Metrics for Eccentricity of an ellipse

start0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated

analyze35.0ms (0.7%)

Memory

-13.8MiB live, 24.5MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	37.5%	62.5%	0%	0%	0%	0
0%	0%	37.5%	62.5%	0%	0%	0%	1
0%	0%	18.7%	62.5%	0%	18.7%	0%	2
0%	0%	9.4%	62.5%	0%	28.1%	0%	3
0%	0%	9.4%	62.5%	0%	28.1%	0%	4
0%	0%	7%	62.5%	0%	30.4%	0%	5
20%	1.2%	4.7%	62.5%	0%	31.6%	0%	6
25%	1.2%	3.5%	62.5%	0%	32.8%	0%	7
40%	1.8%	2.6%	62.5%	0%	33.1%	0%	8
51.9%	2%	1.9%	62.5%	0%	33.5%	0%	9
64.7%	2.4%	1.3%	62.5%	0%	33.7%	0%	10
72.9%	2.6%	1%	62.5%	0%	33.9%	0%	11
80.2%	2.7%	0.7%	62.5%	0%	34%	0%	12

Compiler

Compiled 25 to 16 computations (36% saved)

sample1.1s (23.6%)

Memory

52.6MiB live, 1 184.0MiB allocated

Samples

670.0ms	8 256×	0	valid
77.0ms	762×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 504.0ms

ival-mult: 106.0ms (21% of total)

ival-<=: 95.0ms (18.8% of total)

ival-sub: 80.0ms (15.9% of total)

ival-sqrt: 66.0ms (13.1% of total)

ival-div: 63.0ms (12.5% of total)

ival-fabs: 62.0ms (12.3% of total)

ival-and: 17.0ms (3.4% of total)

exact: 11.0ms (2.2% of total)

ival-assert: 3.0ms (0.6% of total)

Bogosity

explain136.0ms (2.8%)

Memory

-24.5MiB live, 101.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
59	-	-	`(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))`
0	-	-	`(*.f64 a a)`
0	-	-	`a`
0	-	-	`b`
0	-	-	`(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))`
0	-	-	`(fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a)))`
0	-	-	`(-.f64 (.f64 a a) (.f64 b b))`
0	-	-	`(*.f64 b b)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f64`	`(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))`	u/u	59	0
↳	`(*.f64 b b)`	underflow	192
↳	`(-.f64 (.f64 a a) (.f64 b b))`	underflow	59
↳	`(*.f64 a a)`	underflow	59
↳	`(*.f64 a a)`	underflow	59

Confusion

	Predicted +	Predicted -
+	59	0
-	0	197

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	59	0	0
-	0	0	197

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	197
1	59

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

35.0ms

512×

valid

Compiler

Compiled 119 to 28 computations (76.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-mult: 6.0ms (28.6% of total)

ival-sub: 5.0ms (23.8% of total)

ival-div: 3.0ms (14.3% of total)

ival-sqrt: 3.0ms (14.3% of total)

ival-fabs: 2.0ms (9.5% of total)

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

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

preprocess164.0ms (3.4%)

Memory

8.7MiB live, 45.1MiB allocated

Algorithm

1×	egg-herbie

Rules

9 090×	`lower-fma.f64`
9 090×	`lower-fma.f32`
4 304×	`lower-*.f32`
4 300×	`lower-*.f64`
1 434×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	67
1	85	57
2	338	57
3	2529	57
4	6437	57
0	8	13
0	14	13
1	30	11
2	75	11
3	199	11
4	482	11
5	1723	11
6	5645	11
0	8181	10

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs b)

(abs a)

Compiler

Compiled 13 to 8 computations (38.5% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	76.9%	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

Compiler

Compiled 13 to 8 computations (38.5% saved)

simplify150.0ms (3.1%)

Memory

4.8MiB live, 48.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

9 090×	`lower-fma.f64`
9 090×	`lower-fma.f32`
4 304×	`lower-*.f32`
4 300×	`lower-*.f64`
1 340×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	51
0	14	51
1	30	45
2	75	45
3	199	45
4	482	45
5	1723	45
6	5645	45
0	8181	43

Stop Event

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

Calls

Call 1

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

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

localize21.0ms (0.4%)

Memory

13.1MiB live, 13.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a)))
accuracy	0.00390625	(-.f64 (.f64 a a) (.f64 b b))
accuracy	0.01171875	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
accuracy	14.293131230844281	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))

Samples

15.0ms

256×

valid

Compiler

Compiled 53 to 10 computations (81.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-mult: 3.0ms (35.1% of total)

ival-sqrt: 2.0ms (23.4% of total)

ival-sub: 1.0ms (11.7% of total)

ival-div: 1.0ms (11.7% of total)

ival-fabs: 1.0ms (11.7% of total)

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

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

series46.0ms (0.9%)

Memory

-30.8MiB live, 7.8MiB allocated

Counts

5 → 108

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
39.0ms	a	@	inf	((fabs (/ (- (* a a) (* b b)) (* a a))) (- (* a a) (* b b)) (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (* a a) (/ (- (* a a) (* b b)) (* a a)))
1.0ms	b	@	inf	((fabs (/ (- (* a a) (* b b)) (* a a))) (- (* a a) (* b b)) (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (* a a) (/ (- (* a a) (* b b)) (* a a)))
1.0ms	b	@	0	((fabs (/ (- (* a a) (* b b)) (* a a))) (- (* a a) (* b b)) (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (* a a) (/ (- (* a a) (* b b)) (* a a)))
1.0ms	a	@	0	((fabs (/ (- (* a a) (* b b)) (* a a))) (- (* a a) (* b b)) (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (* a a) (/ (- (* a a) (* b b)) (* a a)))
1.0ms	a	@	-inf	((fabs (/ (- (* a a) (* b b)) (* a a))) (- (* a a) (* b b)) (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (* a a) (/ (- (* a a) (* b b)) (* a a)))

simplify168.0ms (3.5%)

Memory

36.8MiB live, 73.0MiB allocated

Algorithm

1×	egg-herbie

Rules

17 628×	`lower-fma.f64`
17 628×	`lower-fma.f32`
5 538×	`lower-*.f64`
5 538×	`lower-*.f32`
1 900×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	990
1	55	876
2	165	876
3	709	876
4	3801	876
0	8016	828

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 108

Calls

Call 1

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

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

rewrite216.0ms (4.5%)

Memory

-2.4MiB live, 80.8MiB allocated

Rules

3 746×	`lower-fma.f64`
3 746×	`lower-fma.f32`
3 566×	`lower-*.f32`
3 562×	`lower-*.f64`
2 844×	`lower-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	46
0	14	46
1	58	40
2	431	34
3	4344	34
0	8225	34

