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

analyze34.0ms (0.4%)

Memory

-58.1MiB live, 14.1MiB 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)

sample758.0ms (9.5%)

Memory

47.0MiB live, 1 147.4MiB allocated

Samples

521.0ms	8 252×	0	valid
13.0ms	253×	0	invalid
0.0ms	3×	2	valid
0.0ms	1×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 245.0ms

ival-sub: 76.0ms (31% of total)

ival-sqrt: 66.0ms (26.9% of total)

ival-mult: 55.0ms (22.4% of total)

ival-add: 36.0ms (14.7% of total)

ival-true: 5.0ms (2% of total)

exact: 4.0ms (1.6% of total)

ival-assert: 3.0ms (1.2% of total)

adjust: 0.0ms (0% of total)

Bogosity

preprocess61.0ms (0.8%)

Memory

-24.5MiB live, 89.9MiB allocated

Algorithm

2×	egg-herbie

Rules

336×	`accelerator-lowering-fma.f32`
336×	`accelerator-lowering-fma.f64`
252×	`sub-neg`
206×	`cancel-sign-sub-inv`
192×	`associate--r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	56
1	59	51
2	173	50
3	475	50
4	972	50
5	1355	50
6	1493	50
7	1515	50
0	7	8
1	15	8
2	34	8
3	61	8
4	125	8
5	243	8
6	372	8
7	420	8
8	443	8
0	443	7

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(+ (- 1 x) (* y (sqrt x)))

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

Call 2

Inputs
(+ (- 1 x) (* y (sqrt x)))
(+ (- 1 (neg x)) (* y (sqrt (neg x))))
(+ (- 1 x) (* (neg y) (sqrt x)))
(neg (+ (- 1 (neg x)) (* y (sqrt (neg x)))))
(neg (+ (- 1 x) (* (neg y) (sqrt x))))
(+ (- 1 y) (* x (sqrt y)))

Outputs
(+ (- 1 x) (* y (sqrt x)))
(+ (- 1 (neg x)) (* y (sqrt (neg x))))
(+ 1 (+ x (* y (sqrt (neg x)))))
(+ (- 1 x) (* (neg y) (sqrt x)))
(- (- 1 x) (* y (sqrt x)))
(neg (+ (- 1 (neg x)) (* y (sqrt (neg x)))))
(- -1 (+ x (* y (sqrt (neg x)))))
(neg (+ (- 1 x) (* (neg y) (sqrt x))))
(+ (* y (sqrt x)) (+ x -1))
(+ (- 1 y) (* x (sqrt y)))

explain79.0ms (1%)

Memory

-10.2MiB live, 128.0MiB 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

34.0ms

512×

valid

Compiler

Compiled 64 to 32 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-add: 8.0ms (43.5% of total)

ival-sqrt: 4.0ms (21.8% of total)

ival-sub: 3.0ms (16.3% of total)

ival-mult: 3.0ms (16.3% of total)

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

exact: 0.0ms (0% of total)

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

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.2MiB live, 1.2MiB 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 10 to 7 computations (30% saved)

simplify20.0ms (0.2%)

Memory

-13.0MiB live, 25.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(*.f64 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×	`accelerator-lowering-fma.f32`
336×	`accelerator-lowering-fma.f64`
144×	`-lowering-.f32`
144×	`-lowering-.f64`
112×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
1	15	20
2	34	20
3	61	20
4	125	20
5	243	20
6	372	20
7	420	20
8	443	20
0	443	19

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ (- 1 x) (* y (sqrt x)))
(- 1 x)
1
x
(* y (sqrt x))
y
(sqrt x)

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

localize25.0ms (0.3%)

Memory

7.0MiB live, 48.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))
✓	accuracy	99.7%	(*.f64 y (sqrt.f64 x))

Samples

17.0ms

256×

valid

Compiler

Compiled 22 to 9 computations (59.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-mult: 2.0ms (31.6% of total)

ival-sqrt: 2.0ms (31.6% of total)

ival-sub: 1.0ms (15.8% of total)

ival-add: 1.0ms (15.8% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Memory

10.0MiB live, 10.0MiB allocated

Counts

4 → 72

Calls

Call 1

Inputs
#<alt (+ (- 1 x) (* y (sqrt x)))>
#<alt (- 1 x)>
#<alt (* y (sqrt x))>
#<alt (sqrt x)>

Outputs
#<alt (+ 1 (* (sqrt x) y))>
#<alt (+ 1 (+ (* -1 x) (* (sqrt x) y)))>
#<alt (+ 1 (+ (* -1 x) (* (sqrt x) y)))>
#<alt (+ 1 (+ (* -1 x) (* (sqrt x) y)))>
#<alt (* x (- (* (sqrt (/ 1 x)) y) 1))>
#<alt (* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))>
#<alt (* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))>
#<alt (* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))>
#<alt (* -1 (* x (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))>
#<alt (* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))>
#<alt (* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))>
#<alt (- 1 x)>
#<alt (- (+ 1 (* (sqrt x) y)) x)>
#<alt (- (+ 1 (* (sqrt x) y)) x)>
#<alt (- (+ 1 (* (sqrt x) y)) x)>
#<alt (* (sqrt x) y)>
#<alt (* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))>
#<alt (* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))>
#<alt (* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))>
#<alt (* (sqrt x) y)>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* -1 (* (sqrt x) (* y (pow (sqrt -1) 2))))>
#<alt (* -1 (* (sqrt x) (* y (pow (sqrt -1) 2))))>
#<alt (* -1 (* (sqrt x) (* y (pow (sqrt -1) 2))))>
#<alt (* -1 (* (sqrt x) (* y (pow (sqrt -1) 2))))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>

Calls

18 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(+ (- 1 x) (* y (sqrt x)))
0.0ms	x	@	0	(+ (- 1 x) (* y (sqrt x)))
0.0ms	x	@	inf	(+ (- 1 x) (* y (sqrt x)))
0.0ms	y	@	0	(+ (- 1 x) (* y (sqrt x)))
0.0ms	y	@	inf	(+ (- 1 x) (* y (sqrt x)))

rewrite414.0ms (5.2%)

Memory

-4.3MiB live, 541.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 324×	`accelerator-lowering-fma.f32`
6 324×	`accelerator-lowering-fma.f64`
4 236×	`-lowering-.f32`
4 236×	`-lowering-.f64`
2 084×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	42	17
2	353	17
3	5351	17
0	9013	16

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 252

Calls

Call 1

Inputs
(+ (- 1 x) (* y (sqrt x)))
(- 1 x)
(* y (sqrt x))
(sqrt x)

