Metrics for Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, E

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze8.0ms (0.2%)

Memory

10.4MiB live, 10.4MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
50%	50%	50%	0.1%	0%	0%	0%	2
50%	50%	50%	0.1%	0%	0%	0%	3
66.7%	50%	25%	0.1%	0%	25%	0%	4
66.7%	50%	25%	0.1%	0%	25%	0%	5
80%	50%	12.5%	0.1%	0%	37.5%	0%	6
80%	50%	12.5%	0.1%	0%	37.5%	0%	7
88.9%	50%	6.2%	0.1%	0%	43.7%	0%	8
88.9%	50%	6.2%	0.1%	0%	43.7%	0%	9
94.1%	50%	3.1%	0.1%	0%	46.8%	0%	10
94.1%	50%	3.1%	0.1%	0%	46.8%	0%	11
97%	50%	1.6%	0.1%	0%	48.4%	0%	12

Compiler

Compiled 10 to 9 computations (10% saved)

sample918.0ms (17%)

Memory

4.4MiB live, 749.9MiB allocated

Samples

451.0ms	8 252×	0	valid
28.0ms	267×	0	invalid
0.0ms	3×	1	valid
0.0ms	1×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 233.0ms

ival-mult: 64.0ms (27.5% of total)

ival-sqrt: 59.0ms (25.4% of total)

ival-sub: 52.0ms (22.4% of total)

ival-add: 43.0ms (18.5% of total)

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

exact: 5.0ms (2.1% of total)

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

adjust: 0.0ms (0% of total)

Bogosity

explain85.0ms (1.6%)

Memory

25.1MiB live, 100.0MiB allocated

FPErrors

Click to see full error table

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

36.0ms	510×	0	valid
0.0ms	2×	1	valid

Compiler

Compiled 52 to 25 computations (51.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-mult: 14.0ms (59.4% of total)

ival-sqrt: 4.0ms (17% of total)

ival-sub: 3.0ms (12.7% of total)

ival-add: 2.0ms (8.5% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

preprocess47.0ms (0.9%)

Memory

-8.6MiB live, 35.1MiB allocated

Algorithm

1×	egg-herbie

Rules

336×	`lower-fma.f64`
336×	`lower-fma.f32`
212×	`sub-neg`
180×	`cancel-sign-sub-inv`
178×	`associate--r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	48
1	54	43
2	160	42
3	433	42
4	878	42
5	1222	42
6	1337	42
7	1357	42
0	7	8
0	11	8
1	19	8
2	38	8
3	65	8
4	129	8
5	247	8
6	389	8
7	437	8
8	460	8
0	460	7

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 8 to 7 computations (12.5% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify19.0ms (0.3%)

Memory

-14.1MiB live, 21.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(*.f64 y (sqrt.f64 x))
cost-diff	0	(-.f64 #s(literal 1 binary64) x)
cost-diff	128	(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))

Rules

336×	`lower-fma.f64`
336×	`lower-fma.f32`
144×	`lower-*.f32`
142×	`lower-*.f64`
112×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
0	11	20
1	19	20
2	38	20
3	65	20
4	129	20
5	247	20
6	389	20
7	437	20
8	460	20
0	460	19

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize21.0ms (0.4%)

Memory

5.8MiB live, 42.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(-.f64 #s(literal 1 binary64) x)
accuracy	0	(sqrt.f64 x)
accuracy	0.0078125	(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))
accuracy	0.2578125	(*.f64 y (sqrt.f64 x))

Samples

16.0ms	255×	0	valid
0.0ms	1×	1	valid

Compiler

Compiled 22 to 9 computations (59.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-sqrt: 5.0ms (51.4% of total)

ival-mult: 2.0ms (20.5% of total)

ival-add: 1.0ms (10.3% of total)

ival-sub: 1.0ms (10.3% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory

12.2MiB live, 12.2MiB allocated

Counts

4 → 72

Calls

Call 1

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

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

Calls

6 calls:

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

simplify132.0ms (2.4%)

Memory

-20.3MiB live, 153.6MiB allocated

Algorithm

1×	egg-herbie

Rules

7 542×	`lower-fma.f64`
7 542×	`lower-fma.f32`
2 696×	`lower-*.f64`
2 696×	`lower-*.f32`
1 866×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	369
1	141	369
2	438	357
3	1298	357
4	4642	357
5	7358	357
0	8082	330

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

Inputs
(- 1 x)
(- (+ 1 (* (sqrt x) y)) x)
(- (+ 1 (* (sqrt x) y)) x)
(- (+ 1 (* (sqrt x) y)) x)
(* (sqrt x) y)
(* (sqrt x) y)
(* (sqrt x) y)
(* (sqrt x) y)
(* (sqrt x) y)
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* (sqrt x) y)
(* (sqrt x) y)
(* (sqrt x) y)
(* (sqrt x) y)
(* (sqrt x) y)
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(* (sqrt x) y)
(* (sqrt x) y)
(* (sqrt x) y)
(* (sqrt x) y)
(+ 1 (* (sqrt x) y))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(* (sqrt x) y)
(* (sqrt x) y)
(* (sqrt x) y)
(* (sqrt x) y)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* x (- (* (sqrt (/ 1 x)) y) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* (sqrt x) y)
(* (sqrt x) y)
(* (sqrt x) y)
(* (sqrt x) y)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* x (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))))))
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* (sqrt x) (* y (pow (sqrt -1) 2))))
(* -1 (* (sqrt x) (* y (pow (sqrt -1) 2))))
(* -1 (* (sqrt x) (* y (pow (sqrt -1) 2))))
(* -1 (* (sqrt x) (* y (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)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))

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

rewrite220.0ms (4.1%)

Memory

2.2MiB live, 161.1MiB allocated

Rules

6 324×	`lower-fma.f64`
6 324×	`lower-fma.f32`
4 236×	`lower-*.f32`
4 234×	`lower-*.f64`
2 084×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
0	11	17
1	46	17
2	357	17
3	5315	17
0	8974	16

Stop Event

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

Counts

4 → 252

Calls

Call 1

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

Outputs
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eval57.0ms (1.1%)

Memory: -8.8MiB live, 78.1MiB allocated
Compiler: Compiled 5 943 to 749 computations (87.4% saved)

prune16.0ms (0.3%)

Memory

4.6MiB live, 42.9MiB allocated

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	310	14	324
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	311	14	325

Accuracy

100.0%

Counts

325 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.7%	(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (*.f64 (pow.f64 x #s(literal 1/4 binary64)) y) (-.f64 #s(literal 1 binary64) x))
	76.6%	(fma.f64 (-.f64 #s(literal 1 binary64) x) (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 x) y x))) (neg.f64 (/.f64 (.f64 (.f64 y x) y) (-.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 x) y x)))))
▶	99.9%	(fma.f64 (sqrt.f64 x) y (-.f64 #s(literal 1 binary64) x))
▶	99.8%	(/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (sqrt.f64 x) y (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
	48.4%	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (sqrt.f64 x) y (fma.f64 #s(literal -1 binary64) x #s(literal -1 binary64))) (-.f64 (.f64 (.f64 y x) y) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
▶	48.7%	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 x) y x)) (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 x (*.f64 (sqrt.f64 x) y)) #s(literal 2 binary64)))))
	67.0%	(+.f64 (/.f64 (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal -1 binary64))) (*.f64 y (sqrt.f64 x)))
	99.8%	(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))))
	77.6%	(+.f64 (-.f64 #s(literal 1 binary64) x) (.f64 y (pow.f64 (.f64 x x) #s(literal 1/4 binary64))))
	92.7%	(.f64 (fma.f64 (sqrt.f64 x) y (-.f64 #s(literal 1 binary64) x)) (.f64 (-.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 x) y x)) (pow.f64 (-.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 x) y x)) #s(literal -1 binary64))))
	69.0%	#s(approx (+ (- 1 x) (* y (sqrt x))) (fma.f64 y (sqrt.f64 x) #s(literal 1 binary64)))
▶	63.1%	#s(approx (+ (- 1 x) (* y (sqrt x))) (-.f64 #s(literal 1 binary64) x))
▶	62.5%	#s(approx (+ (- 1 x) (* y (sqrt x))) (*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y #s(literal -1 binary64)) x))
	38.1%	#s(approx (+ (- 1 x) (* y (sqrt x))) (*.f64 y (sqrt.f64 x)))

Compiler

Compiled 380 to 266 computations (30% saved)

simplify325.0ms (6%)

Memory

6.4MiB live, 160.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 (sqrt.f64 x) y x)
cost-diff	0	(-.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 x) y x))
cost-diff	0	(/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 x) y x)) (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 x (*.f64 (sqrt.f64 x) y)) #s(literal 2 binary64))))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 x) y x)) (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 x (*.f64 (sqrt.f64 x) y)) #s(literal 2 binary64)))))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(fma.f64 (sqrt.f64 x) y (-.f64 #s(literal 1 binary64) x))
cost-diff	0	(pow.f64 (fma.f64 (sqrt.f64 x) y (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
cost-diff	7168	(/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (sqrt.f64 x) y (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
cost-diff	0	(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y #s(literal -1 binary64))
cost-diff	0	(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y #s(literal -1 binary64)) x)
cost-diff	0	#s(approx (+ (- 1 x) (* y (sqrt x))) (*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y #s(literal -1 binary64)) x))
cost-diff	0	(-.f64 #s(literal 1 binary64) x)
cost-diff	0	#s(approx (+ (- 1 x) (* y (sqrt x))) (-.f64 #s(literal 1 binary64) x))
cost-diff	0	(-.f64 #s(literal 1 binary64) x)
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(fma.f64 (sqrt.f64 x) y (-.f64 #s(literal 1 binary64) x))

Rules

10 072×	`lower-fma.f32`
10 066×	`lower-fma.f64`
2 396×	`lower-*.f32`
2 392×	`lower-*.f64`
1 684×	`lower--.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	28	197
0	46	191
1	81	191
2	146	189
3	382	189
4	1210	189
5	4459	189
0	8209	189

Stop Event

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

Calls

Call 1

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

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

localize84.0ms (1.6%)

Memory

17.0MiB live, 90.6MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.12890625	(fma.f64 (sqrt.f64 x) y x)
accuracy	0.1328125	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 x) y x)) (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 x (*.f64 (sqrt.f64 x) y)) #s(literal 2 binary64)))))
accuracy	0.2578125	(*.f64 (sqrt.f64 x) y)
accuracy	21.736912680523844	(/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 x) y x)) (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 x (*.f64 (sqrt.f64 x) y)) #s(literal 2 binary64))))
accuracy	0	(sqrt.f64 x)
accuracy	0.0859375	(fma.f64 (sqrt.f64 x) y (-.f64 #s(literal 1 binary64) x))
accuracy	0.12890625	(/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (sqrt.f64 x) y (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
accuracy	0.2923182774472468	(pow.f64 (fma.f64 (sqrt.f64 x) y (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
accuracy	0.11328125	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy	0.12109375	(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y #s(literal -1 binary64))
accuracy	3.207784621031485	(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y #s(literal -1 binary64)) x)
accuracy	20.804585654102873	#s(approx (+ (- 1 x) (* y (sqrt x))) (*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y #s(literal -1 binary64)) x))
accuracy	0	(-.f64 #s(literal 1 binary64) x)
accuracy	23.608575991597185	#s(approx (+ (- 1 x) (* y (sqrt x))) (-.f64 #s(literal 1 binary64) x))
accuracy	0	(-.f64 #s(literal 1 binary64) x)
accuracy	0	(sqrt.f64 x)
accuracy	0.0859375	(fma.f64 (sqrt.f64 x) y (-.f64 #s(literal 1 binary64) x))

Samples

66.0ms	255×	0	valid
0.0ms	1×	1	valid

Compiler

Compiled 195 to 27 computations (86.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 47.0ms

ival-add: 20.0ms (42.6% of total)

ival-div: 6.0ms (12.8% of total)

ival-mult: 6.0ms (12.8% of total)

ival-sub: 4.0ms (8.5% of total)

ival-sqrt: 4.0ms (8.5% of total)

ival-pow: 4.0ms (8.5% of total)

ival-pow2: 2.0ms (4.3% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series56.0ms (1%)

Memory

-10.0MiB live, 43.2MiB allocated

Counts

15 → 324

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
24.0ms	x	@	0	((+ (* (sqrt x) y) (- 1 x)) (sqrt x) (- 1 x) (+ (- 1 x) (* y (sqrt x))) (+ (- 1 x) (* y (sqrt x))) (* (+ (* (sqrt (/ 1 x)) y) -1) x) (+ (* (sqrt (/ 1 x)) y) -1) (sqrt (/ 1 x)) (/ 1 (pow (+ (* (sqrt x) y) (- 1 x)) -1)) (pow (+ (* (sqrt x) y) (- 1 x)) -1) (/ 1 (/ (- 1 (+ (* (sqrt x) y) x)) (- 1 (pow (- x (* (sqrt x) y)) 2)))) (/ (- 1 (+ (* (sqrt x) y) x)) (- 1 (pow (- x (* (sqrt x) y)) 2))) (- 1 (+ (* (sqrt x) y) x)) (+ (* (sqrt x) y) x) (* (sqrt x) y))
5.0ms	x	@	-inf	((+ (* (sqrt x) y) (- 1 x)) (sqrt x) (- 1 x) (+ (- 1 x) (* y (sqrt x))) (+ (- 1 x) (* y (sqrt x))) (* (+ (* (sqrt (/ 1 x)) y) -1) x) (+ (* (sqrt (/ 1 x)) y) -1) (sqrt (/ 1 x)) (/ 1 (pow (+ (* (sqrt x) y) (- 1 x)) -1)) (pow (+ (* (sqrt x) y) (- 1 x)) -1) (/ 1 (/ (- 1 (+ (* (sqrt x) y) x)) (- 1 (pow (- x (* (sqrt x) y)) 2)))) (/ (- 1 (+ (* (sqrt x) y) x)) (- 1 (pow (- x (* (sqrt x) y)) 2))) (- 1 (+ (* (sqrt x) y) x)) (+ (* (sqrt x) y) x) (* (sqrt x) y))
4.0ms	y	@	-inf	((+ (* (sqrt x) y) (- 1 x)) (sqrt x) (- 1 x) (+ (- 1 x) (* y (sqrt x))) (+ (- 1 x) (* y (sqrt x))) (* (+ (* (sqrt (/ 1 x)) y) -1) x) (+ (* (sqrt (/ 1 x)) y) -1) (sqrt (/ 1 x)) (/ 1 (pow (+ (* (sqrt x) y) (- 1 x)) -1)) (pow (+ (* (sqrt x) y) (- 1 x)) -1) (/ 1 (/ (- 1 (+ (* (sqrt x) y) x)) (- 1 (pow (- x (* (sqrt x) y)) 2)))) (/ (- 1 (+ (* (sqrt x) y) x)) (- 1 (pow (- x (* (sqrt x) y)) 2))) (- 1 (+ (* (sqrt x) y) x)) (+ (* (sqrt x) y) x) (* (sqrt x) y))
4.0ms	y	@	0	((+ (* (sqrt x) y) (- 1 x)) (sqrt x) (- 1 x) (+ (- 1 x) (* y (sqrt x))) (+ (- 1 x) (* y (sqrt x))) (* (+ (* (sqrt (/ 1 x)) y) -1) x) (+ (* (sqrt (/ 1 x)) y) -1) (sqrt (/ 1 x)) (/ 1 (pow (+ (* (sqrt x) y) (- 1 x)) -1)) (pow (+ (* (sqrt x) y) (- 1 x)) -1) (/ 1 (/ (- 1 (+ (* (sqrt x) y) x)) (- 1 (pow (- x (* (sqrt x) y)) 2)))) (/ (- 1 (+ (* (sqrt x) y) x)) (- 1 (pow (- x (* (sqrt x) y)) 2))) (- 1 (+ (* (sqrt x) y) x)) (+ (* (sqrt x) y) x) (* (sqrt x) y))
3.0ms	x	@	inf	((+ (* (sqrt x) y) (- 1 x)) (sqrt x) (- 1 x) (+ (- 1 x) (* y (sqrt x))) (+ (- 1 x) (* y (sqrt x))) (* (+ (* (sqrt (/ 1 x)) y) -1) x) (+ (* (sqrt (/ 1 x)) y) -1) (sqrt (/ 1 x)) (/ 1 (pow (+ (* (sqrt x) y) (- 1 x)) -1)) (pow (+ (* (sqrt x) y) (- 1 x)) -1) (/ 1 (/ (- 1 (+ (* (sqrt x) y) x)) (- 1 (pow (- x (* (sqrt x) y)) 2)))) (/ (- 1 (+ (* (sqrt x) y) x)) (- 1 (pow (- x (* (sqrt x) y)) 2))) (- 1 (+ (* (sqrt x) y) x)) (+ (* (sqrt x) y) x) (* (sqrt x) y))

simplify176.0ms (3.3%)