Stop Event

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

Counts

5 → 416

Calls

Call 1

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

Outputs
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eval117.0ms (2.4%)

Memory: -11.4MiB live, 63.7MiB allocated
Compiler: Compiled 10 830 to 1 903 computations (82.4% saved)

prune49.0ms (1%)

Memory

-14.1MiB live, 25.3MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	556	5	561
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	557	5	562

Accuracy

100.0%

Counts

562 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	76.8%	(/.f64 (sqrt.f64 (fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a)))) a)
▶	76.9%	(sqrt.f64 (/.f64 (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a))) (.f64 a a)))
▶	100.0%	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))))
▶	97.7%	(sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))))
▶	100.0%	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))))

Compiler

Compiled 112 to 90 computations (19.6% saved)

simplify178.0ms (3.7%)

Memory

-17.8MiB live, 57.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(/.f64 (/.f64 b a) a)
cost-diff	0	(fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))
cost-diff	0	#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64))))
cost-diff	0	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))))
cost-diff	0	(-.f64 a b)
cost-diff	0	(*.f64 (-.f64 a b) (+.f64 b a))
cost-diff	0	(fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
cost-diff	0	(sqrt.f64 (/.f64 (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a))) (.f64 a a)))
cost-diff	0	(*.f64 (-.f64 a b) (+.f64 b a))
cost-diff	0	(fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
cost-diff	0	(sqrt.f64 (fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a))))
cost-diff	0	(/.f64 (sqrt.f64 (fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a)))) a)
cost-diff	0	#s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))
cost-diff	0	(fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64)))
cost-diff	0	(sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))))
cost-diff	0	(-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 4 binary64)))
cost-diff	0	(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))
cost-diff	0	(fabs.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))))
cost-diff	0	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))))

Rules

13 160×	`lower-fma.f32`
13 158×	`lower-fma.f64`
2 620×	`lower-+.f32`
2 616×	`lower-+.f64`
2 456×	`lower-*.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	36	290
0	60	293
1	107	258
2	188	258
3	363	258
4	731	258
5	2362	258
6	7055	258
0	8217	258

Stop Event

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

Calls

Call 1

Inputs
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))))
(fabs.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))
(-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 4 binary64)))
#s(literal 1 binary64)
(pow.f64 (/.f64 b a) #s(literal 4 binary64))
(/.f64 b a)
b
a
#s(literal 4 binary64)
(+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))
(pow.f64 (/.f64 b a) #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))))
(fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64)))
#s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))
#s(literal 1 binary64)
(/.f64 (sqrt.f64 (fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a)))) a)
(sqrt.f64 (fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a))))
(fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
(*.f64 (-.f64 a b) (+.f64 b a))
(-.f64 a b)
a
b
(+.f64 b a)
(sqrt.f64 (/.f64 (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a))) (.f64 a a)))
(/.f64 (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a))) (.f64 a a))
(fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
(*.f64 (-.f64 a b) (+.f64 b a))
(-.f64 a b)
a
b
(+.f64 b a)
(*.f64 a a)
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))))
#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64))))
(fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))
(fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64))
(/.f64 (/.f64 b a) a)
(/.f64 b a)
b
a
#s(literal -1 binary64)

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

localize108.0ms (2.2%)

Memory

9.6MiB live, 48.3MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	(fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))
accuracy	0	#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64))))
accuracy	0.01171875	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))))
accuracy	0.2578125	(/.f64 (/.f64 b a) a)
accuracy	0	(fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
accuracy	0.00390625	(*.f64 (-.f64 a b) (+.f64 b a))
accuracy	0.01171875	(sqrt.f64 (/.f64 (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a))) (.f64 a a)))
accuracy	14.293131230844281	(/.f64 (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a))) (.f64 a a))
accuracy	0	(fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
accuracy	0.00390625	(*.f64 (-.f64 a b) (+.f64 b a))
accuracy	0.0234375	(/.f64 (sqrt.f64 (fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a)))) a)
accuracy	14.438666732822963	(sqrt.f64 (fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a))))
accuracy	0	(fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64)))
accuracy	0.01171875	(sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))))
accuracy	1.5374468011429867	#s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))
accuracy	0.01171875	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))))
accuracy	0.01953125	(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))
accuracy	0.3741952637479346	(pow.f64 (/.f64 b a) #s(literal 4 binary64))
accuracy	0.3935737793053261	(pow.f64 (/.f64 b a) #s(literal 2 binary64))

Samples

86.0ms

256×

valid

Compiler

Compiled 268 to 34 computations (87.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 69.0ms

ival-mult: 37.0ms (53.7% of total)

ival-div: 9.0ms (13.1% of total)

ival-sqrt: 6.0ms (8.7% of total)

ival-fabs: 4.0ms (5.8% of total)

ival-add: 3.0ms (4.4% of total)

ival-sub: 3.0ms (4.4% of total)

ival-pow: 3.0ms (4.4% of total)

ival-pow2: 2.0ms (2.9% of total)

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

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

exact: 0.0ms (0% of total)

series108.0ms (2.2%)

Memory

-19.4MiB live, 57.7MiB allocated

Counts

20 → 480

Calls

Call 1

Inputs
#s(alt (sqrt.f64 (fabs.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))))) (patch (sqrt.f64 (fabs.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))))) #<representation binary64>) () ())
#s(alt (fabs.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))) (patch (fabs.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))) (patch (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 4 binary64))) (patch (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 4 binary64))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64)))) (patch (sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))) (patch (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64)) (patch #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (sqrt.f64 (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a)))) a) (patch (/.f64 (sqrt.f64 (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a)))) a) #<representation binary64>) () ())
#s(alt (sqrt.f64 (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a)))) (patch (sqrt.f64 (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a)))) #<representation binary64>) () ())
#s(alt (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a))) (patch (fabs.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 (sqrt.f64 (/.f64 (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a))) (.f64 a a))) (patch (sqrt.f64 (/.f64 (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a))) (.f64 a a))) #<representation binary64>) () ())
#s(alt (-.f64 a b) (patch (-.f64 a b) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64))))) (patch (sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64))))) #<representation binary64>) () ())
#s(alt #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))) (patch #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))) #<representation binary64>) () ())
#s(alt (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64))) (patch (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 (/.f64 b a) a) (patch (/.f64 (/.f64 b a) a) #<representation binary64>) () ())
#s(alt (pow.f64 (/.f64 b a) #s(literal 2 binary64)) (patch (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (pow.f64 (/.f64 b a) #s(literal 4 binary64)) (patch (pow.f64 (/.f64 b a) #s(literal 4 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a))) (.f64 a a)) (patch (/.f64 (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a))) (.f64 a a)) #<representation binary64>) () ())