Outputs
(+.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) (neg.f64 x)))
(+.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))
(+.f64 (*.f64 y (sqrt.f64 x)) (+.f64 #s(literal 1 binary64) x))
(+.f64 (neg.f64 x) (fma.f64 y (sqrt.f64 x) #s(literal 1 binary64)))
(+.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) x))) (neg.f64 (/.f64 (.f64 x (*.f64 y y)) (-.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) x)))))
(+.f64 (fma.f64 y (sqrt.f64 x) #s(literal 1 binary64)) (neg.f64 x))
(+.f64 (fma.f64 y (sqrt.f64 x) (neg.f64 x)) #s(literal 1 binary64))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) (+.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)))
(-.f64 #s(literal 1 binary64) (-.f64 x (*.f64 y (sqrt.f64 x))))
(-.f64 (+.f64 #s(literal 1 binary64) x) (neg.f64 (*.f64 y (sqrt.f64 x))))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (-.f64 (/.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (*.f64 y (sqrt.f64 x))))
(-.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) x))) (/.f64 (.f64 x (*.f64 y y)) (-.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) x))))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (-.f64 (/.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) x)) (.f64 y (sqrt.f64 x))))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) x))) (/.f64 (.f64 (-.f64 x (.f64 y (sqrt.f64 x))) (-.f64 x (*.f64 y (sqrt.f64 x)))) (-.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) x))))
(-.f64 (fma.f64 y (sqrt.f64 x) #s(literal 1 binary64)) x)
(-.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 x (.f64 y (sqrt.f64 x))) (-.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) x)) #s(literal 1 binary64))) (/.f64 (.f64 (-.f64 x (.f64 y (sqrt.f64 x))) (.f64 (-.f64 x (.f64 y (sqrt.f64 x))) (-.f64 x (.f64 y (sqrt.f64 x))))) (fma.f64 (-.f64 x (*.f64 y (sqrt.f64 x))) (-.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) x)) #s(literal 1 binary64))))
(-.f64 (/.f64 (.f64 x (.f64 y y)) (+.f64 (-.f64 (.f64 y (sqrt.f64 x)) #s(literal 1 binary64)) x)) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 (-.f64 (*.f64 y (sqrt.f64 x)) #s(literal 1 binary64)) x)))
(-.f64 (fma.f64 y (sqrt.f64 x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))) (/.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))))
(-.f64 (fma.f64 y (sqrt.f64 x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (/.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) x)))
(-.f64 (+.f64 (fma.f64 y (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 0 binary64)) x)
(fma.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))
(fma.f64 #s(literal 1 binary64) (neg.f64 x) (fma.f64 y (sqrt.f64 x) #s(literal 1 binary64)))
(fma.f64 x #s(literal -1 binary64) (fma.f64 y (sqrt.f64 x) #s(literal 1 binary64)))
(fma.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64) (*.f64 y (sqrt.f64 x)))
(fma.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) x))) (neg.f64 (/.f64 (.f64 x (.f64 y y)) (-.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) x)))))
(fma.f64 y (sqrt.f64 x) (+.f64 #s(literal 1 binary64) x))
(fma.f64 (sqrt.f64 x) y (+.f64 #s(literal 1 binary64) x))
(fma.f64 (sqrt.f64 x) (exp.f64 (log.f64 y)) (+.f64 #s(literal 1 binary64) x))
(fma.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) x))) (neg.f64 (/.f64 (.f64 x (*.f64 y y)) (-.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) x)))))
(fma.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (.f64 y (sqrt.f64 x)))
(fma.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) #s(literal 1 binary64)) (*.f64 y (sqrt.f64 x)))
(fma.f64 (neg.f64 x) #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) #s(literal 1 binary64)))
(fma.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (.f64 y (sqrt.f64 x)))
(fma.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (*.f64 y (sqrt.f64 x)))
(fma.f64 (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (fma.f64 x x x))) (*.f64 y (sqrt.f64 x)))
(fma.f64 (+.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 (neg.f64 x) #s(literal -1 binary64))) (.f64 y (sqrt.f64 x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (.f64 y (sqrt.f64 x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 y (sqrt.f64 x)))
(fma.f64 #s(literal -1 binary64) x (fma.f64 y (sqrt.f64 x) #s(literal 1 binary64)))
(fma.f64 #s(literal -1 binary64) (-.f64 x (*.f64 y (sqrt.f64 x))) #s(literal 1 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))
(fma.f64 (.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (*.f64 y (sqrt.f64 x)))
(fma.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (*.f64 y (sqrt.f64 x)))
(fma.f64 (*.f64 y (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)) (+.f64 #s(literal 1 binary64) x))
(fma.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 x x x)) (*.f64 y (sqrt.f64 x)))
(fma.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x x))) (+.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))
(fma.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (fma.f64 (.f64 (fma.f64 x x x) (fma.f64 x x x)) (fma.f64 x x x) #s(literal 1 binary64))) (fma.f64 (fma.f64 x x x) (-.f64 (fma.f64 x x x) #s(literal 1 binary64)) #s(literal 1 binary64)) (*.f64 y (sqrt.f64 x)))
(fma.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x x) (fma.f64 x x x)))) (+.f64 #s(literal 1 binary64) (fma.f64 x x x)) (*.f64 y (sqrt.f64 x)))
(fma.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (.f64 y (sqrt.f64 x)))
(fma.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x x)))) (+.f64 #s(literal -1 binary64) (fma.f64 x x x)) (.f64 y (sqrt.f64 x)))
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(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x (.f64 x x)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) x)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) x)))
(/.f64 (.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))) (+.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x)))) (+.f64 #s(literal -1 binary64) (fma.f64 x x x)))
(/.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (.f64 x x))) (+.f64 (neg.f64 x) #s(literal -1 binary64)))
(/.f64 (.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x))) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) (fma.f64 x x x)))
(/.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 x x)) #s(literal 1 binary64)) (+.f64 (neg.f64 x) #s(literal -1 binary64)))
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x x)))) (neg.f64 (+.f64 #s(literal -1 binary64) (fma.f64 x x x))))
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (*.f64 x x))) (+.f64 #s(literal 1 binary64) x))
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)) (.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)) (.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))))))) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)) (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))) (fma.f64 (/.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (/.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (/.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))))))
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) x) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) x) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (fma.f64 (/.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) x)) (/.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) x)) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (/.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) x))))))
(/.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))
(/.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64)))
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)) (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))) (.f64 (/.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (/.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (/.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))))
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (.f64 (/.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) x)) (/.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) x)))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (/.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) x))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))) (fma.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (fma.f64 x x #s(literal 1 binary64)))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(/.f64 (exp.f64 (log1p.f64 (.f64 x (.f64 x x)))) (exp.f64 (log1p.f64 (fma.f64 x x x))))
(/.f64 (exp.f64 (log1p.f64 (*.f64 x (neg.f64 x)))) (+.f64 #s(literal 1 binary64) x))
(/.f64 (exp.f64 (log.f64 (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))))) (exp.f64 (log.f64 (+.f64 #s(literal -1 binary64) (fma.f64 x x x)))))
(/.f64 (exp.f64 (log.f64 (+.f64 #s(literal -1 binary64) (*.f64 x x)))) (exp.f64 (log.f64 (+.f64 (neg.f64 x) #s(literal -1 binary64)))))
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))
(*.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))))
(.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) #s(literal 1 binary64)))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(.f64 (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (fma.f64 x x x))))
(.f64 (+.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 (neg.f64 x) #s(literal -1 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) (fma.f64 x (.f64 x x) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))))
(.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (fma.f64 (*.f64 (fma.f64 x x x) (fma.f64 x x x)) (fma.f64 x x x) #s(literal 1 binary64))) (fma.f64 (fma.f64 x x x) (-.f64 (fma.f64 x x x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x x) (fma.f64 x x x)))) (+.f64 #s(literal 1 binary64) (fma.f64 x x x)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x x)))) (+.f64 #s(literal -1 binary64) (fma.f64 x x x)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal -1 binary64) (*.f64 x x))) (+.f64 (neg.f64 x) #s(literal -1 binary64)))
(.f64 (exp.f64 (log1p.f64 (.f64 x (*.f64 x x)))) (exp.f64 (neg.f64 (log1p.f64 (fma.f64 x x x)))))
(.f64 (exp.f64 (log1p.f64 (.f64 x (neg.f64 x)))) (exp.f64 (neg.f64 (log1p.f64 x))))
(exp.f64 (log.f64 (*.f64 y (sqrt.f64 x))))
(exp.f64 (.f64 (log.f64 (.f64 y (sqrt.f64 x))) #s(literal 1 binary64)))
(pow.f64 (*.f64 y (sqrt.f64 x)) #s(literal 1 binary64))
(*.f64 y (sqrt.f64 x))
(*.f64 (sqrt.f64 x) y)
(*.f64 (sqrt.f64 x) (exp.f64 (log.f64 y)))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (pow.f64 x #s(literal 1/4 binary64)) y))
(.f64 (.f64 y (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (exp.f64 (log.f64 y)) (sqrt.f64 x))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)))
(exp.f64 (.f64 (log.f64 (.f64 x x)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 x #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 1/4 binary64) (*.f64 (log.f64 x) #s(literal 1/4 binary64))))
(sqrt.f64 x)
(pow.f64 x #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 (neg.f64 x) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 x))
(*.f64 #s(literal 1 binary64) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) #s(literal 1 binary64))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))

simplify271.0ms (3.4%)

Memory

26.4MiB live, 339.3MiB allocated

Algorithm

1×	egg-herbie

Rules

7 542×	`accelerator-lowering-fma.f32`
7 542×	`accelerator-lowering-fma.f64`
2 696×	`-lowering-.f32`
2 696×	`-lowering-.f64`
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	4657	357
5	7379	357
0	8084	330

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

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

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

eval61.0ms (0.8%)

Memory: -2.4MiB live, 75.1MiB allocated
Compiler: Compiled 7 322 to 720 computations (90.2% saved)

prune42.0ms (0.5%)

Memory

-7.7MiB live, 106.2MiB allocated

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	312	12	324
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	312	13	325

Accuracy

100.0%

Counts

325 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	68.9%	(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))
▶	69.6%	(fma.f64 (sqrt.f64 x) y #s(literal 1 binary64))
	93.9%	(fma.f64 x (fma.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) #s(literal 1 binary64))
	99.9%	(-.f64 (fma.f64 (sqrt.f64 x) y #s(literal 1 binary64)) x)
▶	57.5%	(-.f64 #s(literal 1 binary64) x)
▶	99.9%	(+.f64 (fma.f64 y (sqrt.f64 x) (neg.f64 x)) #s(literal 1 binary64))
	99.7%	(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))))
	72.7%	(+.f64 (-.f64 #s(literal 1 binary64) x) (.f64 y (pow.f64 (.f64 x x) #s(literal 1/4 binary64))))
✓	99.9%	(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))
	97.4%	(+.f64 (-.f64 #s(literal 1 binary64) x) (.f64 y (exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 x)))))
▶	62.4%	(.f64 (fma.f64 y (sqrt.f64 x) (+.f64 #s(literal 1 binary64) x)) (.f64 (-.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) x)))))
	43.1%	(*.f64 (sqrt.f64 x) y)
▶	64.6%	(*.f64 x (fma.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))

Compiler

Compiled 290 to 187 computations (35.5% saved)

simplify442.0ms (5.5%)

Memory

-11.1MiB live, 804.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(fma.f64 y (sqrt.f64 x) (+.f64 #s(literal 1 binary64) x))
✓	cost-diff	320	(.f64 (fma.f64 y (sqrt.f64 x) (+.f64 #s(literal 1 binary64) x)) (.f64 (-.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) x)))))
✓	cost-diff	3456	(*.f64 (-.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) x))))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(fma.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
✓	cost-diff	0	(*.f64 x (fma.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(fma.f64 (sqrt.f64 x) y #s(literal 1 binary64))
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(neg.f64 x)
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(fma.f64 y (sqrt.f64 x) (neg.f64 x))
✓	cost-diff	128	(+.f64 (fma.f64 y (sqrt.f64 x) (neg.f64 x)) #s(literal 1 binary64))

Rules

15 618×	`accelerator-lowering-fma.f32`
15 618×	`accelerator-lowering-fma.f64`
3 960×	`-lowering-.f32`
3 960×	`-lowering-.f64`
2 382×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	119
1	60	115
2	130	115
3	369	115
4	2413	115
5	6354	115
0	8279	106

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(+ (+ (* y (sqrt x)) (neg x)) 1)
(+ (* y (sqrt x)) (neg x))
y
(sqrt x)
x
(neg x)
1
(- 1 x)
1
x
(+ (* (sqrt x) y) 1)
(sqrt x)
x
y
1
(* x (+ (* y (sqrt (/ 1 x))) -1))
x
(+ (* y (sqrt (/ 1 x))) -1)
y
(sqrt (/ 1 x))
(/ 1 x)
1
-1
(* (+ (* y (sqrt x)) (+ 1 x)) (* (- 1 (+ (* y (sqrt x)) x)) (/ 1 (- 1 (+ (* y (sqrt x)) x)))))
(+ (* y (sqrt x)) (+ 1 x))
y
(sqrt x)
x
(+ 1 x)
1
(* (- 1 (+ (* y (sqrt x)) x)) (/ 1 (- 1 (+ (* y (sqrt x)) x))))
(- 1 (+ (* y (sqrt x)) x))
(+ (* y (sqrt x)) x)
(/ 1 (- 1 (+ (* y (sqrt x)) x)))

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

localize89.0ms (1.1%)

Memory

26.0MiB live, 182.4MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(fma.f64 y (sqrt.f64 x) (+.f64 #s(literal 1 binary64) x))
✓	accuracy	99.8%	(fma.f64 y (sqrt.f64 x) x)
✓	accuracy	99.2%	(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) x)))
✓	accuracy	93.3%	(*.f64 (-.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) x))))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	accuracy	99.8%	(fma.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	93.9%	(*.f64 x (fma.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.8%	(fma.f64 (sqrt.f64 x) y #s(literal 1 binary64))
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(neg.f64 x)
✓	accuracy	100.0%	(+.f64 (fma.f64 y (sqrt.f64 x) (neg.f64 x)) #s(literal 1 binary64))
✓	accuracy	99.8%	(fma.f64 y (sqrt.f64 x) (neg.f64 x))

Samples

48.0ms

256×

valid

Compiler

Compiled 143 to 26 computations (81.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 29.0ms

ival-mult: 10.0ms (35.1% of total)

ival-add: 8.0ms (28.1% of total)

ival-sqrt: 4.0ms (14% of total)

ival-div: 3.0ms (10.5% of total)

ival-sub: 2.0ms (7% of total)

ival-neg: 1.0ms (3.5% of total)

