Metrics for sqrt times

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze1.0ms (0%)

Memory

1.8MiB live, 1.8MiB 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)

sample636.0ms (16%)

Memory

27.6MiB live, 739.7MiB allocated

Samples

405.0ms	8 249×	0	valid
1.0ms	7×	1	valid
1.0ms	12×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 229.0ms

ival-sqrt: 110.0ms (48% of total)

ival-mult: 54.0ms (23.6% of total)

ival-sub: 50.0ms (21.8% of total)

ival-true: 6.0ms (2.6% of total)

exact: 5.0ms (2.2% of total)

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

adjust: 0.0ms (0% of total)

Bogosity

explain94.0ms (2.4%)

Memory

20.3MiB live, 144.6MiB 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

26.0ms

512×

valid

Compiler

Compiled 101 to 52 computations (48.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-sqrt: 7.0ms (48.4% of total)

ival-sub: 3.0ms (20.7% of total)

ival-mult: 3.0ms (20.7% of total)

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

exact: 0.0ms (0% of total)

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

preprocess20.0ms (0.5%)

Memory

-21.7MiB live, 17.2MiB 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

0.8MiB live, 0.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.3%	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0.1%)

Memory

3.0MiB live, 3.0MiB 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)

localize34.0ms (0.8%)

Memory

-18.1MiB live, 25.3MiB 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	0.4765625	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Samples

13.0ms

256×

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 (43% of total)

ival-sub: 2.0ms (28.6% of total)

ival-mult: 2.0ms (28.6% of total)

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

exact: 0.0ms (0% of total)

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

series7.0ms (0.2%)

Memory

8.0MiB live, 8.0MiB 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
2.0ms	x	@	-inf	((* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) (sqrt x))
2.0ms	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))

simplify415.0ms (10.4%)

Memory

-3.6MiB live, 172.4MiB 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)

rewrite164.0ms (4.1%)

Memory

-14.5MiB live, 182.1MiB 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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eval56.0ms (1.4%)

Memory: 26.8MiB live, 143.0MiB allocated
Compiler: Compiled 8 893 to 1 545 computations (82.6% saved)

prune11.0ms (0.3%)

Memory

13.2MiB live, 51.0MiB allocated

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	408	5	413
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	408	6	414

Accuracy

100.0%

Counts

414 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	37.2%	(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
✓	99.3%	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	53.8%	(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))))
▶	98.9%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
▶	97.3%	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Compiler

Compiled 71 to 58 computations (18.3% saved)

simplify303.0ms (7.6%)

Memory

-8.8MiB live, 217.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	25	113
0	39	113
1	58	113
2	97	113
3	203	110
4	379	110
5	947	110
6	2375	110
7	2979	110
8	3140	110
9	3195	110
10	3215	110
11	3220	110
0	8187	110

Stop Event

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

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

Outputs
#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)
#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)
(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)
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
(sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x))
(sqrt.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) x))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) x)
(-.f64 (pow.f64 x #s(literal 3 binary64)) x)
(fma.f64 x x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(sqrt.f64 (-.f64 x #s(literal -1 binary64)))
(-.f64 x #s(literal -1 binary64))

localize147.0ms (3.7%)

Memory

-5.2MiB live, 133.7MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 (-.f64 x #s(literal -1 binary64)))
accuracy	0.078125	(*.f64 (fma.f64 x x #s(literal -1 binary64)) x)
accuracy	18.709570610337828	(sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x))
accuracy	21.189978495975048	(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
accuracy	0	(-.f64 x #s(literal 1 binary64))
accuracy	0	(*.f64 (-.f64 x #s(literal 1 binary64)) x)
accuracy	29.566664404133075	(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
accuracy	0	(-.f64 x #s(literal 1/2 binary64))
accuracy	0.7034145493838815	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
accuracy	1.6983722941129002	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
accuracy	0	(/.f64 #s(literal -1/8 binary64) x)
accuracy	0	(-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
accuracy	0	(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
accuracy	0.46722644600420593	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))

