Metrics for Eccentricity of an ellipse

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze12.0ms (0.2%)

Memory

14.6MiB live, 14.6MiB 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)

sample1.3s (22.6%)

Memory

21.0MiB live, 1 095.6MiB allocated

Samples

868.0ms	8 256×	0	valid
82.0ms	829×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 659.0ms

ival-mult: 188.0ms (28.5% of total)

ival-fabs: 150.0ms (22.8% of total)

ival-sqrt: 115.0ms (17.5% of total)

ival-div: 67.0ms (10.2% of total)

ival-<=: 62.0ms (9.4% of total)

ival-sub: 43.0ms (6.5% of total)

ival-and: 17.0ms (2.6% of total)

exact: 11.0ms (1.7% of total)

ival-assert: 4.0ms (0.6% of total)

Bogosity

explain109.0ms (1.9%)

Memory

-19.6MiB live, 140.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
70	-	-	`(/.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	70	0
↳	`(*.f64 b b)`	underflow	198
↳	`(-.f64 (.f64 a a) (.f64 b b))`	underflow	70
↳	`(*.f64 a a)`	underflow	70
↳	`(*.f64 a a)`	underflow	70

Confusion

	Predicted +	Predicted -
+	70	0
-	0	186

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	70	0	0
-	0	0	186

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	186
1	70

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

56.0ms

512×

valid

Compiler

Compiled 119 to 28 computations (76.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-mult: 7.0ms (37.8% of total)

ival-div: 3.0ms (16.2% of total)

ival-sqrt: 3.0ms (16.2% of total)

ival-sub: 2.0ms (10.8% of total)

ival-fabs: 2.0ms (10.8% of total)

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

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

preprocess172.0ms (2.9%)

Memory

-11.3MiB live, 183.2MiB 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: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	72.6%	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

Compiler

Compiled 13 to 8 computations (38.5% saved)

simplify117.0ms (2%)

Memory

13.5MiB live, 135.7MiB 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

localize29.0ms (0.5%)

Memory

-10.9MiB live, 28.2MiB 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	0.0078125	(-.f64 (.f64 a a) (.f64 b b))
accuracy	0.015625	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
accuracy	16.961130073574523	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))

Samples

23.0ms

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 (33.6% of total)

ival-div: 2.0ms (22.4% of total)

ival-sqrt: 2.0ms (22.4% of total)

ival-sub: 1.0ms (11.2% of total)

ival-fabs: 1.0ms (11.2% of total)

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

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

series8.0ms (0.1%)

Memory

11.2MiB live, 11.2MiB 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
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	@	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	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)))

simplify177.0ms (3%)

Memory

19.7MiB live, 178.6MiB 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)

rewrite204.0ms (3.4%)

Memory

-10.8MiB live, 145.2MiB 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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eval115.0ms (1.9%)

Memory: -8.9MiB live, 111.9MiB allocated
Compiler: Compiled 10 830 to 1 903 computations (82.4% saved)

prune28.0ms (0.5%)

Memory

0.9MiB live, 40.3MiB allocated

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	554	7	561
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	554	8	562

Accuracy

100.0%

Counts

562 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	72.4%	(/.f64 (sqrt.f64 (fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a)))) a)
▶	72.6%	(sqrt.f64 (/.f64 (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a))) (.f64 a a)))
▶	100.0%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))) #s(literal -1 binary64))))
✓	72.6%	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
▶	72.2%	(sqrt.f64 (fabs.f64 (.f64 (-.f64 a b) (/.f64 (+.f64 b a) (.f64 a a)))))
	100.0%	(sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a))))
▶	98.0%	(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 167 to 132 computations (21% saved)

simplify186.0ms (3.1%)