Memory

2.3MiB live, 226.0MiB allocated

Algorithm

1×	egg-herbie

Rules

7 284×	`lower-fma.f64`
7 284×	`lower-fma.f32`
5 614×	`lower-*.f64`
5 614×	`lower-*.f32`
3 344×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	680	6251
1	2171	5674
2	7743	5626
0	8314	5410

Stop Event

1×	iter limit
1×	node limit

Counts

324 → 323

Calls

Call 1

Inputs
(- 1 x)
(- (+ 1 (* (sqrt x) y)) x)
(- (+ 1 (* (sqrt x) y)) x)
(- (+ 1 (* (sqrt x) y)) x)
(- 1 x)
(- (+ 1 (* (sqrt x) y)) x)
(- (+ 1 (* (sqrt x) y)) x)
(- (+ 1 (* (sqrt x) y)) x)
(- 1 x)
(- (+ 1 (* (sqrt x) y)) x)
(- (+ 1 (* (sqrt x) y)) x)
(- (+ 1 (* (sqrt x) y)) x)
(* -1 x)
(+ (* -1 x) (* (sqrt x) y))
(+ (* -1 x) (* (sqrt x) y))
(+ (* -1 x) (* (sqrt x) y))
-1
(- (* (sqrt (/ 1 x)) y) 1)
(- (* (sqrt (/ 1 x)) y) 1)
(- (* (sqrt (/ 1 x)) y) 1)
(- 1 x)
(- (+ 1 (* (sqrt x) y)) x)
(- (+ 1 (* (sqrt x) y)) x)
(- (+ 1 (* (sqrt x) y)) x)
(/ 1 (- 1 x))
(+ (* -1 (* (sqrt x) (/ y (pow (- 1 x) 2)))) (/ 1 (- 1 x)))
(+ (* y (- (/ (* x y) (pow (- 1 x) 3)) (* (sqrt x) (/ 1 (pow (- 1 x) 2))))) (/ 1 (- 1 x)))
(+ (* y (- (* y (- (* -1 (* (sqrt (pow x 3)) (/ y (pow (- 1 x) 4)))) (* -1 (/ x (pow (- 1 x) 3))))) (* (sqrt x) (/ 1 (pow (- 1 x) 2))))) (/ 1 (- 1 x)))
(/ (- 1 (pow x 2)) (- 1 x))
(- (+ (* y (- (* 2 (* (sqrt (pow x 3)) (/ 1 (- 1 x)))) (* -1 (* (sqrt x) (/ (- 1 (pow x 2)) (pow (- 1 x) 2)))))) (/ 1 (- 1 x))) (/ (pow x 2) (- 1 x)))
(- (+ (* y (- (+ (* 2 (* (sqrt (pow x 3)) (/ 1 (- 1 x)))) (* y (- (* -1 (/ x (- 1 x))) (* -1 (* (sqrt x) (/ (- (* 2 (* (sqrt (pow x 3)) (/ 1 (- 1 x)))) (* -1 (* (sqrt x) (/ (- 1 (pow x 2)) (pow (- 1 x) 2))))) (- 1 x))))))) (* -1 (* (sqrt x) (/ (- 1 (pow x 2)) (pow (- 1 x) 2)))))) (/ 1 (- 1 x))) (/ (pow x 2) (- 1 x)))
(- (+ (* y (- (+ (* 2 (* (sqrt (pow x 3)) (/ 1 (- 1 x)))) (* y (- (+ (* -1 (/ x (- 1 x))) (* (sqrt x) (/ (* y (- (* -1 (/ x (- 1 x))) (* -1 (* (sqrt x) (/ (- (* 2 (* (sqrt (pow x 3)) (/ 1 (- 1 x)))) (* -1 (* (sqrt x) (/ (- 1 (pow x 2)) (pow (- 1 x) 2))))) (- 1 x)))))) (- 1 x)))) (* -1 (* (sqrt x) (/ (- (* 2 (* (sqrt (pow x 3)) (/ 1 (- 1 x)))) (* -1 (* (sqrt x) (/ (- 1 (pow x 2)) (pow (- 1 x) 2))))) (- 1 x))))))) (* -1 (* (sqrt x) (/ (- 1 (pow x 2)) (pow (- 1 x) 2)))))) (/ 1 (- 1 x))) (/ (pow x 2) (- 1 x)))
(/ (- 1 x) (- 1 (pow x 2)))
(- (+ (* y (- (* -1 (* (sqrt x) (/ 1 (- 1 (pow x 2))))) (* 2 (* (sqrt (pow x 3)) (/ (- 1 x) (pow (- 1 (pow x 2)) 2)))))) (/ 1 (- 1 (pow x 2)))) (/ x (- 1 (pow x 2))))
(- (+ (* y (- (+ (* -1 (* y (+ (* -1 (/ (* x (- 1 x)) (pow (- 1 (pow x 2)) 2))) (* 2 (* (sqrt (pow x 3)) (/ (- (* -1 (* (sqrt x) (/ 1 (- 1 (pow x 2))))) (* 2 (* (sqrt (pow x 3)) (/ (- 1 x) (pow (- 1 (pow x 2)) 2))))) (- 1 (pow x 2)))))))) (* -1 (* (sqrt x) (/ 1 (- 1 (pow x 2)))))) (* 2 (* (sqrt (pow x 3)) (/ (- 1 x) (pow (- 1 (pow x 2)) 2)))))) (/ 1 (- 1 (pow x 2)))) (/ x (- 1 (pow x 2))))
(- (+ (* y (- (+ (* -1 (* (sqrt x) (/ 1 (- 1 (pow x 2))))) (* y (- (* -1 (* y (+ (* -2 (* (sqrt (pow x 3)) (/ (+ (* -1 (/ (* x (- 1 x)) (pow (- 1 (pow x 2)) 2))) (* 2 (* (sqrt (pow x 3)) (/ (- (* -1 (* (sqrt x) (/ 1 (- 1 (pow x 2))))) (* 2 (* (sqrt (pow x 3)) (/ (- 1 x) (pow (- 1 (pow x 2)) 2))))) (- 1 (pow x 2)))))) (- 1 (pow x 2))))) (* -1 (/ (* x (- (* -1 (* (sqrt x) (/ 1 (- 1 (pow x 2))))) (* 2 (* (sqrt (pow x 3)) (/ (- 1 x) (pow (- 1 (pow x 2)) 2)))))) (- 1 (pow x 2))))))) (+ (* -1 (/ (* x (- 1 x)) (pow (- 1 (pow x 2)) 2))) (* 2 (* (sqrt (pow x 3)) (/ (- (* -1 (* (sqrt x) (/ 1 (- 1 (pow x 2))))) (* 2 (* (sqrt (pow x 3)) (/ (- 1 x) (pow (- 1 (pow x 2)) 2))))) (- 1 (pow x 2))))))))) (* 2 (* (sqrt (pow x 3)) (/ (- 1 x) (pow (- 1 (pow x 2)) 2)))))) (/ 1 (- 1 (pow x 2)))) (/ x (- 1 (pow x 2))))
(- 1 x)
(- (+ 1 (* -1 (* (sqrt x) y))) x)
(- (+ 1 (* -1 (* (sqrt x) y))) x)
(- (+ 1 (* -1 (* (sqrt x) y))) x)
x
(+ x (* (sqrt x) y))
(+ x (* (sqrt x) y))
(+ x (* (sqrt x) y))
(* (sqrt x) y)
(* (sqrt x) y)
(* (sqrt x) y)
(* (sqrt x) y)
(* (sqrt x) y)
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* (sqrt x) y)
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* (sqrt x) y)
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* (sqrt x) y)
(* y (+ (sqrt x) (* -1 (/ x y))))
(* y (+ (sqrt x) (* -1 (/ x y))))
(* y (+ (sqrt x) (* -1 (/ x y))))
(* (sqrt (/ 1 x)) y)
(* y (- (sqrt (/ 1 x)) (/ 1 y)))
(* y (- (sqrt (/ 1 x)) (/ 1 y)))
(* y (- (sqrt (/ 1 x)) (/ 1 y)))
(* (sqrt x) y)
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* (sqrt (/ 1 x)) (/ 1 y))
(/ (- (+ (sqrt (/ 1 x)) (/ 1 y)) (/ 1 (* x y))) y)
(/ (- (+ (sqrt (/ 1 x)) (+ (* -1 (* (sqrt (/ 1 x)) (/ (* (- 1 x) (- 1 (/ 1 x))) (pow y 2)))) (/ 1 y))) (/ 1 (* x y))) y)
(/ (- (+ (sqrt (/ 1 x)) (+ (/ 1 y) (/ (* (pow (- 1 x) 2) (- 1 (/ 1 x))) (* x (pow y 3))))) (+ (* (sqrt (/ 1 x)) (/ (* (- 1 x) (- 1 (/ 1 x))) (pow y 2))) (/ 1 (* x y)))) y)
(* (sqrt x) y)
(* y (- (+ (sqrt x) (* -2 (/ x y))) (* -1 (/ (- 1 x) y))))
(* y (- (+ (sqrt x) (+ (* -2 (/ x y)) (* -1 (* (sqrt (/ 1 x)) (/ (- 1 (pow x 2)) (pow y 2)))))) (+ (* -1 (* (sqrt (/ 1 x)) (/ (* (- 1 x) (- (* -2 x) (* -1 (- 1 x)))) (pow y 2)))) (* -1 (/ (- 1 x) y)))))
(* y (- (+ (sqrt x) (+ (* -2 (/ x y)) (+ (* -1 (* (sqrt (/ 1 x)) (/ (- 1 (pow x 2)) (pow y 2)))) (* (sqrt (/ 1 x)) (/ (* (- 1 x) (- (* -1 (* (sqrt (/ 1 x)) (- 1 (pow x 2)))) (* -1 (* (sqrt (/ 1 x)) (* (- 1 x) (- (* -2 x) (* -1 (- 1 x)))))))) (pow y 3)))))) (+ (* -1 (* (sqrt (/ 1 x)) (/ (* (- 1 x) (- (* -2 x) (* -1 (- 1 x)))) (pow y 2)))) (* -1 (/ (- 1 x) y)))))
(* (sqrt (/ 1 x)) (/ 1 y))
(/ (+ (sqrt (/ 1 x)) (+ (* -1 (/ (- 1 x) (* x y))) (* 2 (/ 1 y)))) y)
(/ (+ (sqrt (/ 1 x)) (+ (* -1 (/ (+ (* -2 (* (sqrt x) (+ 2 (* -1 (/ (- 1 x) x))))) (* -1 (* (sqrt (/ 1 (pow x 3))) (- 1 (pow x 2))))) (pow y 2))) (+ (* -1 (/ (- 1 x) (* x y))) (* 2 (/ 1 y))))) y)
(/ (- (+ (sqrt (/ 1 x)) (+ (* -1 (/ (+ (* -1 (/ (* (+ 2 (* -1 (/ (- 1 x) x))) (- 1 (pow x 2))) x)) (* 2 (* (sqrt x) (+ (* -2 (* (sqrt x) (+ 2 (* -1 (/ (- 1 x) x))))) (* -1 (* (sqrt (/ 1 (pow x 3))) (- 1 (pow x 2)))))))) (pow y 3))) (+ (* -1 (/ (- 1 x) (* x y))) (* 2 (/ 1 y))))) (+ (* -2 (* (sqrt x) (/ (+ 2 (* -1 (/ (- 1 x) x))) (pow y 2)))) (* -1 (* (sqrt (/ 1 (pow x 3))) (/ (- 1 (pow x 2)) (pow y 2)))))) y)
(* -1 (* (sqrt x) y))
(* y (- (/ 1 y) (+ (sqrt x) (/ x y))))
(* y (- (/ 1 y) (+ (sqrt x) (/ x y))))
(* y (- (/ 1 y) (+ (sqrt x) (/ x y))))
(* (sqrt x) y)
(* y (+ (sqrt x) (/ x y)))
(* y (+ (sqrt x) (/ x y)))
(* y (+ (sqrt x) (/ x y)))
(* (sqrt x) y)
(* (sqrt x) y)
(* (sqrt x) y)
(* (sqrt x) y)
(* (sqrt x) y)
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
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1
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(- 1 (* (sqrt x) y))
(- (+ 1 (* -1 x)) (* (sqrt x) y))
(- (+ 1 (* -1 x)) (* (sqrt x) y))
(- (+ 1 (* -1 x)) (* (sqrt x) y))
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(+ x (* (sqrt x) y))
(* (sqrt x) y)
(* (sqrt x) y)
(* (sqrt x) y)
(* (sqrt x) y)
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(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
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(sqrt x)
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(* -1 x)
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(* x (- (/ 1 x) 1))
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(* x (- (* (sqrt (/ 1 x)) y) 1))
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(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(* x (- (* (sqrt (/ 1 x)) y) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(* x (- (* (sqrt (/ 1 x)) y) 1))
(* x (- (* (sqrt (/ 1 x)) y) 1))
(* x (- (* (sqrt (/ 1 x)) y) 1))
(* x (- (* (sqrt (/ 1 x)) y) 1))
(- (* (sqrt (/ 1 x)) y) 1)
(- (* (sqrt (/ 1 x)) y) 1)
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(sqrt (/ 1 x))
(sqrt (/ 1 x))
(* x (- (* (sqrt (/ 1 x)) y) 1))
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(/ 1 (* x (- (* (sqrt (/ 1 x)) y) 1)))
(/ (- (/ 1 (- (* (sqrt (/ 1 x)) y) 1)) (/ 1 (* x (pow (- (* (sqrt (/ 1 x)) y) 1) 2)))) x)
(/ (- (+ (/ 1 (* (pow x 2) (pow (- (* (sqrt (/ 1 x)) y) 1) 3))) (/ 1 (- (* (sqrt (/ 1 x)) y) 1))) (/ 1 (* x (pow (- (* (sqrt (/ 1 x)) y) 1) 2)))) x)
(/ (- (+ (/ 1 (* (pow x 2) (pow (- (* (sqrt (/ 1 x)) y) 1) 3))) (/ 1 (- (* (sqrt (/ 1 x)) y) 1))) (+ (/ 1 (* x (pow (- (* (sqrt (/ 1 x)) y) 1) 2))) (/ 1 (* (pow x 3) (pow (- (* (sqrt (/ 1 x)) y) 1) 4))))) x)
(/ (* x (pow (- 1 (* (sqrt (/ 1 x)) y)) 2)) (+ 1 (* (sqrt (/ 1 x)) y)))
(* x (+ (/ (pow (- 1 (* (sqrt (/ 1 x)) y)) 2) (* x (pow (+ 1 (* (sqrt (/ 1 x)) y)) 2))) (/ (pow (- 1 (* (sqrt (/ 1 x)) y)) 2) (+ 1 (* (sqrt (/ 1 x)) y)))))
(* x (- (+ (* -1 (/ (+ (* -1 (/ (pow (- 1 (* (sqrt (/ 1 x)) y)) 2) (pow (+ 1 (* (sqrt (/ 1 x)) y)) 3))) (/ 1 (+ 1 (* (sqrt (/ 1 x)) y)))) (pow x 2))) (/ (pow (- 1 (* (sqrt (/ 1 x)) y)) 2) (+ 1 (* (sqrt (/ 1 x)) y)))) (* -1 (/ (pow (- 1 (* (sqrt (/ 1 x)) y)) 2) (* x (pow (+ 1 (* (sqrt (/ 1 x)) y)) 2))))))
(* x (- (+ (* -1 (/ (+ (* -1 (/ (pow (- 1 (* (sqrt (/ 1 x)) y)) 2) (pow (+ 1 (* (sqrt (/ 1 x)) y)) 4))) (/ 1 (pow (+ 1 (* (sqrt (/ 1 x)) y)) 2))) (pow x 3))) (/ (pow (- 1 (* (sqrt (/ 1 x)) y)) 2) (+ 1 (* (sqrt (/ 1 x)) y)))) (+ (* -1 (/ (pow (- 1 (* (sqrt (/ 1 x)) y)) 2) (* x (pow (+ 1 (* (sqrt (/ 1 x)) y)) 2)))) (+ (* -1 (/ (pow (- 1 (* (sqrt (/ 1 x)) y)) 2) (* (pow x 2) (pow (+ 1 (* (sqrt (/ 1 x)) y)) 3)))) (/ 1 (* (pow x 2) (+ 1 (* (sqrt (/ 1 x)) y))))))))
(/ (+ 1 (* (sqrt (/ 1 x)) y)) (* x (pow (- 1 (* (sqrt (/ 1 x)) y)) 2)))
(/ (- (+ (* (sqrt (/ 1 x)) (/ y (pow (- 1 (* (sqrt (/ 1 x)) y)) 2))) (/ 1 (pow (- 1 (* (sqrt (/ 1 x)) y)) 2))) (/ 1 (* x (pow (- 1 (* (sqrt (/ 1 x)) y)) 2)))) x)
(/ (- (+ (* (sqrt (/ 1 x)) (/ y (pow (- 1 (* (sqrt (/ 1 x)) y)) 2))) (+ (* (sqrt (/ 1 (pow x 5))) (/ y (pow (- 1 (* (sqrt (/ 1 x)) y)) 4))) (+ (/ 1 (* (pow x 2) (pow (- 1 (* (sqrt (/ 1 x)) y)) 4))) (/ 1 (pow (- 1 (* (sqrt (/ 1 x)) y)) 2))))) (/ 1 (* x (pow (- 1 (* (sqrt (/ 1 x)) y)) 2)))) x)
(/ (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* (sqrt (/ 1 x)) y)) (pow (- 1 (* (sqrt (/ 1 x)) y)) 4))) (/ 1 (* x (pow (- 1 (* (sqrt (/ 1 x)) y)) 4)))) (pow x 2))) (+ (* (sqrt (/ 1 x)) (/ y (pow (- 1 (* (sqrt (/ 1 x)) y)) 2))) (/ 1 (pow (- 1 (* (sqrt (/ 1 x)) y)) 2)))) (/ 1 (* x (pow (- 1 (* (sqrt (/ 1 x)) y)) 2)))) x)
(* -1 (* x (+ 1 (* (sqrt (/ 1 x)) y))))
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(* x (- (/ 1 x) (+ 1 (* (sqrt (/ 1 x)) y))))
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(* (sqrt x) y)
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(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
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(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
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(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
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(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
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(* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) 1))
(* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) 1))
(* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) 1))
(- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) 1)
(- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) 1)
(- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) 1)
(- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) 1)
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
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(* -1 (* x (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))))))
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(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
(/ -1 (* x (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))))))
(* -1 (/ (+ (/ 1 (* x (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2))) (/ 1 (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))))) x))
(* -1 (/ (+ (/ 1 (* x (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2))) (+ (/ 1 (* (pow x 2) (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 3))) (/ 1 (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))))))) x))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (+ (/ 1 (* x (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 4))) (/ 1 (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 3))) x)) (/ 1 (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2))) x)) (/ 1 (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))))) x))
(/ (* x (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2)) (- 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1 (/ (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2) (* x (pow (- 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2)))) (* -1 (/ (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2) (- 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))))))))
(* -1 (* x (+ (* -1 (/ (- (* -1 (/ (- (/ 1 (- 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))))) (/ (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2) (pow (- 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 3))) x)) (* -1 (/ (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2) (pow (- 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2)))) x)) (* -1 (/ (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2) (- 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))))))))
(* -1 (* x (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (/ (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2) (pow (- 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 4)) (/ 1 (pow (- 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2))) x)) (/ 1 (- 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))))) (/ (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2) (pow (- 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 3))) x)) (* -1 (/ (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2) (pow (- 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2)))) x)) (* -1 (/ (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2) (- 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))))))))
(/ (- 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (* x (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2)))
(* -1 (/ (+ (* -1 (/ (- 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2))) (/ 1 (* x (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2)))) x))
(* -1 (/ (+ (* -1 (/ (- 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2))) (* -1 (/ (- (* -1 (/ (- (* (sqrt (/ 1 x)) (/ (* y (pow (sqrt -1) 2)) (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 4))) (/ 1 (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 4))) x)) (/ 1 (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2))) x))) x))
(* -1 (/ (+ (* -1 (/ (- 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2))) (* -1 (/ (- (* -1 (/ (- (+ (* (sqrt (/ 1 x)) (/ (* y (pow (sqrt -1) 2)) (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 4))) (/ 1 (* x (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 4)))) (/ 1 (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 4))) x)) (/ 1 (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2))) x))) x))
(* -1 (* x (- 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))))))
(* -1 (* x (- 1 (+ (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) (/ 1 x)))))
(* -1 (* x (- 1 (+ (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) (/ 1 x)))))
(* -1 (* x (- 1 (+ (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) (/ 1 x)))))
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(* -1 (* (sqrt x) (* y (pow (sqrt -1) 2))))
(* -1 (* (sqrt x) (* y (pow (sqrt -1) 2))))
(* -1 (* (sqrt x) (* y (pow (sqrt -1) 2))))