Samples

66.0ms

256×

valid

Compiler

Compiled 197 to 45 computations (77.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 54.0ms

ival-mult: 26.0ms (48.5% of total)

ival-div: 11.0ms (20.5% of total)

ival-sqrt: 8.0ms (14.9% of total)

ival-sub: 6.0ms (11.2% of total)

ival-add: 1.0ms (1.9% of total)

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

exact: 0.0ms (0% of total)

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

series50.0ms (1.2%)

Memory

-17.3MiB live, 18.3MiB allocated

Counts

15 → 180

Calls

Call 1

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

Outputs
#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 #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 (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 (* (sqrt x) (sqrt -1)) (taylor 0 x) (#s(alt (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))) (patch (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))) #<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 (fma.f64 x x #s(literal -1 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))) (patch (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal -1 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 (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))) (patch (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal -1 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 (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))) (patch (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt -1)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (patch (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (sqrt (pow x 5)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1))) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (patch (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt x) (sqrt -1)) (* (pow x 3) (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1))))))) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (patch (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt x) (sqrt -1)) (* (pow x 3) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 3) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt x) (/ 1 (pow (sqrt -1) 5))))))))) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (patch (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt 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 (* 1/2 x)) (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 (* x (+ 1/2 (* -1/8 x)))) (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 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
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#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) (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>) () ())) ())
#s(alt (* -1 (* x (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))) (patch (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (/ 1 x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))) (patch (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ (- (* 1/8 (/ 1 (* x (pow (sqrt -1) 2)))) 1/2) x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))) (patch (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 (* x (pow (sqrt -1) 4)))) (* 1/8 (/ 1 (pow (sqrt -1) 2)))) x)) 1/2) x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))) (patch (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (pow x 3)) (pow (sqrt -1) 2)) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (patch (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (patch (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (patch (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (pow (sqrt -1) 2))) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (pow x 3))) (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))) (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (patch (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<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)))) (* (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))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (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))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (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 (pow x 3) (taylor -inf x) (#s(alt (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (patch (.f64 (fma.f64 x x #s(literal -1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1))) (taylor -inf x) (#s(alt (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (patch (.f64 (fma.f64 x x #s(literal -1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1))) (taylor -inf x) (#s(alt (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (patch (.f64 (fma.f64 x x #s(literal -1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1))) (taylor -inf x) (#s(alt (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (patch (.f64 (fma.f64 x x #s(literal -1 binary64)) x) #<representation binary64>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
4.0ms	x	@	-inf	((* (sqrt (- x 1)) (sqrt x)) (- x (- 1/2 (/ -1/8 x))) (- 1/2 (/ -1/8 x)) (/ -1/8 x) (* (sqrt (- x 1)) (sqrt x)) (* (sqrt (- x 1)) (sqrt x)) (- x 1/2) (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1) (/ (sqrt (* (+ (* x x) -1) x)) (sqrt (- x -1))) (sqrt (* (+ (* x x) -1) x)) (+ (* x x) -1) (sqrt (- x -1)) (* (+ (* x x) -1) x))
2.0ms	x	@	0	((* (sqrt (- x 1)) (sqrt x)) (- x (- 1/2 (/ -1/8 x))) (- 1/2 (/ -1/8 x)) (/ -1/8 x) (* (sqrt (- x 1)) (sqrt x)) (* (sqrt (- x 1)) (sqrt x)) (- x 1/2) (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1) (/ (sqrt (* (+ (* x x) -1) x)) (sqrt (- x -1))) (sqrt (* (+ (* x x) -1) x)) (+ (* x x) -1) (sqrt (- x -1)) (* (+ (* x x) -1) x))
2.0ms	x	@	inf	((* (sqrt (- x 1)) (sqrt x)) (- x (- 1/2 (/ -1/8 x))) (- 1/2 (/ -1/8 x)) (/ -1/8 x) (* (sqrt (- x 1)) (sqrt x)) (* (sqrt (- x 1)) (sqrt x)) (- x 1/2) (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1) (/ (sqrt (* (+ (* x x) -1) x)) (sqrt (- x -1))) (sqrt (* (+ (* x x) -1) x)) (+ (* x x) -1) (sqrt (- x -1)) (* (+ (* x x) -1) x))

Time

Variable

Point

Expression

4.0ms

-inf

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

2.0ms

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

2.0ms

inf

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

simplify165.0ms (4.1%)