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

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

exact: 0.0ms (0% of total)

series42.0ms (0.5%)

Memory

-13.6MiB live, 24.8MiB allocated

Counts

15 → 300

Calls

Call 1

Inputs
#<alt (+ (+ (* y (sqrt x)) (neg x)) 1)>
#<alt (+ (* y (sqrt x)) (neg x))>
#<alt (sqrt x)>
#<alt (neg x)>
#<alt (- 1 x)>
#<alt (+ (* (sqrt x) y) 1)>
#<alt (* x (+ (* y (sqrt (/ 1 x))) -1))>
#<alt (+ (* y (sqrt (/ 1 x))) -1)>
#<alt (sqrt (/ 1 x))>
#<alt (/ 1 x)>
#<alt (* (- 1 (+ (* y (sqrt x)) x)) (/ 1 (- 1 (+ (* y (sqrt x)) x))))>
#<alt (* (+ (* y (sqrt x)) (+ 1 x)) (* (- 1 (+ (* y (sqrt x)) x)) (/ 1 (- 1 (+ (* y (sqrt x)) x)))))>
#<alt (+ (* y (sqrt x)) (+ 1 x))>
#<alt (/ 1 (- 1 (+ (* y (sqrt x)) x)))>
#<alt (+ (* y (sqrt x)) x)>

Outputs
#<alt (- 1 x)>
#<alt (- (+ 1 (* (sqrt x) y)) x)>
#<alt (- (+ 1 (* (sqrt x) y)) x)>
#<alt (- (+ 1 (* (sqrt x) y)) x)>
#<alt (* (sqrt x) y)>
#<alt (* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))>
#<alt (* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))>
#<alt (* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))>
#<alt (* (sqrt x) y)>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))>
#<alt (+ 1 (* (sqrt x) y))>
#<alt (+ 1 (+ (* -1 x) (* (sqrt x) y)))>
#<alt (+ 1 (+ (* -1 x) (* (sqrt x) y)))>
#<alt (+ 1 (+ (* -1 x) (* (sqrt x) y)))>
#<alt (* x (- (* (sqrt (/ 1 x)) y) 1))>
#<alt (* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))>
#<alt (* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))>
#<alt (* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))>
#<alt (* -1 (* x (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))>
#<alt (* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))>
#<alt (* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))>
#<alt (* -1 x)>
#<alt (- (* (sqrt x) y) x)>
#<alt (- (* (sqrt x) y) x)>
#<alt (- (* (sqrt x) y) x)>
#<alt (* (sqrt x) y)>
#<alt (* y (+ (sqrt x) (* -1 (/ x y))))>
#<alt (* y (+ (sqrt x) (* -1 (/ x y))))>
#<alt (* y (+ (sqrt x) (* -1 (/ x y))))>
#<alt (* (sqrt x) y)>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (/ x y))))>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (/ x y))))>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (/ x y))))>
#<alt (* (sqrt x) y)>
#<alt (+ (* -1 x) (* (sqrt x) y))>
#<alt (+ (* -1 x) (* (sqrt x) y))>
#<alt (+ (* -1 x) (* (sqrt x) y))>
#<alt (* x (- (* (sqrt (/ 1 x)) y) 1))>
#<alt (* x (- (* (sqrt (/ 1 x)) y) 1))>
#<alt (* x (- (* (sqrt (/ 1 x)) y) 1))>
#<alt (* x (- (* (sqrt (/ 1 x)) y) 1))>
#<alt (* -1 (* x (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))))))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (+ 1 (* (sqrt x) y))>
#<alt (+ 1 (* (sqrt x) y))>
#<alt (+ 1 (* (sqrt x) y))>
#<alt (+ 1 (* (sqrt x) y))>
#<alt (* (sqrt x) y)>
#<alt (* x (+ (* (sqrt (/ 1 x)) y) (/ 1 x)))>
#<alt (* x (+ (* (sqrt (/ 1 x)) y) (/ 1 x)))>
#<alt (* x (+ (* (sqrt (/ 1 x)) y) (/ 1 x)))>
#<alt (* -1 (* (sqrt x) (* y (pow (sqrt -1) 2))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) (/ 1 x))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) (/ 1 x))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) (/ 1 x))))>
#<alt 1>
#<alt (+ 1 (* (sqrt x) y))>
#<alt (+ 1 (* (sqrt x) y))>
#<alt (+ 1 (* (sqrt x) y))>
#<alt (* (sqrt x) y)>
#<alt (* y (+ (sqrt x) (/ 1 y)))>
#<alt (* y (+ (sqrt x) (/ 1 y)))>
#<alt (* y (+ (sqrt x) (/ 1 y)))>
#<alt (* (sqrt x) y)>
#<alt (* -1 (* y (- (* -1 (sqrt x)) (/ 1 y))))>
#<alt (* -1 (* y (- (* -1 (sqrt x)) (/ 1 y))))>
#<alt (* -1 (* y (- (* -1 (sqrt x)) (/ 1 y))))>
#<alt (* (sqrt x) y)>
#<alt (+ (* -1 x) (* (sqrt x) y))>
#<alt (+ (* -1 x) (* (sqrt x) y))>
#<alt (+ (* -1 x) (* (sqrt x) y))>
#<alt (* x (- (* (sqrt (/ 1 x)) y) 1))>
#<alt (* x (- (* (sqrt (/ 1 x)) y) 1))>
#<alt (* x (- (* (sqrt (/ 1 x)) y) 1))>
#<alt (* x (- (* (sqrt (/ 1 x)) y) 1))>
#<alt (* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) 1))>
#<alt (* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) 1))>
#<alt (* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) 1))>
#<alt (* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) 1))>
#<alt (* -1 x)>
#<alt (+ (* -1 x) (* (sqrt x) y))>
#<alt (+ (* -1 x) (* (sqrt x) y))>
#<alt (+ (* -1 x) (* (sqrt x) y))>
#<alt (* (sqrt x) y)>
#<alt (* y (+ (sqrt x) (* -1 (/ x y))))>
#<alt (* y (+ (sqrt x) (* -1 (/ x y))))>
#<alt (* y (+ (sqrt x) (* -1 (/ x y))))>
#<alt (* (sqrt x) y)>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (/ x y))))>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (/ x y))))>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (/ x y))))>
#<alt -1>
#<alt (- (* (sqrt (/ 1 x)) y) 1)>
#<alt (- (* (sqrt (/ 1 x)) y) 1)>
#<alt (- (* (sqrt (/ 1 x)) y) 1)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* y (- (sqrt (/ 1 x)) (/ 1 y)))>
#<alt (* y (- (sqrt (/ 1 x)) (/ 1 y)))>
#<alt (* y (- (sqrt (/ 1 x)) (/ 1 y)))>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* -1 (* y (+ (* -1 (sqrt (/ 1 x))) (/ 1 y))))>
#<alt (* -1 (* y (+ (* -1 (sqrt (/ 1 x))) (/ 1 y))))>
#<alt (* -1 (* y (+ (* -1 (sqrt (/ 1 x))) (/ 1 y))))>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (/ (+ (* -1 x) (* (sqrt x) y)) x)>
#<alt (/ (+ (* -1 x) (* (sqrt x) y)) x)>
#<alt (/ (+ (* -1 x) (* (sqrt x) y)) x)>
#<alt (- (* (sqrt (/ 1 x)) y) 1)>
#<alt (- (* (sqrt (/ 1 x)) y) 1)>
#<alt (- (* (sqrt (/ 1 x)) y) 1)>
#<alt (- (* (sqrt (/ 1 x)) y) 1)>
#<alt (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) 1)>
#<alt (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) 1)>
#<alt (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) 1)>
#<alt (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) 1)>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 (+ x (* (sqrt x) y)))>
#<alt (+ 1 (+ x (* (sqrt x) y)))>
#<alt (+ 1 (+ x (* (sqrt x) y)))>
#<alt (* (sqrt x) y)>
#<alt (* y (+ (sqrt x) (+ (/ 1 y) (/ x y))))>
#<alt (* y (+ (sqrt x) (+ (/ 1 y) (/ x y))))>
#<alt (* y (+ (sqrt x) (+ (/ 1 y) (/ x y))))>
#<alt (* (sqrt x) y)>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (+ 1 x) y)))))>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (+ 1 x) y)))))>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (+ 1 x) y)))))>
#<alt (+ 1 (* (sqrt x) y))>
#<alt (+ 1 (+ x (* (sqrt x) y)))>
#<alt (+ 1 (+ x (* (sqrt x) y)))>
#<alt (+ 1 (+ x (* (sqrt x) y)))>
#<alt (* x (+ 1 (* (sqrt (/ 1 x)) y)))>
#<alt (* x (+ 1 (+ (* (sqrt (/ 1 x)) y) (/ 1 x))))>
#<alt (* x (+ 1 (+ (* (sqrt (/ 1 x)) y) (/ 1 x))))>
#<alt (* x (+ 1 (+ (* (sqrt (/ 1 x)) y) (/ 1 x))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) 1)))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) (+ 1 (/ 1 x)))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) (+ 1 (/ 1 x)))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) (+ 1 (/ 1 x)))))>
#<alt (+ 1 x)>
#<alt (+ 1 (+ x (* (sqrt x) y)))>
#<alt (+ 1 (+ x (* (sqrt x) y)))>
#<alt (+ 1 (+ x (* (sqrt x) y)))>
#<alt (* (sqrt x) y)>
#<alt (* y (+ (sqrt x) (+ (/ 1 y) (/ x y))))>
#<alt (* y (+ (sqrt x) (+ (/ 1 y) (/ x y))))>
#<alt (* y (+ (sqrt x) (+ (/ 1 y) (/ x y))))>
#<alt (* (sqrt x) y)>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (+ 1 x) y)))))>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (+ 1 x) y)))))>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (+ 1 x) y)))))>
#<alt (+ 1 (* (sqrt x) y))>
#<alt (+ 1 (+ x (* (sqrt x) y)))>
#<alt (+ 1 (+ x (* (sqrt x) y)))>
#<alt (+ 1 (+ x (* (sqrt x) y)))>
#<alt (* x (+ 1 (* (sqrt (/ 1 x)) y)))>
#<alt (* x (+ 1 (+ (* (sqrt (/ 1 x)) y) (/ 1 x))))>
#<alt (* x (+ 1 (+ (* (sqrt (/ 1 x)) y) (/ 1 x))))>
#<alt (* x (+ 1 (+ (* (sqrt (/ 1 x)) y) (/ 1 x))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) 1)))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) (+ 1 (/ 1 x)))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) (+ 1 (/ 1 x)))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) (+ 1 (/ 1 x)))))>
#<alt (/ 1 (- 1 x))>
#<alt (+ (* (sqrt x) (/ y (pow (- 1 x) 2))) (/ 1 (- 1 x)))>
#<alt (+ (* y (- (/ (* x y) (pow (- 1 x) 3)) (* -1 (* (sqrt x) (/ 1 (pow (- 1 x) 2)))))) (/ 1 (- 1 x)))>
#<alt (+ (* y (- (* y (- (* (sqrt (pow x 3)) (/ y (pow (- 1 x) 4))) (* -1 (/ x (pow (- 1 x) 3))))) (* -1 (* (sqrt x) (/ 1 (pow (- 1 x) 2)))))) (/ 1 (- 1 x)))>
#<alt (* -1 (* (sqrt (/ 1 x)) (/ 1 y)))>
#<alt (/ (- (+ (* -1 (sqrt (/ 1 x))) (/ 1 y)) (/ 1 (* x y))) y)>
#<alt (/ (- (+ (* -1 (sqrt (/ 1 x))) (+ (* (sqrt (/ 1 x)) (/ (* (- 1 x) (- 1 (/ 1 x))) (pow y 2))) (/ 1 y))) (/ 1 (* x y))) y)>
#<alt (/ (- (+ (* -1 (sqrt (/ 1 x))) (+ (/ 1 y) (/ (* (pow (- 1 x) 2) (- 1 (/ 1 x))) (* x (pow y 3))))) (+ (* -1 (* (sqrt (/ 1 x)) (/ (* (- 1 x) (- 1 (/ 1 x))) (pow y 2)))) (/ 1 (* x y)))) y)>
#<alt (* -1 (* (sqrt (/ 1 x)) (/ 1 y)))>
#<alt (* -1 (/ (+ (sqrt (/ 1 x)) (* -1 (/ (- 1 (/ 1 x)) y))) y))>
#<alt (* -1 (/ (+ (sqrt (/ 1 x)) (* -1 (/ (- (+ 1 (* (sqrt (/ 1 x)) (/ (* (- 1 x) (- 1 (/ 1 x))) y))) (/ 1 x)) y))) y))>
#<alt (* -1 (/ (+ (sqrt (/ 1 x)) (* -1 (/ (- (+ 1 (* -1 (/ (- (* -1 (/ (* (pow (- 1 x) 2) (- 1 (/ 1 x))) (* x y))) (* (sqrt (/ 1 x)) (* (- 1 x) (- 1 (/ 1 x))))) y))) (/ 1 x)) y))) y))>
#<alt (/ 1 (- 1 (* (sqrt x) y)))>
#<alt (+ (/ 1 (- 1 (* (sqrt x) y))) (/ x (pow (- 1 (* (sqrt x) y)) 2)))>
#<alt (+ (* x (+ (/ 1 (pow (- 1 (* (sqrt x) y)) 2)) (/ x (pow (- 1 (* (sqrt x) y)) 3)))) (/ 1 (- 1 (* (sqrt x) y))))>
#<alt (+ (* 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))))>
#<alt (/ -1 (* x (+ 1 (* (sqrt (/ 1 x)) y))))>
#<alt (* -1 (/ (+ (/ 1 (* x (pow (+ 1 (* (sqrt (/ 1 x)) y)) 2))) (/ 1 (+ 1 (* (sqrt (/ 1 x)) y)))) x))>
#<alt (/ (- (* -1 (/ (+ (/ 1 (* x (pow (+ 1 (* (sqrt (/ 1 x)) y)) 3))) (/ 1 (pow (+ 1 (* (sqrt (/ 1 x)) y)) 2))) x)) (/ 1 (+ 1 (* (sqrt (/ 1 x)) y)))) x)>
#<alt (/ (- (* -1 (/ (+ (/ 1 (* x (pow (+ 1 (* (sqrt (/ 1 x)) y)) 4))) (/ 1 (pow (+ 1 (* (sqrt (/ 1 x)) y)) 3))) (pow x 2))) (+ (/ 1 (* x (pow (+ 1 (* (sqrt (/ 1 x)) y)) 2))) (/ 1 (+ 1 (* (sqrt (/ 1 x)) y))))) x)>
#<alt (/ -1 (* x (- 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))))))>
#<alt (* -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))>
#<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))>
#<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))>
#<alt x>
#<alt (+ x (* (sqrt x) y))>
#<alt (+ x (* (sqrt x) y))>
#<alt (+ x (* (sqrt x) y))>
#<alt (* (sqrt x) y)>
#<alt (* y (+ (sqrt x) (/ x y)))>
#<alt (* y (+ (sqrt x) (/ x y)))>
#<alt (* y (+ (sqrt x) (/ x y)))>
#<alt (* (sqrt x) y)>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ x y)))))>
#<alt (* (sqrt x) y)>
#<alt (+ x (* (sqrt x) y))>
#<alt (+ x (* (sqrt x) y))>
#<alt (+ x (* (sqrt x) y))>
#<alt (* x (+ 1 (* (sqrt (/ 1 x)) y)))>
#<alt (* x (+ 1 (* (sqrt (/ 1 x)) y)))>
#<alt (* x (+ 1 (* (sqrt (/ 1 x)) y)))>
#<alt (* x (+ 1 (* (sqrt (/ 1 x)) y)))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) 1)))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) 1)))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) 1)))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) 1)))>