Outputs
(- 1 x)
(-.f64 #s(literal 1 binary64) x)
(- (+ 1 (* (sqrt x) y)) x)
(fma.f64 y (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x))
(- (+ 1 (* (sqrt x) y)) x)
(fma.f64 y (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x))
(- (+ 1 (* (sqrt x) y)) x)
(fma.f64 y (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x))
(- 1 x)
(-.f64 #s(literal 1 binary64) x)
(- (+ 1 (* (sqrt x) y)) x)
(fma.f64 y (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x))
(- (+ 1 (* (sqrt x) y)) x)
(fma.f64 y (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x))
(- (+ 1 (* (sqrt x) y)) x)
(fma.f64 y (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x))
(- 1 x)
(-.f64 #s(literal 1 binary64) x)
(- (+ 1 (* (sqrt x) y)) x)
(fma.f64 y (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x))
(- (+ 1 (* (sqrt x) y)) x)
(fma.f64 y (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x))
(- (+ 1 (* (sqrt x) y)) x)
(fma.f64 y (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x))
(* -1 x)
(neg.f64 x)
(+ (* -1 x) (* (sqrt x) y))
(-.f64 (*.f64 y (sqrt.f64 x)) x)
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(* -1 (* x (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (/ (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2) (pow (- 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 4)) (/ 1 (pow (- 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2))) x)) (/ 1 (- 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))))) (/ (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2) (pow (- 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 3))) x)) (* -1 (/ (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2) (pow (- 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2)))) x)) (* -1 (/ (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2) (- 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))))))))
(*.f64 (neg.f64 x) (-.f64 (/.f64 (fma.f64 (/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 (neg.f64 y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (/.f64 (-.f64 (/.f64 (pow.f64 (fma.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64)) (pow.f64 (fma.f64 (neg.f64 (neg.f64 y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (neg.f64 (neg.f64 y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64)))) x)) (/.f64 (pow.f64 (fma.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64)) (pow.f64 (fma.f64 (neg.f64 (neg.f64 y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal 3 binary64)))) x) #s(literal -1 binary64) (/.f64 (pow.f64 (fma.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64)) (pow.f64 (fma.f64 (neg.f64 (neg.f64 y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64)))) (neg.f64 x)) (/.f64 (pow.f64 (fma.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64)) (fma.f64 (neg.f64 (neg.f64 y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))))
(/ (- 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (* x (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2)))
(/.f64 (/.f64 (fma.f64 (neg.f64 (neg.f64 y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) x) (pow.f64 (fma.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64)))
(* -1 (/ (+ (* -1 (/ (- 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2))) (/ 1 (* x (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2)))) x))
(/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (fma.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64))) (/.f64 (fma.f64 (neg.f64 (neg.f64 y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (pow.f64 (fma.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64)))) (neg.f64 x))
(* -1 (/ (+ (* -1 (/ (- 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2))) (* -1 (/ (- (* -1 (/ (- (* (sqrt (/ 1 x)) (/ (* y (pow (sqrt -1) 2)) (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 4))) (/ 1 (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 4))) x)) (/ 1 (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2))) x))) x))
(/.f64 (-.f64 (/.f64 (neg.f64 (fma.f64 (neg.f64 (neg.f64 y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (pow.f64 (fma.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64))) (/.f64 (fma.f64 (/.f64 (/.f64 (fma.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal 4 binary64))) x) #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64)))) x)) (neg.f64 x))
(* -1 (/ (+ (* -1 (/ (- 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2))) (* -1 (/ (- (* -1 (/ (- (+ (* (sqrt (/ 1 x)) (/ (* y (pow (sqrt -1) 2)) (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 4))) (/ 1 (* x (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 4)))) (/ 1 (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 4))) x)) (/ 1 (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2))) x))) x))
(/.f64 (-.f64 (/.f64 (fma.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (fma.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal 4 binary64))) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y #s(literal 1 binary64)) (pow.f64 (fma.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal 4 binary64)))) x) #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64)))) (neg.f64 x)) (/.f64 (fma.f64 (neg.f64 (neg.f64 y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (pow.f64 (fma.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64)))) (neg.f64 x))
(* -1 (* x (- 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))))))
(*.f64 (neg.f64 x) (fma.f64 (neg.f64 (neg.f64 y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(* -1 (* x (- 1 (+ (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) (/ 1 x)))))
(*.f64 (neg.f64 x) (-.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) x))))
(* -1 (* x (- 1 (+ (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) (/ 1 x)))))
(*.f64 (neg.f64 x) (-.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) x))))
(* -1 (* x (- 1 (+ (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) (/ 1 x)))))
(*.f64 (neg.f64 x) (-.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) x))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) 1)))
(*.f64 (fma.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) (neg.f64 x))
(* -1 (* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) 1)))
(*.f64 (fma.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) (neg.f64 x))
(* -1 (* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) 1)))
(*.f64 (fma.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) (neg.f64 x))
(* -1 (* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) 1)))
(*.f64 (fma.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) (neg.f64 x))
(* -1 (* (sqrt x) (* y (pow (sqrt -1) 2))))
(*.f64 y (sqrt.f64 x))
(* -1 (* (sqrt x) (* y (pow (sqrt -1) 2))))
(*.f64 y (sqrt.f64 x))
(* -1 (* (sqrt x) (* y (pow (sqrt -1) 2))))
(*.f64 y (sqrt.f64 x))
(* -1 (* (sqrt x) (* y (pow (sqrt -1) 2))))
(*.f64 y (sqrt.f64 x))

rewrite250.0ms (4.6%)

Memory

6.5MiB live, 246.5MiB allocated

Rules

4 178×	`lower-/.f32`
4 170×	`lower-/.f64`
4 040×	`lower-*.f32`
4 036×	`lower-*.f64`
3 914×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	136
0	46	130
1	213	124
2	1569	124
0	8542	124

Stop Event

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

Counts

15 → 683

Calls

Call 1

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

Outputs
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eval250.0ms (4.6%)

Memory: 8.5MiB live, 349.8MiB allocated
Compiler: Compiled 34 905 to 3 309 computations (90.5% saved)

prune63.0ms (1.2%)

Memory

-6.9MiB live, 114.0MiB allocated

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	1 278	14	1 292
Fresh	8	1	9
Picked	4	1	5
Done	0	0	0
Total	1 290	16	1 306

