Metrics for bug366, discussion (missed optimization)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze29.0ms (0.6%)

Memory

14.5MiB live, 51.0MiB 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
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
0%	0%	99.9%	0.1%	0%	0%	0%	4
30.8%	25%	56.2%	0.1%	0%	18.7%	0%	5
32%	25%	53.1%	0.1%	0%	21.9%	0%	6
55.8%	37.5%	29.7%	0.1%	0%	32.8%	0%	7
57.8%	37.5%	27.3%	0.1%	0%	35.1%	0%	8
74.2%	43.7%	15.2%	0.1%	0%	41%	0%	9
75.9%	43.7%	13.9%	0.1%	0%	42.3%	0%	10
85.9%	46.8%	7.7%	0.1%	0%	45.4%	0%	11
87%	46.8%	7%	0.1%	0%	46.1%	0%	12

Compiler

Compiled 10 to 8 computations (20% saved)

sample854.0ms (17.5%)

Memory

9.3MiB live, 800.3MiB allocated

Samples

560.0ms	8 256×	0	valid
75.0ms	669×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 278.0ms

ival-mult: 166.0ms (59.8% of total)

ival-sqrt: 63.0ms (22.7% of total)

ival-sub: 39.0ms (14% of total)

ival-true: 6.0ms (2.2% of total)

ival-assert: 3.0ms (1.1% of total)

Bogosity

explain108.0ms (2.2%)

Memory

-4.2MiB live, 94.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
139	-	-	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`
22	-	-	`(-.f64 (.f64 a a) (.f64 b b))`
0	-	-	`(*.f64 a a)`
0	-	-	`a`
0	-	-	`b`
0	-	-	`(*.f64 b b)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`	oflow-rescue	126	0
↳	`(*.f64 b b)`	overflow	22
↳	`(-.f64 (.f64 a a) (.f64 b b))`	overflow	126
↳	`(*.f64 a a)`	overflow	126
`-.f64`	`(-.f64 (.f64 a a) (.f64 b b))`	nan-rescue	22	0
↳	`(*.f64 a a)`	overflow	126
↳	`(*.f64 b b)`	overflow	22
`sqrt.f64`	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`	uflow-rescue	13	0
↳	`(*.f64 b b)`	underflow	108
↳	`(-.f64 (.f64 a a) (.f64 b b))`	underflow	13
↳	`(*.f64 a a)`	underflow	13

Confusion

	Predicted +	Predicted -
+	139	0
-	0	117

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	139	0	0
-	0	0	117

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	117
1	117
2	22

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

67.0ms

512×

valid

Compiler

Compiled 58 to 22 computations (62.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-mult: 7.0ms (45.9% of total)

ival-sqrt: 5.0ms (32.8% of total)

ival-sub: 2.0ms (13.1% of total)

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

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

preprocess416.0ms (8.5%)

Memory

2.3MiB live, 226.6MiB allocated

Algorithm

1×	egg-herbie

Rules

24 584×	`lower-fma.f64`
24 584×	`lower-fma.f32`
5 200×	`lower-+.f64`
5 200×	`lower-+.f32`
3 968×	`associate-+r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	42
1	54	42
2	128	42
3	331	42
4	827	42
5	1200	42
6	1876	42
7	2756	42
8	3566	42
9	4032	42
10	4138	42
11	4184	42
12	4202	42
13	6464	42
14	7171	42
15	7815	42
0	6	8
0	10	8
1	18	8
2	29	8
3	55	8
4	115	8
5	318	8
6	587	8
7	1257	8
8	2531	8
9	4197	8
10	5056	8
11	5425	8
12	5655	8
13	5769	8
14	5769	8
15	6729	8
16	6889	8
17	7209	8
18	7209	8
19	7609	8
20	7769	8
21	7849	8
22	7849	8
23	7849	8
0	10335	8

Stop Event

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

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))

Outputs
(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
(sqrt.f64 (*.f64 (-.f64 a b) (+.f64 b a)))

Symmetry

(abs b)

(abs a)

Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

Memory: 0.7MiB live, 0.7MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune1.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	48.9%	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify481.0ms (9.9%)

Memory

0.8MiB live, 212.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 b b)
cost-diff	0	(*.f64 a a)
cost-diff	0	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
cost-diff	128	(-.f64 (.f64 a a) (.f64 b b))

Rules

24 584×	`lower-fma.f64`
24 584×	`lower-fma.f32`
5 200×	`lower-+.f64`
5 200×	`lower-+.f32`
3 968×	`associate-+r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	23
0	10	23
1	18	23
2	29	23
3	55	23
4	115	23
5	318	23
6	587	23
7	1257	23
8	2531	23
9	4197	23
10	5056	23
11	5425	23
12	5655	23
13	5769	23
14	5769	23
15	6729	23
16	6889	23
17	7209	23
18	7209	23
19	7609	23
20	7769	23
21	7849	23
22	7849	23
23	7849	23
0	10335	23

Stop Event

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

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
(-.f64 (.f64 a a) (.f64 b b))
(*.f64 a a)
a
(*.f64 b b)
b

Outputs
(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
(sqrt.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
(-.f64 (.f64 a a) (.f64 b b))
(*.f64 (-.f64 a b) (+.f64 b a))
(*.f64 a a)
a
(*.f64 b b)
b

localize63.0ms (1.3%)

Memory

-14.0MiB live, 22.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 b b)
accuracy	0	(*.f64 a a)
accuracy	4.382812500000001	(-.f64 (.f64 a a) (.f64 b b))
accuracy	32.30399915420999	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))

Samples

58.0ms

256×

valid

Compiler

Compiled 25 to 8 computations (68% saved)

Precisions

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

ival-mult: 3.0ms (47.8% of total)

ival-sqrt: 2.0ms (31.9% of total)

ival-sub: 1.0ms (15.9% of total)

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

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

series6.0ms (0.1%)

Memory

8.9MiB live, 8.9MiB allocated

Counts

4 → 72

Calls

Call 1

Inputs
#s(alt (-.f64 (.f64 a a) (.f64 b b)) (patch (-.f64 (.f64 a a) (.f64 b b)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (patch (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) #<representation binary64>) () ())
#s(alt (.f64 a a) (patch (.f64 a a) #<representation binary64>) () ())
#s(alt (.f64 b b) (patch (.f64 b b) #<representation binary64>) () ())