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

Calls

6 calls:

Time	Variable		Point	Expression
67.0ms	b	@	-inf	((sqrt (fabs (/ (- 1 (pow (/ b a) 4)) (+ 1 (pow (/ b a) 2))))) (fabs (/ (- 1 (pow (/ b a) 4)) (+ 1 (pow (/ b a) 2)))) (/ (- 1 (pow (/ b a) 4)) (+ 1 (pow (/ b a) 2))) (- 1 (pow (/ b a) 4)) (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (/ (- (* a a) (* b b)) (* a a)) (/ (sqrt (fabs (* (- a b) (+ b a)))) a) (sqrt (fabs (* (- a b) (+ b a)))) (fabs (* (- a b) (+ b a))) (* (- a b) (+ b a)) (sqrt (/ (fabs (* (- a b) (+ b a))) (* a a))) (- a b) (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs (+ (* (/ (/ b a) a) b) -1)) (/ (/ b a) a) (pow (/ b a) 2) (pow (/ b a) 4) (/ (fabs (* (- a b) (+ b a))) (* a a)))
6.0ms	a	@	-inf	((sqrt (fabs (/ (- 1 (pow (/ b a) 4)) (+ 1 (pow (/ b a) 2))))) (fabs (/ (- 1 (pow (/ b a) 4)) (+ 1 (pow (/ b a) 2)))) (/ (- 1 (pow (/ b a) 4)) (+ 1 (pow (/ b a) 2))) (- 1 (pow (/ b a) 4)) (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (/ (- (* a a) (* b b)) (* a a)) (/ (sqrt (fabs (* (- a b) (+ b a)))) a) (sqrt (fabs (* (- a b) (+ b a)))) (fabs (* (- a b) (+ b a))) (* (- a b) (+ b a)) (sqrt (/ (fabs (* (- a b) (+ b a))) (* a a))) (- a b) (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs (+ (* (/ (/ b a) a) b) -1)) (/ (/ b a) a) (pow (/ b a) 2) (pow (/ b a) 4) (/ (fabs (* (- a b) (+ b a))) (* a a)))
6.0ms	b	@	inf	((sqrt (fabs (/ (- 1 (pow (/ b a) 4)) (+ 1 (pow (/ b a) 2))))) (fabs (/ (- 1 (pow (/ b a) 4)) (+ 1 (pow (/ b a) 2)))) (/ (- 1 (pow (/ b a) 4)) (+ 1 (pow (/ b a) 2))) (- 1 (pow (/ b a) 4)) (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (/ (- (* a a) (* b b)) (* a a)) (/ (sqrt (fabs (* (- a b) (+ b a)))) a) (sqrt (fabs (* (- a b) (+ b a)))) (fabs (* (- a b) (+ b a))) (* (- a b) (+ b a)) (sqrt (/ (fabs (* (- a b) (+ b a))) (* a a))) (- a b) (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs (+ (* (/ (/ b a) a) b) -1)) (/ (/ b a) a) (pow (/ b a) 2) (pow (/ b a) 4) (/ (fabs (* (- a b) (+ b a))) (* a a)))
5.0ms	b	@	0	((sqrt (fabs (/ (- 1 (pow (/ b a) 4)) (+ 1 (pow (/ b a) 2))))) (fabs (/ (- 1 (pow (/ b a) 4)) (+ 1 (pow (/ b a) 2)))) (/ (- 1 (pow (/ b a) 4)) (+ 1 (pow (/ b a) 2))) (- 1 (pow (/ b a) 4)) (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (/ (- (* a a) (* b b)) (* a a)) (/ (sqrt (fabs (* (- a b) (+ b a)))) a) (sqrt (fabs (* (- a b) (+ b a)))) (fabs (* (- a b) (+ b a))) (* (- a b) (+ b a)) (sqrt (/ (fabs (* (- a b) (+ b a))) (* a a))) (- a b) (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs (+ (* (/ (/ b a) a) b) -1)) (/ (/ b a) a) (pow (/ b a) 2) (pow (/ b a) 4) (/ (fabs (* (- a b) (+ b a))) (* a a)))
4.0ms	a	@	0	((sqrt (fabs (/ (- 1 (pow (/ b a) 4)) (+ 1 (pow (/ b a) 2))))) (fabs (/ (- 1 (pow (/ b a) 4)) (+ 1 (pow (/ b a) 2)))) (/ (- 1 (pow (/ b a) 4)) (+ 1 (pow (/ b a) 2))) (- 1 (pow (/ b a) 4)) (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (/ (- (* a a) (* b b)) (* a a)) (/ (sqrt (fabs (* (- a b) (+ b a)))) a) (sqrt (fabs (* (- a b) (+ b a)))) (fabs (* (- a b) (+ b a))) (* (- a b) (+ b a)) (sqrt (/ (fabs (* (- a b) (+ b a))) (* a a))) (- a b) (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs (+ (* (/ (/ b a) a) b) -1)) (/ (/ b a) a) (pow (/ b a) 2) (pow (/ b a) 4) (/ (fabs (* (- a b) (+ b a))) (* a a)))

simplify248.0ms (5.1%)

Memory

13.0MiB live, 168.3MiB allocated

Algorithm

1×	egg-herbie

Rules

19 630×	`lower-fma.f64`
19 630×	`lower-fma.f32`
3 276×	`lower-*.f64`
3 276×	`lower-*.f32`
1 804×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	128	5116
1	359	4624
2	1032	4624
3	4602	4624
0	8701	4432

Stop Event

1×	iter limit
1×	node limit

Counts

480 → 477

Calls

Call 1

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

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

rewrite227.0ms (4.7%)

Memory

20.9MiB live, 260.7MiB allocated

Rules

5 308×	`lower-/.f32`
5 298×	`lower-/.f64`
4 240×	`lower-*.f32`
4 236×	`lower-*.f64`
3 608×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	36	229
0	60	250
1	237	172
2	1682	172
0	8461	172