Calls

75 calls:

Time	Variable		Point	Expression
29.0ms	x	@	-inf	(* (+ (* y (sqrt x)) (+ 1 x)) (* (- 1 (+ (* y (sqrt x)) x)) (/ 1 (- 1 (+ (* y (sqrt x)) x)))))
2.0ms	y	@	inf	(/ 1 (- 1 (+ (* y (sqrt x)) x)))
1.0ms	x	@	-inf	(/ 1 (- 1 (+ (* y (sqrt x)) x)))
1.0ms	x	@	-inf	(* x (+ (* y (sqrt (/ 1 x))) -1))
1.0ms	x	@	0	(* x (+ (* y (sqrt (/ 1 x))) -1))

rewrite445.0ms (5.6%)

Memory

31.4MiB live, 823.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 812×	`accelerator-lowering-fma.f32`
4 812×	`accelerator-lowering-fma.f64`
4 406×	`-lowering-.f32`
4 406×	`-lowering-.f64`
4 156×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	81
1	171	78
2	1471	78
0	8697	72

Stop Event

1×	iter limit
1×	node limit

Counts

15 → 1 303

Calls

Call 1

Inputs
(+ (+ (* y (sqrt x)) (neg x)) 1)
(+ (* y (sqrt x)) (neg x))
(sqrt x)
(neg x)
(- 1 x)
(+ (* (sqrt x) y) 1)
(* x (+ (* y (sqrt (/ 1 x))) -1))
(+ (* y (sqrt (/ 1 x))) -1)
(sqrt (/ 1 x))
(/ 1 x)
(* (- 1 (+ (* y (sqrt x)) x)) (/ 1 (- 1 (+ (* y (sqrt x)) x))))
(* (+ (* y (sqrt x)) (+ 1 x)) (* (- 1 (+ (* y (sqrt x)) x)) (/ 1 (- 1 (+ (* y (sqrt x)) x)))))
(+ (* y (sqrt x)) (+ 1 x))
(/ 1 (- 1 (+ (* y (sqrt x)) x)))
(+ (* y (sqrt x)) x)

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

simplify399.0ms (5%)

Memory

-28.3MiB live, 609.2MiB allocated

Algorithm

1×	egg-herbie

Rules

9 690×	`accelerator-lowering-fma.f32`
9 690×	`accelerator-lowering-fma.f64`
4 246×	`-lowering-.f32`
4 246×	`-lowering-.f64`
2 818×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	257	2465
1	745	2335
2	2228	2293
3	7477	2293
0	8737	2112

Stop Event

1×	iter limit
1×	node limit

Counts

300 → 300

Calls

Call 1

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

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

eval316.0ms (4%)

Memory: 25.6MiB live, 460.8MiB allocated
Compiler: Compiled 51 809 to 2 689 computations (94.8% saved)

prune232.0ms (2.9%)

Memory

-17.8MiB live, 436.7MiB allocated

Pruning

19 alts after pruning (16 fresh and 3 done)

	Pruned	Kept	Total
New	1 785	13	1 798
Fresh	4	3	7
Picked	3	2	5
Done	0	1	1
Total	1 792	19	1 811

Accuracy

100.0%

Counts

1 811 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
	69.4%	(fma.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) y #s(literal 1 binary64))
	57.8%	(fma.f64 (pow.f64 (*.f64 x x) #s(literal 1/4 binary64)) y #s(literal 1 binary64))
	68.9%	(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))
	63.6%	(fma.f64 (/.f64 y (sqrt.f64 x)) x #s(literal 1 binary64))
	63.6%	(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 y x) #s(literal 1 binary64))
	63.7%	(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 x y) #s(literal 1 binary64))
	70.6%	(fma.f64 (sqrt.f64 x) y (neg.f64 x))
✓	69.6%	(fma.f64 (sqrt.f64 x) y #s(literal 1 binary64))
▶	99.9%	(-.f64 (fma.f64 (sqrt.f64 x) y #s(literal 1 binary64)) x)
▶	70.6%	(-.f64 (*.f64 y (sqrt.f64 x)) x)
✓	57.5%	(-.f64 #s(literal 1 binary64) x)
✓	99.9%	(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))
	28.5%	(+.f64 x #s(literal 1 binary64))
	43.1%	(*.f64 (sqrt.f64 x) y)
▶	60.3%	(*.f64 x (fma.f64 (sqrt.f64 x) (/.f64 y x) #s(literal -1 binary64)))
▶	64.6%	(*.f64 x (fma.f64 y (sqrt.f64 (pow.f64 (sqrt.f64 x) #s(literal -2 binary64))) #s(literal -1 binary64)))
	37.1%	(.f64 x (.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
	29.1%	(neg.f64 x)
▶	28.3%	#s(literal 1 binary64)

Compiler

Compiled 304 to 208 computations (31.6% saved)

simplify518.0ms (6.5%)

Memory

18.9MiB live, 683.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(pow.f64 (sqrt.f64 x) #s(literal -2 binary64))
✓	cost-diff	0	(sqrt.f64 (pow.f64 (sqrt.f64 x) #s(literal -2 binary64)))
✓	cost-diff	0	(fma.f64 y (sqrt.f64 (pow.f64 (sqrt.f64 x) #s(literal -2 binary64))) #s(literal -1 binary64))
✓	cost-diff	0	(*.f64 x (fma.f64 y (sqrt.f64 (pow.f64 (sqrt.f64 x) #s(literal -2 binary64))) #s(literal -1 binary64)))
✓	cost-diff	0	(/.f64 y x)
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(fma.f64 (sqrt.f64 x) (/.f64 y x) #s(literal -1 binary64))
✓	cost-diff	896	(*.f64 x (fma.f64 (sqrt.f64 x) (/.f64 y x) #s(literal -1 binary64)))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(*.f64 y (sqrt.f64 x))
✓	cost-diff	0	(-.f64 (*.f64 y (sqrt.f64 x)) x)
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(fma.f64 (sqrt.f64 x) y #s(literal 1 binary64))
✓	cost-diff	0	(-.f64 (fma.f64 (sqrt.f64 x) y #s(literal 1 binary64)) x)