Memory

-1.6MiB live, 240.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	271	1925
1	797	1747
2	2807	1625
3	7589	1607
0	8200	1530

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 169

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)))))))))
(/ -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)))))))))
(* (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 x)
(* x (- x 1))
(* x (- x 1))
(* x (- x 1))
-1
(- x 1)
(- x 1)
(- x 1)
(* (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 5)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 3) (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 3) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 3) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt x) (/ 1 (pow (sqrt -1) 5)))))))))
-1
(- (pow x 2) 1)
(- (pow x 2) 1)
(- (pow x 2) 1)
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(* -1 x)
(* x (- (pow x 2) 1))
(* x (- (pow x 2) 1))
(* x (- (pow x 2) 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 (/ (+ 1/2 (* 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))))
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))))
(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)))
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 (pow x 3))
(* (pow x 2) (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))))
(* (pow x 2) (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* -1/8 (sqrt (/ 1 (pow x 9)))))))
(* (pow x 2) (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (sqrt (/ 1 (pow x 9)))) (* -1/16 (sqrt (/ 1 (pow x 13))))))))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(pow x 3)
(* (pow x 3) (- 1 (/ 1 (pow x 2))))
(* (pow x 3) (- 1 (/ 1 (pow x 2))))
(* (pow x 3) (- 1 (/ 1 (pow x 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 (- (+ (/ 1/8 (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 (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)
(* -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)))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (/ 1 x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (- (* 1/8 (/ 1 (* x (pow (sqrt -1) 2)))) 1/2) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 (* x (pow (sqrt -1) 4)))) (* 1/8 (/ 1 (pow (sqrt -1) 2)))) x)) 1/2) x)) (pow (sqrt -1) 2))))
(* (sqrt (pow x 3)) (pow (sqrt -1) 2))
(* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (pow (sqrt -1) 2))) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (pow x 3))) (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))) (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(pow x 3)
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1)))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1)))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 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 (/.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 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.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 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 x #s(literal 1/2 binary64)) (/.f64 #s(literal 1/8 binary64) x))
(/ (- (* x (- x 1/2)) 1/8) x)
(-.f64 (-.f64 x #s(literal 1/2 binary64)) (/.f64 #s(literal 1/8 binary64) x))
(/ 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 (/.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 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.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 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 (/.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 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.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 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 (/.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 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.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 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))
(* (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 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.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 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 5)) (/ 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 5 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 3) (+ (* -1/8 (* (sqrt (pow x 3)) (/ 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 (pow.f64 x #s(literal 3 binary64))) (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (pow.f64 x #s(literal 3 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 3) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 3) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt 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 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (sqrt.f64 x))) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 x #s(literal 3 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
-1
#s(literal -1 binary64)
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(* -1 x)
(neg.f64 x)
(* x (- (pow x 2) 1))
(-.f64 (pow.f64 x #s(literal 3 binary64)) x)
(* x (- (pow x 2) 1))
(-.f64 (pow.f64 x #s(literal 3 binary64)) x)
(* x (- (pow x 2) 1))
(-.f64 (pow.f64 x #s(literal 3 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 x (-.f64 (/.f64 #s(literal 1/8 binary64) 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 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal -1/2 binary64)) #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 x (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(-.f64 x (-.f64 (/.f64 #s(literal 1/8 binary64) 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 x (-.f64 (/.f64 #s(literal 1/8 binary64) 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 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal -1/2 binary64)) #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 x (-.f64 (/.f64 #s(literal 1/8 binary64) 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 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal -1/2 binary64)) #s(literal 1 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))))
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x
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x
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x
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(* (pow x 3) (- 1 (/ 1 (pow x 2))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) x)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (- 1 (/ 1 (pow x 2))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) x)) (pow.f64 x #s(literal 3 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 x (-.f64 (/.f64 #s(literal 1/8 binary64) 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))))
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x
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
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(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(-.f64 x (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(-.f64 x (-.f64 (/.f64 #s(literal 1/8 binary64) 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 (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 (/.f64 #s(literal 1/8 binary64) 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))))
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(* -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 (/.f64 #s(literal 1/8 binary64) 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 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal -1/2 binary64)) #s(literal 1 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)
(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)))))
(neg.f64 (fma.f64 (fma.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) x) x) #s(literal 1/2 binary64)) #s(literal -1 binary64) (/.f64 #s(literal -1/8 binary64) x)) #s(literal 1 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
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(* -1 (* x (- (/ 1 x) 1)))
(-.f64 x #s(literal 1 binary64))
(* -1 (* x (- (/ 1 x) 1)))
(-.f64 x #s(literal 1 binary64))
(* -1 (* x (pow (sqrt -1) 2)))
x
(* -1 (* x (+ (* 1/2 (/ 1 x)) (pow (sqrt -1) 2))))
(-.f64 x #s(literal 1/2 binary64))
(* -1 (* x (+ (* -1 (/ (- (* 1/8 (/ 1 (* x (pow (sqrt -1) 2)))) 1/2) x)) (pow (sqrt -1) 2))))
(-.f64 x (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))
(* -1 (* x (+ (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 (* x (pow (sqrt -1) 4)))) (* 1/8 (/ 1 (pow (sqrt -1) 2)))) x)) 1/2) x)) (pow (sqrt -1) 2))))
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(* (sqrt (pow x 3)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))))
(* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
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(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
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(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
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(pow x 3)
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(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) x)) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) x)) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) x)) (pow.f64 x #s(literal 3 binary64)))