Stop Event

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

Counts

20 → 1 059

Calls

Call 1

Inputs
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))))
(fabs.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))
(-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 4 binary64)))
(sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))))
(fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64)))
#s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))
(/.f64 (sqrt.f64 (fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a)))) a)
(sqrt.f64 (fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a))))
(fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
(*.f64 (-.f64 a b) (+.f64 b a))
(sqrt.f64 (/.f64 (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a))) (.f64 a a)))
(-.f64 a b)
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))))
#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64))))
(fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))
(/.f64 (/.f64 b a) a)
(pow.f64 (/.f64 b a) #s(literal 2 binary64))
(pow.f64 (/.f64 b a) #s(literal 4 binary64))
(/.f64 (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a))) (.f64 a a))

Outputs
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eval329.0ms (6.8%)

Memory: -22.8MiB live, 402.7MiB allocated
Compiler: Compiled 39 539 to 4 338 computations (89% saved)

prune49.0ms (1%)

Memory

22.1MiB live, 101.1MiB allocated

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	1 845	3	1 848
Fresh	0	0	0
Picked	2	3	5
Done	0	0	0
Total	1 847	6	1 853

Accuracy

100.0%

Counts

1 853 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.1%	(/.f64 (*.f64 (sqrt.f64 (fabs.f64 (-.f64 b a))) (sqrt.f64 (fabs.f64 (+.f64 a b)))) a)
✓	76.8%	(/.f64 (sqrt.f64 (fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a)))) a)
▶	4.4%	(/.f64 (sqrt.f64 (fabs.f64 #s(approx (* (- a b) (+ b a)) (*.f64 (neg.f64 b) b)))) a)
✓	97.7%	(sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))))
✓	100.0%	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))))
▶	77.7%	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64)))))

Compiler

Compiled 59 to 50 computations (15.3% saved)

simplify114.0ms (2.4%)

Memory

17.6MiB live, 136.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

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

Rules

9 038×	`lower-fma.f32`
9 036×	`lower-fma.f64`
2 344×	`lower-*.f32`
2 338×	`lower-*.f64`
2 266×	`lower--.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	31	186
0	50	186
1	86	182
2	160	180
3	360	180
4	758	180
5	2497	180
6	6697	180
0	8206	180

Stop Event

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

Calls

Call 1

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

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

localize97.0ms (2%)

Memory

-21.3MiB live, 114.0MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(sqrt.f64 (fabs.f64 (+.f64 a b)))
accuracy	0.0078125	(sqrt.f64 (fabs.f64 (-.f64 b a)))
accuracy	0.0234375	(/.f64 (*.f64 (sqrt.f64 (fabs.f64 (-.f64 b a))) (sqrt.f64 (fabs.f64 (+.f64 a b)))) a)
accuracy	0.515625	(*.f64 (sqrt.f64 (fabs.f64 (-.f64 b a))) (sqrt.f64 (fabs.f64 (+.f64 a b))))
accuracy	0	(fabs.f64 #s(approx (* (- a b) (+ b a)) (*.f64 (neg.f64 b) b)))
accuracy	0.0234375	(/.f64 (sqrt.f64 (fabs.f64 #s(approx (* (- a b) (+ b a)) (*.f64 (neg.f64 b) b)))) a)
accuracy	14.438666732822963	(sqrt.f64 (fabs.f64 #s(approx (* (- a b) (+ b a)) (*.f64 (neg.f64 b) b))))
accuracy	45.97345558673093	#s(approx (* (- a b) (+ b a)) (*.f64 (neg.f64 b) b))
accuracy	0	(fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64)))
accuracy	0	#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64))))
accuracy	0.01171875	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64)))))
accuracy	14.750769563853018	(/.f64 b (*.f64 a a))

Samples

71.0ms

256×

valid

Compiler

Compiled 150 to 31 computations (79.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 52.0ms

ival-fabs: 23.0ms (44.2% of total)

ival-mult: 9.0ms (17.3% of total)

ival-div: 6.0ms (11.5% of total)

ival-sqrt: 6.0ms (11.5% of total)

ival-add: 3.0ms (5.8% of total)

ival-sub: 3.0ms (5.8% of total)

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

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

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

exact: 0.0ms (0% of total)

series44.0ms (0.9%)

Memory

1.2MiB live, 40.3MiB allocated

Counts

14 → 336

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
24.0ms	b	@	inf	((sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs (+ (* (/ b (* a a)) b) -1)) (+ (* (/ b (* a a)) b) -1) (/ (sqrt (fabs (* (- a b) (+ b a)))) a) (sqrt (fabs (* (- a b) (+ b a)))) (fabs (* (- a b) (+ b a))) (* (- a b) (+ b a)) (/ (* (sqrt (fabs (- b a))) (sqrt (fabs (+ a b)))) a) (* (sqrt (fabs (- b a))) (sqrt (fabs (+ a b)))) (sqrt (fabs (- b a))) (fabs (- b a)) (/ b (* a a)) (sqrt (fabs (+ a b))))
3.0ms	b	@	-inf	((sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs (+ (* (/ b (* a a)) b) -1)) (+ (* (/ b (* a a)) b) -1) (/ (sqrt (fabs (* (- a b) (+ b a)))) a) (sqrt (fabs (* (- a b) (+ b a)))) (fabs (* (- a b) (+ b a))) (* (- a b) (+ b a)) (/ (* (sqrt (fabs (- b a))) (sqrt (fabs (+ a b)))) a) (* (sqrt (fabs (- b a))) (sqrt (fabs (+ a b)))) (sqrt (fabs (- b a))) (fabs (- b a)) (/ b (* a a)) (sqrt (fabs (+ a b))))
2.0ms	b	@	0	((sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs (+ (* (/ b (* a a)) b) -1)) (+ (* (/ b (* a a)) b) -1) (/ (sqrt (fabs (* (- a b) (+ b a)))) a) (sqrt (fabs (* (- a b) (+ b a)))) (fabs (* (- a b) (+ b a))) (* (- a b) (+ b a)) (/ (* (sqrt (fabs (- b a))) (sqrt (fabs (+ a b)))) a) (* (sqrt (fabs (- b a))) (sqrt (fabs (+ a b)))) (sqrt (fabs (- b a))) (fabs (- b a)) (/ b (* a a)) (sqrt (fabs (+ a b))))
2.0ms	a	@	inf	((sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs (+ (* (/ b (* a a)) b) -1)) (+ (* (/ b (* a a)) b) -1) (/ (sqrt (fabs (* (- a b) (+ b a)))) a) (sqrt (fabs (* (- a b) (+ b a)))) (fabs (* (- a b) (+ b a))) (* (- a b) (+ b a)) (/ (* (sqrt (fabs (- b a))) (sqrt (fabs (+ a b)))) a) (* (sqrt (fabs (- b a))) (sqrt (fabs (+ a b)))) (sqrt (fabs (- b a))) (fabs (- b a)) (/ b (* a a)) (sqrt (fabs (+ a b))))
2.0ms	a	@	-inf	((sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs (+ (* (/ b (* a a)) b) -1)) (+ (* (/ b (* a a)) b) -1) (/ (sqrt (fabs (* (- a b) (+ b a)))) a) (sqrt (fabs (* (- a b) (+ b a)))) (fabs (* (- a b) (+ b a))) (* (- a b) (+ b a)) (/ (* (sqrt (fabs (- b a))) (sqrt (fabs (+ a b)))) a) (* (sqrt (fabs (- b a))) (sqrt (fabs (+ a b)))) (sqrt (fabs (- b a))) (fabs (- b a)) (/ b (* a a)) (sqrt (fabs (+ a b))))

simplify133.0ms (2.7%)