Rules

18 776×	`accelerator-lowering-fma.f32`
18 776×	`accelerator-lowering-fma.f64`
2 790×	`-lowering-.f32`
2 790×	`-lowering-.f64`
1 680×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	91
1	47	91
2	81	91
3	123	91
4	215	91
5	399	91
6	1112	91
7	3493	91
8	4841	91
9	5692	91
10	5932	91
11	6046	91
12	6208	91
13	7256	91
14	7374	91
15	7474	91
16	7482	91
17	7490	91
18	7506	91
19	7506	91
0	8081	86

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize73.0ms (0.9%)

Memory

-13.4MiB live, 181.3MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(fma.f64 y (sqrt.f64 (pow.f64 (sqrt.f64 x) #s(literal -2 binary64))) #s(literal -1 binary64))
✓	accuracy	99.8%	(sqrt.f64 (pow.f64 (sqrt.f64 x) #s(literal -2 binary64)))
✓	accuracy	99.2%	(pow.f64 (sqrt.f64 x) #s(literal -2 binary64))
✓	accuracy	93.9%	(*.f64 x (fma.f64 y (sqrt.f64 (pow.f64 (sqrt.f64 x) #s(literal -2 binary64))) #s(literal -1 binary64)))
✓	accuracy	100.0%	(/.f64 y x)
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	93.9%	(*.f64 x (fma.f64 (sqrt.f64 x) (/.f64 y x) #s(literal -1 binary64)))
✓	accuracy	93.7%	(fma.f64 (sqrt.f64 x) (/.f64 y x) #s(literal -1 binary64))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(-.f64 (*.f64 y (sqrt.f64 x)) x)
✓	accuracy	99.7%	(*.f64 y (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(-.f64 (fma.f64 (sqrt.f64 x) y #s(literal 1 binary64)) x)
✓	accuracy	99.8%	(fma.f64 (sqrt.f64 x) y #s(literal 1 binary64))

Samples

42.0ms

256×

valid

Compiler

Compiled 91 to 22 computations (75.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-mult: 9.0ms (36.7% of total)

ival-sqrt: 5.0ms (20.4% of total)

ival-add: 3.0ms (12.2% of total)

ival-div: 2.0ms (8.2% of total)

ival-sub: 2.0ms (8.2% of total)

ival-pow: 2.0ms (8.2% of total)

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

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

exact: 0.0ms (0% of total)

series9.0ms (0.1%)

Memory

29.8MiB live, 29.8MiB allocated

Counts

12 → 252

Calls

Call 1

Inputs
#<alt (- (+ (* (sqrt x) y) 1) x)>
#<alt (+ (* (sqrt x) y) 1)>
#<alt (sqrt x)>
#<alt (- (* y (sqrt x)) x)>
#<alt (* y (sqrt x))>
#<alt (* x (+ (* (sqrt x) (/ y x)) -1))>
#<alt (+ (* (sqrt x) (/ y x)) -1)>
#<alt (/ y x)>
#<alt (* x (+ (* y (sqrt (pow (sqrt x) -2))) -1))>
#<alt (+ (* y (sqrt (pow (sqrt x) -2))) -1)>
#<alt (sqrt (pow (sqrt x) -2))>
#<alt (pow (sqrt x) -2)>

Outputs
#<alt (+ 1 (* (sqrt x) y))>
#<alt (+ 1 (+ (* -1 x) (* (sqrt x) y)))>
#<alt (+ 1 (+ (* -1 x) (* (sqrt x) y)))>
#<alt (+ 1 (+ (* -1 x) (* (sqrt x) y)))>
#<alt (* x (- (* (sqrt (/ 1 x)) y) 1))>
#<alt (* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))>
#<alt (* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))>
#<alt (* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))>
#<alt (* -1 (* x (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))>
#<alt (* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))>
#<alt (* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))>
#<alt (- 1 x)>
#<alt (- (+ 1 (* (sqrt x) y)) x)>
#<alt (- (+ 1 (* (sqrt x) y)) x)>
#<alt (- (+ 1 (* (sqrt x) y)) x)>
#<alt (* (sqrt x) y)>
#<alt (* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))>
#<alt (* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))>
#<alt (* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))>
#<alt (* (sqrt x) y)>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))>
#<alt (+ 1 (* (sqrt x) y))>
#<alt (+ 1 (* (sqrt x) y))>
#<alt (+ 1 (* (sqrt x) y))>
#<alt (+ 1 (* (sqrt x) y))>
#<alt (* (sqrt x) y)>
#<alt (* x (+ (* (sqrt (/ 1 x)) y) (/ 1 x)))>
#<alt (* x (+ (* (sqrt (/ 1 x)) y) (/ 1 x)))>
#<alt (* x (+ (* (sqrt (/ 1 x)) y) (/ 1 x)))>
#<alt (* -1 (* (sqrt x) (* y (pow (sqrt -1) 2))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) (/ 1 x))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) (/ 1 x))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))) (/ 1 x))))>
#<alt 1>
#<alt (+ 1 (* (sqrt x) y))>
#<alt (+ 1 (* (sqrt x) y))>
#<alt (+ 1 (* (sqrt x) y))>
#<alt (* (sqrt x) y)>
#<alt (* y (+ (sqrt x) (/ 1 y)))>
#<alt (* y (+ (sqrt x) (/ 1 y)))>
#<alt (* y (+ (sqrt x) (/ 1 y)))>
#<alt (* (sqrt x) y)>
#<alt (* -1 (* y (- (* -1 (sqrt x)) (/ 1 y))))>
#<alt (* -1 (* y (- (* -1 (sqrt x)) (/ 1 y))))>
#<alt (* -1 (* y (- (* -1 (sqrt x)) (/ 1 y))))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 x)>
#<alt (- (* (sqrt x) y) x)>
#<alt (- (* (sqrt x) y) x)>
#<alt (- (* (sqrt x) y) x)>
#<alt (* (sqrt x) y)>
#<alt (* y (+ (sqrt x) (* -1 (/ x y))))>
#<alt (* y (+ (sqrt x) (* -1 (/ x y))))>
#<alt (* y (+ (sqrt x) (* -1 (/ x y))))>
#<alt (* (sqrt x) y)>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (/ x y))))>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (/ x y))))>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (/ x y))))>
#<alt (* (sqrt x) y)>
#<alt (+ (* -1 x) (* (sqrt x) y))>
#<alt (+ (* -1 x) (* (sqrt x) y))>
#<alt (+ (* -1 x) (* (sqrt x) y))>
#<alt (* x (- (* (sqrt (/ 1 x)) y) 1))>
#<alt (* x (- (* (sqrt (/ 1 x)) y) 1))>
#<alt (* x (- (* (sqrt (/ 1 x)) y) 1))>
#<alt (* x (- (* (sqrt (/ 1 x)) y) 1))>
#<alt (* -1 (* x (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))))))>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* -1 (* (sqrt x) (* y (pow (sqrt -1) 2))))>
#<alt (* -1 (* (sqrt x) (* y (pow (sqrt -1) 2))))>
#<alt (* -1 (* (sqrt x) (* y (pow (sqrt -1) 2))))>
#<alt (* -1 (* (sqrt x) (* y (pow (sqrt -1) 2))))>
#<alt (* (sqrt x) y)>
#<alt (+ (* -1 x) (* (sqrt x) y))>
#<alt (+ (* -1 x) (* (sqrt x) y))>
#<alt (+ (* -1 x) (* (sqrt x) y))>
#<alt (* x (- (* (sqrt (/ 1 x)) y) 1))>
#<alt (* x (- (* (sqrt (/ 1 x)) y) 1))>
#<alt (* x (- (* (sqrt (/ 1 x)) y) 1))>
#<alt (* x (- (* (sqrt (/ 1 x)) y) 1))>
#<alt (* x (- (* -1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 1))>
#<alt (* x (- (* -1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 1))>
#<alt (* x (- (* -1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 1))>
#<alt (* x (- (* -1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 1))>
#<alt (* -1 x)>
#<alt (+ (* -1 x) (* (sqrt x) y))>
#<alt (+ (* -1 x) (* (sqrt x) y))>
#<alt (+ (* -1 x) (* (sqrt x) y))>
#<alt (* (sqrt x) y)>
#<alt (* y (+ (sqrt x) (* -1 (/ x y))))>
#<alt (* y (+ (sqrt x) (* -1 (/ x y))))>
#<alt (* y (+ (sqrt x) (* -1 (/ x y))))>
#<alt (* (sqrt x) y)>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (/ x y))))>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (/ x y))))>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (/ x y))))>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (/ (+ (* -1 x) (* (sqrt x) y)) x)>
#<alt (/ (+ (* -1 x) (* (sqrt x) y)) x)>
#<alt (/ (+ (* -1 x) (* (sqrt x) y)) x)>
#<alt (- (* (sqrt (/ 1 x)) y) 1)>
#<alt (- (* (sqrt (/ 1 x)) y) 1)>
#<alt (- (* (sqrt (/ 1 x)) y) 1)>
#<alt (- (* (sqrt (/ 1 x)) y) 1)>
#<alt (- (* -1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 1)>
#<alt (- (* -1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 1)>
#<alt (- (* -1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 1)>
#<alt (- (* -1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) 1)>
#<alt -1>
#<alt (- (* (sqrt (/ 1 x)) y) 1)>
#<alt (- (* (sqrt (/ 1 x)) y) 1)>
#<alt (- (* (sqrt (/ 1 x)) y) 1)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* y (- (sqrt (/ 1 x)) (/ 1 y)))>
#<alt (* y (- (sqrt (/ 1 x)) (/ 1 y)))>
#<alt (* y (- (sqrt (/ 1 x)) (/ 1 y)))>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* -1 (* y (+ (* -1 (sqrt (/ 1 x))) (/ 1 y))))>
#<alt (* -1 (* y (+ (* -1 (sqrt (/ 1 x))) (/ 1 y))))>
#<alt (* -1 (* y (+ (* -1 (sqrt (/ 1 x))) (/ 1 y))))>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (* (sqrt x) y)>
#<alt (+ (* -1 x) (* (sqrt x) y))>
#<alt (+ (* -1 x) (* (sqrt x) y))>
#<alt (+ (* -1 x) (* (sqrt x) y))>
#<alt (* x (- (* (sqrt (/ 1 x)) y) 1))>
#<alt (* x (- (* (sqrt (/ 1 x)) y) 1))>
#<alt (* x (- (* (sqrt (/ 1 x)) y) 1))>
#<alt (* x (- (* (sqrt (/ 1 x)) y) 1))>
#<alt (* x (- (* (sqrt (/ 1 x)) y) 1))>
#<alt (* x (- (* (sqrt (/ 1 x)) y) 1))>
#<alt (* x (- (* (sqrt (/ 1 x)) y) 1))>
#<alt (* x (- (* (sqrt (/ 1 x)) y) 1))>
#<alt (* -1 x)>
#<alt (+ (* -1 x) (* (sqrt x) y))>
#<alt (+ (* -1 x) (* (sqrt x) y))>
#<alt (+ (* -1 x) (* (sqrt x) y))>
#<alt (* (sqrt x) y)>
#<alt (* y (+ (sqrt x) (* -1 (/ x y))))>
#<alt (* y (+ (sqrt x) (* -1 (/ x y))))>
#<alt (* y (+ (sqrt x) (* -1 (/ x y))))>
#<alt (* (sqrt x) y)>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (/ x y))))>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (/ x y))))>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (/ x y))))>
#<alt -1>
#<alt (- (* (sqrt (/ 1 x)) y) 1)>
#<alt (- (* (sqrt (/ 1 x)) y) 1)>
#<alt (- (* (sqrt (/ 1 x)) y) 1)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* y (- (sqrt (/ 1 x)) (/ 1 y)))>
#<alt (* y (- (sqrt (/ 1 x)) (/ 1 y)))>
#<alt (* y (- (sqrt (/ 1 x)) (/ 1 y)))>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* -1 (* y (+ (* -1 (sqrt (/ 1 x))) (/ 1 y))))>
#<alt (* -1 (* y (+ (* -1 (sqrt (/ 1 x))) (/ 1 y))))>
#<alt (* -1 (* y (+ (* -1 (sqrt (/ 1 x))) (/ 1 y))))>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (/ (+ (* -1 x) (* (sqrt x) y)) x)>
#<alt (/ (+ (* -1 x) (* (sqrt x) y)) x)>
#<alt (/ (+ (* -1 x) (* (sqrt x) y)) x)>
#<alt (- (* (sqrt (/ 1 x)) y) 1)>
#<alt (- (* (sqrt (/ 1 x)) y) 1)>
#<alt (- (* (sqrt (/ 1 x)) y) 1)>
#<alt (- (* (sqrt (/ 1 x)) y) 1)>
#<alt (- (* (sqrt (/ 1 x)) y) 1)>
#<alt (- (* (sqrt (/ 1 x)) y) 1)>
#<alt (- (* (sqrt (/ 1 x)) y) 1)>
#<alt (- (* (sqrt (/ 1 x)) y) 1)>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ -1 (* x (pow (sqrt -1) 2)))>
#<alt (/ -1 (* x (pow (sqrt -1) 2)))>
#<alt (/ -1 (* x (pow (sqrt -1) 2)))>
#<alt (/ -1 (* x (pow (sqrt -1) 2)))>