rewrite178.0ms (4.5%)

Memory

42.5MiB live, 194.0MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	25	100
0	39	91
1	144	91
2	1015	89
0	8649	89

Stop Event

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

Counts

15 → 759

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

Outputs
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eval240.0ms (6%)

Memory: -4.9MiB live, 331.4MiB allocated
Compiler: Compiled 18 034 to 2 947 computations (83.7% saved)

prune41.0ms (1%)

Memory

-4.4MiB live, 83.2MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	927	1	928
Fresh	0	0	0
Picked	1	4	5
Done	0	1	1
Total	928	6	934

Accuracy

100.0%

Counts

934 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.3%	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	53.7%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 x #s(literal 1 binary64)) x))))
✓	53.8%	(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))))
✓	98.9%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
✓	97.3%	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Compiler

Compiled 37 to 31 computations (16.2% saved)

simplify26.0ms (0.7%)

Memory

5.8MiB live, 45.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
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 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 x #s(literal 1 binary64)) x))))
cost-diff	1792	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 x #s(literal 1 binary64)) x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	36
0	12	28
1	25	28
2	42	28
3	72	28
4	89	28
5	107	28
6	149	28
7	200	28
8	321	28
9	472	28
10	661	28
11	712	28
12	729	28
13	732	28
14	733	28
0	733	28

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize24.0ms (0.6%)

Memory

0.3MiB live, 78.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 (-.f64 x #s(literal 1 binary64)) x)
accuracy	0.15625	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 x #s(literal 1 binary64)) x)))
accuracy	0.8397116448092165	(/.f64 #s(literal 1 binary64) (*.f64 (-.f64 x #s(literal 1 binary64)) x))
accuracy	29.566664404133075	(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 x #s(literal 1 binary64)) x))))

Samples

18.0ms

256×

valid

Compiler

Compiled 74 to 16 computations (78.4% saved)

Precisions

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

ival-div: 4.0ms (37.7% of total)

ival-sqrt: 3.0ms (28.3% of total)

ival-sub: 2.0ms (18.8% of total)

ival-mult: 2.0ms (18.8% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

3.9MiB live, 3.9MiB allocated

Counts

5 → 60

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

0.0ms

inf

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

0.0ms

-inf

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

0.0ms

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

simplify193.0ms (4.8%)

Memory

23.3MiB live, 131.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	105	459
1	277	443
2	835	417
3	2524	403
4	7029	385
0	8549	378