Outputs
#s(alt (pow a 2) (taylor 0 b) (#s(alt (-.f64 (.f64 a a) (.f64 b b)) (patch (-.f64 (.f64 a a) (.f64 b b)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow b 2)) (pow a 2)) (taylor 0 b) (#s(alt (-.f64 (.f64 a a) (.f64 b b)) (patch (-.f64 (.f64 a a) (.f64 b b)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow b 2)) (pow a 2)) (taylor 0 b) (#s(alt (-.f64 (.f64 a a) (.f64 b b)) (patch (-.f64 (.f64 a a) (.f64 b b)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow b 2)) (pow a 2)) (taylor 0 b) (#s(alt (-.f64 (.f64 a a) (.f64 b b)) (patch (-.f64 (.f64 a a) (.f64 b b)) #<representation binary64>) () ())) ())
#s(alt a (taylor 0 b) (#s(alt (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (patch (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) #<representation binary64>) () ())) ())
#s(alt (+ a (* -1/2 (/ (pow b 2) a))) (taylor 0 b) (#s(alt (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (patch (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) #<representation binary64>) () ())) ())
#s(alt (+ a (* (pow b 2) (- (* -1/8 (/ (pow b 2) (pow a 3))) (* 1/2 (/ 1 a))))) (taylor 0 b) (#s(alt (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (patch (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) #<representation binary64>) () ())) ())
#s(alt (+ a (* (pow b 2) (- (* (pow b 2) (- (* -1/16 (/ (pow b 2) (pow a 5))) (* 1/8 (/ 1 (pow a 3))))) (* 1/2 (/ 1 a))))) (taylor 0 b) (#s(alt (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (patch (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) #<representation binary64>) () ())) ())
#s(alt (pow b 2) (taylor 0 b) (#s(alt (.f64 b b) (patch (.f64 b b) #<representation binary64>) () ())) ())
#s(alt (pow b 2) (taylor 0 b) (#s(alt (.f64 b b) (patch (.f64 b b) #<representation binary64>) () ())) ())
#s(alt (pow b 2) (taylor 0 b) (#s(alt (.f64 b b) (patch (.f64 b b) #<representation binary64>) () ())) ())
#s(alt (pow b 2) (taylor 0 b) (#s(alt (.f64 b b) (patch (.f64 b b) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow b 2)) (taylor inf b) (#s(alt (-.f64 (.f64 a a) (.f64 b b)) (patch (-.f64 (.f64 a a) (.f64 b b)) #<representation binary64>) () ())) ())
#s(alt (* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1)) (taylor inf b) (#s(alt (-.f64 (.f64 a a) (.f64 b b)) (patch (-.f64 (.f64 a a) (.f64 b b)) #<representation binary64>) () ())) ())
#s(alt (* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1)) (taylor inf b) (#s(alt (-.f64 (.f64 a a) (.f64 b b)) (patch (-.f64 (.f64 a a) (.f64 b b)) #<representation binary64>) () ())) ())
#s(alt (* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1)) (taylor inf b) (#s(alt (-.f64 (.f64 a a) (.f64 b b)) (patch (-.f64 (.f64 a a) (.f64 b b)) #<representation binary64>) () ())) ())
#s(alt (* b (sqrt -1)) (taylor inf b) (#s(alt (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (patch (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) #<representation binary64>) () ())) ())
#s(alt (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))) (taylor inf b) (#s(alt (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (patch (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) #<representation binary64>) () ())) ())
#s(alt (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))) (taylor inf b) (#s(alt (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (patch (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) #<representation binary64>) () ())) ())
#s(alt (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))) (taylor inf b) (#s(alt (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (patch (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) #<representation binary64>) () ())) ())
#s(alt (pow b 2) (taylor inf b) (#s(alt (.f64 b b) (patch (.f64 b b) #<representation binary64>) () ())) ())
#s(alt (pow b 2) (taylor inf b) (#s(alt (.f64 b b) (patch (.f64 b b) #<representation binary64>) () ())) ())
#s(alt (pow b 2) (taylor inf b) (#s(alt (.f64 b b) (patch (.f64 b b) #<representation binary64>) () ())) ())
#s(alt (pow b 2) (taylor inf b) (#s(alt (.f64 b b) (patch (.f64 b b) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow b 2)) (taylor -inf b) (#s(alt (-.f64 (.f64 a a) (.f64 b b)) (patch (-.f64 (.f64 a a) (.f64 b b)) #<representation binary64>) () ())) ())
#s(alt (* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1)) (taylor -inf b) (#s(alt (-.f64 (.f64 a a) (.f64 b b)) (patch (-.f64 (.f64 a a) (.f64 b b)) #<representation binary64>) () ())) ())
#s(alt (* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1)) (taylor -inf b) (#s(alt (-.f64 (.f64 a a) (.f64 b b)) (patch (-.f64 (.f64 a a) (.f64 b b)) #<representation binary64>) () ())) ())
#s(alt (* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1)) (taylor -inf b) (#s(alt (-.f64 (.f64 a a) (.f64 b b)) (patch (-.f64 (.f64 a a) (.f64 b b)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* b (sqrt -1))) (taylor -inf b) (#s(alt (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (patch (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))) (taylor -inf b) (#s(alt (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (patch (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))) (taylor -inf b) (#s(alt (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (patch (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))) (taylor -inf b) (#s(alt (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (patch (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) #<representation binary64>) () ())) ())
#s(alt (pow b 2) (taylor -inf b) (#s(alt (.f64 b b) (patch (.f64 b b) #<representation binary64>) () ())) ())
#s(alt (pow b 2) (taylor -inf b) (#s(alt (.f64 b b) (patch (.f64 b b) #<representation binary64>) () ())) ())
#s(alt (pow b 2) (taylor -inf b) (#s(alt (.f64 b b) (patch (.f64 b b) #<representation binary64>) () ())) ())
#s(alt (pow b 2) (taylor -inf b) (#s(alt (.f64 b b) (patch (.f64 b b) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow b 2)) (taylor 0 a) (#s(alt (-.f64 (.f64 a a) (.f64 b b)) (patch (-.f64 (.f64 a a) (.f64 b b)) #<representation binary64>) () ())) ())
#s(alt (- (pow a 2) (pow b 2)) (taylor 0 a) (#s(alt (-.f64 (.f64 a a) (.f64 b b)) (patch (-.f64 (.f64 a a) (.f64 b b)) #<representation binary64>) () ())) ())
#s(alt (- (pow a 2) (pow b 2)) (taylor 0 a) (#s(alt (-.f64 (.f64 a a) (.f64 b b)) (patch (-.f64 (.f64 a a) (.f64 b b)) #<representation binary64>) () ())) ())
#s(alt (- (pow a 2) (pow b 2)) (taylor 0 a) (#s(alt (-.f64 (.f64 a a) (.f64 b b)) (patch (-.f64 (.f64 a a) (.f64 b b)) #<representation binary64>) () ())) ())
#s(alt (* b (sqrt -1)) (taylor 0 a) (#s(alt (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (patch (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (/ (pow a 2) (* b (sqrt -1)))) (* b (sqrt -1))) (taylor 0 a) (#s(alt (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (patch (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) #<representation binary64>) () ())) ())
#s(alt (+ (* b (sqrt -1)) (* (pow a 2) (+ (* -1/8 (/ (pow a 2) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* b (sqrt -1))))))) (taylor 0 a) (#s(alt (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (patch (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) #<representation binary64>) () ())) ())
#s(alt (+ (* b (sqrt -1)) (* (pow a 2) (+ (* (pow a 2) (- (* 1/16 (/ (pow a 2) (* (pow b 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow b 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* b (sqrt -1))))))) (taylor 0 a) (#s(alt (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (patch (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) #<representation binary64>) () ())) ())
#s(alt (pow a 2) (taylor 0 a) (#s(alt (.f64 a a) (patch (.f64 a a) #<representation binary64>) () ())) ())
#s(alt (pow a 2) (taylor 0 a) (#s(alt (.f64 a a) (patch (.f64 a a) #<representation binary64>) () ())) ())
#s(alt (pow a 2) (taylor 0 a) (#s(alt (.f64 a a) (patch (.f64 a a) #<representation binary64>) () ())) ())
#s(alt (pow a 2) (taylor 0 a) (#s(alt (.f64 a a) (patch (.f64 a a) #<representation binary64>) () ())) ())
#s(alt (pow a 2) (taylor inf a) (#s(alt (-.f64 (.f64 a a) (.f64 b b)) (patch (-.f64 (.f64 a a) (.f64 b b)) #<representation binary64>) () ())) ())
#s(alt (* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2))))) (taylor inf a) (#s(alt (-.f64 (.f64 a a) (.f64 b b)) (patch (-.f64 (.f64 a a) (.f64 b b)) #<representation binary64>) () ())) ())
#s(alt (* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2))))) (taylor inf a) (#s(alt (-.f64 (.f64 a a) (.f64 b b)) (patch (-.f64 (.f64 a a) (.f64 b b)) #<representation binary64>) () ())) ())
#s(alt (* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2))))) (taylor inf a) (#s(alt (-.f64 (.f64 a a) (.f64 b b)) (patch (-.f64 (.f64 a a) (.f64 b b)) #<representation binary64>) () ())) ())
#s(alt a (taylor inf a) (#s(alt (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (patch (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) #<representation binary64>) () ())) ())
#s(alt (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2))))) (taylor inf a) (#s(alt (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (patch (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) #<representation binary64>) () ())) ())
#s(alt (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4)))))) (taylor inf a) (#s(alt (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (patch (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) #<representation binary64>) () ())) ())
#s(alt (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6))))))) (taylor inf a) (#s(alt (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (patch (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) #<representation binary64>) () ())) ())
#s(alt (pow a 2) (taylor inf a) (#s(alt (.f64 a a) (patch (.f64 a a) #<representation binary64>) () ())) ())
#s(alt (pow a 2) (taylor inf a) (#s(alt (.f64 a a) (patch (.f64 a a) #<representation binary64>) () ())) ())
#s(alt (pow a 2) (taylor inf a) (#s(alt (.f64 a a) (patch (.f64 a a) #<representation binary64>) () ())) ())
#s(alt (pow a 2) (taylor inf a) (#s(alt (.f64 a a) (patch (.f64 a a) #<representation binary64>) () ())) ())
#s(alt (pow a 2) (taylor -inf a) (#s(alt (-.f64 (.f64 a a) (.f64 b b)) (patch (-.f64 (.f64 a a) (.f64 b b)) #<representation binary64>) () ())) ())
#s(alt (* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2))))) (taylor -inf a) (#s(alt (-.f64 (.f64 a a) (.f64 b b)) (patch (-.f64 (.f64 a a) (.f64 b b)) #<representation binary64>) () ())) ())
#s(alt (* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2))))) (taylor -inf a) (#s(alt (-.f64 (.f64 a a) (.f64 b b)) (patch (-.f64 (.f64 a a) (.f64 b b)) #<representation binary64>) () ())) ())
#s(alt (* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2))))) (taylor -inf a) (#s(alt (-.f64 (.f64 a a) (.f64 b b)) (patch (-.f64 (.f64 a a) (.f64 b b)) #<representation binary64>) () ())) ())
#s(alt (* -1 a) (taylor -inf a) (#s(alt (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (patch (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))) (taylor -inf a) (#s(alt (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (patch (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4))))))) (taylor -inf a) (#s(alt (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (patch (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6)))))))) (taylor -inf a) (#s(alt (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (patch (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) #<representation binary64>) () ())) ())
#s(alt (pow a 2) (taylor -inf a) (#s(alt (.f64 a a) (patch (.f64 a a) #<representation binary64>) () ())) ())
#s(alt (pow a 2) (taylor -inf a) (#s(alt (.f64 a a) (patch (.f64 a a) #<representation binary64>) () ())) ())
#s(alt (pow a 2) (taylor -inf a) (#s(alt (.f64 a a) (patch (.f64 a a) #<representation binary64>) () ())) ())
#s(alt (pow a 2) (taylor -inf a) (#s(alt (.f64 a a) (patch (.f64 a a) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	b	@	inf	((- (* a a) (* b b)) (sqrt (- (* a a) (* b b))) (* a a) (* b b))
1.0ms	b	@	0	((- (* a a) (* b b)) (sqrt (- (* a a) (* b b))) (* a a) (* b b))
1.0ms	a	@	0	((- (* a a) (* b b)) (sqrt (- (* a a) (* b b))) (* a a) (* b b))
1.0ms	a	@	inf	((- (* a a) (* b b)) (sqrt (- (* a a) (* b b))) (* a a) (* b b))
1.0ms	b	@	-inf	((- (* a a) (* b b)) (sqrt (- (* a a) (* b b))) (* a a) (* b b))

simplify389.0ms (8%)

Memory

12.0MiB live, 172.8MiB allocated

Algorithm

1×	egg-herbie

Rules

18 934×	`lower-fma.f64`
18 934×	`lower-fma.f32`
5 608×	`lower-*.f64`
5 608×	`lower-*.f32`
3 030×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	119	757
1	332	757
2	1128	744
3	4541	722
0	8122	682

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 70

Calls

Call 1

Inputs
(pow a 2)
(+ (* -1 (pow b 2)) (pow a 2))
(+ (* -1 (pow b 2)) (pow a 2))
(+ (* -1 (pow b 2)) (pow a 2))
a
(+ a (* -1/2 (/ (pow b 2) a)))
(+ a (* (pow b 2) (- (* -1/8 (/ (pow b 2) (pow a 3))) (* 1/2 (/ 1 a)))))
(+ a (* (pow b 2) (- (* (pow b 2) (- (* -1/16 (/ (pow b 2) (pow a 5))) (* 1/8 (/ 1 (pow a 3))))) (* 1/2 (/ 1 a)))))
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(* -1 (pow b 2))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* b (sqrt -1))
(* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))
(* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))
(* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(* -1 (pow b 2))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* -1 (* b (sqrt -1)))
(* -1 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))
(* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))
(* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(* -1 (pow b 2))
(- (pow a 2) (pow b 2))
(- (pow a 2) (pow b 2))
(- (pow a 2) (pow b 2))
(* b (sqrt -1))
(+ (* 1/2 (/ (pow a 2) (* b (sqrt -1)))) (* b (sqrt -1)))
(+ (* b (sqrt -1)) (* (pow a 2) (+ (* -1/8 (/ (pow a 2) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* b (sqrt -1)))))))
(+ (* b (sqrt -1)) (* (pow a 2) (+ (* (pow a 2) (- (* 1/16 (/ (pow a 2) (* (pow b 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow b 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* b (sqrt -1)))))))
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
a
(* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))
(* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4))))))
(* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6)))))))
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* -1 a)
(* -1 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2))))))
(* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4)))))))
(* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6))))))))
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)

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

rewrite259.0ms (5.3%)

Memory

3.5MiB live, 123.3MiB allocated

Rules

6 736×	`lower-fma.f64`
6 736×	`lower-fma.f32`
3 576×	`lower-/.f64`
3 576×	`lower-/.f32`
3 476×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	21
0	10	21
1	36	21
2	239	21
3	2135	21
0	9378	21

Stop Event

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

Counts

4 → 326

Calls

Call 1

Inputs
(-.f64 (.f64 a a) (.f64 b b))
(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
(*.f64 a a)
(*.f64 b b)