Calls

63 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(* x (+ (* y (sqrt (pow (sqrt x) -2))) -1))
1.0ms	x	@	-inf	(* x (+ (* (sqrt x) (/ y x)) -1))
1.0ms	x	@	-inf	(pow (sqrt x) -2)
1.0ms	x	@	-inf	(sqrt (pow (sqrt x) -2))
0.0ms	y	@	inf	(/ y x)

rewrite508.0ms (6.4%)

Memory

-29.3MiB live, 609.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 312×	`accelerator-lowering-fma.f32`
6 312×	`accelerator-lowering-fma.f64`
3 996×	`-lowering-.f32`
3 996×	`-lowering-.f64`
3 388×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	64
1	126	63
2	907	59
0	8773	57

Stop Event

1×	iter limit
1×	node limit

Counts

12 → 635

Calls

Call 1

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

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

simplify291.0ms (3.6%)

Memory

4.0MiB live, 498.9MiB allocated

Algorithm

1×	egg-herbie

Rules

9 168×	`accelerator-lowering-fma.f32`
9 168×	`accelerator-lowering-fma.f64`
3 542×	`-lowering-.f32`
3 542×	`-lowering-.f64`
1 660×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	74	1516
1	218	1498
2	657	1492
3	1743	1492
4	4811	1492
0	8355	1382

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 252

Calls

Call 1

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

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

eval152.0ms (1.9%)

Memory: -7.3MiB live, 220.6MiB allocated
Compiler: Compiled 17 588 to 1 304 computations (92.6% saved)

prune123.0ms (1.5%)

Memory

0.7MiB live, 121.5MiB allocated

Pruning

17 alts after pruning (12 fresh and 5 done)

	Pruned	Kept	Total
New	951	5	956
Fresh	4	7	11
Picked	2	3	5
Done	1	2	3
Total	958	17	975

Accuracy

100.0%

Counts

975 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	63.6%	(fma.f64 (/.f64 y (sqrt.f64 x)) x #s(literal 1 binary64))
	99.8%	(fma.f64 (/.f64 x (sqrt.f64 x)) y (-.f64 #s(literal 1 binary64) x))
▶	70.6%	(fma.f64 (/.f64 x (sqrt.f64 x)) y (neg.f64 x))
	63.6%	(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 y x) #s(literal 1 binary64))
▶	99.9%	(fma.f64 (sqrt.f64 x) y (-.f64 #s(literal 1 binary64) x))
	70.6%	(fma.f64 (sqrt.f64 x) y (neg.f64 x))
✓	69.6%	(fma.f64 (sqrt.f64 x) y #s(literal 1 binary64))
	48.8%	(-.f64 (/.f64 (*.f64 x (sqrt.f64 x)) (/.f64 x y)) x)
	61.4%	(-.f64 (/.f64 (*.f64 x y) (sqrt.f64 x)) x)
✓	70.6%	(-.f64 (*.f64 y (sqrt.f64 x)) x)
✓	57.5%	(-.f64 #s(literal 1 binary64) x)
	28.5%	(+.f64 x #s(literal 1 binary64))
▶	43.1%	(*.f64 (sqrt.f64 x) y)
✓	60.3%	(*.f64 x (fma.f64 (sqrt.f64 x) (/.f64 y x) #s(literal -1 binary64)))
	37.1%	(.f64 x (.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
▶	29.1%	(neg.f64 x)
✓	28.3%	#s(literal 1 binary64)

Compiler

Compiled 244 to 160 computations (34.4% saved)

simplify83.0ms (1%)

Memory

3.4MiB live, 42.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

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

Rules

752×	`accelerator-lowering-fma.f32`
752×	`accelerator-lowering-fma.f64`
384×	`-lowering-.f32`
384×	`-lowering-.f64`
218×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	62
1	33	62
2	49	62
3	96	62
4	176	62
5	357	62
6	684	62
7	1396	62
8	1544	62
9	1587	62
10	1642	62
11	1643	62
0	1643	60

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ (* (sqrt x) y) (- 1 x))
(sqrt x)
x
y
(- 1 x)
1
(neg x)
x
(* (sqrt x) y)
(sqrt x)
x
y
(+ (* (/ y (sqrt x)) x) 1)
(/ y (sqrt x))
y
(sqrt x)
x
1
(+ (* (/ x (sqrt x)) y) (neg x))
(/ x (sqrt x))
x
(sqrt x)
y
(neg x)

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

localize61.0ms (0.8%)

Memory

32.4MiB live, 69.8MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(neg.f64 x)
✓	accuracy	99.8%	(fma.f64 (/.f64 x (sqrt.f64 x)) y (neg.f64 x))
✓	accuracy	99.3%	(/.f64 x (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.6%	(/.f64 y (sqrt.f64 x))
✓	accuracy	93.9%	(fma.f64 (/.f64 y (sqrt.f64 x)) x #s(literal 1 binary64))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.7%	(*.f64 (sqrt.f64 x) y)
✓	accuracy	100.0%	(neg.f64 x)
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.9%	(fma.f64 (sqrt.f64 x) y (-.f64 #s(literal 1 binary64) x))

Samples

44.0ms

256×

valid

Compiler

Compiled 62 to 16 computations (74.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-mult: 4.0ms (25.5% of total)

ival-div: 3.0ms (19.1% of total)

ival-add: 3.0ms (19.1% of total)

ival-sqrt: 2.0ms (12.8% of total)

ival-sub: 1.0ms (6.4% of total)

ival-neg: 1.0ms (6.4% of total)

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

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

exact: 0.0ms (0% of total)

series50.0ms (0.6%)

Memory

-47.9MiB live, 4.7MiB allocated

Counts

9 → 168

Calls

Call 1

Inputs
#<alt (+ (* (sqrt x) y) (- 1 x))>
#<alt (sqrt x)>
#<alt (- 1 x)>
#<alt (neg x)>
#<alt (* (sqrt x) y)>
#<alt (+ (* (/ y (sqrt x)) x) 1)>
#<alt (/ y (sqrt x))>
#<alt (+ (* (/ x (sqrt x)) y) (neg x))>
#<alt (/ x (sqrt x))>