Accuracy

100.0%

Counts

1 306 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.7%	(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (*.f64 (pow.f64 x #s(literal 1/4 binary64)) y) (-.f64 #s(literal 1 binary64) x))
▶	99.8%	(fma.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64))) y (-.f64 #s(literal 1 binary64) x))
	67.4%	(fma.f64 (sqrt.f64 x) y #s(approx (- 1 x) (neg.f64 x)))
▶	69.0%	(fma.f64 (sqrt.f64 x) y #s(approx (- 1 x) #s(literal 1 binary64)))
	38.1%	(/.f64 #s(literal 1 binary64) #s(approx (pow (+ (* (sqrt x) y) (- 1 x)) -1) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y)))
▶	69.0%	(/.f64 #s(literal 1 binary64) #s(approx (pow (+ (* (sqrt x) y) (- 1 x)) -1) (/.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) #s(literal 1 binary64)))))
	51.4%	(*.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x))))
	38.1%	#s(approx (/ 1 (pow (+ (* (sqrt x) y) (- 1 x)) -1)) (*.f64 y (sqrt.f64 x)))
	43.2%	#s(approx (/ 1 (/ (- 1 (+ (* (sqrt x) y) x)) (- 1 (pow (- x (* (sqrt x) y)) 2)))) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 y y) x)) (-.f64 #s(literal 1 binary64) (*.f64 y (sqrt.f64 x)))))
▶	62.5%	#s(approx (+ (- 1 x) (* y (sqrt x))) (fma.f64 (/.f64 y (sqrt.f64 x)) x (neg.f64 x)))
✓	63.1%	#s(approx (+ (- 1 x) (* y (sqrt x))) (-.f64 #s(literal 1 binary64) x))
	62.5%	#s(approx (+ (- 1 x) (* y (sqrt x))) (*.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) y #s(literal -1 binary64)) x))
	33.2%	#s(approx (+ (- 1 x) (* y (sqrt x))) (.f64 #s(approx (+ ( (sqrt (/ 1 x)) y) -1) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y)) x))
	63.0%	#s(approx (+ (- 1 x) (* y (sqrt x))) #s(approx (- 1 x) (*.f64 (neg.f64 x) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)))))
	31.1%	#s(approx (+ (- 1 x) (* y (sqrt x))) #s(approx (- 1 x) (neg.f64 x)))
▶	32.8%	#s(approx (+ (- 1 x) (* y (sqrt x))) #s(approx (- 1 x) #s(literal 1 binary64)))

Compiler

Compiled 278 to 229 computations (17.6% saved)

simplify70.0ms (1.3%)

Memory

35.5MiB live, 72.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 y (sqrt.f64 x) #s(literal 1 binary64))
cost-diff	0	(/.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) #s(literal 1 binary64)))
cost-diff	0	#s(approx (pow (+ (* (sqrt x) y) (- 1 x)) -1) (/.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) #s(literal 1 binary64))))
cost-diff	0	(/.f64 #s(literal 1 binary64) #s(approx (pow (+ (* (sqrt x) y) (- 1 x)) -1) (/.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) #s(literal 1 binary64)))))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(/.f64 y (sqrt.f64 x))
cost-diff	0	(fma.f64 (/.f64 y (sqrt.f64 x)) x (neg.f64 x))
cost-diff	0	#s(approx (+ (- 1 x) (* y (sqrt x))) (fma.f64 (/.f64 y (sqrt.f64 x)) x (neg.f64 x)))
cost-diff	0	#s(approx (- 1 x) #s(literal 1 binary64))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(fma.f64 (sqrt.f64 x) y #s(approx (- 1 x) #s(literal 1 binary64)))
cost-diff	0	#s(approx (- 1 x) #s(literal 1 binary64))
cost-diff	0	#s(approx (+ (- 1 x) (* y (sqrt x))) #s(approx (- 1 x) #s(literal 1 binary64)))
cost-diff	0	(-.f64 #s(literal 1 binary64) x)
cost-diff	0	(pow.f64 x #s(literal -1/2 binary64))
cost-diff	0	(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64)))
cost-diff	192	(fma.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64))) y (-.f64 #s(literal 1 binary64) x))

Rules

1 072×	`lower-fma.f32`
1 064×	`lower-fma.f64`
544×	`lower-*.f64`
544×	`lower-*.f32`
312×	`lower-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	154
0	45	150
1	75	149
2	116	149
3	214	149
4	385	149
5	780	149
6	1444	149
7	1601	149
8	1682	149
9	1761	149
10	1776	149
11	1782	149
12	1783	149
0	1783	149

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize131.0ms (2.4%)

Memory

-0.5MiB live, 153.8MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.11328125	(fma.f64 y (sqrt.f64 x) #s(literal 1 binary64))
accuracy	0.12890625	(/.f64 #s(literal 1 binary64) #s(approx (pow (+ (* (sqrt x) y) (- 1 x)) -1) (/.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) #s(literal 1 binary64)))))
accuracy	0.3001307774472468	(/.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) #s(literal 1 binary64)))
accuracy	19.517137268316375	#s(approx (pow (+ (* (sqrt x) y) (- 1 x)) -1) (/.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) #s(literal 1 binary64))))
accuracy	0	(neg.f64 x)
accuracy	0.2265625	(/.f64 y (sqrt.f64 x))
accuracy	3.180440871031485	(fma.f64 (/.f64 y (sqrt.f64 x)) x (neg.f64 x))
accuracy	20.804585654102873	#s(approx (+ (- 1 x) (* y (sqrt x))) (fma.f64 (/.f64 y (sqrt.f64 x)) x (neg.f64 x)))
accuracy	0	(sqrt.f64 x)
accuracy	0.0859375	(fma.f64 (sqrt.f64 x) y #s(approx (- 1 x) #s(literal 1 binary64)))
accuracy	31.962539748183463	#s(approx (- 1 x) #s(literal 1 binary64))
accuracy	23.608575991597185	#s(approx (+ (- 1 x) (* y (sqrt x))) #s(approx (- 1 x) #s(literal 1 binary64)))
accuracy	31.962539748183463	#s(approx (- 1 x) #s(literal 1 binary64))
accuracy	0	(pow.f64 x #s(literal -1/2 binary64))
accuracy	0	(-.f64 #s(literal 1 binary64) x)
accuracy	0.0859375	(fma.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64))) y (-.f64 #s(literal 1 binary64) x))
accuracy	0.2578125	(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64)))

Samples

113.0ms	255×	0	valid
0.0ms	1×	1	valid

Compiler

Compiled 124 to 25 computations (79.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 95.0ms

ival-pow: 67.0ms (70.2% of total)

ival-mult: 10.0ms (10.5% of total)

ival-div: 9.0ms (9.4% of total)

ival-add: 5.0ms (5.2% of total)

ival-sqrt: 2.0ms (2.1% of total)

ival-sub: 1.0ms (1% of total)

ival-neg: 1.0ms (1% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series35.0ms (0.7%)

Memory

-17.9MiB live, 19.6MiB allocated

Counts

16 → 312

Calls

Call 1

Inputs
#s(alt (fma.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64))) y (-.f64 #s(literal 1 binary64) x)) (patch (fma.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64))) y (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64))) (patch (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64))) #<representation binary64>) () ())
#s(alt (pow.f64 x #s(literal -1/2 binary64)) (patch (pow.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())
#s(alt #s(approx (+ (- 1 x) (* y (sqrt x))) #s(approx (- 1 x) #s(literal 1 binary64))) (patch #s(approx (+ (- 1 x) (* y (sqrt x))) #s(approx (- 1 x) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (- 1 x) #s(literal 1 binary64)) (patch #s(approx (- 1 x) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (sqrt.f64 x) y #s(approx (- 1 x) #s(literal 1 binary64))) (patch (fma.f64 (sqrt.f64 x) y #s(approx (- 1 x) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())
#s(alt #s(approx (+ (- 1 x) (* y (sqrt x))) (fma.f64 (/.f64 y (sqrt.f64 x)) x (neg.f64 x))) (patch #s(approx (+ (- 1 x) (* y (sqrt x))) (fma.f64 (/.f64 y (sqrt.f64 x)) x (neg.f64 x))) #<representation binary64>) () ())
#s(alt (fma.f64 (/.f64 y (sqrt.f64 x)) x (neg.f64 x)) (patch (fma.f64 (/.f64 y (sqrt.f64 x)) x (neg.f64 x)) #<representation binary64>) () ())
#s(alt (/.f64 y (sqrt.f64 x)) (patch (/.f64 y (sqrt.f64 x)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) #s(approx (pow (+ (* (sqrt x) y) (- 1 x)) -1) (/.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) #s(literal 1 binary64))))) (patch (/.f64 #s(literal 1 binary64) #s(approx (pow (+ (* (sqrt x) y) (- 1 x)) -1) (/.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt #s(approx (pow (+ (* (sqrt x) y) (- 1 x)) -1) (/.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) #s(literal 1 binary64)))) (patch #s(approx (pow (+ (* (sqrt x) y) (- 1 x)) -1) (/.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 y (sqrt.f64 x) #s(literal 1 binary64)) (patch (fma.f64 y (sqrt.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())

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

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	x	@	0	((+ (* (/ 1 (pow x -1/2)) y) (- 1 x)) (/ 1 (pow x -1/2)) (pow x -1/2) (- 1 x) (+ (- 1 x) (* y (sqrt x))) (- 1 x) (+ (* (sqrt x) y) (- 1 x)) (sqrt x) (+ (- 1 x) (* y (sqrt x))) (+ (* (/ y (sqrt x)) x) (neg x)) (/ y (sqrt x)) (/ 1 (pow (+ (* (sqrt x) y) (- 1 x)) -1)) (pow (+ (* (sqrt x) y) (- 1 x)) -1) (/ 1 (+ (* y (sqrt x)) 1)) (+ (* y (sqrt x)) 1) (neg x))
4.0ms	x	@	-inf	((+ (* (/ 1 (pow x -1/2)) y) (- 1 x)) (/ 1 (pow x -1/2)) (pow x -1/2) (- 1 x) (+ (- 1 x) (* y (sqrt x))) (- 1 x) (+ (* (sqrt x) y) (- 1 x)) (sqrt x) (+ (- 1 x) (* y (sqrt x))) (+ (* (/ y (sqrt x)) x) (neg x)) (/ y (sqrt x)) (/ 1 (pow (+ (* (sqrt x) y) (- 1 x)) -1)) (pow (+ (* (sqrt x) y) (- 1 x)) -1) (/ 1 (+ (* y (sqrt x)) 1)) (+ (* y (sqrt x)) 1) (neg x))
2.0ms	x	@	inf	((+ (* (/ 1 (pow x -1/2)) y) (- 1 x)) (/ 1 (pow x -1/2)) (pow x -1/2) (- 1 x) (+ (- 1 x) (* y (sqrt x))) (- 1 x) (+ (* (sqrt x) y) (- 1 x)) (sqrt x) (+ (- 1 x) (* y (sqrt x))) (+ (* (/ y (sqrt x)) x) (neg x)) (/ y (sqrt x)) (/ 1 (pow (+ (* (sqrt x) y) (- 1 x)) -1)) (pow (+ (* (sqrt x) y) (- 1 x)) -1) (/ 1 (+ (* y (sqrt x)) 1)) (+ (* y (sqrt x)) 1) (neg x))
1.0ms	y	@	-inf	((+ (* (/ 1 (pow x -1/2)) y) (- 1 x)) (/ 1 (pow x -1/2)) (pow x -1/2) (- 1 x) (+ (- 1 x) (* y (sqrt x))) (- 1 x) (+ (* (sqrt x) y) (- 1 x)) (sqrt x) (+ (- 1 x) (* y (sqrt x))) (+ (* (/ y (sqrt x)) x) (neg x)) (/ y (sqrt x)) (/ 1 (pow (+ (* (sqrt x) y) (- 1 x)) -1)) (pow (+ (* (sqrt x) y) (- 1 x)) -1) (/ 1 (+ (* y (sqrt x)) 1)) (+ (* y (sqrt x)) 1) (neg x))
1.0ms	y	@	inf	((+ (* (/ 1 (pow x -1/2)) y) (- 1 x)) (/ 1 (pow x -1/2)) (pow x -1/2) (- 1 x) (+ (- 1 x) (* y (sqrt x))) (- 1 x) (+ (* (sqrt x) y) (- 1 x)) (sqrt x) (+ (- 1 x) (* y (sqrt x))) (+ (* (/ y (sqrt x)) x) (neg x)) (/ y (sqrt x)) (/ 1 (pow (+ (* (sqrt x) y) (- 1 x)) -1)) (pow (+ (* (sqrt x) y) (- 1 x)) -1) (/ 1 (+ (* y (sqrt x)) 1)) (+ (* y (sqrt x)) 1) (neg x))

simplify172.0ms (3.2%)

Memory

7.3MiB live, 188.6MiB allocated

Algorithm

1×	egg-herbie

Rules

7 880×	`lower-fma.f64`
7 880×	`lower-fma.f32`
4 012×	`lower-*.f64`
4 012×	`lower-*.f32`
3 494×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	324	3037
1	969	2812
2	2894	2765
0	8849	2596