Outputs
(.f64 (exp.f64 (log.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))))) (exp.f64 (neg.f64 (log.f64 (fma.f64 b b (.f64 a a))))))
(.f64 (exp.f64 (log.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))))) (exp.f64 (neg.f64 (log.f64 (fma.f64 (fma.f64 b b (.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64)))))))
(*.f64 (exp.f64 (log.f64 (+.f64 b a))) (exp.f64 (log.f64 (-.f64 a b))))
(*.f64 (exp.f64 (log.f64 (-.f64 a b))) (exp.f64 (log.f64 (+.f64 b a))))
(.f64 (pow.f64 (/.f64 (fma.f64 b b (.f64 a a)) (-.f64 (pow.f64 a #s(literal 8 binary64)) (pow.f64 b #s(literal 8 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 a #s(literal 4 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 b b (.f64 a a)) (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (+.f64 (pow.f64 (*.f64 b a) #s(literal 4 binary64)) (pow.f64 b #s(literal 8 binary64))) (pow.f64 a #s(literal 8 binary64))) #s(literal -1 binary64)))
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(/.f64 (sqrt.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (fma.f64 (fma.f64 b b (.f64 a a)) (.f64 b b) (pow.f64 a #s(literal 4 binary64)))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 b #s(literal 6 binary64)) (fma.f64 (fma.f64 b b (.f64 a a)) (.f64 b b) (pow.f64 a #s(literal 4 binary64)))) #s(literal 2 binary64)))) (sqrt.f64 (+.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (fma.f64 (fma.f64 b b (.f64 a a)) (.f64 b b) (pow.f64 a #s(literal 4 binary64)))) (/.f64 (pow.f64 b #s(literal 6 binary64)) (fma.f64 (fma.f64 b b (.f64 a a)) (.f64 b b) (pow.f64 a #s(literal 4 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 (/.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 (fma.f64 b b (.f64 a a)) #s(literal 3 binary64))) (/.f64 (pow.f64 b #s(literal 12 binary64)) (pow.f64 (fma.f64 b b (.f64 a a)) #s(literal 3 binary64))))) (sqrt.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))) (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (*.f64 a a))))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (fma.f64 (fma.f64 b b (.f64 a a)) (.f64 b b) (pow.f64 a #s(literal 4 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 b #s(literal 6 binary64)) (fma.f64 (fma.f64 b b (.f64 a a)) (.f64 b b) (pow.f64 a #s(literal 4 binary64)))) #s(literal 3 binary64)))) (sqrt.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (fma.f64 (fma.f64 b b (.f64 a a)) (.f64 b b) (pow.f64 a #s(literal 4 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 b #s(literal 6 binary64)) (fma.f64 (fma.f64 b b (.f64 a a)) (.f64 b b) (pow.f64 a #s(literal 4 binary64)))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (fma.f64 (fma.f64 b b (.f64 a a)) (.f64 b b) (pow.f64 a #s(literal 4 binary64)))) (/.f64 (pow.f64 b #s(literal 6 binary64)) (fma.f64 (fma.f64 b b (.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64)))))))))
(/.f64 (sqrt.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64)))))) (sqrt.f64 (neg.f64 (neg.f64 (fma.f64 b b (*.f64 a a))))))
(/.f64 (sqrt.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))))) (sqrt.f64 (neg.f64 (neg.f64 (fma.f64 (fma.f64 b b (.f64 a a)) (.f64 b b) (pow.f64 a #s(literal 4 binary64)))))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (+.f64 (pow.f64 b #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64))))) (sqrt.f64 (.f64 (fma.f64 b (+.f64 b a) (.f64 a a)) (fma.f64 b (-.f64 b a) (.f64 a a)))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (.f64 (-.f64 a b) (+.f64 b a)))) (sqrt.f64 (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))))
(/.f64 (sqrt.f64 (.f64 (.f64 (-.f64 a b) (+.f64 b a)) (+.f64 (pow.f64 b #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64))))) (sqrt.f64 (.f64 (+.f64 b a) (fma.f64 b (-.f64 b a) (.f64 a a)))))
(/.f64 (sqrt.f64 (.f64 (+.f64 (pow.f64 b #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64))) (.f64 (-.f64 a b) (+.f64 b a)))) (hypot.f64 (pow.f64 b #s(literal 3/2 binary64)) (pow.f64 a #s(literal 3/2 binary64))))
(/.f64 (sqrt.f64 (.f64 (.f64 (-.f64 a b) (+.f64 b a)) (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))))) (sqrt.f64 (.f64 (-.f64 a b) (fma.f64 b (+.f64 b a) (.f64 a a)))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 a #s(literal 8 binary64)) (pow.f64 b #s(literal 8 binary64))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (+.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 a #s(literal 4 binary64))) (fma.f64 b b (*.f64 a a)))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (+.f64 (+.f64 (pow.f64 (.f64 b a) #s(literal 4 binary64)) (pow.f64 b #s(literal 8 binary64))) (pow.f64 a #s(literal 8 binary64))) (fma.f64 b b (.f64 a a)))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (fma.f64 (fma.f64 b b (.f64 a a)) (.f64 b b) (pow.f64 a #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 a #s(literal 18 binary64)) (pow.f64 b #s(literal 18 binary64))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (+.f64 (+.f64 (pow.f64 (.f64 b a) #s(literal 6 binary64)) (pow.f64 b #s(literal 12 binary64))) (pow.f64 a #s(literal 12 binary64))) (fma.f64 (fma.f64 b b (.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))) (.f64 (fma.f64 b b (.f64 a a)) (pow.f64 b #s(literal 4 binary64))))) (sqrt.f64 (pow.f64 (fma.f64 b b (*.f64 a a)) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (pow.f64 a #s(literal 6 binary64)) (fma.f64 (fma.f64 b b (.f64 a a)) (.f64 b b) (pow.f64 a #s(literal 4 binary64)))) (.f64 (fma.f64 (fma.f64 b b (.f64 a a)) (.f64 b b) (pow.f64 a #s(literal 4 binary64))) (pow.f64 b #s(literal 6 binary64))))) (sqrt.f64 (pow.f64 (fma.f64 (fma.f64 b b (.f64 a a)) (.f64 b b) (pow.f64 a #s(literal 4 binary64))) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (pow.f64 (.f64 (-.f64 a b) (+.f64 b a)) #s(literal 2 binary64))) (sqrt.f64 (.f64 (-.f64 a b) (+.f64 b a))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 a #s(literal 4 binary64)))) (sqrt.f64 (-.f64 (.f64 (neg.f64 b) b) (.f64 a a))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 (fma.f64 b b (.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64)))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) #s(literal 1 binary64))) (hypot.f64 b a))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (pow.f64 (*.f64 (-.f64 a b) (+.f64 b a)) #s(literal -1 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))))) (neg.f64 (hypot.f64 b a)))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 b #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 (fma.f64 b b (.f64 a a)) (.f64 b b) (pow.f64 a #s(literal 4 binary64))))))
(/.f64 (hypot.f64 (pow.f64 a #s(literal 9 binary64)) (pow.f64 b #s(literal 9 binary64))) (sqrt.f64 (.f64 (fma.f64 (fma.f64 b b (.f64 a a)) (.f64 b b) (pow.f64 a #s(literal 4 binary64))) (+.f64 (+.f64 (pow.f64 (.f64 b a) #s(literal 6 binary64)) (pow.f64 b #s(literal 12 binary64))) (pow.f64 a #s(literal 12 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 a #s(literal 8 binary64)) (pow.f64 b #s(literal 8 binary64)))) (sqrt.f64 (.f64 (fma.f64 b b (.f64 a a)) (+.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 a #s(literal 4 binary64))))))
(/.f64 (hypot.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (sqrt.f64 (.f64 (fma.f64 b b (.f64 a a)) (+.f64 (+.f64 (pow.f64 (*.f64 b a) #s(literal 4 binary64)) (pow.f64 b #s(literal 8 binary64))) (pow.f64 a #s(literal 8 binary64))))))
(/.f64 (hypot.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (sqrt.f64 (.f64 (fma.f64 (fma.f64 b b (.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64))) (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (hypot.f64 b a)))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 (fma.f64 b b (.f64 a a)) (.f64 b b) (pow.f64 a #s(literal 4 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (-.f64 a b) (+.f64 b a))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (-.f64 a b) (+.f64 b a)) #s(literal -1 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (-.f64 a b) (+.f64 b a)))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64)))) (hypot.f64 b a))
(/.f64 (hypot.f64 (pow.f64 b #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64))) (sqrt.f64 (+.f64 (pow.f64 b #s(literal 4 binary64)) (-.f64 (pow.f64 a #s(literal 4 binary64)) (neg.f64 (pow.f64 (*.f64 b a) #s(literal 2 binary64)))))))
(/.f64 (hypot.f64 (pow.f64 b #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64))) (sqrt.f64 (.f64 (fma.f64 b (-.f64 b a) (.f64 a a)) (fma.f64 b (+.f64 b a) (*.f64 a a)))))
(/.f64 (hypot.f64 (pow.f64 b #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64))) (sqrt.f64 (fma.f64 (fma.f64 b b (.f64 a a)) (.f64 b b) (pow.f64 a #s(literal 4 binary64)))))
(sqrt.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
(exp.f64 (fma.f64 (log.f64 (.f64 (-.f64 a b) (+.f64 b a))) #s(literal 1/4 binary64) (.f64 (log.f64 (*.f64 (-.f64 a b) (+.f64 b a))) #s(literal 1/4 binary64))))
(exp.f64 (fma.f64 (log.f64 (-.f64 a b)) #s(literal 1/2 binary64) (*.f64 (log.f64 (+.f64 b a)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 (+.f64 b a)) #s(literal 1/2 binary64) (*.f64 (log.f64 (-.f64 a b)) #s(literal 1/2 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 (-.f64 a b) (+.f64 b a))) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (-.f64 a b) (+.f64 b a)) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (-.f64 a b) (+.f64 b a)) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (-.f64 a b) (+.f64 b a))) #s(literal 1/2 binary64)))
(*.f64 a a)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 a))
(pow.f64 (*.f64 a a) #s(literal 1 binary64))
(pow.f64 a #s(literal 2 binary64))
(exp.f64 (.f64 (.f64 (log.f64 a) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 a) #s(literal 2 binary64)))
(*.f64 (neg.f64 b) (neg.f64 b))
(*.f64 b b)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 b))
(pow.f64 (neg.f64 b) #s(literal 2 binary64))
(pow.f64 (*.f64 b b) #s(literal 1 binary64))
(pow.f64 b #s(literal 2 binary64))
(exp.f64 (.f64 (.f64 (log.f64 b) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 b) #s(literal 2 binary64)))

eval78.0ms (1.6%)

Memory: -22.7MiB live, 51.3MiB allocated
Compiler: Compiled 10 807 to 1 293 computations (88% saved)

prune103.0ms (2.1%)

Memory

-3.4MiB live, 80.5MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	391	5	396
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	392	5	397

Accuracy

100.0%

Counts

397 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.3%	(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 b a)))
▶	49.5%	(sqrt.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
▶	48.9%	(sqrt.f64 #s(approx (- (* a a) (* b b)) (*.f64 a a)))
▶	99.3%	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a))
▶	1.0%	#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))

Compiler

Compiled 68 to 58 computations (14.7% saved)

simplify149.0ms (3%)

Memory

18.6MiB live, 174.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(sqrt.f64 (+.f64 b a))
cost-diff	0	(-.f64 a b)
cost-diff	0	(sqrt.f64 (-.f64 a b))
cost-diff	0	(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 b a)))
cost-diff	0	(+.f64 b a)
cost-diff	0	(-.f64 a b)
cost-diff	0	(*.f64 (-.f64 a b) (+.f64 b a))
cost-diff	0	(sqrt.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
cost-diff	0	(*.f64 a a)
cost-diff	0	#s(approx (- (* a a) (* b b)) (*.f64 a a))
cost-diff	0	(sqrt.f64 #s(approx (- (* a a) (* b b)) (*.f64 a a)))
cost-diff	0	(neg.f64 a)
cost-diff	0	#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))
cost-diff	0	(/.f64 #s(literal -1/2 binary64) a)
cost-diff	0	(*.f64 (/.f64 #s(literal -1/2 binary64) a) b)
cost-diff	0	(fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a)
cost-diff	0	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a))

Rules

13 330×	`lower-fma.f32`
13 328×	`lower-fma.f64`
3 318×	`lower--.f32`
3 316×	`lower--.f64`
2 170×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	125
0	37	125
1	64	125
2	102	125
3	171	125
4	290	125
5	617	125
6	1582	125
7	3325	125
8	6529	125
0	8154	125

Stop Event

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

Calls

Call 1

Inputs
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a))
(fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a)
(*.f64 (/.f64 #s(literal -1/2 binary64) a) b)
(/.f64 #s(literal -1/2 binary64) a)
#s(literal -1/2 binary64)
a
b
#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))
(neg.f64 a)
a
(sqrt.f64 #s(approx (- (* a a) (* b b)) (*.f64 a a)))
#s(approx (- (* a a) (* b b)) (*.f64 a a))
(*.f64 a a)
a
(sqrt.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
(*.f64 (-.f64 a b) (+.f64 b a))
(-.f64 a b)
a
b
(+.f64 b a)
(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 b a)))
(sqrt.f64 (-.f64 a b))
(-.f64 a b)
a
b
(sqrt.f64 (+.f64 b a))
(+.f64 b a)

Outputs
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a))
(fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a)
(*.f64 (/.f64 #s(literal -1/2 binary64) a) b)
(/.f64 #s(literal -1/2 binary64) a)
#s(literal -1/2 binary64)
a
b
#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))
(neg.f64 a)
a
(sqrt.f64 #s(approx (- (* a a) (* b b)) (*.f64 a a)))
#s(approx (- (* a a) (* b b)) (*.f64 a a))
(*.f64 a a)
a
(sqrt.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
(sqrt.f64 (*.f64 (+.f64 b a) (-.f64 a b)))
(*.f64 (-.f64 a b) (+.f64 b a))
(*.f64 (+.f64 b a) (-.f64 a b))
(-.f64 a b)
a
b
(+.f64 b a)
(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 b a)))
(*.f64 (sqrt.f64 (+.f64 b a)) (sqrt.f64 (-.f64 a b)))
(sqrt.f64 (-.f64 a b))
(-.f64 a b)
a
b
(sqrt.f64 (+.f64 b a))
(+.f64 b a)

localize54.0ms (1.1%)