Outputs
#<alt (+ 1 (* (sqrt x) y))>
#<alt (+ 1 (+ (* -1 x) (* (sqrt x) y)))>
#<alt (+ 1 (+ (* -1 x) (* (sqrt x) y)))>
#<alt (+ 1 (+ (* -1 x) (* (sqrt x) y)))>
#<alt (* x (- (* (sqrt (/ 1 x)) y) 1))>
#<alt (* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))>
#<alt (* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))>
#<alt (* x (- (+ (* (sqrt (/ 1 x)) y) (/ 1 x)) 1))>
#<alt (* -1 (* x (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))>
#<alt (* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))>
#<alt (* -1 (* x (- (+ 1 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2)))) (/ 1 x))))>
#<alt (- 1 x)>
#<alt (- (+ 1 (* (sqrt x) y)) x)>
#<alt (- (+ 1 (* (sqrt x) y)) x)>
#<alt (- (+ 1 (* (sqrt x) y)) x)>
#<alt (* (sqrt x) y)>
#<alt (* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))>
#<alt (* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))>
#<alt (* y (- (+ (sqrt x) (/ 1 y)) (/ x y)))>
#<alt (* (sqrt x) y)>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (* -1 (/ (- 1 x) y)))))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* -1 (* (sqrt x) (* y (pow (sqrt -1) 2))))>
#<alt (* -1 (* (sqrt x) (* y (pow (sqrt -1) 2))))>
#<alt (* -1 (* (sqrt x) (* y (pow (sqrt -1) 2))))>
#<alt (* -1 (* (sqrt x) (* y (pow (sqrt -1) 2))))>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt 1>
#<alt (+ 1 (* (sqrt x) y))>
#<alt (+ 1 (* (sqrt x) y))>
#<alt (+ 1 (* (sqrt x) y))>
#<alt (* (sqrt x) y)>
#<alt (* y (+ (sqrt x) (/ 1 y)))>
#<alt (* y (+ (sqrt x) (/ 1 y)))>
#<alt (* y (+ (sqrt x) (/ 1 y)))>
#<alt (* (sqrt x) y)>
#<alt (* -1 (* y (- (* -1 (sqrt x)) (/ 1 y))))>
#<alt (* -1 (* y (- (* -1 (sqrt x)) (/ 1 y))))>
#<alt (* -1 (* y (- (* -1 (sqrt x)) (/ 1 y))))>
#<alt (+ 1 (* (sqrt x) y))>
#<alt (+ 1 (* (sqrt x) y))>
#<alt (+ 1 (* (sqrt x) y))>
#<alt (+ 1 (* (sqrt x) y))>
#<alt (* (sqrt x) y)>
#<alt (* x (+ (* (sqrt (/ 1 x)) y) (/ 1 x)))>
#<alt (* x (+ (* (sqrt (/ 1 x)) y) (/ 1 x)))>
#<alt (* x (+ (* (sqrt (/ 1 x)) y) (/ 1 x)))>
#<alt (* (sqrt x) y)>
#<alt (* -1 (* x (- (* -1 (* (sqrt (/ 1 x)) y)) (/ 1 x))))>
#<alt (* -1 (* x (- (* -1 (* (sqrt (/ 1 x)) y)) (/ 1 x))))>
#<alt (* -1 (* x (- (* -1 (* (sqrt (/ 1 x)) y)) (/ 1 x))))>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt (/ 1 x)) y)>
#<alt (* (sqrt x) y)>
#<alt (+ (* -1 x) (* (sqrt x) y))>
#<alt (+ (* -1 x) (* (sqrt x) y))>
#<alt (+ (* -1 x) (* (sqrt x) y))>
#<alt (* x (- (* (sqrt (/ 1 x)) y) 1))>
#<alt (* x (- (* (sqrt (/ 1 x)) y) 1))>
#<alt (* x (- (* (sqrt (/ 1 x)) y) 1))>
#<alt (* x (- (* (sqrt (/ 1 x)) y) 1))>
#<alt (* -1 (* x (+ 1 (* -1 (* (sqrt (/ 1 x)) y)))))>
#<alt (* -1 (* x (+ 1 (* -1 (* (sqrt (/ 1 x)) y)))))>
#<alt (* -1 (* x (+ 1 (* -1 (* (sqrt (/ 1 x)) y)))))>
#<alt (* -1 (* x (+ 1 (* -1 (* (sqrt (/ 1 x)) y)))))>
#<alt (* -1 x)>
#<alt (- (* (sqrt x) y) x)>
#<alt (- (* (sqrt x) y) x)>
#<alt (- (* (sqrt x) y) x)>
#<alt (* (sqrt x) y)>
#<alt (* y (+ (sqrt x) (* -1 (/ x y))))>
#<alt (* y (+ (sqrt x) (* -1 (/ x y))))>
#<alt (* y (+ (sqrt x) (* -1 (/ x y))))>
#<alt (* (sqrt x) y)>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (/ x y))))>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (/ x y))))>
#<alt (* -1 (* y (+ (* -1 (sqrt x)) (/ x y))))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>

Calls

42 calls:

Time	Variable		Point	Expression
44.0ms	x	@	inf	(/ x (sqrt x))
3.0ms	x	@	-inf	(/ x (sqrt x))
0.0ms	x	@	-inf	(+ (* (/ y (sqrt x)) x) 1)
0.0ms	y	@	0	(/ y (sqrt x))
0.0ms	x	@	-inf	(+ (* (/ x (sqrt x)) y) (neg x))

rewrite417.0ms (5.2%)

Memory

17.6MiB live, 407.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

10 082×	`accelerator-lowering-fma.f32`
10 082×	`accelerator-lowering-fma.f64`
3 584×	`-lowering-.f32`
3 584×	`-lowering-.f64`
2 640×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	41
1	93	41
2	816	36
0	9910	33

Stop Event

1×	iter limit
1×	node limit

Counts

9 → 642

Calls

Call 1

Inputs
(+ (* (sqrt x) y) (- 1 x))
(sqrt x)
(- 1 x)
(neg x)
(* (sqrt x) y)
(+ (* (/ y (sqrt x)) x) 1)
(/ y (sqrt x))
(+ (* (/ x (sqrt x)) y) (neg x))
(/ x (sqrt x))

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

simplify253.0ms (3.2%)

Memory

10.9MiB live, 452.1MiB allocated

Algorithm

1×	egg-herbie

Rules

8 328×	`accelerator-lowering-fma.f32`
8 328×	`accelerator-lowering-fma.f64`
3 210×	`-lowering-.f32`
3 210×	`-lowering-.f64`
1 654×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	894
1	216	870
2	653	870
3	1581	870
4	3804	870
5	6608	870
0	8088	816

Stop Event

1×	iter limit
1×	node limit

Counts

168 → 168

Calls

Call 1

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

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

eval127.0ms (1.6%)

Memory: 2.1MiB live, 304.2MiB allocated
Compiler: Compiled 13 404 to 1 462 computations (89.1% saved)

prune122.0ms (1.5%)

Memory

22.1MiB live, 349.7MiB allocated

Pruning

18 alts after pruning (10 fresh and 8 done)

	Pruned	Kept	Total
New	1 005	5	1 010
Fresh	2	5	7
Picked	1	4	5
Done	1	4	5
Total	1 009	18	1 027

Accuracy

100.0%

Counts

1 027 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	63.6%	(fma.f64 (/.f64 y (sqrt.f64 x)) x #s(literal 1 binary64))
	99.8%	(fma.f64 (/.f64 x (sqrt.f64 x)) y (-.f64 #s(literal 1 binary64) x))
	63.6%	(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 y x) #s(literal 1 binary64))
✓	99.9%	(fma.f64 (sqrt.f64 x) y (-.f64 #s(literal 1 binary64) x))
	70.6%	(fma.f64 (sqrt.f64 x) y (neg.f64 x))
✓	69.6%	(fma.f64 (sqrt.f64 x) y #s(literal 1 binary64))
	37.2%	(/.f64 (*.f64 x y) (sqrt.f64 x))
	43.1%	(/.f64 y (/.f64 (sqrt.f64 x) x))
✓	70.6%	(-.f64 (*.f64 y (sqrt.f64 x)) x)
✓	57.5%	(-.f64 #s(literal 1 binary64) x)
	28.5%	(+.f64 x #s(literal 1 binary64))
	37.1%	(*.f64 (/.f64 y (sqrt.f64 x)) x)
	43.1%	(*.f64 (/.f64 x (sqrt.f64 x)) y)
✓	43.1%	(*.f64 (sqrt.f64 x) y)
	37.1%	(.f64 x (.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
✓	29.1%	(neg.f64 x)
	3.2%	x
✓	28.3%	#s(literal 1 binary64)

Compiler

Compiled 410 to 168 computations (59% saved)

regimes34.0ms (0.4%)

Memory

-29.4MiB live, 89.8MiB allocated

Counts

36 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)
x
(neg.f64 x)
(+.f64 x #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) x)
(*.f64 (sqrt.f64 x) y)
(fma.f64 (sqrt.f64 x) y #s(literal 1 binary64))
(-.f64 (*.f64 y (sqrt.f64 x)) x)
(fma.f64 (sqrt.f64 x) y (neg.f64 x))
(-.f64 (fma.f64 (sqrt.f64 x) y #s(literal 1 binary64)) x)
(fma.f64 (sqrt.f64 x) y (-.f64 #s(literal 1 binary64) x))
(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))
(+.f64 (fma.f64 y (sqrt.f64 x) (neg.f64 x)) #s(literal 1 binary64))
(*.f64 (/.f64 x (sqrt.f64 x)) y)
(*.f64 (/.f64 y (sqrt.f64 x)) x)
(/.f64 (*.f64 x y) (sqrt.f64 x))
(fma.f64 (/.f64 y (sqrt.f64 x)) x #s(literal 1 binary64))
(-.f64 (/.f64 (*.f64 x y) (sqrt.f64 x)) x)
(fma.f64 (/.f64 x (sqrt.f64 x)) y (neg.f64 x))
(fma.f64 (/.f64 x (sqrt.f64 x)) y (-.f64 #s(literal 1 binary64) x))
(.f64 x (.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(*.f64 x (fma.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
(*.f64 x (fma.f64 (sqrt.f64 x) (/.f64 y x) #s(literal -1 binary64)))
(/.f64 y (/.f64 (sqrt.f64 x) x))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 x y) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 y x) #s(literal 1 binary64))
(fma.f64 x (fma.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) #s(literal 1 binary64))
(-.f64 (/.f64 (*.f64 x (sqrt.f64 x)) (/.f64 x y)) x)
(.f64 (fma.f64 y (sqrt.f64 x) (+.f64 #s(literal 1 binary64) x)) (.f64 (-.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (fma.f64 y (sqrt.f64 x) x)))))
(fma.f64 (pow.f64 (*.f64 x x) #s(literal 1/4 binary64)) y #s(literal 1 binary64))
(+.f64 (-.f64 #s(literal 1 binary64) x) (.f64 y (pow.f64 (.f64 x x) #s(literal 1/4 binary64))))
(*.f64 x (fma.f64 y (sqrt.f64 (pow.f64 (sqrt.f64 x) #s(literal -2 binary64))) #s(literal -1 binary64)))
(fma.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) y #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))))
(+.f64 (-.f64 #s(literal 1 binary64) x) (.f64 y (exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 x)))))
(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	(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))
10.0ms	y
10.0ms	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 16 to 11 computations (31.3% saved)

regimes12.0ms (0.2%)

Memory

-1.7MiB live, 37.3MiB allocated

Counts

10 → 1

Calls

Call 1

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

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

Calls

3 calls:

4.0ms	y
4.0ms	x
4.0ms	(+.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 16 to 11 computations (31.3% saved)

regimes11.0ms (0.1%)

Memory

32.3MiB live, 32.3MiB allocated

Counts

9 → 2

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.6%	2	`x`
96.0%	3	`y`
98.9%	3	`(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))`

