8 x)
(/ -1/8 x)
(/ -1/8 x)
(* -1 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x)))))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (- 1 (/ 1 x)))
x
(* -1 (* x (- (/ 1 x) 1)))
(* -1 (* x (- (/ 1 x) 1)))
(* -1 (* x (- (/ 1 x) 1)))

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

rewrite181.0ms (7.6%)

Memory

-20.3MiB live, 168.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	67
0	25	64
1	95	64
2	694	64
0	8472	64

Stop Event

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

Counts

10 → 519

Calls

Call 1

Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
(-.f64 x #s(literal 1/2 binary64))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
(/.f64 #s(literal -1/8 binary64) x)
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(-.f64 x #s(literal 1 binary64))

Outputs
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eval155.0ms (6.5%)

Memory: 18.6MiB live, 147.6MiB allocated
Compiler: Compiled 12 748 to 2 037 computations (84% saved)

prune32.0ms (1.3%)

Memory

4.3MiB live, 41.1MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	629	0	629
Fresh	0	0	0
Picked	0	4	4
Done	0	1	1
Total	629	5	634

Accuracy

100.0%

Counts

634 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	54.8%	(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
✓	99.3%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
✓	99.0%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
✓	97.5%	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Compiler

Compiled 54 to 41 computations (24.1% saved)

regimes5.0ms (0.2%)

Memory

9.7MiB live, 9.7MiB allocated

Counts

5 → 1

Calls

Call 1

Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))

Calls

2 calls:

2.0ms	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
2.0ms	x

Results

Accuracy	Segments	Branch
99.3%	1	`x`
99.3%	1	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes12.0ms (0.5%)

Memory

-27.7MiB live, 7.9MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

2 calls:

11.0ms	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
2.0ms	x

Results

Accuracy	Segments	Branch
99.0%	1	`x`
99.0%	1	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes3.0ms (0.1%)

Memory

7.2MiB live, 7.2MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Calls

2 calls:

1.0ms	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
1.0ms	x

Results

Accuracy	Segments	Branch
97.5%	1	`x`
97.5%	1	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify33.0ms (1.4%)

Memory

-5.9MiB live, 45.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	35
1	24	35
2	40	35
3	62	35
4	92	35
5	126	35
6	163	35
7	235	35
8	337	35
9	357	35
10	359	35

Stop Event

1×

saturated

Calls

Call 1

Inputs

#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))

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

#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Outputs

#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))

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

#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

soundness294.0ms (12.4%)

Memory

-3.9MiB live, 184.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	150	492
1	442	431
2	1561	410
3	4077	392
0	8270	368

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 15 to 12 computations (20% saved)

preprocess57.0ms (2.4%)

Memory: 15.3MiB live, 91.7MiB allocated
Compiler: Compiled 42 to 32 computations (23.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	8	19
1	22	19
2	38	17
3	59	17
4	77	17
5	97	17
6	116	17
7	131	17
8	132	17
0	6	7
0	10	7
1	16	7
2	17	7
0	17	7

Iter	Nodes	Cost
0	18	75
0	25	75
1	40	75
2	64	75
3	110	75
4	189	75
5	372	75
6	598	75
7	650	75
8	652	75
0	652	75

Iter	Nodes	Cost
0	15	35
1	24	35
2	40	35
3	62	35
4	92	35
5	126	35
6	163	35
7	235	35
8	337	35
9	357	35
10	359	35

Iter	Nodes	Cost
0	8	19
1	22	19
2	38	17
3	59	17
4	77	17
5	97	17
6	116	17
7	131	17
8	132	17
0	6	7
0	10	7
1	16	7
2	17	7
0	17	7

Iter	Nodes	Cost
0	18	75
0	25	75
1	40	75
2	64	75
3	110	75
4	189	75
5	372	75
6	598	75
7	650	75
8	652	75
0	652	75

Iter	Nodes	Cost
0	15	35
1	24	35
2	40	35
3	62	35
4	92	35
5	126	35
6	163	35
7	235	35
8	337	35
9	357	35
10	359	35

start0.0ms (0%)

analyze1.0ms (0.1%)

sample598.0ms (25.2%)

explain74.0ms (3.1%)

preprocess14.0ms (0.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify8.0ms (0.3%)

localize18.0ms (0.8%)

series10.0ms (0.4%)

simplify147.0ms (6.2%)

rewrite332.0ms (14%)

eval154.0ms (6.5%)

prune8.0ms (0.4%)

simplify19.0ms (0.8%)

localize72.0ms (3%)

series6.0ms (0.2%)

simplify139.0ms (5.9%)

rewrite181.0ms (7.6%)

eval155.0ms (6.5%)

prune32.0ms (1.3%)

regimes5.0ms (0.2%)

regimes12.0ms (0.5%)

regimes3.0ms (0.1%)

simplify33.0ms (1.4%)

soundness294.0ms (12.4%)

preprocess57.0ms (2.4%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	19
1	22	19
2	38	17
3	59	17
4	77	17
5	97	17
6	116	17
7	131	17
8	132	17
0	6	7
0	10	7
1	16	7
2	17	7
0	17	7

Iter	Nodes	Cost
0	18	75
0	25	75
1	40	75
2	64	75
3	110	75
4	189	75
5	372	75
6	598	75
7	650	75
8	652	75
0	652	75

Iter	Nodes	Cost
0	15	35
1	24	35
2	40	35
3	62	35
4	92	35
5	126	35
6	163	35
7	235	35
8	337	35
9	357	35
10	359	35