Memory

-6.7MiB live, 108.0MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 b a)
accuracy	0	(sqrt.f64 (-.f64 a b))
accuracy	0.00390625	(sqrt.f64 (+.f64 b a))
accuracy	0.47265625	(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 b a)))
accuracy	0	(-.f64 a b)
accuracy	0	(+.f64 b a)
accuracy	0	(*.f64 (-.f64 a b) (+.f64 b a))
accuracy	32.30399915420999	(sqrt.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
accuracy	0	(*.f64 a a)
accuracy	0.39302537978655727	#s(approx (- (* a a) (* b b)) (*.f64 a a))
accuracy	32.30399915420999	(sqrt.f64 #s(approx (- (* a a) (* b b)) (*.f64 a a)))
accuracy	0	(neg.f64 a)
accuracy	63.345505421668	#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))
accuracy	0	(fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a)
accuracy	0	(/.f64 #s(literal -1/2 binary64) a)
accuracy	0.228847509768442	(*.f64 (/.f64 #s(literal -1/2 binary64) a) b)
accuracy	0.4359196283768829	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a))

Samples

39.0ms

256×

valid

Compiler

Compiled 108 to 21 computations (80.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 27.0ms

ival-mult: 9.0ms (33.3% of total)

ival-sqrt: 8.0ms (29.6% of total)

ival-neg: 3.0ms (11.1% of total)

ival-div: 2.0ms (7.4% of total)

ival-add: 2.0ms (7.4% of total)

ival-sub: 2.0ms (7.4% of total)

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

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

exact: 0.0ms (0% of total)

series81.0ms (1.7%)

Memory

-11.8MiB live, 77.8MiB allocated

Counts

16 → 348

Calls

Call 1

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

Outputs
#s(alt a (taylor 0 b) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a)) (patch #s(approx (sqrt (- ( a a) (* b b))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a)) #<representation binary64>) () ())) ())
#s(alt (+ a (* -1/2 (/ (pow b 2) a))) (taylor 0 b) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a)) (patch #s(approx (sqrt (- ( a a) (* b b))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a)) #<representation binary64>) () ())) ())
#s(alt (+ a (* (pow b 2) (- (* -1/8 (/ (pow b 2) (pow a 3))) (* 1/2 (/ 1 a))))) (taylor 0 b) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a)) (patch #s(approx (sqrt (- ( a a) (* b b))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a)) #<representation binary64>) () ())) ())
#s(alt (+ a (* (pow b 2) (- (* (pow b 2) (- (* -1/16 (/ (pow b 2) (pow a 5))) (* 1/8 (/ 1 (pow a 3))))) (* 1/2 (/ 1 a))))) (taylor 0 b) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a)) (patch #s(approx (sqrt (- ( a a) (* b b))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a)) #<representation binary64>) () ())) ())
#s(alt a (taylor 0 b) (#s(alt (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a) (patch (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a) #<representation binary64>) () ())) ())
#s(alt (+ a (* -1/2 (/ (pow b 2) a))) (taylor 0 b) (#s(alt (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a) (patch (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a) #<representation binary64>) () ())) ())
#s(alt (+ a (* -1/2 (/ (pow b 2) a))) (taylor 0 b) (#s(alt (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a) (patch (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a) #<representation binary64>) () ())) ())
#s(alt (+ a (* -1/2 (/ (pow b 2) a))) (taylor 0 b) (#s(alt (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a) (patch (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (/ b a)) (taylor 0 b) (#s(alt (.f64 (/.f64 #s(literal -1/2 binary64) a) b) (patch (.f64 (/.f64 #s(literal -1/2 binary64) a) b) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (/ b a)) (taylor 0 b) (#s(alt (.f64 (/.f64 #s(literal -1/2 binary64) a) b) (patch (.f64 (/.f64 #s(literal -1/2 binary64) a) b) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (/ b a)) (taylor 0 b) (#s(alt (.f64 (/.f64 #s(literal -1/2 binary64) a) b) (patch (.f64 (/.f64 #s(literal -1/2 binary64) a) b) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (/ b a)) (taylor 0 b) (#s(alt (.f64 (/.f64 #s(literal -1/2 binary64) a) b) (patch (.f64 (/.f64 #s(literal -1/2 binary64) a) b) #<representation binary64>) () ())) ())
#s(alt a (taylor 0 b) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a)) (patch #s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a)) #<representation binary64>) () ())) ())
#s(alt (+ a (* -1/2 (/ (pow b 2) a))) (taylor 0 b) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a)) (patch #s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a)) #<representation binary64>) () ())) ())
#s(alt (+ a (* (pow b 2) (- (* -1/8 (/ (pow b 2) (pow a 3))) (* 1/2 (/ 1 a))))) (taylor 0 b) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a)) (patch #s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a)) #<representation binary64>) () ())) ())
#s(alt (+ a (* (pow b 2) (- (* (pow b 2) (- (* -1/16 (/ (pow b 2) (pow a 5))) (* 1/8 (/ 1 (pow a 3))))) (* 1/2 (/ 1 a))))) (taylor 0 b) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a)) (patch #s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a)) #<representation binary64>) () ())) ())
#s(alt a (taylor 0 b) (#s(alt (sqrt.f64 #s(approx (- (* a a) (* b b)) (.f64 a a))) (patch (sqrt.f64 #s(approx (- ( a a) (* b b)) (*.f64 a a))) #<representation binary64>) () ())) ())
#s(alt (+ a (* -1/2 (/ (pow b 2) a))) (taylor 0 b) (#s(alt (sqrt.f64 #s(approx (- (* a a) (* b b)) (.f64 a a))) (patch (sqrt.f64 #s(approx (- ( a a) (* b b)) (*.f64 a a))) #<representation binary64>) () ())) ())
#s(alt (+ a (* (pow b 2) (- (* -1/8 (/ (pow b 2) (pow a 3))) (* 1/2 (/ 1 a))))) (taylor 0 b) (#s(alt (sqrt.f64 #s(approx (- (* a a) (* b b)) (.f64 a a))) (patch (sqrt.f64 #s(approx (- ( a a) (* b b)) (*.f64 a a))) #<representation binary64>) () ())) ())
#s(alt (+ a (* (pow b 2) (- (* (pow b 2) (- (* -1/16 (/ (pow b 2) (pow a 5))) (* 1/8 (/ 1 (pow a 3))))) (* 1/2 (/ 1 a))))) (taylor 0 b) (#s(alt (sqrt.f64 #s(approx (- (* a a) (* b b)) (.f64 a a))) (patch (sqrt.f64 #s(approx (- ( a a) (* b b)) (*.f64 a a))) #<representation binary64>) () ())) ())
#s(alt (pow a 2) (taylor 0 b) (#s(alt #s(approx (- (* a a) (* b b)) (.f64 a a)) (patch #s(approx (- ( a a) (* b b)) (*.f64 a a)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow b 2)) (pow a 2)) (taylor 0 b) (#s(alt #s(approx (- (* a a) (* b b)) (.f64 a a)) (patch #s(approx (- ( a a) (* b b)) (*.f64 a a)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow b 2)) (pow a 2)) (taylor 0 b) (#s(alt #s(approx (- (* a a) (* b b)) (.f64 a a)) (patch #s(approx (- ( a a) (* b b)) (*.f64 a a)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow b 2)) (pow a 2)) (taylor 0 b) (#s(alt #s(approx (- (* a a) (* b b)) (.f64 a a)) (patch #s(approx (- ( a a) (* b b)) (*.f64 a a)) #<representation binary64>) () ())) ())
#s(alt a (taylor 0 b) (#s(alt (sqrt.f64 (.f64 (-.f64 a b) (+.f64 b a))) (patch (sqrt.f64 (.f64 (-.f64 a b) (+.f64 b a))) #<representation binary64>) () ())) ())
#s(alt (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a))) (taylor 0 b) (#s(alt (sqrt.f64 (.f64 (-.f64 a b) (+.f64 b a))) (patch (sqrt.f64 (.f64 (-.f64 a b) (+.f64 b a))) #<representation binary64>) () ())) ())
#s(alt (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) (taylor 0 b) (#s(alt (sqrt.f64 (.f64 (-.f64 a b) (+.f64 b a))) (patch (sqrt.f64 (.f64 (-.f64 a b) (+.f64 b a))) #<representation binary64>) () ())) ())
#s(alt (+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3)))))))) (taylor 0 b) (#s(alt (sqrt.f64 (.f64 (-.f64 a b) (+.f64 b a))) (patch (sqrt.f64 (.f64 (-.f64 a b) (+.f64 b a))) #<representation binary64>) () ())) ())
#s(alt (pow a 2) (taylor 0 b) (#s(alt (.f64 (-.f64 a b) (+.f64 b a)) (patch (.f64 (-.f64 a b) (+.f64 b a)) #<representation binary64>) () ())) ())
#s(alt (+ (* b (+ a (* -1 a))) (pow a 2)) (taylor 0 b) (#s(alt (.f64 (-.f64 a b) (+.f64 b a)) (patch (.f64 (-.f64 a b) (+.f64 b a)) #<representation binary64>) () ())) ())
#s(alt (+ (* b (+ a (+ (* -1 a) (* -1 b)))) (pow a 2)) (taylor 0 b) (#s(alt (.f64 (-.f64 a b) (+.f64 b a)) (patch (.f64 (-.f64 a b) (+.f64 b a)) #<representation binary64>) () ())) ())
#s(alt (+ (* b (+ a (+ (* -1 a) (* -1 b)))) (pow a 2)) (taylor 0 b) (#s(alt (.f64 (-.f64 a b) (+.f64 b a)) (patch (.f64 (-.f64 a b) (+.f64 b a)) #<representation binary64>) () ())) ())
#s(alt a (taylor 0 b) (#s(alt (-.f64 a b) (patch (-.f64 a b) #<representation binary64>) () ())) ())
#s(alt (+ a (* -1 b)) (taylor 0 b) (#s(alt (-.f64 a b) (patch (-.f64 a b) #<representation binary64>) () ())) ())
#s(alt (+ a (* -1 b)) (taylor 0 b) (#s(alt (-.f64 a b) (patch (-.f64 a b) #<representation binary64>) () ())) ())
#s(alt (+ a (* -1 b)) (taylor 0 b) (#s(alt (-.f64 a b) (patch (-.f64 a b) #<representation binary64>) () ())) ())
#s(alt a (taylor 0 b) (#s(alt (+.f64 b a) (patch (+.f64 b a) #<representation binary64>) () ())) ())
#s(alt (+ a b) (taylor 0 b) (#s(alt (+.f64 b a) (patch (+.f64 b a) #<representation binary64>) () ())) ())
#s(alt (+ a b) (taylor 0 b) (#s(alt (+.f64 b a) (patch (+.f64 b a) #<representation binary64>) () ())) ())
#s(alt (+ a b) (taylor 0 b) (#s(alt (+.f64 b a) (patch (+.f64 b a) #<representation binary64>) () ())) ())
#s(alt a (taylor 0 b) (#s(alt (.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 b a))) (patch (.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 b a))) #<representation binary64>) () ())) ())
#s(alt (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a))) (taylor 0 b) (#s(alt (.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 b a))) (patch (.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 b a))) #<representation binary64>) () ())) ())
#s(alt (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) (taylor 0 b) (#s(alt (.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 b a))) (patch (.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 b a))) #<representation binary64>) () ())) ())
#s(alt (+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3)))))))) (taylor 0 b) (#s(alt (.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 b a))) (patch (.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 b a))) #<representation binary64>) () ())) ())
#s(alt (sqrt a) (taylor 0 b) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt a) (* -1/2 (* (sqrt (/ 1 a)) b))) (taylor 0 b) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* -1/8 (* (sqrt (/ 1 (pow a 3))) b))))) (taylor 0 b) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* -1/16 (* (sqrt (/ 1 (pow a 5))) b))))))) (taylor 0 b) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (sqrt a) (taylor 0 b) (#s(alt (sqrt.f64 (+.f64 b a)) (patch (sqrt.f64 (+.f64 b a)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt a) (* 1/2 (* (sqrt (/ 1 a)) b))) (taylor 0 b) (#s(alt (sqrt.f64 (+.f64 b a)) (patch (sqrt.f64 (+.f64 b a)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt a) (* b (+ (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)) (* 1/2 (sqrt (/ 1 a)))))) (taylor 0 b) (#s(alt (sqrt.f64 (+.f64 b a)) (patch (sqrt.f64 (+.f64 b a)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt a) (* b (+ (* 1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* 1/16 (* (sqrt (/ 1 (pow a 5))) b))))))) (taylor 0 b) (#s(alt (sqrt.f64 (+.f64 b a)) (patch (sqrt.f64 (+.f64 b a)) #<representation binary64>) () ())) ())