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 57

Calls

Call 1

Inputs
(* -1 x)
(* x (- x 1))
(* x (- x 1))
(* x (- x 1))
(* (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)
(/ -1 x)
(/ (- (* -1 x) 1) x)
(/ (- (* x (- (* -1 x) 1)) 1) x)
(/ (- (* x (- (* x (- (* -1 x) 1)) 1)) 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 (* 1/2 (/ 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 (pow x 2))
(/ (+ 1 (/ 1 x)) (pow x 2))
(/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) (pow x 2))
(/ (+ 1 (+ (/ 1 x) (+ (/ 1 (pow x 2)) (/ 1 (pow x 3))))) (pow x 2))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (- 1 (/ 1 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)))
(/ 1 (pow x 2))
(/ (+ 1 (/ 1 x)) (pow x 2))
(/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) (pow x 2))
(/ (+ 1 (* -1 (/ (- (* -1 (/ (+ 1 (/ 1 x)) x)) 1) x))) (pow x 2))

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

rewrite120.0ms (3%)

Memory

-62.6MiB live, 89.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	34
0	12	26
1	55	26
2	293	26
0	2346	26

Stop Event

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

Counts

5 → 418

Calls

Call 1

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

Outputs
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eval77.0ms (1.9%)

Memory: 2.8MiB live, 120.8MiB allocated
Compiler: Compiled 7 638 to 1 660 computations (78.3% saved)

prune10.0ms (0.3%)

Memory

23.5MiB live, 23.5MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	475	0	475
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	475	6	481

Accuracy

100.0%

Counts

481 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.3%	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	53.7%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 x #s(literal 1 binary64)) x))))
✓	53.8%	(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))))
✓	98.9%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
✓	97.3%	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Compiler

Compiled 86 to 58 computations (32.6% saved)

regimes6.0ms (0.2%)

Memory

10.6MiB live, 10.6MiB allocated

Counts

7 → 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))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 x #s(literal 1 binary64)) x))))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))

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:

3.0ms	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
3.0ms	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)

regimes37.0ms (0.9%)

Memory

-29.7MiB live, 9.4MiB 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:

35.0ms	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
2.0ms	x

Results

Accuracy	Segments	Branch
98.9%	1	`x`
98.9%	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

8.6MiB live, 8.6MiB 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
97.3%	1	`x`
97.3%	1	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify30.0ms (0.8%)

Memory

-9.6MiB live, 65.7MiB 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)

soundness625.0ms (15.7%)

Memory

0.6MiB live, 202.2MiB 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)

preprocess255.0ms (6.4%)

Memory: 18.2MiB live, 56.4MiB 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	7	36
0	12	28
1	25	28
2	42	28
3	72	28
4	89	28
5	107	28
6	149	28
7	200	28
8	321	28
9	472	28
10	661	28
11	712	28
12	729	28
13	732	28
14	733	28
0	733	28

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	7	36
0	12	28
1	25	28
2	42	28
3	72	28
4	89	28
5	107	28
6	149	28
7	200	28
8	321	28
9	472	28
10	661	28
11	712	28
12	729	28
13	732	28
14	733	28
0	733	28

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%)

sample636.0ms (16%)

explain94.0ms (2.4%)

preprocess20.0ms (0.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0.1%)

localize34.0ms (0.8%)

series7.0ms (0.2%)

simplify415.0ms (10.4%)

rewrite164.0ms (4.1%)

eval56.0ms (1.4%)

prune11.0ms (0.3%)

simplify303.0ms (7.6%)

localize147.0ms (3.7%)

series50.0ms (1.2%)

simplify165.0ms (4.1%)

rewrite178.0ms (4.5%)

eval240.0ms (6%)

prune41.0ms (1%)

simplify26.0ms (0.7%)

localize24.0ms (0.6%)

series3.0ms (0.1%)

simplify193.0ms (4.8%)

rewrite120.0ms (3%)

eval77.0ms (1.9%)

prune10.0ms (0.3%)

regimes6.0ms (0.2%)

regimes37.0ms (0.9%)

regimes3.0ms (0.1%)

simplify30.0ms (0.8%)

soundness625.0ms (15.7%)

preprocess255.0ms (6.4%)

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	7	36
0	12	28
1	25	28
2	42	28
3	72	28
4	89	28
5	107	28
6	149	28
7	200	28
8	321	28
9	472	28
10	661	28
11	712	28
12	729	28
13	732	28
14	733	28
0	733	28

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