Stop Event

1×	iter limit
1×	node limit

Counts

312 → 312

Calls

Call 1

Inputs
(- 1 x)
(- (+ 1 (* (sqrt x) y)) x)
(- (+ 1 (* (sqrt x) y)) x)
(- (+ 1 (* (sqrt x) y)) x)
(- 1 x)
(- (+ 1 (* (sqrt x) y)) x)
(- (+ 1 (* (sqrt x) y)) x)
(- (+ 1 (* (sqrt x) y)) x)
(- 1 x)
(- (+ 1 (* (sqrt x) y)) x)
(- (+ 1 (* (sqrt x) y)) x)
(- (+ 1 (* (sqrt x) y)) x)
(- 1 x)
(- (+ 1 (* (sqrt x) y)) x)
(- (+ 1 (* (sqrt x) y)) x)
(- (+ 1 (* (sqrt x) y)) x)
(* -1 x)
(- (* (sqrt x) y) x)
(- (* (sqrt x) y) x)
(- (* (sqrt x) y) x)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(- 1 x)
(- (+ 1 (* (sqrt x) y)) x)
(- (+ 1 (* (sqrt x) y)) x)
(- (+ 1 (* (sqrt x) y)) x)
(/ 1 (- 1 x))
(+ (* -1 (* (sqrt x) (/ y (pow (- 1 x) 2)))) (/ 1 (- 1 x)))
(+ (* y (- (/ (* x y) (pow (- 1 x) 3)) (* (sqrt x) (/ 1 (pow (- 1 x) 2))))) (/ 1 (- 1 x)))
(+ (* y (- (* y (- (* -1 (* (sqrt (pow x 3)) (/ y (pow (- 1 x) 4)))) (* -1 (/ x (pow (- 1 x) 3))))) (* (sqrt x) (/ 1 (pow (- 1 x) 2))))) (/ 1 (- 1 x)))
1
(+ 1 (* -1 (* (sqrt x) y)))
(+ 1 (* y (- (* x y) (sqrt x))))
(+ 1 (* y (- (* y (- (* -1 (* (sqrt (pow x 3)) y)) (* -1 x))) (sqrt x))))
1
(+ 1 (* (sqrt x) y))
(+ 1 (* (sqrt x) y))
(+ 1 (* (sqrt x) y))
(* (sqrt x) y)
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* (sqrt x) y)
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* (sqrt x) y)
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* (sqrt x) y)
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* (sqrt x) y)
(* y (+ (sqrt x) (* -1 (/ x y))))
(* y (+ (sqrt x) (* -1 (/ x y))))
(* y (+ (sqrt x) (* -1 (/ x y))))
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt x) y)
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* (sqrt (/ 1 x)) (/ 1 y))
(/ (- (+ (sqrt (/ 1 x)) (/ 1 y)) (/ 1 (* x y))) y)
(/ (- (+ (sqrt (/ 1 x)) (+ (* -1 (* (sqrt (/ 1 x)) (/ (* (- 1 x) (- 1 (/ 1 x))) (pow y 2)))) (/ 1 y))) (/ 1 (* x y))) y)
(/ (- (+ (sqrt (/ 1 x)) (+ (/ 1 y) (/ (* (pow (- 1 x) 2) (- 1 (/ 1 x))) (* x (pow y 3))))) (+ (* (sqrt (/ 1 x)) (/ (* (- 1 x) (- 1 (/ 1 x))) (pow y 2))) (/ 1 (* x y)))) y)
(* (sqrt (/ 1 x)) (/ 1 y))
(/ (- (sqrt (/ 1 x)) (/ 1 (* x y))) y)
(/ (- (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow y 2)))) (/ 1 (* x y))) y)
(/ (- (+ (sqrt (/ 1 x)) (* -1 (/ (+ (* -1 (sqrt (/ 1 (pow x 3)))) (/ 1 (* (pow x 2) y))) (pow y 2)))) (/ 1 (* x y))) y)
(* (sqrt x) y)
(* y (+ (sqrt x) (/ 1 y)))
(* y (+ (sqrt x) (/ 1 y)))
(* y (+ (sqrt x) (/ 1 y)))
(* (sqrt x) y)
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(* (sqrt x) y)
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(* (sqrt x) y)
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(* (sqrt x) y)
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(* (sqrt x) y)
(* -1 (* y (+ (* -1 (sqrt x)) (/ x y))))
(* -1 (* y (+ (* -1 (sqrt x)) (/ x y))))
(* -1 (* y (+ (* -1 (sqrt x)) (/ x y))))
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt x) y)
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(* (sqrt (/ 1 x)) (/ 1 y))
(* -1 (/ (+ (* -1 (sqrt (/ 1 x))) (* -1 (/ (- 1 (/ 1 x)) y))) y))
(* -1 (/ (+ (* -1 (sqrt (/ 1 x))) (* -1 (/ (- (+ 1 (* -1 (* (sqrt (/ 1 x)) (/ (* (- 1 x) (- 1 (/ 1 x))) y)))) (/ 1 x)) y))) y))
(* -1 (/ (+ (* -1 (sqrt (/ 1 x))) (* -1 (/ (- (+ 1 (* -1 (/ (- (* -1 (/ (* (pow (- 1 x) 2) (- 1 (/ 1 x))) (* x y))) (* -1 (* (sqrt (/ 1 x)) (* (- 1 x) (- 1 (/ 1 x)))))) y))) (/ 1 x)) y))) y))
(* (sqrt (/ 1 x)) (/ 1 y))
(* -1 (/ (+ (* -1 (sqrt (/ 1 x))) (/ 1 (* x y))) y))
(* -1 (/ (+ (* -1 (sqrt (/ 1 x))) (* -1 (/ (- (* (sqrt (/ 1 (pow x 3))) (/ 1 y)) (/ 1 x)) y))) y))
(* -1 (/ (+ (* -1 (sqrt (/ 1 x))) (* -1 (/ (- (* -1 (/ (- (/ 1 (* (pow x 2) y)) (sqrt (/ 1 (pow x 3)))) y)) (/ 1 x)) y))) y))
(* (sqrt x) y)
(* -1 (* y (- (* -1 (sqrt x)) (/ 1 y))))
(* -1 (* y (- (* -1 (sqrt x)) (/ 1 y))))
(* -1 (* y (- (* -1 (sqrt x)) (/ 1 y))))
(+ 1 (* (sqrt x) y))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* (sqrt x) y))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* (sqrt x) y))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(+ 1 (* (sqrt x) y))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
(* (sqrt x) y)
(+ (* -1 x) (* (sqrt x) y))
(+ (* -1 x) (* (sqrt x) y))
(+ (* -1 x) (* (sqrt x) y))
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(+ 1 (* (sqrt x) y))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
(/ 1 (+ 1 (* (sqrt x) y)))
(+ (/ 1 (+ 1 (* (sqrt x) y))) (/ x (pow (+ 1 (* (sqrt x) y)) 2)))
(+ (* x (+ (/ 1 (pow (+ 1 (* (sqrt x) y)) 2)) (/ x (pow (+ 1 (* (sqrt x) y)) 3)))) (/ 1 (+ 1 (* (sqrt x) y))))
(+ (* x (+ (* x (+ (/ 1 (pow (+ 1 (* (sqrt x) y)) 3)) (/ x (pow (+ 1 (* (sqrt x) y)) 4)))) (/ 1 (pow (+ 1 (* (sqrt x) y)) 2)))) (/ 1 (+ 1 (* (sqrt x) y))))
(/ 1 (+ 1 (* (sqrt x) y)))
(/ 1 (+ 1 (* (sqrt x) y)))
(/ 1 (+ 1 (* (sqrt x) y)))
(/ 1 (+ 1 (* (sqrt x) y)))
(+ 1 (* (sqrt x) y))
(+ 1 (* (sqrt x) y))
(+ 1 (* (sqrt x) y))
(+ 1 (* (sqrt x) y))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* x (- (* (sqrt (/ 1 x)) y) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (* (sqrt (/ 1 x)) y) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (* (sqrt (/ 1 x)) y) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* x (- (* (sqrt (/ 1 x)) y) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(* x (- (* (sqrt (/ 1 x)) y) 1))
(* x (- (* (sqrt (/ 1 x)) y) 1))
(* x (- (* (sqrt (/ 1 x)) y) 1))
(* x (- (* (sqrt (/ 1 x)) y) 1))
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* x (- (* (sqrt (/ 1 x)) y) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(/ 1 (* x (- (* (sqrt (/ 1 x)) y) 1)))
(/ (- (/ 1 (- (* (sqrt (/ 1 x)) y) 1)) (/ 1 (* x (pow (- (* (sqrt (/ 1 x)) y) 1) 2)))) x)
(/ (- (+ (/ 1 (* (pow x 2) (pow (- (* (sqrt (/ 1 x)) y) 1) 3))) (/ 1 (- (* (sqrt (/ 1 x)) y) 1))) (/ 1 (* x (pow (- (* (sqrt (/ 1 x)) y) 1) 2)))) x)
(/ (- (+ (/ 1 (* (pow x 2) (pow (- (* (sqrt (/ 1 x)) y) 1) 3))) (/ 1 (- (* (sqrt (/ 1 x)) y) 1))) (+ (/ 1 (* x (pow (- (* (sqrt (/ 1 x)) y) 1) 2))) (/ 1 (* (pow x 3) (pow (- (* (sqrt (/ 1 x)) y) 1) 4))))) x)
(* (sqrt (/ 1 x)) (/ 1 y))
(/ (- (* (sqrt x) (/ 1 y)) (/ 1 (pow y 2))) x)
(/ (- (+ (* (sqrt x) (/ 1 y)) (* (sqrt (/ 1 x)) (/ 1 (pow y 3)))) (/ 1 (pow y 2))) x)
(/ (- (* (sqrt x) (/ 1 y)) (+ (* -1 (* (sqrt (/ 1 x)) (/ 1 (pow y 3)))) (+ (/ 1 (* x (pow y 4))) (/ 1 (pow y 2))))) x)
(* (sqrt x) y)
(* x (+ (* (sqrt (/ 1 x)) y) (/ 1 x)))
(* x (+ (* (sqrt (/ 1 x)) y) (/ 1 x)))
(* x (+ (* (sqrt (/ 1 x)) y) (/ 1 x)))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 (* x (+ 1 (* (sqrt (/ 1 x)) y))))
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) y)) (/ 1 x))))
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) y)) (/ 1 x))))
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) y)) (/ 1 x))))
(* -1 (sqrt x))
(* -1 (sqrt x))
(* -1 (sqrt x))
(* -1 (sqrt x))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))))))
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))))))
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
(* -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)))
(* -1 (* x (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))))))
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
(* -1 (* x (+ 1 (* -1 (* (sqrt (/ 1 x)) y)))))
(* -1 (* x (+ 1 (* -1 (* (sqrt (/ 1 x)) y)))))
(* -1 (* x (+ 1 (* -1 (* (sqrt (/ 1 x)) y)))))
(* -1 (* x (+ 1 (* -1 (* (sqrt (/ 1 x)) y)))))
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* -1 (* x (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))))))
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
(/ -1 (* x (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))))))
(* -1 (/ (+ (/ 1 (* x (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2))) (/ 1 (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))))) x))
(* -1 (/ (+ (/ 1 (* x (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2))) (+ (/ 1 (* (pow x 2) (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 3))) (/ 1 (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))))))) x))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (+ (/ 1 (* x (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 4))) (/ 1 (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 3))) x)) (/ 1 (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2))) x)) (/ 1 (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))))) x))
(* -1 (* (sqrt (/ 1 x)) (/ 1 y)))
(* -1 (/ (- (* (sqrt x) (/ 1 y)) (/ 1 (* (pow y 2) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -1 (/ (- (* -1 (* (sqrt x) (/ 1 (* (pow y 3) (pow (sqrt -1) 2))))) (* -1 (/ x (* (pow y 2) (pow (sqrt -1) 2))))) x)) (* (sqrt x) (/ 1 y))) x))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (/ x (* (pow y 4) (pow (sqrt -1) 4))) (* -1 (* (sqrt (pow x 3)) (/ 1 (* (pow y 3) (pow (sqrt -1) 2)))))) x)) (* -1 (/ x (* (pow y 2) (pow (sqrt -1) 2))))) x)) (* (sqrt x) (/ 1 y))) x))
(* -1 (* (sqrt x) (* y (pow (sqrt -1) 2))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) (/ 1 x))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) (/ 1 x))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) (/ 1 x))))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)