#s(alt (* b (sqrt -1)) (taylor inf b) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a)) (patch #s(approx (sqrt (- ( a a) (* b b))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a)) #<representation binary64>) () ())) ())
#s(alt (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))) (taylor inf b) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a)) (patch #s(approx (sqrt (- ( a a) (* b b))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a)) #<representation binary64>) () ())) ())
#s(alt (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))) (taylor inf b) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a)) (patch #s(approx (sqrt (- ( a a) (* b b))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a)) #<representation binary64>) () ())) ())
#s(alt (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))) (taylor inf b) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a)) (patch #s(approx (sqrt (- ( a a) (* b b))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (/ (pow b 2) a)) (taylor inf b) (#s(alt (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a) (patch (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a) #<representation binary64>) () ())) ())
#s(alt (* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a)))) (taylor inf b) (#s(alt (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a) (patch (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a) #<representation binary64>) () ())) ())
#s(alt (* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a)))) (taylor inf b) (#s(alt (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a) (patch (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a) #<representation binary64>) () ())) ())
#s(alt (* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a)))) (taylor inf b) (#s(alt (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a) (patch (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (/ b a)) (taylor inf b) (#s(alt (.f64 (/.f64 #s(literal -1/2 binary64) a) b) (patch (.f64 (/.f64 #s(literal -1/2 binary64) a) b) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (/ b a)) (taylor inf b) (#s(alt (.f64 (/.f64 #s(literal -1/2 binary64) a) b) (patch (.f64 (/.f64 #s(literal -1/2 binary64) a) b) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (/ b a)) (taylor inf b) (#s(alt (.f64 (/.f64 #s(literal -1/2 binary64) a) b) (patch (.f64 (/.f64 #s(literal -1/2 binary64) a) b) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (/ b a)) (taylor inf b) (#s(alt (.f64 (/.f64 #s(literal -1/2 binary64) a) b) (patch (.f64 (/.f64 #s(literal -1/2 binary64) a) b) #<representation binary64>) () ())) ())
#s(alt (* b (sqrt -1)) (taylor inf b) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a)) (patch #s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a)) #<representation binary64>) () ())) ())
#s(alt (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))) (taylor inf b) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a)) (patch #s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a)) #<representation binary64>) () ())) ())
#s(alt (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))) (taylor inf b) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a)) (patch #s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a)) #<representation binary64>) () ())) ())
#s(alt (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))) (taylor inf b) (#s(alt #s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a)) (patch #s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a)) #<representation binary64>) () ())) ())
#s(alt (* b (sqrt -1)) (taylor inf b) (#s(alt (sqrt.f64 #s(approx (- (* a a) (* b b)) (.f64 a a))) (patch (sqrt.f64 #s(approx (- ( a a) (* b b)) (*.f64 a a))) #<representation binary64>) () ())) ())
#s(alt (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))) (taylor inf b) (#s(alt (sqrt.f64 #s(approx (- (* a a) (* b b)) (.f64 a a))) (patch (sqrt.f64 #s(approx (- ( a a) (* b b)) (*.f64 a a))) #<representation binary64>) () ())) ())
#s(alt (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))) (taylor inf b) (#s(alt (sqrt.f64 #s(approx (- (* a a) (* b b)) (.f64 a a))) (patch (sqrt.f64 #s(approx (- ( a a) (* b b)) (*.f64 a a))) #<representation binary64>) () ())) ())
#s(alt (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))) (taylor inf b) (#s(alt (sqrt.f64 #s(approx (- (* a a) (* b b)) (.f64 a a))) (patch (sqrt.f64 #s(approx (- ( a a) (* b b)) (*.f64 a a))) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow b 2)) (taylor inf b) (#s(alt #s(approx (- (* a a) (* b b)) (.f64 a a)) (patch #s(approx (- ( a a) (* b b)) (*.f64 a a)) #<representation binary64>) () ())) ())
#s(alt (* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1)) (taylor inf b) (#s(alt #s(approx (- (* a a) (* b b)) (.f64 a a)) (patch #s(approx (- ( a a) (* b b)) (*.f64 a a)) #<representation binary64>) () ())) ())
#s(alt (* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1)) (taylor inf b) (#s(alt #s(approx (- (* a a) (* b b)) (.f64 a a)) (patch #s(approx (- ( a a) (* b b)) (*.f64 a a)) #<representation binary64>) () ())) ())
#s(alt (* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1)) (taylor inf b) (#s(alt #s(approx (- (* a a) (* b b)) (.f64 a a)) (patch #s(approx (- ( a a) (* b b)) (*.f64 a a)) #<representation binary64>) () ())) ())
#s(alt (* b (sqrt -1)) (taylor inf b) (#s(alt (sqrt.f64 (.f64 (-.f64 a b) (+.f64 b a))) (patch (sqrt.f64 (.f64 (-.f64 a b) (+.f64 b a))) #<representation binary64>) () ())) ())
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#s(alt (* (pow a 2) (+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a)))) (taylor -inf a) (#s(alt (.f64 (-.f64 a b) (+.f64 b a)) (patch (.f64 (-.f64 a b) (+.f64 b a)) #<representation binary64>) () ())) ())
#s(alt (* (pow a 2) (+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a)))) (taylor -inf a) (#s(alt (.f64 (-.f64 a b) (+.f64 b a)) (patch (.f64 (-.f64 a b) (+.f64 b a)) #<representation binary64>) () ())) ())
#s(alt a (taylor -inf a) (#s(alt (-.f64 a b) (patch (-.f64 a b) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (- (/ b a) 1))) (taylor -inf a) (#s(alt (-.f64 a b) (patch (-.f64 a b) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (- (/ b a) 1))) (taylor -inf a) (#s(alt (-.f64 a b) (patch (-.f64 a b) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (- (/ b a) 1))) (taylor -inf a) (#s(alt (-.f64 a b) (patch (-.f64 a b) #<representation binary64>) () ())) ())
#s(alt a (taylor -inf a) (#s(alt (+.f64 b a) (patch (+.f64 b a) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (- (* -1 (/ b a)) 1))) (taylor -inf a) (#s(alt (+.f64 b a) (patch (+.f64 b a) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (- (* -1 (/ b a)) 1))) (taylor -inf a) (#s(alt (+.f64 b a) (patch (+.f64 b a) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (- (* -1 (/ b a)) 1))) (taylor -inf a) (#s(alt (+.f64 b a) (patch (+.f64 b a) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (pow (sqrt -1) 2))) (taylor -inf a) (#s(alt (.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 b a))) (patch (.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 b a))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2)))) (taylor -inf a) (#s(alt (.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 b a))) (patch (.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 b a))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2)))) (taylor -inf a) (#s(alt (.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 b a))) (patch (.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 b a))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2)))) (taylor -inf a) (#s(alt (.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 b a))) (patch (.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 b a))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt a) (pow (sqrt -1) 2))) (taylor -inf a) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))) (taylor -inf a) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (* (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))) (taylor -inf a) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (* (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (* (pow b 3) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))) (taylor -inf a) (#s(alt (sqrt.f64 (-.f64 a b)) (patch (sqrt.f64 (-.f64 a b)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt a) (pow (sqrt -1) 2))) (taylor -inf a) (#s(alt (sqrt.f64 (+.f64 b a)) (patch (sqrt.f64 (+.f64 b a)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))) (taylor -inf a) (#s(alt (sqrt.f64 (+.f64 b a)) (patch (sqrt.f64 (+.f64 b a)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))) (taylor -inf a) (#s(alt (sqrt.f64 (+.f64 b a)) (patch (sqrt.f64 (+.f64 b a)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (/ (pow b 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))) (taylor -inf a) (#s(alt (sqrt.f64 (+.f64 b a)) (patch (sqrt.f64 (+.f64 b a)) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
46.0ms	a	@	0	((sqrt (- (* a a) (* b b))) (+ (* (* (/ -1/2 a) b) b) a) (* (/ -1/2 a) b) (/ -1/2 a) (sqrt (- (* a a) (* b b))) (neg a) (sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* a a) (sqrt (* (- a b) (+ b a))) (* (- a b) (+ b a)) (- a b) (+ b a) (* (sqrt (- a b)) (sqrt (+ b a))) (sqrt (- a b)) (sqrt (+ b a)))
6.0ms	a	@	-inf	((sqrt (- (* a a) (* b b))) (+ (* (* (/ -1/2 a) b) b) a) (* (/ -1/2 a) b) (/ -1/2 a) (sqrt (- (* a a) (* b b))) (neg a) (sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* a a) (sqrt (* (- a b) (+ b a))) (* (- a b) (+ b a)) (- a b) (+ b a) (* (sqrt (- a b)) (sqrt (+ b a))) (sqrt (- a b)) (sqrt (+ b a)))
5.0ms	b	@	inf	((sqrt (- (* a a) (* b b))) (+ (* (* (/ -1/2 a) b) b) a) (* (/ -1/2 a) b) (/ -1/2 a) (sqrt (- (* a a) (* b b))) (neg a) (sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* a a) (sqrt (* (- a b) (+ b a))) (* (- a b) (+ b a)) (- a b) (+ b a) (* (sqrt (- a b)) (sqrt (+ b a))) (sqrt (- a b)) (sqrt (+ b a)))
3.0ms	a	@	inf	((sqrt (- (* a a) (* b b))) (+ (* (* (/ -1/2 a) b) b) a) (* (/ -1/2 a) b) (/ -1/2 a) (sqrt (- (* a a) (* b b))) (neg a) (sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* a a) (sqrt (* (- a b) (+ b a))) (* (- a b) (+ b a)) (- a b) (+ b a) (* (sqrt (- a b)) (sqrt (+ b a))) (sqrt (- a b)) (sqrt (+ b a)))
3.0ms	b	@	-inf	((sqrt (- (* a a) (* b b))) (+ (* (* (/ -1/2 a) b) b) a) (* (/ -1/2 a) b) (/ -1/2 a) (sqrt (- (* a a) (* b b))) (neg a) (sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* a a) (sqrt (* (- a b) (+ b a))) (* (- a b) (+ b a)) (- a b) (+ b a) (* (sqrt (- a b)) (sqrt (+ b a))) (sqrt (- a b)) (sqrt (+ b a)))