Memory

6.9MiB live, 163.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
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 b a)
cost-diff	0	(-.f64 a b)
cost-diff	0	(fabs.f64 (.f64 (-.f64 a b) (/.f64 (+.f64 b a) (.f64 a a))))
cost-diff	0	(sqrt.f64 (fabs.f64 (.f64 (-.f64 a b) (/.f64 (+.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	(fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))
cost-diff	0	(pow.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))) #s(literal -1 binary64))
cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))) #s(literal -1 binary64))))
cost-diff	7168	(/.f64 #s(literal 1 binary64) (pow.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))) #s(literal -1 binary64)))

Rules

15 724×	`lower-fma.f64`
15 724×	`lower-fma.f32`
2 752×	`lower-*.f32`
2 746×	`lower-*.f64`
2 452×	`lower-+.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	32	254
0	55	254
1	96	214
2	192	214
3	380	214
4	832	214
5	2756	214
6	7225	214
0	8405	214

Stop Event

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

Calls

Call 1

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

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

localize198.0ms (3.3%)

Memory

-20.3MiB live, 146.3MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 a a)
accuracy	0	(fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
accuracy	0.015625	(sqrt.f64 (/.f64 (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a))) (.f64 a a)))
accuracy	16.961130073574523	(/.f64 (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a))) (.f64 a a))
accuracy	0	(fabs.f64 (.f64 (-.f64 a b) (/.f64 (+.f64 b a) (.f64 a a))))
accuracy	0.015625	(sqrt.f64 (fabs.f64 (.f64 (-.f64 a b) (/.f64 (+.f64 b a) (.f64 a a)))))
accuracy	0.1796875	(.f64 (-.f64 a b) (/.f64 (+.f64 b a) (.f64 a a)))
accuracy	17.313334775697427	(/.f64 (+.f64 b a) (*.f64 a a))
accuracy	0	(*.f64 (-.f64 a b) (+.f64 b a))
accuracy	0	(fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
accuracy	0.03125	(/.f64 (sqrt.f64 (fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a)))) a)
accuracy	17.121933967217515	(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	0.015625	(sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))))
accuracy	1.3404224947129366	#s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))
accuracy	0.0078125	(pow.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))) #s(literal -1 binary64))
accuracy	0.015625	(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))) #s(literal -1 binary64))))
accuracy	0.03125	(/.f64 #s(literal 1 binary64) (pow.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))) #s(literal -1 binary64)))
accuracy	0.4036712890737681	(pow.f64 (/.f64 b a) #s(literal 2 binary64))

Samples

94.0ms

256×

valid

Compiler

Compiled 250 to 32 computations (87.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 62.0ms

ival-pow: 27.0ms (43.6% of total)

ival-div: 10.0ms (16.1% of total)

ival-sqrt: 7.0ms (11.3% of total)

ival-mult: 6.0ms (9.7% of total)

ival-fabs: 4.0ms (6.5% of total)

ival-sub: 3.0ms (4.8% of total)

ival-pow2: 2.0ms (3.2% of total)

ival-add: 1.0ms (1.6% of total)

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

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

exact: 0.0ms (0% of total)

series43.0ms (0.7%)

Memory

17.3MiB live, 56.0MiB allocated

Counts

21 → 492

Calls

Call 1

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

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

Calls

6 calls:

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

simplify253.0ms (4.3%)

Memory

8.0MiB live, 163.3MiB allocated

Algorithm

1×	egg-herbie

Rules

14 098×	`lower-fma.f64`
14 098×	`lower-fma.f32`
3 060×	`lower-*.f64`
3 060×	`lower-*.f32`
1 468×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	144	4388
1	409	4220
2	1150	4184
3	5464	4184
0	8485	3968

Stop Event

1×	iter limit
1×	node limit

Counts

492 → 483

Calls

Call 1

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

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

rewrite353.0ms (6%)

Memory

11.5MiB live, 252.8MiB allocated

Rules

4 316×	`lower-/.f32`
4 306×	`lower-/.f64`
3 786×	`lower-fma.f64`
3 786×	`lower-fma.f32`
3 758×	`lower-*.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	32	202
0	55	192
1	211	160
2	1407	160
0	8377	160