Outputs
(- 1 x)
(-.f64 #s(literal 1 binary64) x)
(- (+ 1 (* (sqrt x) y)) x)
(fma.f64 y (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x))
(- (+ 1 (* (sqrt x) y)) x)
(fma.f64 y (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x))
(- (+ 1 (* (sqrt x) y)) x)
(fma.f64 y (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x))
(- 1 x)
(-.f64 #s(literal 1 binary64) x)
(- (+ 1 (* (sqrt x) y)) x)
(fma.f64 y (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x))
(- (+ 1 (* (sqrt x) y)) x)
(fma.f64 y (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x))
(- (+ 1 (* (sqrt x) y)) x)
(fma.f64 y (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x))
(- 1 x)
(-.f64 #s(literal 1 binary64) x)
(- (+ 1 (* (sqrt x) y)) x)
(fma.f64 y (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x))
(- (+ 1 (* (sqrt x) y)) x)
(fma.f64 y (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x))
(- (+ 1 (* (sqrt x) y)) x)
(fma.f64 y (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x))
(- 1 x)
(-.f64 #s(literal 1 binary64) x)
(- (+ 1 (* (sqrt x) y)) x)
(fma.f64 y (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x))
(- (+ 1 (* (sqrt x) y)) x)
(fma.f64 y (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x))
(- (+ 1 (* (sqrt x) y)) x)
(fma.f64 y (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x))
(* -1 x)
(neg.f64 x)
(- (* (sqrt x) y) x)
(fma.f64 y (sqrt.f64 x) (neg.f64 x))
(- (* (sqrt x) y) x)
(fma.f64 y (sqrt.f64 x) (neg.f64 x))
(- (* (sqrt x) y) x)
(fma.f64 y (sqrt.f64 x) (neg.f64 x))
(* (sqrt (/ 1 x)) y)
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y)
(* (sqrt (/ 1 x)) y)
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y)
(* (sqrt (/ 1 x)) y)
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y)
(* (sqrt (/ 1 x)) y)
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y)
(- 1 x)
(-.f64 #s(literal 1 binary64) x)
(- (+ 1 (* (sqrt x) y)) x)
(fma.f64 y (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x))
(- (+ 1 (* (sqrt x) y)) x)
(fma.f64 y (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x))
(- (+ 1 (* (sqrt x) y)) x)
(fma.f64 y (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x))
(/ 1 (- 1 x))
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))
(+ (* -1 (* (sqrt x) (/ y (pow (- 1 x) 2)))) (/ 1 (- 1 x)))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (*.f64 (/.f64 y (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))) (sqrt.f64 x)))
(+ (* y (- (/ (* x y) (pow (- 1 x) 3)) (* (sqrt x) (/ 1 (pow (- 1 x) 2))))) (/ 1 (- 1 x)))
(fma.f64 (fma.f64 (/.f64 y (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3 binary64))) x (/.f64 (neg.f64 (sqrt.f64 x)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) y (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
(+ (* y (- (* y (- (* -1 (* (sqrt (pow x 3)) (/ y (pow (- 1 x) 4)))) (* -1 (/ x (pow (- 1 x) 3))))) (* (sqrt x) (/ 1 (pow (- 1 x) 2))))) (/ 1 (- 1 x)))
(fma.f64 (fma.f64 (-.f64 (/.f64 x (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3 binary64))) (*.f64 (/.f64 y (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 4 binary64))) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))))) y (/.f64 (neg.f64 (sqrt.f64 x)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))) y (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
1
#s(literal 1 binary64)
(+ 1 (* -1 (* (sqrt x) y)))
(fma.f64 (neg.f64 y) (sqrt.f64 x) #s(literal 1 binary64))
(+ 1 (* y (- (* x y) (sqrt x))))
(fma.f64 (-.f64 (*.f64 y x) (sqrt.f64 x)) y #s(literal 1 binary64))
(+ 1 (* y (- (* y (- (* -1 (* (sqrt (pow x 3)) y)) (* -1 x))) (sqrt x))))
(fma.f64 (fma.f64 (fma.f64 (neg.f64 y) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) x) y (neg.f64 (sqrt.f64 x))) y #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* (sqrt x) y))
(fma.f64 y (sqrt.f64 x) #s(literal 1 binary64))
(+ 1 (* (sqrt x) y))
(fma.f64 y (sqrt.f64 x) #s(literal 1 binary64))
(+ 1 (* (sqrt x) y))
(fma.f64 y (sqrt.f64 x) #s(literal 1 binary64))
(* (sqrt x) y)
(*.f64 y (sqrt.f64 x))
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) y) (sqrt.f64 x)) y)
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) y) (sqrt.f64 x)) y)
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) y) (sqrt.f64 x)) y)
(* (sqrt x) y)
(*.f64 y (sqrt.f64 x))
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) y) (sqrt.f64 x)) y)
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) y) (sqrt.f64 x)) y)
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) y) (sqrt.f64 x)) y)
(* (sqrt x) y)
(*.f64 y (sqrt.f64 x))
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) y) (sqrt.f64 x)) y)
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) y) (sqrt.f64 x)) y)
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) y) (sqrt.f64 x)) y)
(* (sqrt x) y)
(*.f64 y (sqrt.f64 x))
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) y) (sqrt.f64 x)) y)
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) y) (sqrt.f64 x)) y)
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) y) (sqrt.f64 x)) y)
(* (sqrt x) y)
(*.f64 y (sqrt.f64 x))
(* y (+ (sqrt x) (* -1 (/ x y))))
(*.f64 (-.f64 (sqrt.f64 x) (/.f64 x y)) y)
(* y (+ (sqrt x) (* -1 (/ x y))))
(*.f64 (-.f64 (sqrt.f64 x) (/.f64 x y)) y)
(* y (+ (sqrt x) (* -1 (/ x y))))
(*.f64 (-.f64 (sqrt.f64 x) (/.f64 x y)) y)
(* (sqrt (/ 1 x)) y)
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y)
(* (sqrt (/ 1 x)) y)
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y)
(* (sqrt (/ 1 x)) y)
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y)
(* (sqrt (/ 1 x)) y)
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y)
(* (sqrt x) y)
(*.f64 y (sqrt.f64 x))
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) y) (sqrt.f64 x)) y)
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) y) (sqrt.f64 x)) y)
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) y) (sqrt.f64 x)) y)
(* (sqrt (/ 1 x)) (/ 1 y))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y)
(/ (- (+ (sqrt (/ 1 x)) (/ 1 y)) (/ 1 (* x y))) y)
(/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) y)
(/ (- (+ (sqrt (/ 1 x)) (+ (* -1 (* (sqrt (/ 1 x)) (/ (* (- 1 x) (- 1 (/ 1 x))) (pow y 2)))) (/ 1 y))) (/ 1 (* x y))) y)
(/.f64 (fma.f64 (+.f64 (/.f64 (/.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) y) x) y) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) y)) y)
(/ (- (+ (sqrt (/ 1 x)) (+ (/ 1 y) (/ (* (pow (- 1 x) 2) (- 1 (/ 1 x))) (* x (pow y 3))))) (+ (* (sqrt (/ 1 x)) (/ (* (- 1 x) (- 1 (/ 1 x))) (pow y 2))) (/ 1 (* x y)))) y)
(/.f64 (fma.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (pow.f64 y #s(literal 3 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x) (fma.f64 (+.f64 (/.f64 (/.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) y) x) y) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) y))) y)
(* (sqrt (/ 1 x)) (/ 1 y))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y)
(/ (- (sqrt (/ 1 x)) (/ 1 (* x y))) y)
(/.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 (/.f64 #s(literal 1 binary64) y) x)) y)
(/ (- (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow y 2)))) (/ 1 (* x y))) y)
(/.f64 (+.f64 (/.f64 (-.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) y) (/.f64 #s(literal 1 binary64) x)) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) y)
(/ (- (+ (sqrt (/ 1 x)) (* -1 (/ (+ (* -1 (sqrt (/ 1 (pow x 3)))) (/ 1 (* (pow x 2) y))) (pow y 2)))) (/ 1 (* x y))) y)
(/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (-.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) y) x) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) y)) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) y)
(* (sqrt x) y)
(*.f64 y (sqrt.f64 x))
(* y (+ (sqrt x) (/ 1 y)))
(fma.f64 y (sqrt.f64 x) #s(literal 1 binary64))
(* y (+ (sqrt x) (/ 1 y)))
(fma.f64 y (sqrt.f64 x) #s(literal 1 binary64))
(* y (+ (sqrt x) (/ 1 y)))
(fma.f64 y (sqrt.f64 x) #s(literal 1 binary64))
(* (sqrt x) y)
(*.f64 y (sqrt.f64 x))
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) y) (sqrt.f64 x)) y)
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) y) (sqrt.f64 x)) y)
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) y) (sqrt.f64 x)) y)
(* (sqrt x) y)
(*.f64 y (sqrt.f64 x))
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) y) (sqrt.f64 x)) y)
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) y) (sqrt.f64 x)) y)
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) y) (sqrt.f64 x)) y)
(* (sqrt x) y)
(*.f64 y (sqrt.f64 x))
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) y) (sqrt.f64 x)) y)
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) y) (sqrt.f64 x)) y)
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) y) (sqrt.f64 x)) y)
(* (sqrt x) y)
(*.f64 y (sqrt.f64 x))
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) y) (sqrt.f64 x)) y)
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) y) (sqrt.f64 x)) y)
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) y) (sqrt.f64 x)) y)
(* (sqrt x) y)
(*.f64 y (sqrt.f64 x))
(* -1 (* y (+ (* -1 (sqrt x)) (/ x y))))
(*.f64 (-.f64 (sqrt.f64 x) (/.f64 x y)) y)
(* -1 (* y (+ (* -1 (sqrt x)) (/ x y))))
(*.f64 (-.f64 (sqrt.f64 x) (/.f64 x y)) y)
(* -1 (* y (+ (* -1 (sqrt x)) (/ x y))))
(*.f64 (-.f64 (sqrt.f64 x) (/.f64 x y)) y)
(* (sqrt (/ 1 x)) y)
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y)
(* (sqrt (/ 1 x)) y)
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y)
(* (sqrt (/ 1 x)) y)
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y)
(* (sqrt (/ 1 x)) y)
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y)
(* (sqrt x) y)
(*.f64 y (sqrt.f64 x))
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) y) (sqrt.f64 x)) y)
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) y) (sqrt.f64 x)) y)
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) y) (sqrt.f64 x)) y)
(* (sqrt (/ 1 x)) (/ 1 y))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y)
(* -1 (/ (+ (* -1 (sqrt (/ 1 x))) (* -1 (/ (- 1 (/ 1 x)) y))) y))
(/.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) y)
(* -1 (/ (+ (* -1 (sqrt (/ 1 x))) (* -1 (/ (- (+ 1 (* -1 (* (sqrt (/ 1 x)) (/ (* (- 1 x) (- 1 (/ 1 x))) y)))) (/ 1 x)) y))) y))
(/.f64 (fma.f64 (+.f64 (/.f64 (/.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) y) x) y) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) y)) y)
(* -1 (/ (+ (* -1 (sqrt (/ 1 x))) (* -1 (/ (- (+ 1 (* -1 (/ (- (* -1 (/ (* (pow (- 1 x) 2) (- 1 (/ 1 x))) (* x y))) (* -1 (* (sqrt (/ 1 x)) (* (- 1 x) (- 1 (/ 1 x)))))) y))) (/ 1 x)) y))) y))
(/.f64 (+.f64 (/.f64 (-.f64 (+.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (-.f64 (/.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) y) x) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)))) y) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x)) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) y)
(* (sqrt (/ 1 x)) (/ 1 y))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y)
(* -1 (/ (+ (* -1 (sqrt (/ 1 x))) (/ 1 (* x y))) y))
(/.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 (/.f64 #s(literal 1 binary64) y) x)) y)
(* -1 (/ (+ (* -1 (sqrt (/ 1 x))) (* -1 (/ (- (* (sqrt (/ 1 (pow x 3))) (/ 1 y)) (/ 1 x)) y))) y))
(/.f64 (+.f64 (/.f64 (-.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) y) (/.f64 #s(literal 1 binary64) x)) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) y)
(* -1 (/ (+ (* -1 (sqrt (/ 1 x))) (* -1 (/ (- (* -1 (/ (- (/ 1 (* (pow x 2) y)) (sqrt (/ 1 (pow x 3)))) y)) (/ 1 x)) y))) y))
(/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (-.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) y) x) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) y)) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) y)
(* (sqrt x) y)
(*.f64 y (sqrt.f64 x))
(* -1 (* y (- (* -1 (sqrt x)) (/ 1 y))))
(fma.f64 y (sqrt.f64 x) #s(literal 1 binary64))
(* -1 (* y (- (* -1 (sqrt x)) (/ 1 y))))
(fma.f64 y (sqrt.f64 x) #s(literal 1 binary64))
(* -1 (* y (- (* -1 (sqrt x)) (/ 1 y))))
(fma.f64 y (sqrt.f64 x) #s(literal 1 binary64))
(+ 1 (* (sqrt x) y))
(fma.f64 y (sqrt.f64 x) #s(literal 1 binary64))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
(fma.f64 y (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
(fma.f64 y (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
(fma.f64 y (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* (sqrt x) y))
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(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y #s(literal -1 binary64)) x)
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
(fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y #s(literal -1 binary64)) x #s(literal 1 binary64))
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
(fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y #s(literal -1 binary64)) x #s(literal 1 binary64))
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
(fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y #s(literal -1 binary64)) x #s(literal 1 binary64))
(/ -1 (* x (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))))))
(/.f64 (/.f64 #s(literal -1 binary64) x) (fma.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(* -1 (/ (+ (/ 1 (* x (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2))) (/ 1 (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))))) x))
(/.f64 (+.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) (pow.f64 (fma.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) x)
(* -1 (/ (+ (/ 1 (* x (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2))) (+ (/ 1 (* (pow x 2) (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 3))) (/ 1 (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))))))) x))
(/.f64 (fma.f64 (+.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) (pow.f64 (fma.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal 3 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (fma.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64)))) #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (fma.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))) x)
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (+ (/ 1 (* x (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 4))) (/ 1 (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 3))) x)) (/ 1 (pow (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 2))) x)) (/ 1 (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))))) x))
(/.f64 (+.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64))) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal 3 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (fma.f64 (neg.f64 y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal 4 binary64)))) x)) x)) x)
(* -1 (* (sqrt (/ 1 x)) (/ 1 y)))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 y))
(* -1 (/ (- (* (sqrt x) (/ 1 y)) (/ 1 (* (pow y 2) (pow (sqrt -1) 2)))) x))
(/.f64 (fma.f64 (/.f64 (sqrt.f64 x) y) #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 y y))) x)
(* -1 (/ (+ (* -1 (/ (- (* -1 (* (sqrt x) (/ 1 (* (pow y 3) (pow (sqrt -1) 2))))) (* -1 (/ x (* (pow y 2) (pow (sqrt -1) 2))))) x)) (* (sqrt x) (/ 1 y))) x))
(/.f64 (-.f64 (/.f64 (sqrt.f64 x) y) (/.f64 (-.f64 (/.f64 (sqrt.f64 x) (pow.f64 y #s(literal 3 binary64))) (/.f64 (/.f64 x y) y)) x)) (neg.f64 x))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (/ x (* (pow y 4) (pow (sqrt -1) 4))) (* -1 (* (sqrt (pow x 3)) (/ 1 (* (pow y 3) (pow (sqrt -1) 2)))))) x)) (* -1 (/ x (* (pow y 2) (pow (sqrt -1) 2))))) x)) (* (sqrt x) (/ 1 y))) x))
(/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (-.f64 (/.f64 (/.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64))) x) (/.f64 (/.f64 x y) y))) x) (/.f64 (sqrt.f64 x) y)) (neg.f64 x))
(* -1 (* (sqrt x) (* y (pow (sqrt -1) 2))))
(*.f64 y (sqrt.f64 x))
(* -1 (* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) (/ 1 x))))
(fma.f64 (*.f64 y x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(* -1 (* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) (/ 1 x))))
(fma.f64 (*.f64 y x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(* -1 (* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) (/ 1 x))))
(fma.f64 (*.f64 y x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)

rewrite183.0ms (3.4%)

Memory

0.7MiB live, 310.0MiB allocated

Rules

7 420×	`lower-fma.f32`
7 412×	`lower-fma.f64`
4 412×	`lower-/.f32`
4 404×	`lower-/.f64`
3 884×	`lower-*.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	28	132
0	45	122
1	206	122
2	1256	118
0	8316	118

Stop Event

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

Counts

16 → 649

Calls

Call 1

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

Outputs
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eval254.0ms (4.7%)

Memory: -2.4MiB live, 384.8MiB allocated
Compiler: Compiled 17 820 to 2 627 computations (85.3% saved)

prune29.0ms (0.5%)

Memory

29.5MiB live, 104.0MiB allocated

Pruning

16 alts after pruning (12 fresh and 4 done)

	Pruned	Kept	Total
New	1 055	3	1 058
Fresh	1	9	10
Picked	2	3	5
Done	0	1	1
Total	1 058	16	1 074

Accuracy

100.0%

Counts

1 074 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	64.2%	(fma.f64 (/.f64 y (sqrt.f64 x)) x #s(approx (- 1 x) #s(literal 1 binary64)))
▶	99.8%	(fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) y (-.f64 #s(literal 1 binary64) x))
▶	67.4%	(fma.f64 (sqrt.f64 x) y #s(approx (- 1 x) (neg.f64 x)))
✓	69.0%	(fma.f64 (sqrt.f64 x) y #s(approx (- 1 x) #s(literal 1 binary64)))
▶	69.0%	(fma.f64 y (/.f64 x (sqrt.f64 x)) #s(approx (- 1 x) #s(literal 1 binary64)))
	38.1%	(/.f64 #s(literal 1 binary64) #s(approx (pow (+ (* (sqrt x) y) (- 1 x)) -1) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y)))
	51.4%	(*.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x))))
	38.1%	#s(approx (/ 1 (pow (+ (* (sqrt x) y) (- 1 x)) -1)) (*.f64 y (sqrt.f64 x)))
	43.2%	#s(approx (/ 1 (/ (- 1 (+ (* (sqrt x) y) x)) (- 1 (pow (- x (* (sqrt x) y)) 2)))) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 y y) x)) (-.f64 #s(literal 1 binary64) (*.f64 y (sqrt.f64 x)))))
✓	62.5%	#s(approx (+ (- 1 x) (* y (sqrt x))) (fma.f64 (/.f64 y (sqrt.f64 x)) x (neg.f64 x)))
✓	63.1%	#s(approx (+ (- 1 x) (* y (sqrt x))) (-.f64 #s(literal 1 binary64) x))
	62.5%	#s(approx (+ (- 1 x) (* y (sqrt x))) (*.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) y #s(literal -1 binary64)) x))
▶	33.2%	#s(approx (+ (- 1 x) (* y (sqrt x))) (.f64 #s(approx (+ ( (sqrt (/ 1 x)) y) -1) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y)) x))
	63.0%	#s(approx (+ (- 1 x) (* y (sqrt x))) #s(approx (- 1 x) (*.f64 (neg.f64 x) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)))))
▶	31.1%	#s(approx (+ (- 1 x) (* y (sqrt x))) #s(approx (- 1 x) (neg.f64 x)))
✓	32.8%	#s(approx (+ (- 1 x) (* y (sqrt x))) #s(approx (- 1 x) #s(literal 1 binary64)))

Compiler

Compiled 250 to 207 computations (17.2% saved)

simplify66.0ms (1.2%)