simplify155.0ms (3.2%)

Memory

36.8MiB live, 224.6MiB allocated

Algorithm

1×	egg-herbie

Rules

11 938×	`lower-fma.f64`
11 938×	`lower-fma.f32`
4 572×	`lower-*.f64`
4 572×	`lower-*.f32`
2 664×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	576	5107
1	1872	4323
2	7580	4315
0	8030	4070

Stop Event

1×	iter limit
1×	node limit

Counts

348 → 326

Calls

Call 1

Inputs
a
(+ a (* -1/2 (/ (pow b 2) a)))
(+ a (* (pow b 2) (- (* -1/8 (/ (pow b 2) (pow a 3))) (* 1/2 (/ 1 a)))))
(+ a (* (pow b 2) (- (* (pow b 2) (- (* -1/16 (/ (pow b 2) (pow a 5))) (* 1/8 (/ 1 (pow a 3))))) (* 1/2 (/ 1 a)))))
a
(+ a (* -1/2 (/ (pow b 2) a)))
(+ a (* -1/2 (/ (pow b 2) a)))
(+ a (* -1/2 (/ (pow b 2) a)))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
a
(+ a (* -1/2 (/ (pow b 2) a)))
(+ a (* (pow b 2) (- (* -1/8 (/ (pow b 2) (pow a 3))) (* 1/2 (/ 1 a)))))
(+ a (* (pow b 2) (- (* (pow b 2) (- (* -1/16 (/ (pow b 2) (pow a 5))) (* 1/8 (/ 1 (pow a 3))))) (* 1/2 (/ 1 a)))))
a
(+ a (* -1/2 (/ (pow b 2) a)))
(+ a (* (pow b 2) (- (* -1/8 (/ (pow b 2) (pow a 3))) (* 1/2 (/ 1 a)))))
(+ a (* (pow b 2) (- (* (pow b 2) (- (* -1/16 (/ (pow b 2) (pow a 5))) (* 1/8 (/ 1 (pow a 3))))) (* 1/2 (/ 1 a)))))
(pow a 2)
(+ (* -1 (pow b 2)) (pow a 2))
(+ (* -1 (pow b 2)) (pow a 2))
(+ (* -1 (pow b 2)) (pow a 2))
a
(+ a (* 1/2 (/ (* b (+ a (* -1 a))) a)))
(+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))
(+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3))))))))
(pow a 2)
(+ (* b (+ a (* -1 a))) (pow a 2))
(+ (* b (+ a (+ (* -1 a) (* -1 b)))) (pow a 2))
(+ (* b (+ a (+ (* -1 a) (* -1 b)))) (pow a 2))
a
(+ a (* -1 b))
(+ a (* -1 b))
(+ a (* -1 b))
a
(+ a b)
(+ a b)
(+ a b)
a
(+ a (* 1/2 (/ (* b (+ a (* -1 a))) a)))
(+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))
(+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3))))))))
(sqrt a)
(+ (sqrt a) (* -1/2 (* (sqrt (/ 1 a)) b)))
(+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)))))
(+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* -1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))
(sqrt a)
(+ (sqrt a) (* 1/2 (* (sqrt (/ 1 a)) b)))
(+ (sqrt a) (* b (+ (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)) (* 1/2 (sqrt (/ 1 a))))))
(+ (sqrt a) (* b (+ (* 1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* 1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))
(* b (sqrt -1))
(* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))
(* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))
(* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))
(* -1/2 (/ (pow b 2) a))
(* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))
(* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))
(* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* b (sqrt -1))
(* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))
(* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))
(* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))
(* b (sqrt -1))
(* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))
(* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))
(* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))
(* -1 (pow b 2))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* b (sqrt -1))
(* b (+ (sqrt -1) (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))
(* b (+ (sqrt -1) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1)))))))
(* b (+ (sqrt -1) (+ (* -1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* (pow b 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1))))))))
(* -1 (pow b 2))
(* (pow b 2) (- (+ (* -1 (/ a b)) (/ a b)) 1))
(* (pow b 2) (- (+ (* -1 (/ a b)) (+ (/ a b) (/ (pow a 2) (pow b 2)))) 1))
(* (pow b 2) (- (+ (* -1 (/ a b)) (+ (/ a b) (/ (pow a 2) (pow b 2)))) 1))
(* -1 b)
(* b (- (/ a b) 1))
(* b (- (/ a b) 1))
(* b (- (/ a b) 1))
b
(* b (+ 1 (/ a b)))
(* b (+ 1 (/ a b)))
(* b (+ 1 (/ a b)))
(* b (sqrt -1))
(* b (+ (sqrt -1) (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))
(* b (+ (sqrt -1) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1)))))))
(* b (+ (sqrt -1) (+ (* -1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* (pow b 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1))))))))
(* (sqrt b) (sqrt -1))
(* b (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))
(* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))
(* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))
(sqrt b)
(* b (+ (sqrt (/ 1 b)) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))
(* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3))))))))
(* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (pow a 3) (sqrt (/ 1 (pow b 7))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))))
(* -1 (* b (sqrt -1)))
(* -1 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))
(* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))
(* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))
(* -1/2 (/ (pow b 2) a))
(* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))
(* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))
(* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1 (* b (sqrt -1)))
(* -1 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))
(* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))
(* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))
(* -1 (* b (sqrt -1)))
(* -1 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))
(* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))
(* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))
(* -1 (pow b 2))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* -1 (* b (sqrt -1)))
(* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(* -1 (pow b 2))
(* (pow b 2) (- (* -1 (/ (+ a (* -1 a)) b)) 1))
(* (pow b 2) (- (* -1 (/ (+ a (+ (* -1 a) (* -1 (/ (pow a 2) b)))) b)) 1))
(* (pow b 2) (- (* -1 (/ (+ a (+ (* -1 a) (* -1 (/ (pow a 2) b)))) b)) 1))
(* -1 b)
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
b
(* -1 (* b (- (* -1 (/ a b)) 1)))
(* -1 (* b (- (* -1 (/ a b)) 1)))
(* -1 (* b (- (* -1 (/ a b)) 1)))
(* -1 (* b (sqrt -1)))
(* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(* -1 (* (sqrt b) (sqrt -1)))
(* -1 (* b (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))
(* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))
(* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (* (pow a 3) (sqrt -1)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))))
(* -1 (* (sqrt b) (pow (sqrt -1) 2)))
(* -1 (* b (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))
(* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2))))))
(* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))))
(* b (sqrt -1))
(+ (* 1/2 (/ (pow a 2) (* b (sqrt -1)))) (* b (sqrt -1)))
(+ (* b (sqrt -1)) (* (pow a 2) (+ (* -1/8 (/ (pow a 2) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* b (sqrt -1)))))))
(+ (* b (sqrt -1)) (* (pow a 2) (+ (* (pow a 2) (- (* 1/16 (/ (pow a 2) (* (pow b 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow b 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* b (sqrt -1)))))))
(* -1/2 (/ (pow b 2) a))
(/ (+ (* -1/2 (pow b 2)) (pow a 2)) a)
(/ (+ (* -1/2 (pow b 2)) (pow a 2)) a)
(/ (+ (* -1/2 (pow b 2)) (pow a 2)) a)
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(/ -1/2 a)
(/ -1/2 a)
(/ -1/2 a)
(/ -1/2 a)
(* b (sqrt -1))
(+ (* 1/2 (/ (pow a 2) (* b (sqrt -1)))) (* b (sqrt -1)))
(+ (* b (sqrt -1)) (* (pow a 2) (+ (* -1/8 (/ (pow a 2) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* b (sqrt -1)))))))
(+ (* b (sqrt -1)) (* (pow a 2) (+ (* (pow a 2) (- (* 1/16 (/ (pow a 2) (* (pow b 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow b 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* b (sqrt -1)))))))
(* -1 a)
(* -1 a)
(* -1 a)
(* -1 a)
(* b (sqrt -1))
(+ (* 1/2 (/ (pow a 2) (* b (sqrt -1)))) (* b (sqrt -1)))
(+ (* b (sqrt -1)) (* (pow a 2) (+ (* -1/8 (/ (pow a 2) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* b (sqrt -1)))))))
(+ (* b (sqrt -1)) (* (pow a 2) (+ (* (pow a 2) (- (* 1/16 (/ (pow a 2) (* (pow b 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow b 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* b (sqrt -1)))))))
(* -1 (pow b 2))
(- (pow a 2) (pow b 2))
(- (pow a 2) (pow b 2))
(- (pow a 2) (pow b 2))
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(* b (sqrt -1))
(+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))
(+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))
(+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))
(* -1 (pow b 2))
(+ (* -1 (pow b 2)) (* a (+ b (* -1 b))))
(+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b)))))
(+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b)))))
(* -1 b)
(- a b)
(- a b)
(- a b)
b
(+ a b)
(+ a b)
(+ a b)
(* b (sqrt -1))
(+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))
(+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))
(+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))
(* (sqrt b) (sqrt -1))
(+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 b)))) (* (sqrt b) (sqrt -1)))
(+ (* a (+ (* -1/8 (* (/ a (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 3))))) (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))))) (* (sqrt b) (sqrt -1)))
(+ (* a (+ (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))) (* a (+ (* -1/8 (* (sqrt (/ 1 (pow b 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (/ a (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 5))))))))) (* (sqrt b) (sqrt -1)))
(sqrt b)
(+ (sqrt b) (* 1/2 (* a (sqrt (/ 1 b)))))
(+ (sqrt b) (* a (+ (* -1/8 (* a (sqrt (/ 1 (pow b 3))))) (* 1/2 (sqrt (/ 1 b))))))
(+ (sqrt b) (* a (+ (* 1/2 (sqrt (/ 1 b))) (* a (+ (* -1/8 (sqrt (/ 1 (pow b 3)))) (* 1/16 (* a (sqrt (/ 1 (pow b 5))))))))))
a
(* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))
(* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4))))))
(* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6)))))))
a
(* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))
(* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))
(* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(/ -1/2 a)
(/ -1/2 a)
(/ -1/2 a)
(/ -1/2 a)
a
(* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))
(* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4))))))
(* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6)))))))
(* -1 a)
(* -1 a)
(* -1 a)
(* -1 a)
a
(* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))
(* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4))))))
(* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6)))))))
(pow a 2)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
a
(* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))
(* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))
(* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))))
(pow a 2)
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (/ b a))))
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a)))))
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a)))))
a
(* a (+ 1 (* -1 (/ b a))))
(* a (+ 1 (* -1 (/ b a))))
(* a (+ 1 (* -1 (/ b a))))
a
(* a (+ 1 (/ b a)))
(* a (+ 1 (/ b a)))
(* a (+ 1 (/ b a)))
a
(* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))
(* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))
(* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))))
(sqrt a)
(* a (+ (sqrt (/ 1 a)) (* -1/2 (* (sqrt (/ 1 (pow a 3))) b))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* -1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3)))))))
(sqrt a)
(* a (+ (sqrt (/ 1 a)) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))))
(* -1 a)
(* -1 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2))))))
(* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4)))))))
(* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6))))))))
a
(* -1 (* a (- (* 1/2 (/ (pow b 2) (pow a 2))) 1)))
(* -1 (* a (- (* 1/2 (/ (pow b 2) (pow a 2))) 1)))
(* -1 (* a (- (* 1/2 (/ (pow b 2) (pow a 2))) 1)))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(* -1/2 (/ b a))
(/ -1/2 a)
(/ -1/2 a)
(/ -1/2 a)
(/ -1/2 a)
(* -1 a)
(* -1 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2))))))
(* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4)))))))
(* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6))))))))
(* -1 a)
(* -1 a)
(* -1 a)
(* -1 a)
(* -1 a)
(* -1 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2))))))
(* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4)))))))
(* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6))))))))
(pow a 2)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(* -1 (* a (pow (sqrt -1) 2)))
(* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2))))
(* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
(* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
(pow a 2)
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (/ b a))))
(* (pow a 2) (+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a))))
(* (pow a 2) (+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a))))
a
(* -1 (* a (- (/ b a) 1)))
(* -1 (* a (- (/ b a) 1)))
(* -1 (* a (- (/ b a) 1)))
a
(* -1 (* a (- (* -1 (/ b a)) 1)))
(* -1 (* a (- (* -1 (/ b a)) 1)))
(* -1 (* a (- (* -1 (/ b a)) 1)))
(* -1 (* a (pow (sqrt -1) 2)))
(* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2))))
(* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
(* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (* (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (* (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (* (pow b 3) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (/ (pow b 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))

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

rewrite197.0ms (4%)

Memory

-15.6MiB live, 262.0MiB allocated

Rules

8 732×	`lower-fma.f32`
8 730×	`lower-fma.f64`
5 492×	`lower-*.f32`
5 484×	`lower-*.f64`
4 164×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	110
0	37	109
1	120	109
2	788	109
0	8375	109

Stop Event

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

Counts

16 → 817

Calls

Call 1

Inputs
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a))
(fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a)
(*.f64 (/.f64 #s(literal -1/2 binary64) a) b)
(/.f64 #s(literal -1/2 binary64) a)
#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))
(neg.f64 a)
(sqrt.f64 #s(approx (- (* a a) (* b b)) (*.f64 a a)))
#s(approx (- (* a a) (* b b)) (*.f64 a a))
(*.f64 a a)
(sqrt.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
(*.f64 (-.f64 a b) (+.f64 b a))
(-.f64 a b)
(+.f64 b a)
(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 b a)))
(sqrt.f64 (-.f64 a b))
(sqrt.f64 (+.f64 b a))