Memory

4.7MiB live, 159.2MiB allocated

Algorithm

1×	egg-herbie

Rules

13 812×	`lower-fma.f64`
13 812×	`lower-fma.f32`
3 576×	`lower-*.f64`
3 576×	`lower-*.f32`
1 646×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	120	3036
1	325	2720
2	849	2708
3	3956	2696
0	8448	2602

Stop Event

1×	iter limit
1×	node limit

Counts

336 → 336

Calls

Call 1

Inputs
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(fabs (- (/ (pow b 2) (pow a 2)) 1))
(fabs (- (/ (pow b 2) (pow a 2)) 1))
(fabs (- (/ (pow b 2) (pow a 2)) 1))
(fabs (- (/ (pow b 2) (pow a 2)) 1))
-1
(- (/ (pow b 2) (pow a 2)) 1)
(- (/ (pow b 2) (pow a 2)) 1)
(- (/ (pow b 2) (pow a 2)) 1)
(* (/ 1 a) (sqrt (fabs (* (+ a b) (- a b)))))
(* (/ 1 a) (sqrt (fabs (* (+ a b) (- a b)))))
(* (/ 1 a) (sqrt (fabs (* (+ a b) (- a b)))))
(* (/ 1 a) (sqrt (fabs (* (+ a b) (- a b)))))
(sqrt (fabs (* (+ a b) (- a b))))
(sqrt (fabs (* (+ a b) (- a b))))
(sqrt (fabs (* (+ a b) (- a b))))
(sqrt (fabs (* (+ a b) (- a b))))
(fabs (* (+ a b) (- a b)))
(fabs (* (+ a b) (- a b)))
(fabs (* (+ a b) (- a b)))
(fabs (* (+ a b) (- a b)))
(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))
(* (/ 1 a) (sqrt (* (fabs (+ a b)) (fabs (- b a)))))
(* (/ 1 a) (sqrt (* (fabs (+ a b)) (fabs (- b a)))))
(* (/ 1 a) (sqrt (* (fabs (+ a b)) (fabs (- b a)))))
(* (/ 1 a) (sqrt (* (fabs (+ a b)) (fabs (- b a)))))
(sqrt (* (fabs (+ a b)) (fabs (- b a))))
(sqrt (* (fabs (+ a b)) (fabs (- b a))))
(sqrt (* (fabs (+ a b)) (fabs (- b a))))
(sqrt (* (fabs (+ a b)) (fabs (- b a))))
(sqrt (fabs (- b a)))
(sqrt (fabs (- b a)))
(sqrt (fabs (- b a)))
(sqrt (fabs (- b a)))
(fabs (- b a))
(fabs (- b a))
(fabs (- b a))
(fabs (- b a))
(/ b (pow a 2))
(/ b (pow a 2))
(/ b (pow a 2))
(/ b (pow a 2))
(sqrt (fabs (+ a b)))
(sqrt (fabs (+ a b)))
(sqrt (fabs (+ a b)))
(sqrt (fabs (+ a b)))
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(fabs (- (/ (pow b 2) (pow a 2)) 1))
(fabs (- (/ (pow b 2) (pow a 2)) 1))
(fabs (- (/ (pow b 2) (pow a 2)) 1))
(fabs (- (/ (pow b 2) (pow a 2)) 1))
(/ (pow b 2) (pow a 2))
(* (pow b 2) (- (/ 1 (pow a 2)) (/ 1 (pow b 2))))
(* (pow b 2) (- (/ 1 (pow a 2)) (/ 1 (pow b 2))))
(* (pow b 2) (- (/ 1 (pow a 2)) (/ 1 (pow b 2))))
(* (/ 1 a) (sqrt (fabs (* (+ a b) (- a b)))))
(* (/ 1 a) (sqrt (fabs (* (+ a b) (- a b)))))
(* (/ 1 a) (sqrt (fabs (* (+ a b) (- a b)))))
(* (/ 1 a) (sqrt (fabs (* (+ a b) (- a b)))))
(sqrt (fabs (* (+ a b) (- a b))))
(sqrt (fabs (* (+ a b) (- a b))))
(sqrt (fabs (* (+ a b) (- a b))))
(sqrt (fabs (* (+ a b) (- a b))))
(fabs (* (+ a b) (- a b)))
(fabs (* (+ a b) (- a b)))
(fabs (* (+ a b) (- a b)))
(fabs (* (+ a b) (- a b)))
(* -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 a) (sqrt (* (fabs (+ a b)) (fabs (- b a)))))
(* (/ 1 a) (sqrt (* (fabs (+ a b)) (fabs (- b a)))))
(* (/ 1 a) (sqrt (* (fabs (+ a b)) (fabs (- b a)))))
(* (/ 1 a) (sqrt (* (fabs (+ a b)) (fabs (- b a)))))
(sqrt (* (fabs (+ a b)) (fabs (- b a))))
(sqrt (* (fabs (+ a b)) (fabs (- b a))))
(sqrt (* (fabs (+ a b)) (fabs (- b a))))
(sqrt (* (fabs (+ a b)) (fabs (- b a))))
(sqrt (fabs (- b a)))
(sqrt (fabs (- b a)))
(sqrt (fabs (- b a)))
(sqrt (fabs (- b a)))
(fabs (- b a))
(fabs (- b a))
(fabs (- b a))
(fabs (- b a))
(/ b (pow a 2))
(/ b (pow a 2))
(/ b (pow a 2))
(/ b (pow a 2))
(sqrt (fabs (+ a b)))
(sqrt (fabs (+ a b)))
(sqrt (fabs (+ a b)))
(sqrt (fabs (+ a b)))
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(fabs (- (/ (pow b 2) (pow a 2)) 1))
(fabs (- (/ (pow b 2) (pow a 2)) 1))
(fabs (- (/ (pow b 2) (pow a 2)) 1))
(fabs (- (/ (pow b 2) (pow a 2)) 1))
(/ (pow b 2) (pow a 2))
(* (pow b 2) (- (/ 1 (pow a 2)) (/ 1 (pow b 2))))
(* (pow b 2) (- (/ 1 (pow a 2)) (/ 1 (pow b 2))))
(* (pow b 2) (- (/ 1 (pow a 2)) (/ 1 (pow b 2))))
(* (/ 1 a) (sqrt (fabs (* (+ a (* -1 b)) (- a (* -1 b))))))
(* (/ 1 a) (sqrt (fabs (* (+ a (* -1 b)) (- a (* -1 b))))))
(* (/ 1 a) (sqrt (fabs (* (+ a (* -1 b)) (- a (* -1 b))))))
(* (/ 1 a) (sqrt (fabs (* (+ a (* -1 b)) (- a (* -1 b))))))
(sqrt (fabs (* (+ a (* -1 b)) (- a (* -1 b)))))
(sqrt (fabs (* (+ a (* -1 b)) (- a (* -1 b)))))
(sqrt (fabs (* (+ a (* -1 b)) (- a (* -1 b)))))
(sqrt (fabs (* (+ a (* -1 b)) (- a (* -1 b)))))
(fabs (* (+ a (* -1 b)) (- a (* -1 b))))
(fabs (* (+ a (* -1 b)) (- a (* -1 b))))
(fabs (* (+ a (* -1 b)) (- a (* -1 b))))
(fabs (* (+ a (* -1 b)) (- a (* -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 a) (sqrt (* (fabs (neg (+ a (* -1 b)))) (fabs (- a (* -1 b))))))
(* (/ 1 a) (sqrt (* (fabs (neg (+ a (* -1 b)))) (fabs (- a (* -1 b))))))
(* (/ 1 a) (sqrt (* (fabs (neg (+ a (* -1 b)))) (fabs (- a (* -1 b))))))
(* (/ 1 a) (sqrt (* (fabs (neg (+ a (* -1 b)))) (fabs (- a (* -1 b))))))
(sqrt (* (fabs (neg (+ a (* -1 b)))) (fabs (- a (* -1 b)))))
(sqrt (* (fabs (neg (+ a (* -1 b)))) (fabs (- a (* -1 b)))))
(sqrt (* (fabs (neg (+ a (* -1 b)))) (fabs (- a (* -1 b)))))
(sqrt (* (fabs (neg (+ a (* -1 b)))) (fabs (- a (* -1 b)))))
(sqrt (fabs (neg (+ a (* -1 b)))))
(sqrt (fabs (neg (+ a (* -1 b)))))
(sqrt (fabs (neg (+ a (* -1 b)))))
(sqrt (fabs (neg (+ a (* -1 b)))))
(fabs (neg (+ a (* -1 b))))
(fabs (neg (+ a (* -1 b))))