Memory

-7.7MiB live, 77.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y)
cost-diff	0	#s(approx (+ (* (sqrt (/ 1 x)) y) -1) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y))
cost-diff	0	(.f64 #s(approx (+ ( (sqrt (/ 1 x)) y) -1) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y)) x)
cost-diff	0	#s(approx (+ (- 1 x) (* y (sqrt x))) (.f64 #s(approx (+ ( (sqrt (/ 1 x)) y) -1) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y)) x))
cost-diff	0	#s(approx (- 1 x) #s(literal 1 binary64))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(/.f64 x (sqrt.f64 x))
cost-diff	0	(fma.f64 y (/.f64 x (sqrt.f64 x)) #s(approx (- 1 x) #s(literal 1 binary64)))
cost-diff	0	(neg.f64 x)
cost-diff	0	#s(approx (- 1 x) (neg.f64 x))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(fma.f64 (sqrt.f64 x) y #s(approx (- 1 x) (neg.f64 x)))
cost-diff	0	(neg.f64 x)
cost-diff	0	#s(approx (- 1 x) (neg.f64 x))
cost-diff	0	#s(approx (+ (- 1 x) (* y (sqrt x))) #s(approx (- 1 x) (neg.f64 x)))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
cost-diff	0	(fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) y (-.f64 #s(literal 1 binary64) x))
cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))

Rules

864×	`lower-fma.f32`
858×	`lower-fma.f64`
512×	`lower-*.f32`
508×	`lower-*.f64`
256×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	174
0	46	164
1	73	164
2	110	164
3	195	164
4	297	164
5	458	164
6	748	164
7	1130	164
8	1259	164
9	1362	164
10	1405	164
11	1433	164
12	1452	164
13	1456	164
0	1456	161

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize105.0ms (1.9%)

Memory

-22.9MiB live, 175.2MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.24609375	(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y)
accuracy	3.207784621031485	(.f64 #s(approx (+ ( (sqrt (/ 1 x)) y) -1) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y)) x)
accuracy	20.804585654102873	#s(approx (+ (- 1 x) (* y (sqrt x))) (.f64 #s(approx (+ ( (sqrt (/ 1 x)) y) -1) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y)) x))
accuracy	31.710022668616094	#s(approx (+ (* (sqrt (/ 1 x)) y) -1) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y))
accuracy	0	(sqrt.f64 x)
accuracy	0.0859375	(fma.f64 y (/.f64 x (sqrt.f64 x)) #s(approx (- 1 x) #s(literal 1 binary64)))
accuracy	0.48828125	(/.f64 x (sqrt.f64 x))
accuracy	31.962539748183463	#s(approx (- 1 x) #s(literal 1 binary64))
accuracy	0	(sqrt.f64 x)
accuracy	0	(neg.f64 x)
accuracy	0.0859375	(fma.f64 (sqrt.f64 x) y #s(approx (- 1 x) (neg.f64 x)))
accuracy	32.63635138826412	#s(approx (- 1 x) (neg.f64 x))
accuracy	0	(neg.f64 x)
accuracy	23.608575991597185	#s(approx (+ (- 1 x) (* y (sqrt x))) #s(approx (- 1 x) (neg.f64 x)))
accuracy	32.63635138826412	#s(approx (- 1 x) (neg.f64 x))
accuracy	0	(sqrt.f64 x)
accuracy	0.0859375	(fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) y (-.f64 #s(literal 1 binary64) x))
accuracy	0.24609375	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
accuracy	0.2578125	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))

Samples

45.0ms	255×	0	valid
0.0ms	1×	1	valid

Compiler

Compiled 127 to 25 computations (80.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 28.0ms

ival-mult: 9.0ms (32.2% of total)

ival-div: 8.0ms (28.6% of total)

ival-add: 5.0ms (17.9% of total)

ival-sqrt: 4.0ms (14.3% of total)

ival-sub: 1.0ms (3.6% of total)

ival-neg: 1.0ms (3.6% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series15.0ms (0.3%)

Memory

20.8MiB live, 20.8MiB allocated

Counts

15 → 276

Calls

Call 1

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

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

Calls

6 calls:

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

simplify156.0ms (2.9%)

Memory

-26.2MiB live, 147.7MiB allocated

Algorithm

1×	egg-herbie

Rules

8 404×	`lower-fma.f64`
8 404×	`lower-fma.f32`
3 860×	`lower-*.f64`
3 860×	`lower-*.f32`
1 978×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	1857
1	212	1794
2	635	1726
3	1637	1726
4	4024	1726
5	7595	1726
0	8256	1571

Stop Event

1×	iter limit
1×	node limit

Counts

276 → 276

Calls

Call 1

Inputs
(- 1 x)
(- (+ 1 (* (sqrt x) y)) x)
(- (+ 1 (* (sqrt x) y)) x)
(- (+ 1 (* (sqrt x) y)) x)
(- 1 x)
(- (+ 1 (* (sqrt x) y)) x)
(- (+ 1 (* (sqrt x) y)) x)
(- (+ 1 (* (sqrt x) y)) x)
(- 1 x)
(- (+ 1 (* (sqrt x) y)) x)
(- (+ 1 (* (sqrt x) y)) x)
(- (+ 1 (* (sqrt x) y)) x)
(- 1 x)
(- (+ 1 (* (sqrt x) y)) x)
(- (+ 1 (* (sqrt x) y)) x)
(- (+ 1 (* (sqrt x) y)) x)
(- 1 x)
(- (+ 1 (* (sqrt x) y)) x)
(- (+ 1 (* (sqrt x) y)) x)
(- (+ 1 (* (sqrt x) y)) x)
(* -1 x)
(+ (* -1 x) (* (sqrt x) y))
(+ (* -1 x) (* (sqrt x) y))
(+ (* -1 x) (* (sqrt x) y))
-1
(- (* (sqrt (/ 1 x)) y) 1)
(- (* (sqrt (/ 1 x)) y) 1)
(- (* (sqrt (/ 1 x)) y) 1)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt x) y)
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* (sqrt x) y)
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* (sqrt x) y)
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* (sqrt x) y)
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* (sqrt x) y)
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))
(* (sqrt x) y)
(* y (+ (sqrt x) (* -1 (/ x y))))
(* y (+ (sqrt x) (* -1 (/ x y))))
(* y (+ (sqrt x) (* -1 (/ x y))))
(* (sqrt (/ 1 x)) y)
(* y (- (sqrt (/ 1 x)) (/ 1 y)))
(* y (- (sqrt (/ 1 x)) (/ 1 y)))
(* y (- (sqrt (/ 1 x)) (/ 1 y)))
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt x) y)
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(* (sqrt x) y)
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(* (sqrt x) y)
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(* (sqrt x) y)
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(* (sqrt x) y)
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))
(* (sqrt x) y)
(* -1 (* y (+ (* -1 (sqrt x)) (/ x y))))
(* -1 (* y (+ (* -1 (sqrt x)) (/ x y))))
(* -1 (* y (+ (* -1 (sqrt x)) (/ x y))))
(* (sqrt (/ 1 x)) y)
(* -1 (* y (+ (* -1 (sqrt (/ 1 x))) (/ 1 y))))
(* -1 (* y (+ (* -1 (sqrt (/ 1 x))) (/ 1 y))))
(* -1 (* y (+ (* -1 (sqrt (/ 1 x))) (/ 1 y))))
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(+ 1 (* (sqrt x) y))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(+ 1 (* (sqrt x) y))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(+ 1 (* (sqrt x) y))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
(+ 1 (* (sqrt x) y))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* (sqrt x) y))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
(* (sqrt x) y)
(+ (* -1 x) (* (sqrt x) y))
(+ (* -1 x) (* (sqrt x) y))
(+ (* -1 x) (* (sqrt x) y))
(* (sqrt (/ 1 x)) y)
(/ (+ (* -1 x) (* (sqrt x) y)) x)
(/ (+ (* -1 x) (* (sqrt x) y)) x)
(/ (+ (* -1 x) (* (sqrt x) y)) x)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* x (- (* (sqrt (/ 1 x)) y) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* x (- (* (sqrt (/ 1 x)) y) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* x (- (* (sqrt (/ 1 x)) y) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(* x (- (* (sqrt (/ 1 x)) y) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (* (sqrt (/ 1 x)) y) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))
(* x (- (* (sqrt (/ 1 x)) y) 1))
(* x (- (* (sqrt (/ 1 x)) y) 1))
(* x (- (* (sqrt (/ 1 x)) y) 1))
(* x (- (* (sqrt (/ 1 x)) y) 1))
(- (* (sqrt (/ 1 x)) y) 1)
(- (* (sqrt (/ 1 x)) y) 1)
(- (* (sqrt (/ 1 x)) y) 1)
(- (* (sqrt (/ 1 x)) y) 1)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* (sqrt (/ 1 x)) y)
(* -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)))
(* -1 (* x (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))))))
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(* -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)))
(* -1 (* x (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))))))
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 (* x (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))))))
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
(* -1 (* x (+ 1 (* -1 (* (sqrt (/ 1 x)) y)))))
(* -1 (* x (- (+ 1 (* -1 (* (sqrt (/ 1 x)) y))) (/ 1 x))))
(* -1 (* x (- (+ 1 (* -1 (* (sqrt (/ 1 x)) y))) (/ 1 x))))
(* -1 (* x (- (+ 1 (* -1 (* (sqrt (/ 1 x)) y))) (/ 1 x))))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))))))
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
(* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))
(* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) 1))
(* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) 1))
(* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) 1))
(* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) 1))
(- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) 1)
(- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) 1)
(- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) 1)
(- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) 1)
(* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))
(* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))
(* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))
(* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))

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

rewrite187.0ms (3.5%)

Memory

33.6MiB live, 222.4MiB allocated

Rules

6 592×	`lower-fma.f32`
6 586×	`lower-fma.f64`
4 236×	`lower-/.f32`
4 228×	`lower-/.f64`
3 560×	`lower-*.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	140
0	46	128
1	184	113
2	1161	111
0	8520	111

Stop Event

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

Counts

15 → 472

Calls

Call 1

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

Outputs
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eval226.0ms (4.2%)

Memory: -25.8MiB live, 286.7MiB allocated
Compiler: Compiled 12 650 to 1 492 computations (88.2% saved)

prune86.0ms (1.6%)

Memory

-13.2MiB live, 125.4MiB allocated

Pruning

15 alts after pruning (7 fresh and 8 done)

	Pruned	Kept	Total
New	895	3	898
Fresh	3	4	7
Picked	1	4	5
Done	0	4	4
Total	899	15	914

Accuracy

100.0%

Counts

914 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
	65.3%	(fma.f64 (*.f64 (neg.f64 x) y) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #s(approx (- 1 x) #s(literal 1 binary64)))
✓	67.4%	(fma.f64 (sqrt.f64 x) y #s(approx (- 1 x) (neg.f64 x)))
✓	69.0%	(fma.f64 (sqrt.f64 x) y #s(approx (- 1 x) #s(literal 1 binary64)))
✓	69.0%	(fma.f64 y (/.f64 x (sqrt.f64 x)) #s(approx (- 1 x) #s(literal 1 binary64)))
	69.0%	(fma.f64 #s(literal -1 binary64) (/.f64 y (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) #s(approx (- 1 x) #s(literal 1 binary64)))
	38.1%	#s(approx (/ 1 (pow (+ (* (sqrt x) y) (- 1 x)) -1)) (*.f64 y (sqrt.f64 x)))
	43.2%	#s(approx (/ 1 (/ (- 1 (+ (* (sqrt x) y) x)) (- 1 (pow (- x (* (sqrt x) y)) 2)))) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 y y) x)) (-.f64 #s(literal 1 binary64) (*.f64 y (sqrt.f64 x)))))
✓	62.5%	#s(approx (+ (- 1 x) (* y (sqrt x))) (fma.f64 (/.f64 y (sqrt.f64 x)) x (neg.f64 x)))
✓	63.1%	#s(approx (+ (- 1 x) (* y (sqrt x))) (-.f64 #s(literal 1 binary64) x))
	62.5%	#s(approx (+ (- 1 x) (* y (sqrt x))) (*.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) y #s(literal -1 binary64)) x))
	33.3%	#s(approx (+ (- 1 x) (* y (sqrt x))) (.f64 #s(approx (+ ( (sqrt (/ 1 x)) y) -1) (/.f64 y (sqrt.f64 x))) x))
✓	33.2%	#s(approx (+ (- 1 x) (* y (sqrt x))) (.f64 #s(approx (+ ( (sqrt (/ 1 x)) y) -1) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y)) x))
	63.0%	#s(approx (+ (- 1 x) (* y (sqrt x))) #s(approx (- 1 x) (*.f64 (neg.f64 x) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)))))
✓	31.1%	#s(approx (+ (- 1 x) (* y (sqrt x))) #s(approx (- 1 x) (neg.f64 x)))
✓	32.8%	#s(approx (+ (- 1 x) (* y (sqrt x))) #s(approx (- 1 x) #s(literal 1 binary64)))

Compiler

Compiled 499 to 226 computations (54.7% saved)

regimes31.0ms (0.6%)

Memory

29.6MiB live, 67.2MiB allocated

Counts

35 → 1

Calls

Call 1

Inputs
#s(approx (+ (- 1 x) (* y (sqrt x))) #s(approx (- 1 x) #s(literal 1 binary64)))
#s(approx (+ (- 1 x) (* y (sqrt x))) #s(approx (- 1 x) (neg.f64 x)))
#s(approx (+ (- 1 x) (* y (sqrt x))) (-.f64 #s(literal 1 binary64) x))
#s(approx (+ (- 1 x) (* y (sqrt x))) (*.f64 y (sqrt.f64 x)))
#s(approx (/ 1 (pow (+ (* (sqrt x) y) (- 1 x)) -1)) (*.f64 y (sqrt.f64 x)))
#s(approx (+ (- 1 x) (* y (sqrt x))) (fma.f64 y (sqrt.f64 x) #s(literal 1 binary64)))
(fma.f64 (sqrt.f64 x) y #s(approx (- 1 x) #s(literal 1 binary64)))
(fma.f64 (sqrt.f64 x) y #s(approx (- 1 x) (neg.f64 x)))
(fma.f64 (sqrt.f64 x) y (-.f64 #s(literal 1 binary64) x))
#s(approx (+ (- 1 x) (* y (sqrt x))) #s(approx (- 1 x) (*.f64 (neg.f64 x) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)))))
(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))
#s(approx (+ (- 1 x) (* y (sqrt x))) (.f64 #s(approx (+ ( (sqrt (/ 1 x)) y) -1) (/.f64 y (sqrt.f64 x))) x))
(fma.f64 y (/.f64 x (sqrt.f64 x)) #s(approx (- 1 x) #s(literal 1 binary64)))
(fma.f64 (/.f64 y (sqrt.f64 x)) x #s(approx (- 1 x) #s(literal 1 binary64)))
#s(approx (+ (- 1 x) (* y (sqrt x))) (fma.f64 (/.f64 y (sqrt.f64 x)) x (neg.f64 x)))
#s(approx (+ (- 1 x) (* y (sqrt x))) (.f64 #s(approx (+ ( (sqrt (/ 1 x)) y) -1) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y)) x))
#s(approx (+ (- 1 x) (* y (sqrt x))) (*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y #s(literal -1 binary64)) x))
#s(approx (+ (- 1 x) (* y (sqrt x))) (*.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) y #s(literal -1 binary64)) x))
(fma.f64 (*.f64 (neg.f64 x) y) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #s(approx (- 1 x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) #s(approx (pow (+ (* (sqrt x) y) (- 1 x)) -1) (/.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) #s(literal 1 binary64)))))
(fma.f64 #s(literal -1 binary64) (/.f64 y (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) #s(approx (- 1 x) #s(literal 1 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) y (-.f64 #s(literal 1 binary64) x))
#s(approx (/ 1 (/ (- 1 (+ (* (sqrt x) y) x)) (- 1 (pow (- x (* (sqrt x) y)) 2)))) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 y y) x)) (-.f64 #s(literal 1 binary64) (*.f64 y (sqrt.f64 x)))))
(/.f64 #s(literal 1 binary64) #s(approx (pow (+ (* (sqrt x) y) (- 1 x)) -1) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y)))
(*.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (-.f64 #s(literal 1 binary64) x) (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 x) y x))) (neg.f64 (/.f64 (.f64 (.f64 y x) y) (-.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 x) y x)))))
(+.f64 (-.f64 #s(literal 1 binary64) x) (.f64 y (pow.f64 (.f64 x x) #s(literal 1/4 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64))) y (-.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (sqrt.f64 x) y (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
(+.f64 (/.f64 (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal -1 binary64))) (*.f64 y (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (sqrt.f64 x) y (fma.f64 #s(literal -1 binary64) x #s(literal -1 binary64))) (-.f64 (.f64 (.f64 y x) y) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 x) y x)) (-.f64 #s(literal 1 binary64) (pow.f64 (-.f64 x (*.f64 (sqrt.f64 x) y)) #s(literal 2 binary64)))))
(.f64 (fma.f64 (sqrt.f64 x) y (-.f64 #s(literal 1 binary64) x)) (.f64 (-.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 x) y x)) (pow.f64 (-.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 x) y x)) #s(literal -1 binary64))))
(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))))
(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (*.f64 (pow.f64 x #s(literal 1/4 binary64)) y) (-.f64 #s(literal 1 binary64) x))