Outputs
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a))
(.f64 (-.f64 (.f64 a a) (pow.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 a (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b))))
(.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 a #s(literal -2 binary64)) #s(literal -2 binary64)) (pow.f64 b #s(literal 4 binary64)) (.f64 (neg.f64 a) a))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a)))
(.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (pow.f64 (.f64 a #s(literal -2 binary64)) #s(literal -2 binary64)) (pow.f64 b #s(literal 4 binary64)) (.f64 a (-.f64 a (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b)))))))
(.f64 (fma.f64 (pow.f64 (.f64 a #s(literal -2 binary64)) #s(literal -2 binary64)) (pow.f64 b #s(literal 4 binary64)) (.f64 (neg.f64 a) a)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a)))
(.f64 #s(literal 1 binary64) (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a))
(.f64 (fma.f64 (pow.f64 (.f64 a #s(literal -2 binary64)) #s(literal -2 binary64)) (pow.f64 b #s(literal 4 binary64)) (.f64 a (-.f64 a (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b)))) (.f64 (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a) (pow.f64 (fma.f64 (pow.f64 (.f64 a #s(literal -2 binary64)) #s(literal -2 binary64)) (pow.f64 b #s(literal 4 binary64)) (.f64 a (-.f64 a (.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b)))) #s(literal -1 binary64))))
(.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 a a (.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b) (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b (neg.f64 a))))))
(.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64))) (pow.f64 (fma.f64 (pow.f64 (.f64 a #s(literal -2 binary64)) #s(literal -2 binary64)) (pow.f64 b #s(literal 4 binary64)) (.f64 a (-.f64 a (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b)))) #s(literal -1 binary64)))
(.f64 (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a) (.f64 (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b (neg.f64 a)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 b a) b) a))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a)) #s(literal -1 binary64))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b) #s(literal 4 binary64)) (pow.f64 a #s(literal 4 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a))) (fma.f64 (pow.f64 (.f64 a #s(literal -2 binary64)) #s(literal -2 binary64)) (pow.f64 b #s(literal 4 binary64)) (.f64 a a)))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b) #s(literal 6 binary64)) (pow.f64 a #s(literal 6 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a))) (+.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b) #s(literal 4 binary64)) (+.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 (.f64 (.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b) a) #s(literal 2 binary64)))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b) #s(literal 6 binary64)) (pow.f64 a #s(literal 6 binary64))) (pow.f64 (fma.f64 (pow.f64 (.f64 a #s(literal -2 binary64)) #s(literal -2 binary64)) (pow.f64 b #s(literal 4 binary64)) (.f64 a (-.f64 a (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b)))) #s(literal -1 binary64))) (-.f64 (pow.f64 (.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b) #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64))))
(/.f64 (.f64 (+.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b) #s(literal 9 binary64)) (pow.f64 a #s(literal 9 binary64))) (pow.f64 (fma.f64 (pow.f64 (.f64 a #s(literal -2 binary64)) #s(literal -2 binary64)) (pow.f64 b #s(literal 4 binary64)) (.f64 a (-.f64 a (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b)))) #s(literal -1 binary64))) (-.f64 (+.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b) #s(literal 6 binary64)) (pow.f64 a #s(literal 6 binary64))) (pow.f64 (.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b) a) #s(literal 3 binary64))))
(/.f64 (.f64 (fma.f64 (pow.f64 (.f64 a #s(literal -2 binary64)) #s(literal -2 binary64)) (pow.f64 b #s(literal 4 binary64)) (.f64 (neg.f64 a) a)) #s(literal 1 binary64)) (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b (neg.f64 a)))
(/.f64 (.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64))) #s(literal 1 binary64)) (fma.f64 (pow.f64 (.f64 a #s(literal -2 binary64)) #s(literal -2 binary64)) (pow.f64 b #s(literal 4 binary64)) (.f64 a (-.f64 a (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b)))))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b) #s(literal 2 binary64)) (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b (neg.f64 a))) (/.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b) #s(literal 2 binary64)) (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b (neg.f64 a)))) (.f64 (/.f64 (.f64 (neg.f64 a) a) (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a)) (/.f64 (.f64 (neg.f64 a) a) (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a)))) (fma.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a)) (/.f64 (.f64 (neg.f64 a) a) (fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 b a) b) a))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b) #s(literal 2 binary64)) (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b (neg.f64 a))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 (neg.f64 a) a) (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a)) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b) #s(literal 2 binary64)) (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b (neg.f64 a))) (/.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b) #s(literal 2 binary64)) (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b (neg.f64 a))) (fma.f64 (/.f64 (.f64 (neg.f64 a) a) (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a)) (/.f64 (.f64 (neg.f64 a) a) (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 b a) b) a)) (.f64 (/.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b) #s(literal 2 binary64)) (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b (neg.f64 a))) (/.f64 (.f64 (neg.f64 a) a) (fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 b a) b) a))))))
(/.f64 (neg.f64 (-.f64 (.f64 a a) (pow.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b) #s(literal 2 binary64)))) (neg.f64 (-.f64 a (.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 a #s(literal -2 binary64)) #s(literal -2 binary64)) (pow.f64 b #s(literal 4 binary64)) (.f64 (neg.f64 a) a)))) (neg.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 b a) b) a)))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 a #s(literal -2 binary64)) #s(literal -2 binary64)) (pow.f64 b #s(literal 4 binary64)) (.f64 a (-.f64 a (.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b)))))))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b) #s(literal 2 binary64)) (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b (neg.f64 a))) (.f64 (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b (neg.f64 a)) (.f64 a a))) (.f64 (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b (neg.f64 a)) (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b (neg.f64 a))))
(/.f64 (-.f64 (.f64 a a) (pow.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b) #s(literal 2 binary64))) (-.f64 a (.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b)))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 a #s(literal -2 binary64)) #s(literal -2 binary64)) (pow.f64 b #s(literal 4 binary64)) (.f64 (neg.f64 a) a))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 b a) b) a))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64)))) (neg.f64 (fma.f64 a a (.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b (neg.f64 a))))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64)))) (neg.f64 (fma.f64 (pow.f64 (.f64 a #s(literal -2 binary64)) #s(literal -2 binary64)) (pow.f64 b #s(literal 4 binary64)) (.f64 a (-.f64 a (.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b))))))
(/.f64 (fma.f64 (pow.f64 (.f64 a #s(literal -2 binary64)) #s(literal -2 binary64)) (pow.f64 b #s(literal 4 binary64)) (.f64 (neg.f64 a) a)) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b (neg.f64 a)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 a (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b)) (-.f64 (.f64 a a) (pow.f64 (.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 a a (.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b) (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b (neg.f64 a)))) (fma.f64 #s(literal -1/8 binary64) (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a)))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (/.f64 b a) b) #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64))) (fma.f64 a a (.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) a) b) b) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b (neg.f64 a)))))
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(/.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 b a) (-.f64 a b)))) (neg.f64 (sqrt.f64 (+.f64 b a))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 (+.f64 b a) a (*.f64 b b)))))
(/.f64 (hypot.f64 (pow.f64 a #s(literal 3/2 binary64)) (pow.f64 (neg.f64 b) #s(literal 3/2 binary64))) (sqrt.f64 (fma.f64 a a (*.f64 (neg.f64 b) (-.f64 (neg.f64 b) a)))))
(/.f64 (hypot.f64 (pow.f64 a #s(literal 3/2 binary64)) (pow.f64 (neg.f64 b) #s(literal 3/2 binary64))) (sqrt.f64 (fma.f64 (+.f64 b a) a (*.f64 b b))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64)))) (sqrt.f64 (.f64 (+.f64 b a) (fma.f64 b b (.f64 a a)))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) (sqrt.f64 (.f64 (+.f64 b a) (fma.f64 (.f64 a a) (fma.f64 b b (*.f64 a a)) (pow.f64 b #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (fma.f64 (neg.f64 a) a (*.f64 b b))) (sqrt.f64 (neg.f64 (+.f64 b a))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (+.f64 b a) a (*.f64 b b))) (hypot.f64 (pow.f64 a #s(literal 3/2 binary64)) (pow.f64 (neg.f64 b) #s(literal 3/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 b a)) (sqrt.f64 (*.f64 (+.f64 b a) (-.f64 a b)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 a b))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 b a) (-.f64 a b))) (sqrt.f64 (+.f64 b a)))
(sqrt.f64 (-.f64 a b))
(exp.f64 (-.f64 (.f64 (log.f64 (.f64 (+.f64 b a) (-.f64 a b))) #s(literal 1/2 binary64)) (*.f64 (log.f64 (+.f64 b a)) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (-.f64 a b)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (+.f64 b a) #s(literal 1/4 binary64)) (pow.f64 (+.f64 b a) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (fma.f64 (neg.f64 a) a (.f64 b b))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 b a))))
(.f64 (sqrt.f64 (fma.f64 (neg.f64 a) a (.f64 b b))) (sqrt.f64 (pow.f64 (-.f64 b a) #s(literal -1 binary64))))
(.f64 (sqrt.f64 (fma.f64 (neg.f64 a) a (.f64 b b))) (pow.f64 (pow.f64 (-.f64 b a) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (hypot.f64 (pow.f64 a #s(literal 3/2 binary64)) (pow.f64 b #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 a b) a (.f64 b b)))))
(.f64 (hypot.f64 (pow.f64 a #s(literal 3/2 binary64)) (pow.f64 b #s(literal 3/2 binary64))) (sqrt.f64 (pow.f64 (fma.f64 (-.f64 a b) a (.f64 b b)) #s(literal -1 binary64))))
(.f64 (hypot.f64 (pow.f64 a #s(literal 3/2 binary64)) (pow.f64 b #s(literal 3/2 binary64))) (pow.f64 (pow.f64 (fma.f64 (-.f64 a b) a (.f64 b b)) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(pow.f64 (exp.f64 (log.f64 (+.f64 b a))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (+.f64 b a) (+.f64 b a)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (+.f64 b a) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (+.f64 b a) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (neg.f64 a) a (*.f64 b b)))) (neg.f64 (sqrt.f64 (-.f64 b a))))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 a #s(literal 3/2 binary64)) (pow.f64 b #s(literal 3/2 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 (-.f64 a b) a (*.f64 b b)))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 (-.f64 a b) a (*.f64 b b)))))
(/.f64 (sqrt.f64 (fma.f64 (neg.f64 a) a (*.f64 b b))) (sqrt.f64 (-.f64 b a)))
(/.f64 (hypot.f64 (pow.f64 a #s(literal 3/2 binary64)) (pow.f64 b #s(literal 3/2 binary64))) (sqrt.f64 (fma.f64 (-.f64 a b) a (*.f64 b b))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 b a)) (sqrt.f64 (fma.f64 (neg.f64 a) a (*.f64 b b)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (-.f64 a b) a (*.f64 b b))) (hypot.f64 (pow.f64 a #s(literal 3/2 binary64)) (pow.f64 b #s(literal 3/2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (+.f64 b a) #s(literal -1 binary64))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 b a) (-.f64 a b))) (sqrt.f64 (-.f64 a b)))
(sqrt.f64 (+.f64 b a))
(hypot.f64 (pow.f64 b #s(literal 1/2 binary64)) (pow.f64 a #s(literal 1/2 binary64)))
(hypot.f64 (pow.f64 a #s(literal 1/2 binary64)) (pow.f64 b #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (+.f64 b a)) #s(literal 1/2 binary64)))

eval207.0ms (4.2%)

Memory: 19.2MiB live, 404.2MiB allocated
Compiler: Compiled 30 664 to 3 603 computations (88.3% saved)

prune149.0ms (3.1%)

Memory

-39.2MiB live, 345.3MiB allocated

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	1 401	1	1 402
Fresh	0	0	0
Picked	2	3	5
Done	0	0	0
Total	1 403	4	1 407

Accuracy

100.0%

Counts

1 407 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.3%	(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 b a)))
✓	49.5%	(sqrt.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
▶	98.7%	#s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a)
✓	99.3%	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a))

Compiler

Compiled 28 to 23 computations (17.9% saved)

simplify8.0ms (0.2%)

Memory

10.4MiB live, 10.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
cost-diff	0	#s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a)

Rules

128×	`lower-fma.f64`
128×	`lower-fma.f32`
68×	`lower-*.f64`
68×	`lower-*.f32`
48×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
0	8	12
1	12	12
2	17	12
3	23	12
4	32	12
5	53	12
6	83	12
7	112	12
8	165	12
9	189	12
10	209	12
11	211	12
0	211	12

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
#s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a)
a

Outputs
#s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a)
a

localize17.0ms (0.3%)

Memory

19.1MiB live, 19.1MiB allocated

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
accuracy	0.8020975552953378	#s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a)

Samples

13.0ms

256×

valid

Compiler

Compiled 12 to 9 computations (25% saved)

Precisions

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

ival-sqrt: 3.0ms (39.6% of total)

ival-mult: 2.0ms (26.4% of total)