(fabs (neg (+ a (* -1 b))))
(fabs (neg (+ a (* -1 b))))
(/ b (pow a 2))
(/ b (pow a 2))
(/ b (pow a 2))
(/ b (pow a 2))
(sqrt (fabs (- a (* -1 b))))
(sqrt (fabs (- a (* -1 b))))
(sqrt (fabs (- a (* -1 b))))
(sqrt (fabs (- a (* -1 b))))
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(fabs (- (/ (pow b 2) (pow a 2)) 1))
(fabs (- (/ (pow b 2) (pow a 2)) 1))
(fabs (- (/ (pow b 2) (pow a 2)) 1))
(fabs (- (/ (pow b 2) (pow a 2)) 1))
(/ (pow b 2) (pow a 2))
(/ (+ (* -1 (pow a 2)) (pow b 2)) (pow a 2))
(/ (+ (* -1 (pow a 2)) (pow b 2)) (pow a 2))
(/ (+ (* -1 (pow a 2)) (pow b 2)) (pow a 2))
(* (/ 1 a) (sqrt (fabs (* (+ a b) (- a b)))))
(* (/ 1 a) (sqrt (fabs (* (+ a b) (- a b)))))
(* (/ 1 a) (sqrt (fabs (* (+ a b) (- a b)))))
(* (/ 1 a) (sqrt (fabs (* (+ a b) (- a b)))))
(sqrt (fabs (* (+ a b) (- a b))))
(sqrt (fabs (* (+ a b) (- a b))))
(sqrt (fabs (* (+ a b) (- a b))))
(sqrt (fabs (* (+ a b) (- a b))))
(fabs (* (+ a b) (- a b)))
(fabs (* (+ a b) (- a b)))
(fabs (* (+ a b) (- a b)))
(fabs (* (+ a b) (- a b)))
(* -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 a) (sqrt (* (fabs (+ a b)) (fabs (- b a)))))
(* (/ 1 a) (sqrt (* (fabs (+ a b)) (fabs (- b a)))))
(* (/ 1 a) (sqrt (* (fabs (+ a b)) (fabs (- b a)))))
(* (/ 1 a) (sqrt (* (fabs (+ a b)) (fabs (- b a)))))
(sqrt (* (fabs (+ a b)) (fabs (- b a))))
(sqrt (* (fabs (+ a b)) (fabs (- b a))))
(sqrt (* (fabs (+ a b)) (fabs (- b a))))
(sqrt (* (fabs (+ a b)) (fabs (- b a))))
(sqrt (fabs (- b a)))
(sqrt (fabs (- b a)))
(sqrt (fabs (- b a)))
(sqrt (fabs (- b a)))
(fabs (- b a))
(fabs (- b a))
(fabs (- b a))
(fabs (- b a))
(/ b (pow a 2))
(/ b (pow a 2))
(/ b (pow a 2))
(/ b (pow a 2))
(sqrt (fabs (+ a b)))
(sqrt (fabs (+ a b)))
(sqrt (fabs (+ a b)))
(sqrt (fabs (+ a b)))
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(fabs (- (/ (pow b 2) (pow a 2)) 1))
(fabs (- (/ (pow b 2) (pow a 2)) 1))
(fabs (- (/ (pow b 2) (pow a 2)) 1))
(fabs (- (/ (pow b 2) (pow a 2)) 1))
-1
(- (/ (pow b 2) (pow a 2)) 1)
(- (/ (pow b 2) (pow a 2)) 1)
(- (/ (pow b 2) (pow a 2)) 1)
(* (/ 1 a) (sqrt (fabs (* (+ a b) (- a b)))))
(* (/ 1 a) (sqrt (fabs (* (+ a b) (- a b)))))
(* (/ 1 a) (sqrt (fabs (* (+ a b) (- a b)))))
(* (/ 1 a) (sqrt (fabs (* (+ a b) (- a b)))))
(sqrt (fabs (* (+ a b) (- a b))))
(sqrt (fabs (* (+ a b) (- a b))))
(sqrt (fabs (* (+ a b) (- a b))))
(sqrt (fabs (* (+ a b) (- a b))))
(fabs (* (+ a b) (- a b)))
(fabs (* (+ a b) (- a b)))
(fabs (* (+ a b) (- a b)))
(fabs (* (+ a b) (- a b)))
(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)))))
(* (/ 1 a) (sqrt (* (fabs (+ a b)) (fabs (- b a)))))
(* (/ 1 a) (sqrt (* (fabs (+ a b)) (fabs (- b a)))))
(* (/ 1 a) (sqrt (* (fabs (+ a b)) (fabs (- b a)))))
(* (/ 1 a) (sqrt (* (fabs (+ a b)) (fabs (- b a)))))
(sqrt (* (fabs (+ a b)) (fabs (- b a))))
(sqrt (* (fabs (+ a b)) (fabs (- b a))))
(sqrt (* (fabs (+ a b)) (fabs (- b a))))
(sqrt (* (fabs (+ a b)) (fabs (- b a))))
(sqrt (fabs (- b a)))
(sqrt (fabs (- b a)))
(sqrt (fabs (- b a)))
(sqrt (fabs (- b a)))
(fabs (- b a))
(fabs (- b a))
(fabs (- b a))
(fabs (- b a))
(/ b (pow a 2))
(/ b (pow a 2))
(/ b (pow a 2))
(/ b (pow a 2))
(sqrt (fabs (+ a b)))
(sqrt (fabs (+ a b)))
(sqrt (fabs (+ a b)))
(sqrt (fabs (+ a b)))
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(fabs (- (/ (pow b 2) (pow a 2)) 1))
(fabs (- (/ (pow b 2) (pow a 2)) 1))
(fabs (- (/ (pow b 2) (pow a 2)) 1))
(fabs (- (/ (pow b 2) (pow a 2)) 1))
-1
(- (/ (pow b 2) (pow a 2)) 1)
(- (/ (pow b 2) (pow a 2)) 1)
(- (/ (pow b 2) (pow a 2)) 1)
(* (/ 1 a) (sqrt (fabs (* -1 (* (+ b (* -1 a)) (- b (* -1 a)))))))
(* (/ 1 a) (sqrt (fabs (* -1 (* (+ b (* -1 a)) (- b (* -1 a)))))))
(* (/ 1 a) (sqrt (fabs (* -1 (* (+ b (* -1 a)) (- b (* -1 a)))))))
(* (/ 1 a) (sqrt (fabs (* -1 (* (+ b (* -1 a)) (- b (* -1 a)))))))
(sqrt (fabs (* -1 (* (+ b (* -1 a)) (- b (* -1 a))))))
(sqrt (fabs (* -1 (* (+ b (* -1 a)) (- b (* -1 a))))))
(sqrt (fabs (* -1 (* (+ b (* -1 a)) (- b (* -1 a))))))
(sqrt (fabs (* -1 (* (+ b (* -1 a)) (- b (* -1 a))))))
(fabs (* -1 (* (+ b (* -1 a)) (- b (* -1 a)))))
(fabs (* -1 (* (+ b (* -1 a)) (- b (* -1 a)))))
(fabs (* -1 (* (+ b (* -1 a)) (- b (* -1 a)))))
(fabs (* -1 (* (+ b (* -1 a)) (- b (* -1 a)))))
(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))))
(* (/ 1 a) (sqrt (* (fabs (+ b (* -1 a))) (fabs (- b (* -1 a))))))
(* (/ 1 a) (sqrt (* (fabs (+ b (* -1 a))) (fabs (- b (* -1 a))))))
(* (/ 1 a) (sqrt (* (fabs (+ b (* -1 a))) (fabs (- b (* -1 a))))))
(* (/ 1 a) (sqrt (* (fabs (+ b (* -1 a))) (fabs (- b (* -1 a))))))
(sqrt (* (fabs (+ b (* -1 a))) (fabs (- b (* -1 a)))))
(sqrt (* (fabs (+ b (* -1 a))) (fabs (- b (* -1 a)))))
(sqrt (* (fabs (+ b (* -1 a))) (fabs (- b (* -1 a)))))
(sqrt (* (fabs (+ b (* -1 a))) (fabs (- b (* -1 a)))))
(sqrt (fabs (+ b (* -1 a))))
(sqrt (fabs (+ b (* -1 a))))
(sqrt (fabs (+ b (* -1 a))))
(sqrt (fabs (+ b (* -1 a))))
(fabs (+ b (* -1 a)))
(fabs (+ b (* -1 a)))
(fabs (+ b (* -1 a)))
(fabs (+ b (* -1 a)))
(/ b (pow a 2))
(/ b (pow a 2))
(/ b (pow a 2))
(/ b (pow a 2))
(sqrt (fabs (- b (* -1 a))))
(sqrt (fabs (- b (* -1 a))))
(sqrt (fabs (- b (* -1 a))))
(sqrt (fabs (- b (* -1 a))))