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

Calls

3 calls:

11.0ms	y
9.0ms	x
9.0ms	(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`y`
99.9%	1	`(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))`

Compiler

Compiled 10 to 11 computations (-10% saved)

regimes12.0ms (0.2%)

Memory

-14.9MiB live, 22.3MiB allocated

Counts

8 → 2

Calls

Call 1

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

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

Calls

3 calls:

5.0ms	(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))
3.0ms	x
3.0ms	y

Results

Accuracy	Segments	Branch
98.8%	2	`x`
97.1%	3	`y`
98.4%	2	`(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))`

Compiler

Compiled 10 to 11 computations (-10% saved)

regimes13.0ms (0.3%)

Memory

-23.2MiB live, 20.5MiB allocated

Counts

7 → 3

Calls

Call 1

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

Outputs

#s(approx (+ (- 1 x) (* y (sqrt x))) (fma.f64 y (sqrt.f64 x) #s(literal 1 binary64)))

#s(approx (+ (- 1 x) (* y (sqrt x))) (-.f64 #s(literal 1 binary64) x))

#s(approx (+ (- 1 x) (* y (sqrt x))) (fma.f64 y (sqrt.f64 x) #s(literal 1 binary64)))

Calls

3 calls:

7.0ms	y
3.0ms	x
3.0ms	(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))

Results

Accuracy	Segments	Branch
96.1%	3	`y`
84.4%	3	`(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))`
81.3%	2	`x`

Compiler

Compiled 10 to 11 computations (-10% saved)

regimes3.0ms (0.1%)

Memory

6.6MiB live, 6.6MiB allocated

Counts

5 → 3

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
94.2%	3	`y`

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes6.0ms (0.1%)

Memory

14.6MiB live, 14.6MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

#s(approx (+ (- 1 x) (* y (sqrt x))) #s(approx (- 1 x) #s(literal 1 binary64)))

#s(approx (+ (- 1 x) (* y (sqrt x))) #s(approx (- 1 x) (neg.f64 x)))

#s(approx (+ (- 1 x) (* y (sqrt x))) (-.f64 #s(literal 1 binary64) x))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
63.1%	1	`x`
63.1%	1	`(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))`
63.1%	1	`y`

Compiler

Compiled 10 to 11 computations (-10% saved)

regimes5.0ms (0.1%)

Memory

12.8MiB live, 12.8MiB allocated

Counts

2 → 2

Calls

Call 1

Inputs
#s(approx (+ (- 1 x) (* y (sqrt x))) #s(approx (- 1 x) #s(literal 1 binary64)))
#s(approx (+ (- 1 x) (* y (sqrt x))) #s(approx (- 1 x) (neg.f64 x)))

Outputs
#s(approx (+ (- 1 x) (* y (sqrt x))) #s(approx (- 1 x) (neg.f64 x)))
#s(approx (+ (- 1 x) (* y (sqrt x))) #s(approx (- 1 x) #s(literal 1 binary64)))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
62.0%	2	`x`
39.7%	4	`y`
62.5%	2	`(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))`

Compiler

Compiled 10 to 11 computations (-10% saved)

regimes6.0ms (0.1%)

Memory

-26.5MiB live, 11.2MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (+ (- 1 x) (* y (sqrt x))) #s(approx (- 1 x) #s(literal 1 binary64)))

Outputs
#s(approx (+ (- 1 x) (* y (sqrt x))) #s(approx (- 1 x) #s(literal 1 binary64)))

Calls

3 calls:

3.0ms	x
1.0ms	(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))
1.0ms	y

Results

Accuracy	Segments	Branch
32.8%	1	`y`
32.8%	1	`x`
32.8%	1	`(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))`

Compiler

Compiled 10 to 11 computations (-10% saved)

bsearch12.0ms (0.2%)

Memory

23.5MiB live, 23.5MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
10.0ms	0.00025911806126117546	0.0735340847320045

Samples

6.0ms

128×

valid

Compiler

Compiled 115 to 124 computations (-7.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-sub: 1.0ms (31.8% of total)

ival-add: 1.0ms (31.8% of total)

ival-mult: 1.0ms (31.8% of total)

ival-sqrt: 1.0ms (31.8% of total)

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

exact: 0.0ms (0% of total)

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

bsearch31.0ms (0.6%)

Memory

-21.1MiB live, 52.8MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
13.0ms	4185522989.5054803	5.908727852104171e+20
13.0ms	-1.3633512499664174e+32	-5.386693196868369e+27

Samples

13.0ms

288×

valid

Compiler

Compiled 191 to 246 computations (-28.8% saved)

Precisions

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

ival-sub: 2.0ms (27.5% of total)

ival-mult: 2.0ms (27.5% of total)

ival-sqrt: 2.0ms (27.5% of total)

ival-add: 1.0ms (13.7% of total)

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

exact: 0.0ms (0% of total)

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

bsearch8.0ms (0.2%)

Memory

17.2MiB live, 17.2MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
5.0ms	4.390233191217637e+47	7.095311087647453e+47
2.0ms	-1.3633512499664174e+32	-5.386693196868369e+27

Samples

4.0ms

80×

valid

Compiler

Compiled 119 to 156 computations (-31.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-mult: 1.0ms (48.6% of total)

ival-sqrt: 1.0ms (48.6% of total)

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

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

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

exact: 0.0ms (0% of total)

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

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.1891827424665427	0.9997408819387388

Compiler

Compiled 11 to 12 computations (-9.1% saved)

simplify35.0ms (0.7%)

Memory

-5.7MiB live, 66.8MiB allocated

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative-binary64-+.f64`
4×	`-commutative-binary64-.f64`
4×	`sub-neg-binary64-neg.f64-+.f64--.f64`
2×	`1-exp-binary32-exp.f32`
2×	`1-exp-binary64-exp.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	195
1	48	195
2	51	195
3	52	195

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 (sqrt.f64 x) y (-.f64 #s(literal 1 binary64) x))
(if (<=.f64 x #s(literal 5188146770730811/72057594037927936 binary64)) #s(approx (+ (- 1 x) (* y (sqrt x))) (fma.f64 y (sqrt.f64 x) #s(literal 1 binary64))) (fma.f64 (sqrt.f64 x) y #s(approx (- 1 x) (neg.f64 x))))
(if (<=.f64 y #s(literal -119999999999999995630755539582976 binary64)) #s(approx (+ (- 1 x) (* y (sqrt x))) (fma.f64 y (sqrt.f64 x) #s(literal 1 binary64))) (if (<=.f64 y #s(literal 580000000000000000000 binary64)) #s(approx (+ (- 1 x) (* y (sqrt x))) (-.f64 #s(literal 1 binary64) x)) #s(approx (+ (- 1 x) (* y (sqrt x))) (fma.f64 y (sqrt.f64 x) #s(literal 1 binary64)))))
(if (<=.f64 y #s(literal -135000000000000006343599050457088 binary64)) #s(approx (+ (- 1 x) (* y (sqrt x))) (.f64 y (sqrt.f64 x))) (if (<=.f64 y #s(literal 700000000000000030692090131553338148243833356288 binary64)) #s(approx (+ (- 1 x) ( y (sqrt x))) (-.f64 #s(literal 1 binary64) x)) #s(approx (+ (- 1 x) (* y (sqrt x))) (*.f64 y (sqrt.f64 x)))))
#s(approx (+ (- 1 x) (* y (sqrt x))) (-.f64 #s(literal 1 binary64) x))
(if (<=.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) (.f64 y (sqrt.f64 x))) #s(literal -1 binary64)) #s(approx (+ (- 1 x) ( y (sqrt x))) #s(approx (- 1 x) (neg.f64 x))) #s(approx (+ (- 1 x) (* y (sqrt x))) #s(approx (- 1 x) #s(literal 1 binary64))))
#s(approx (+ (- 1 x) (* y (sqrt x))) #s(approx (- 1 x) #s(literal 1 binary64)))

Outputs
(fma.f64 (sqrt.f64 x) y (-.f64 #s(literal 1 binary64) x))
(if (<=.f64 x #s(literal 5188146770730811/72057594037927936 binary64)) #s(approx (+ (- 1 x) (* y (sqrt x))) (fma.f64 y (sqrt.f64 x) #s(literal 1 binary64))) (fma.f64 (sqrt.f64 x) y #s(approx (- 1 x) (neg.f64 x))))
(if (<=.f64 y #s(literal -119999999999999995630755539582976 binary64)) #s(approx (+ (- 1 x) (* y (sqrt x))) (fma.f64 y (sqrt.f64 x) #s(literal 1 binary64))) (if (<=.f64 y #s(literal 580000000000000000000 binary64)) #s(approx (+ (- 1 x) (* y (sqrt x))) (-.f64 #s(literal 1 binary64) x)) #s(approx (+ (- 1 x) (* y (sqrt x))) (fma.f64 y (sqrt.f64 x) #s(literal 1 binary64)))))
(if (<=.f64 y #s(literal -135000000000000006343599050457088 binary64)) #s(approx (+ (- 1 x) (* y (sqrt x))) (.f64 y (sqrt.f64 x))) (if (<=.f64 y #s(literal 700000000000000030692090131553338148243833356288 binary64)) #s(approx (+ (- 1 x) ( y (sqrt x))) (-.f64 #s(literal 1 binary64) x)) #s(approx (+ (- 1 x) (* y (sqrt x))) (*.f64 y (sqrt.f64 x)))))
#s(approx (+ (- 1 x) (* y (sqrt x))) (-.f64 #s(literal 1 binary64) x))
(if (<=.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) (.f64 y (sqrt.f64 x))) #s(literal -1 binary64)) #s(approx (+ (- 1 x) ( y (sqrt x))) #s(approx (- 1 x) (neg.f64 x))) #s(approx (+ (- 1 x) (* y (sqrt x))) #s(approx (- 1 x) #s(literal 1 binary64))))
(if (<=.f64 (+.f64 (.f64 y (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) #s(approx (+ (- 1 x) ( y (sqrt x))) #s(approx (- 1 x) (neg.f64 x))) #s(approx (+ (- 1 x) (* y (sqrt x))) #s(approx (- 1 x) #s(literal 1 binary64))))
#s(approx (+ (- 1 x) (* y (sqrt x))) #s(approx (- 1 x) #s(literal 1 binary64)))

soundness725.0ms (13.4%)

Memory

9.6MiB live, 460.7MiB allocated

Rules

7 542×	`lower-fma.f64`
7 542×	`lower-fma.f32`
7 284×	`lower-fma.f64`
7 284×	`lower-fma.f32`
6 324×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	369
1	141	369
2	438	357
3	1298	357
4	4642	357
5	7358	357
0	8082	330
0	7	17
0	11	17
1	46	17
2	357	17
3	5315	17
0	8974	16
0	680	6251
1	2171	5674
2	7743	5626
0	8314	5410

Stop Event

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

Compiler

Compiled 167 to 105 computations (37.1% saved)

preprocess59.0ms (1.1%)

Memory: -10.1MiB live, 100.9MiB allocated
Compiler: Compiled 206 to 86 computations (58.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	7	20
0	11	20
1	19	20
2	38	20
3	65	20
4	129	20
5	247	20
6	389	20
7	437	20
8	460	20
0	460	19

Iter	Nodes	Cost
0	7	20
0	11	20
1	19	20
2	38	20
3	65	20
4	129	20
5	247	20
6	389	20
7	437	20
8	460	20
0	460	19

start0.0ms (0%)

analyze8.0ms (0.2%)

sample918.0ms (17%)

explain85.0ms (1.6%)

preprocess47.0ms (0.9%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify19.0ms (0.3%)

localize21.0ms (0.4%)

series6.0ms (0.1%)

simplify132.0ms (2.4%)

rewrite220.0ms (4.1%)

eval57.0ms (1.1%)

prune16.0ms (0.3%)

simplify325.0ms (6%)

localize84.0ms (1.6%)

series56.0ms (1%)

simplify176.0ms (3.3%)

rewrite250.0ms (4.6%)

eval250.0ms (4.6%)

prune63.0ms (1.2%)

simplify70.0ms (1.3%)

localize131.0ms (2.4%)

series35.0ms (0.7%)

simplify172.0ms (3.2%)

rewrite183.0ms (3.4%)

eval254.0ms (4.7%)

prune29.0ms (0.5%)

simplify66.0ms (1.2%)

localize105.0ms (1.9%)

series15.0ms (0.3%)

simplify156.0ms (2.9%)

rewrite187.0ms (3.5%)

eval226.0ms (4.2%)

prune86.0ms (1.6%)

regimes31.0ms (0.6%)

regimes12.0ms (0.2%)

regimes13.0ms (0.3%)

regimes3.0ms (0.1%)

regimes6.0ms (0.1%)

regimes5.0ms (0.1%)

regimes6.0ms (0.1%)

bsearch12.0ms (0.2%)

bsearch31.0ms (0.6%)

bsearch8.0ms (0.2%)

bsearch0.0ms (0%)

simplify35.0ms (0.7%)

soundness725.0ms (13.4%)

preprocess59.0ms (1.1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	7	20
0	11	20
1	19	20
2	38	20
3	65	20
4	129	20
5	247	20
6	389	20
7	437	20
8	460	20
0	460	19