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

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

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

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

series1.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Counts

1 → 24

Calls

Call 1

Inputs
#s(alt #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) (patch #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) #<representation binary64>) () ())

Outputs
#s(alt a (taylor 0 b) (#s(alt #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) (patch #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) #<representation binary64>) () ())) ())
#s(alt (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a))) (taylor 0 b) (#s(alt #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) (patch #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) #<representation binary64>) () ())) ())
#s(alt (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) (taylor 0 b) (#s(alt #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) (patch #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) #<representation binary64>) () ())) ())
#s(alt (+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3)))))))) (taylor 0 b) (#s(alt #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) (patch #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) #<representation binary64>) () ())) ())
#s(alt (* b (sqrt -1)) (taylor inf b) (#s(alt #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) (patch #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) #<representation binary64>) () ())) ())
#s(alt (* b (+ (sqrt -1) (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))) (taylor inf b) (#s(alt #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) (patch #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) #<representation binary64>) () ())) ())
#s(alt (* b (+ (sqrt -1) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1))))))) (taylor inf b) (#s(alt #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) (patch #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) #<representation binary64>) () ())) ())
#s(alt (* b (+ (sqrt -1) (+ (* -1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* (pow b 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1)))))))) (taylor inf b) (#s(alt #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) (patch #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) #<representation binary64>) () ())) ())
#s(alt (* -1 (* b (sqrt -1))) (taylor -inf b) (#s(alt #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) (patch #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) #<representation binary64>) () ())) ())
#s(alt (* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))) (taylor -inf b) (#s(alt #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) (patch #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) #<representation binary64>) () ())) ())
#s(alt (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b))))) (taylor -inf b) (#s(alt #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) (patch #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) #<representation binary64>) () ())) ())
#s(alt (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b))))) (taylor -inf b) (#s(alt #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) (patch #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) #<representation binary64>) () ())) ())
#s(alt (* b (sqrt -1)) (taylor 0 a) (#s(alt #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) (patch #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1))) (taylor 0 a) (#s(alt #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) (patch #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) #<representation binary64>) () ())) ())
#s(alt (+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1))) (taylor 0 a) (#s(alt #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) (patch #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) #<representation binary64>) () ())) ())
#s(alt (+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1))) (taylor 0 a) (#s(alt #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) (patch #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) #<representation binary64>) () ())) ())
#s(alt a (taylor inf a) (#s(alt #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) (patch #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) #<representation binary64>) () ())) ())
#s(alt (* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a)))) (taylor inf a) (#s(alt #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) (patch #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) #<representation binary64>) () ())) ())
#s(alt (* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))) (taylor inf a) (#s(alt #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) (patch #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) #<representation binary64>) () ())) ())
#s(alt (* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))) (taylor inf a) (#s(alt #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) (patch #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (pow (sqrt -1) 2))) (taylor -inf a) (#s(alt #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) (patch #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2)))) (taylor -inf a) (#s(alt #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) (patch #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2)))) (taylor -inf a) (#s(alt #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) (patch #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2)))) (taylor -inf a) (#s(alt #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) (patch #s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	a	@	-inf	((* (sqrt (- a b)) (sqrt (+ b a))))
0.0ms	a	@	inf	((* (sqrt (- a b)) (sqrt (+ b a))))
0.0ms	b	@	0	((* (sqrt (- a b)) (sqrt (+ b a))))
0.0ms	b	@	inf	((* (sqrt (- a b)) (sqrt (+ b a))))
0.0ms	b	@	-inf	((* (sqrt (- a b)) (sqrt (+ b a))))

simplify55.0ms (1.1%)

Memory

4.4MiB live, 42.9MiB allocated

Algorithm

1×	egg-herbie

Rules

1 804×	`lower-fma.f64`
1 804×	`lower-fma.f32`
1 450×	`lower-*.f64`
1 450×	`lower-*.f32`
1 444×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	175	514
1	622	331
2	3012	207
0	8671	198

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 22

Calls

Call 1

Inputs
a
(+ a (* 1/2 (/ (* b (+ a (* -1 a))) a)))
(+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))
(+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3))))))))
(* b (sqrt -1))
(* b (+ (sqrt -1) (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))
(* b (+ (sqrt -1) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1)))))))
(* b (+ (sqrt -1) (+ (* -1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* (pow b 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1))))))))
(* -1 (* b (sqrt -1)))
(* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(* b (sqrt -1))
(+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))
(+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))
(+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))
a
(* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))
(* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))
(* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))))
(* -1 (* a (pow (sqrt -1) 2)))
(* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2))))
(* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
(* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))

Outputs
a
(+ a (* 1/2 (/ (* b (+ a (* -1 a))) a)))
a
(+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))
(fma.f64 (/.f64 b a) (*.f64 #s(literal -1/2 binary64) b) a)
(+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3))))))))
(fma.f64 (/.f64 b a) (*.f64 #s(literal -1/2 binary64) b) a)
(* b (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) b)
(* b (+ (sqrt -1) (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) b #s(literal 0 binary64))
(* b (+ (sqrt -1) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1)))))))
(.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) b) b) (.f64 (/.f64 a (sqrt.f64 #s(literal -1 binary64))) a) (sqrt.f64 #s(literal -1 binary64))) b)
(* b (+ (sqrt -1) (+ (* -1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* (pow b 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1))))))))
(.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) b) b) (.f64 (/.f64 a (sqrt.f64 #s(literal -1 binary64))) a) (sqrt.f64 #s(literal -1 binary64))) b)
(* -1 (* b (sqrt -1)))
(*.f64 (neg.f64 b) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))
(*.f64 (neg.f64 b) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(.f64 (neg.f64 b) (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (*.f64 a a) b)) b)))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(.f64 (neg.f64 b) (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 (/.f64 (.f64 (*.f64 a a) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 b)) b)))
(* b (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) b)
(+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) b #s(literal 0 binary64))
(+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))
(fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) b)) a) a (*.f64 (sqrt.f64 #s(literal -1 binary64)) b))
(+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))
(fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) b)) a) a (*.f64 (sqrt.f64 #s(literal -1 binary64)) b))
a
(* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))
a
(* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))
(fma.f64 (.f64 #s(literal 1/2 binary64) a) (/.f64 (/.f64 (.f64 (neg.f64 b) b) a) a) a)
(* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))))
(fma.f64 (.f64 #s(literal 1/2 binary64) a) (/.f64 (/.f64 (.f64 (neg.f64 b) b) a) a) a)
(* -1 (* a (pow (sqrt -1) 2)))
a
(* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2))))
a
(* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
(fma.f64 (/.f64 (.f64 (/.f64 b a) (.f64 #s(literal -1/2 binary64) b)) a) a a)
(* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
(fma.f64 (.f64 #s(literal 1/2 binary64) a) (/.f64 (/.f64 (.f64 (neg.f64 b) b) a) a) a)

rewrite170.0ms (3.5%)

Memory

-13.7MiB live, 100.2MiB allocated

Rules

4 332×	`lower-*.f64`
4 332×	`lower-*.f32`
2 622×	`lower-fma.f64`
2 622×	`lower-fma.f32`
2 136×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
0	8	10
1	38	10
2	294	10
3	4619	10
0	8580	10

Stop Event

1×	iter limit
1×	node limit
1×	saturated

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a)

Outputs
#s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a)

eval2.0ms (0%)

Memory: 2.5MiB live, 2.5MiB allocated
Compiler: Compiled 220 to 55 computations (75% saved)

prune4.0ms (0.1%)

Memory

5.2MiB live, 5.2MiB allocated

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	23	0	23
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	23	4	27

Accuracy

100.0%

Counts

27 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.3%	(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 b a)))
✓	49.5%	(sqrt.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
✓	98.7%	#s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a)
✓	99.3%	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a))

Compiler

Compiled 72 to 46 computations (36.1% saved)

regimes47.0ms (1%)

Memory

-18.1MiB live, 20.7MiB allocated

Counts

7 → 1

Calls

Call 1

Inputs
#s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a)
#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))
(sqrt.f64 #s(approx (- (* a a) (* b b)) (*.f64 a a)))
(sqrt.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a))
(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 b a)))

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

Calls

6 calls:

33.0ms	b
3.0ms	a
3.0ms	(*.f64 a a)
3.0ms	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
3.0ms	(-.f64 (.f64 a a) (.f64 b b))

Results

Accuracy	Segments	Branch
99.3%	1	`a`
99.3%	1	`b`
99.3%	1	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`
99.3%	1	`(-.f64 (.f64 a a) (.f64 b b))`
99.3%	1	`(*.f64 a a)`
99.3%	1	`(*.f64 b b)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes12.0ms (0.2%)

Memory

22.1MiB live, 22.1MiB allocated

Accuracy

Total -62.5b remaining (-7797.5%)

Threshold costs -62.5b (-7797.5%)

Counts

4 → 1

Calls

Call 1

Inputs
#s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a)
#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))
(sqrt.f64 #s(approx (- (* a a) (* b b)) (*.f64 a a)))
(sqrt.f64 (*.f64 (-.f64 a b) (+.f64 b a)))

Outputs
#s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a)

Calls

6 calls:

2.0ms	b
2.0ms	a
2.0ms	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
2.0ms	(-.f64 (.f64 a a) (.f64 b b))
2.0ms	(*.f64 a a)

Results

Accuracy	Segments	Branch
98.7%	1	`a`
98.7%	1	`b`
98.7%	1	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`
98.7%	1	`(-.f64 (.f64 a a) (.f64 b b))`
98.7%	1	`(*.f64 a a)`
98.7%	1	`(*.f64 b b)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

simplify51.0ms (1%)

Memory

2.2MiB live, 39.3MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`-commutative-binary64-.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	28
1	18	28

Stop Event

1×

saturated

Calls

Call 1

Inputs
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a))
#s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a)

Outputs
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a))
#s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a)

soundness609.0ms (12.5%)

Memory

-17.9MiB live, 256.4MiB allocated

Rules

18 934×	`lower-fma.f64`
18 934×	`lower-fma.f32`
11 938×	`lower-fma.f64`
11 938×	`lower-fma.f32`
6 736×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	21
0	10	21
1	36	21
2	239	21
3	2135	21
0	9378	21
0	119	757
1	332	757
2	1128	744
3	4541	722
0	8122	682
0	576	5107
1	1872	4323
2	7580	4315
0	8030	4070

Stop Event

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

Compiler

Compiled 37 to 27 computations (27% saved)

preprocess126.0ms (2.6%)

Memory: 9.4MiB live, 87.3MiB allocated
Remove: (abs b)
Compiler: Compiled 118 to 88 computations (25.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	8	12
0	8	12
1	12	12
2	17	12
3	23	12
4	32	12
5	53	12
6	83	12
7	112	12
8	165	12
9	189	12
10	209	12
11	211	12
0	211	12

Iter	Nodes	Cost
0	8	12
0	8	12
1	12	12
2	17	12
3	23	12
4	32	12
5	53	12
6	83	12
7	112	12
8	165	12
9	189	12
10	209	12
11	211	12
0	211	12

start0.0ms (0%)

analyze29.0ms (0.6%)

sample854.0ms (17.5%)

explain108.0ms (2.2%)

preprocess416.0ms (8.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify481.0ms (9.9%)

localize63.0ms (1.3%)

series6.0ms (0.1%)

simplify389.0ms (8%)

rewrite259.0ms (5.3%)

eval78.0ms (1.6%)

prune103.0ms (2.1%)

simplify149.0ms (3%)

localize54.0ms (1.1%)

series81.0ms (1.7%)

simplify155.0ms (3.2%)

rewrite197.0ms (4%)

eval207.0ms (4.2%)

prune149.0ms (3.1%)

simplify8.0ms (0.2%)

localize17.0ms (0.3%)

series1.0ms (0%)

simplify55.0ms (1.1%)

rewrite170.0ms (3.5%)

eval2.0ms (0%)

prune4.0ms (0.1%)

regimes47.0ms (1%)

regimes12.0ms (0.2%)

simplify51.0ms (1%)

soundness609.0ms (12.5%)

preprocess126.0ms (2.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	12
0	8	12
1	12	12
2	17	12
3	23	12
4	32	12
5	53	12
6	83	12
7	112	12
8	165	12
9	189	12
10	209	12
11	211	12
0	211	12