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

rewrite141.0ms (2.9%)

Memory

1.7MiB live, 160.9MiB allocated

Rules

4 862×	`lower-/.f32`
4 856×	`lower-/.f64`
3 662×	`lower-fma.f32`
3 660×	`lower-fma.f64`
3 546×	`lower-*.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	31	160
0	50	158
1	180	150
2	1283	144
0	8573	144

Stop Event

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

Counts

14 → 320

Calls

Call 1

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

Outputs
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eval112.0ms (2.3%)

Memory: -18.5MiB live, 140.9MiB allocated
Compiler: Compiled 9 871 to 1 469 computations (85.1% saved)

prune13.0ms (0.3%)

Memory

5.2MiB live, 44.1MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	656	0	656
Fresh	0	0	0
Picked	0	3	3
Done	0	3	3
Total	656	6	662

Accuracy

100.0%

Counts

662 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.1%	(/.f64 (*.f64 (sqrt.f64 (fabs.f64 (-.f64 b a))) (sqrt.f64 (fabs.f64 (+.f64 a b)))) a)
✓	76.8%	(/.f64 (sqrt.f64 (fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a)))) a)
✓	4.4%	(/.f64 (sqrt.f64 (fabs.f64 #s(approx (* (- a b) (+ b a)) (*.f64 (neg.f64 b) b)))) a)
✓	97.7%	(sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))))
✓	100.0%	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))))
✓	77.7%	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64)))))