Compiler

Compiled 16 to 11 computations (31.3% saved)

regimes10.0ms (0.1%)

Memory

-11.2MiB live, 27.8MiB allocated

Counts

7 → 3

Calls

Call 1

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

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

Calls

3 calls:

4.0ms	x
3.0ms	y
3.0ms	(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))

Results

Accuracy	Segments	Branch
95.4%	3	`y`
82.2%	3	`(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))`
78.1%	2	`x`

Compiler

Compiled 16 to 11 computations (31.3% saved)

regimes3.0ms (0%)

Memory

11.3MiB live, 11.3MiB allocated

Counts

6 → 3

Calls

Call 1

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

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
92.8%	3	`y`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes9.0ms (0.1%)

Memory

-15.1MiB live, 24.0MiB allocated

Counts

5 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)
x
(neg.f64 x)
(+.f64 x #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) x)

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

Calls

3 calls:

3.0ms	y
2.0ms	x
2.0ms	(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))

Results

Accuracy	Segments	Branch
57.5%	1	`x`
57.5%	1	`(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))`
57.5%	1	`y`

Compiler

Compiled 16 to 11 computations (31.3% saved)

regimes7.0ms (0.1%)

Memory

23.2MiB live, 23.2MiB allocated

Counts

4 → 2

Calls

Call 1

Inputs
#s(literal 1 binary64)
x
(neg.f64 x)
(+.f64 x #s(literal 1 binary64))

Outputs
(neg.f64 x)
(+.f64 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
36.2%	4	`y`
55.3%	2	`x`
56.3%	2	`(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))`

Compiler

Compiled 16 to 11 computations (31.3% saved)

regimes3.0ms (0%)

Memory

-33.5MiB live, 9.2MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs
#s(literal 1 binary64)
x
(neg.f64 x)

Outputs
(neg.f64 x)
#s(literal 1 binary64)

Calls

1 calls:

3.0ms

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

Results

Accuracy	Segments	Branch
56.0%	2	`(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes5.0ms (0.1%)

Memory

16.9MiB live, 16.8MiB allocated

Accuracy

Total -16.4b remaining (-35.6%)

Threshold costs -16.4b (-35.6%)

Counts

2 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)
x

Outputs
#s(literal 1 binary64)

Calls

3 calls:

2.0ms	(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))
2.0ms	y
1.0ms	x

Results

Accuracy	Segments	Branch
28.3%	1	`y`
28.3%	1	`x`
28.3%	1	`(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))`

Compiler

Compiled 16 to 11 computations (31.3% saved)

bsearch11.0ms (0.1%)

Memory

-13.1MiB live, 25.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
10.0ms	0.23496400132429526	27.33203460284544

Samples

6.0ms

112×

valid

Compiler

Compiled 132 to 96 computations (27.3% saved)

Precisions

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

ival-sub: 1.0ms (36.2% of total)

ival-mult: 1.0ms (36.2% of total)

ival-sqrt: 1.0ms (36.2% 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)

bsearch27.0ms (0.3%)

Memory

28.7MiB live, 67.5MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
13.0ms	2.92484778757791e+23	2.5349768627946908e+51
11.0ms	-1.5968900139794543e+45	-1.3554361190564693e+42

Samples

14.0ms

304×

valid

Compiler

Compiled 279 to 221 computations (20.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-sub: 2.0ms (26.5% of total)

ival-mult: 2.0ms (26.5% of total)

ival-sqrt: 2.0ms (26.5% of total)

ival-add: 1.0ms (13.2% of total)

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

exact: 0.0ms (0% of total)

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

bsearch25.0ms (0.3%)

Memory

-67.1MiB live, 43.9MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
10.0ms	2.5349768627946908e+51	1.2544957044563927e+54
7.0ms	-5.7324624550018507e+82	-2.3390713711338007e+82

Samples

11.0ms

208×

valid

Compiler

Compiled 182 to 142 computations (22% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-sub: 2.0ms (33.1% of total)

ival-sqrt: 2.0ms (33.1% of total)

ival-add: 1.0ms (16.5% of total)

ival-mult: 1.0ms (16.5% of total)

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

exact: 0.0ms (0% of total)

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

bsearch0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-26.33203460284544	0.765035998675827

Compiler

Compiled 13 to 12 computations (7.7% saved)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-26.33203460284544	0.765035998675827

Compiler

Compiled 13 to 12 computations (7.7% saved)

simplify8.0ms (0.1%)

Memory

17.7MiB live, 17.7MiB allocated

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
8×	`sub-neg_binary64`
4×	`*-commutative_binary64`
4×	`if-if-or-not_binary32`
2×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	96
1	52	96
2	57	96
3	58	96

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 (sqrt.f64 x) y (-.f64 #s(literal 1 binary64) x))
(-.f64 (fma.f64 (sqrt.f64 x) y #s(literal 1 binary64)) x)
(if (<=.f64 x #s(literal 1 binary64)) (fma.f64 (sqrt.f64 x) y #s(literal 1 binary64)) (-.f64 (*.f64 y (sqrt.f64 x)) x))
(if (<=.f64 y #s(literal -360000000000000000065636053397386469109137408 binary64)) (fma.f64 (sqrt.f64 x) y #s(literal 1 binary64)) (if (<=.f64 y #s(literal 34999999999999997478122585847332822622741410611200 binary64)) (-.f64 #s(literal 1 binary64) x) (fma.f64 (sqrt.f64 x) y #s(literal 1 binary64))))
(if (<=.f64 y #s(literal -38000000000000003327448936148730946068630784484474925502485656549623112898994765824 binary64)) (.f64 (sqrt.f64 x) y) (if (<=.f64 y #s(literal 1250000000000000012793833775510688937038048516915593216 binary64)) (-.f64 #s(literal 1 binary64) x) (.f64 (sqrt.f64 x) y)))
(-.f64 #s(literal 1 binary64) x)
(if (<=.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x))) #s(literal -20 binary64)) (neg.f64 x) (+.f64 x #s(literal 1 binary64)))
(if (<=.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x))) #s(literal -20 binary64)) (neg.f64 x) #s(literal 1 binary64))
#s(literal 1 binary64)

Outputs
(fma.f64 (sqrt.f64 x) y (-.f64 #s(literal 1 binary64) x))
(-.f64 (fma.f64 (sqrt.f64 x) y #s(literal 1 binary64)) x)
(if (<=.f64 x #s(literal 1 binary64)) (fma.f64 (sqrt.f64 x) y #s(literal 1 binary64)) (-.f64 (*.f64 y (sqrt.f64 x)) x))
(if (<=.f64 x #s(literal 1 binary64)) (fma.f64 (sqrt.f64 x) y #s(literal 1 binary64)) (-.f64 (*.f64 (sqrt.f64 x) y) x))
(if (<=.f64 y #s(literal -360000000000000000065636053397386469109137408 binary64)) (fma.f64 (sqrt.f64 x) y #s(literal 1 binary64)) (if (<=.f64 y #s(literal 34999999999999997478122585847332822622741410611200 binary64)) (-.f64 #s(literal 1 binary64) x) (fma.f64 (sqrt.f64 x) y #s(literal 1 binary64))))
(if (<=.f64 y #s(literal -38000000000000003327448936148730946068630784484474925502485656549623112898994765824 binary64)) (.f64 (sqrt.f64 x) y) (if (<=.f64 y #s(literal 1250000000000000012793833775510688937038048516915593216 binary64)) (-.f64 #s(literal 1 binary64) x) (.f64 (sqrt.f64 x) y)))
(-.f64 #s(literal 1 binary64) x)
(if (<=.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x))) #s(literal -20 binary64)) (neg.f64 x) (+.f64 x #s(literal 1 binary64)))
(if (<=.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) y)) #s(literal -20 binary64)) (neg.f64 x) (+.f64 x #s(literal 1 binary64)))
(if (<=.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x))) #s(literal -20 binary64)) (neg.f64 x) #s(literal 1 binary64))
(if (<=.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) y)) #s(literal -20 binary64)) (neg.f64 x) #s(literal 1 binary64))
#s(literal 1 binary64)

soundness1.1s (13.6%)

Memory

6.8MiB live, 597.6MiB allocated

Rules

9 690×	`accelerator-lowering-fma.f32`
9 690×	`accelerator-lowering-fma.f64`
7 542×	`accelerator-lowering-fma.f32`
7 542×	`accelerator-lowering-fma.f64`
6 312×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	257	2465
1	745	2335
2	2228	2293
3	7477	2293
0	8737	2112
0	20	64
1	126	63
2	907	59
0	8773	57
0	24	81
1	171	78
2	1471	78
0	8697	72
0	52	369
1	141	369
2	438	357
3	1298	357
4	4657	357
5	7379	357
0	8084	330

Stop Event

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

Compiler

Compiled 204 to 108 computations (47.1% saved)

preprocess218.0ms (2.7%)

Memory: -11.7MiB live, 113.9MiB allocated
Compiler: Compiled 230 to 76 computations (67% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze34.0ms (0.4%)

sample758.0ms (9.5%)

preprocess61.0ms (0.8%)

explain79.0ms (1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify20.0ms (0.2%)

localize25.0ms (0.3%)

series5.0ms (0.1%)

rewrite414.0ms (5.2%)

simplify271.0ms (3.4%)

eval61.0ms (0.8%)

prune42.0ms (0.5%)

simplify442.0ms (5.5%)

localize89.0ms (1.1%)

series42.0ms (0.5%)

rewrite445.0ms (5.6%)

simplify399.0ms (5%)

eval316.0ms (4%)

prune232.0ms (2.9%)

simplify518.0ms (6.5%)

localize73.0ms (0.9%)

series9.0ms (0.1%)

rewrite508.0ms (6.4%)

simplify291.0ms (3.6%)

eval152.0ms (1.9%)

prune123.0ms (1.5%)

simplify83.0ms (1%)

localize61.0ms (0.8%)

series50.0ms (0.6%)

rewrite417.0ms (5.2%)

simplify253.0ms (3.2%)

eval127.0ms (1.6%)

prune122.0ms (1.5%)

regimes34.0ms (0.4%)

regimes12.0ms (0.2%)

regimes11.0ms (0.1%)

regimes10.0ms (0.1%)

regimes3.0ms (0%)

regimes9.0ms (0.1%)

regimes7.0ms (0.1%)

regimes3.0ms (0%)

regimes5.0ms (0.1%)

bsearch11.0ms (0.1%)

bsearch27.0ms (0.3%)

bsearch25.0ms (0.3%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify8.0ms (0.1%)

soundness1.1s (13.6%)

preprocess218.0ms (2.7%)

end0.0ms (0%)

Profiling