Compiler

Compiled 161 to 105 computations (34.8% saved)

regimes36.0ms (0.8%)

Memory

-7.5MiB live, 31.9MiB allocated

Counts

9 → 1

Calls

Call 1

Inputs
(sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (fabs.f64 #s(approx (* (- a b) (+ b a)) (*.f64 (neg.f64 b) b)))) a)
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64)))))
(/.f64 (sqrt.f64 (fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a)))) a)
(sqrt.f64 (/.f64 (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a))) (.f64 a a)))
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))))
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
(/.f64 (*.f64 (sqrt.f64 (fabs.f64 (-.f64 b a))) (sqrt.f64 (fabs.f64 (+.f64 a b)))) a)
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))))

Outputs
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))))

Calls

7 calls:

20.0ms	b
3.0ms	a
3.0ms	(*.f64 a a)
2.0ms	(fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a)))
2.0ms	(*.f64 b b)

Results

Accuracy	Segments	Branch
100.0%	1	`a`
100.0%	1	`b`
100.0%	1	`(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))`
100.0%	1	`(fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a)))`
100.0%	1	`(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))`
100.0%	1	`(*.f64 a a)`
100.0%	1	`(*.f64 b b)`

Compiler

Compiled 44 to 31 computations (29.5% saved)

regimes18.0ms (0.4%)

Memory

30.0MiB live, 30.0MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

7 calls:

3.0ms	a
3.0ms	b
3.0ms	(*.f64 a a)
2.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
2.0ms	(*.f64 b b)

Results

Accuracy	Segments	Branch
100.0%	1	`a`
100.0%	1	`b`
100.0%	1	`(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))`
100.0%	1	`(fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a)))`
100.0%	1	`(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))`
100.0%	1	`(*.f64 a a)`
100.0%	1	`(*.f64 b b)`

Compiler

Compiled 44 to 31 computations (29.5% saved)

regimes47.0ms (1%)

Memory

-28.6MiB live, 57.4MiB allocated

Counts

5 → 2

Calls

Call 1

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

Outputs

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

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

Calls

7 calls:

23.0ms	(*.f64 b b)
2.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))
2.0ms	a
2.0ms	b
2.0ms	(*.f64 a a)

Results

Accuracy	Segments	Branch
99.3%	2	`a`
99.3%	2	`b`
99.3%	2	`(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))`
99.3%	2	`(fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a)))`
99.3%	2	`(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))`
99.3%	2	`(*.f64 a a)`
99.3%	2	`(*.f64 b b)`

Compiler

Compiled 44 to 31 computations (29.5% saved)

regimes9.0ms (0.2%)

Memory

20.3MiB live, 20.3MiB allocated

Accuracy

Total -59.7b remaining (-3992.7%)

Threshold costs -59.7b (-3992.7%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

7 calls:

1.0ms	a
1.0ms	b
1.0ms	(*.f64 a a)
1.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
1.0ms	(fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a)))

Results

Accuracy	Segments	Branch
97.7%	1	`a`
97.7%	1	`b`
97.7%	1	`(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))`
97.7%	1	`(fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a)))`
97.7%	1	`(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))`
97.7%	1	`(*.f64 a a)`
97.7%	1	`(*.f64 b b)`

Compiler

Compiled 44 to 31 computations (29.5% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	1.846e-320

Compiler

Compiled 16 to 13 computations (18.8% saved)

simplify23.0ms (0.5%)

Memory

-32.5MiB live, 46.6MiB allocated

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative-binary64-+.f64`
8×	`sub-neg-binary64-neg.f64-+.f64--.f64`
4×	`-commutative-binary64-.f64`
4×	`neg-sub0-binary64--.f64-neg.f64`
4×	`neg-mul-1-binary64-*.f64-neg.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	99
1	45	99
2	50	99
3	54	99
4	58	99
5	63	99

Stop Event

1×

saturated

Calls

Call 1

Inputs
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))))
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))))
(if (<=.f64 (.f64 b b) #s(literal 0 binary64)) (sqrt.f64 (fabs.f64 #s(approx (/ (- ( a a) (* b b)) (* a a)) #s(literal 1 binary64)))) (sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64))))))
(sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))))

Outputs
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))))
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 4 binary64))) (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))))
(if (<=.f64 (.f64 b b) #s(literal 0 binary64)) (sqrt.f64 (fabs.f64 #s(approx (/ (- ( a a) (* b b)) (* a a)) #s(literal 1 binary64)))) (sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64))))))
(sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))))

soundness477.0ms (9.9%)

Memory

6.5MiB live, 284.6MiB allocated

Rules

17 628×	`lower-fma.f64`
17 628×	`lower-fma.f32`
5 538×	`lower-*.f64`
5 538×	`lower-*.f32`
5 308×	`lower-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	46
0	14	46
1	58	40
2	431	34
3	4344	34
0	8225	34
0	36	229
0	60	250
1	237	172
2	1682	172
0	8461	172
0	25	990
1	55	876
2	165	876
3	709	876
4	3801	876
0	8016	828

Stop Event

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

Compiler

Compiled 103 to 75 computations (27.2% saved)

preprocess88.0ms (1.8%)

Memory

-3.3MiB live, 115.9MiB allocated

Remove

(abs a)

(abs b)

Compiler

Compiled 268 to 184 computations (31.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze35.0ms (0.7%)

sample1.1s (23.6%)

explain136.0ms (2.8%)

preprocess164.0ms (3.4%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify150.0ms (3.1%)

localize21.0ms (0.4%)

series46.0ms (0.9%)

simplify168.0ms (3.5%)

rewrite216.0ms (4.5%)

eval117.0ms (2.4%)

prune49.0ms (1%)

simplify178.0ms (3.7%)

localize108.0ms (2.2%)

series108.0ms (2.2%)

simplify248.0ms (5.1%)

rewrite227.0ms (4.7%)

eval329.0ms (6.8%)

prune49.0ms (1%)

simplify114.0ms (2.4%)

localize97.0ms (2%)

series44.0ms (0.9%)

simplify133.0ms (2.7%)

rewrite141.0ms (2.9%)

eval112.0ms (2.3%)

prune13.0ms (0.3%)

regimes36.0ms (0.8%)

regimes18.0ms (0.4%)

regimes47.0ms (1%)

regimes9.0ms (0.2%)

bsearch0.0ms (0%)

simplify23.0ms (0.5%)

soundness477.0ms (9.9%)

preprocess88.0ms (1.8%)

end0.0ms (0%)

Profiling