Stop Event

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

Counts

21 → 1 629

Calls

Call 1

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

Outputs
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eval560.0ms (9.5%)

Memory: -9.5MiB live, 785.3MiB allocated
Compiler: Compiled 62 402 to 6 991 computations (88.8% saved)

prune60.0ms (1%)

Memory

6.5MiB live, 166.0MiB allocated

Pruning

8 alts after pruning (3 fresh and 5 done)

	Pruned	Kept	Total
New	2 850	2	2 852
Fresh	1	1	2
Picked	1	4	5
Done	0	1	1
Total	2 852	8	2 860

Accuracy

100.0%

Counts

2 860 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.2%	(/.f64 (*.f64 (sqrt.f64 (fabs.f64 (-.f64 b a))) (sqrt.f64 (fabs.f64 (+.f64 a b)))) a)
✓	72.4%	(/.f64 (sqrt.f64 (fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a)))) a)
✓	72.6%	(sqrt.f64 (/.f64 (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a))) (.f64 a a)))
✓	72.6%	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
✓	72.2%	(sqrt.f64 (fabs.f64 (.f64 (-.f64 a b) (/.f64 (+.f64 b a) (.f64 a a)))))
▶	100.0%	(sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a))))
✓	98.0%	(sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))))
▶	100.0%	(sqrt.f64 #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))))

Compiler

Compiled 90 to 67 computations (25.6% saved)

simplify131.0ms (2.2%)

Memory

16.0MiB live, 132.6MiB 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	(/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a)
cost-diff	0	#s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a))
cost-diff	0	(fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a)))
cost-diff	0	(sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a))))
cost-diff	0	(fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))
cost-diff	0	(fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))
cost-diff	0	#s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))
cost-diff	0	(sqrt.f64 #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))))

Rules

11 362×	`lower-fma.f32`
11 358×	`lower-fma.f64`
3 140×	`lower-*.f32`
3 138×	`lower-*.f64`
1 480×	`unsub-neg`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	31	207
0	50	207
1	96	201
2	183	201
3	359	201
4	675	201
5	1814	195
6	6394	195
0	8225	195

Stop Event

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

Calls

Call 1

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

localize110.0ms (1.9%)

Memory

-19.1MiB live, 141.7MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(sqrt.f64 (fabs.f64 (+.f64 a b)))
accuracy	0.01171875	(sqrt.f64 (fabs.f64 (-.f64 b a)))
accuracy	0.03125	(/.f64 (*.f64 (sqrt.f64 (fabs.f64 (-.f64 b a))) (sqrt.f64 (fabs.f64 (+.f64 a b)))) a)
accuracy	0.4375	(*.f64 (sqrt.f64 (fabs.f64 (-.f64 b a))) (sqrt.f64 (fabs.f64 (+.f64 a b))))
accuracy	0	(fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a)))
accuracy	0	#s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a))
accuracy	0.015625	(sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a))))
accuracy	0.0234375	(/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a)
accuracy	0	(/.f64 b a)
accuracy	0	(fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))
accuracy	0	#s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))
accuracy	0.015625	(sqrt.f64 #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))))

Samples

81.0ms

256×

valid

Compiler

Compiled 163 to 33 computations (79.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 58.0ms

ival-sqrt: 26.0ms (44.9% of total)

ival-div: 8.0ms (13.8% of total)

ival-mult: 8.0ms (13.8% of total)

ival-fabs: 5.0ms (8.6% of total)

ival-add: 4.0ms (6.9% of total)

ival-sub: 4.0ms (6.9% of total)

ival-neg: 1.0ms (1.7% of total)

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

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

exact: 0.0ms (0% of total)

series46.0ms (0.8%)

Memory

0.6MiB live, 41.0MiB allocated

Counts

14 → 336

Calls

Call 1

Inputs
#s(alt (sqrt.f64 #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))) (patch (sqrt.f64 #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))) #<representation binary64>) () ())
#s(alt #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))) (patch #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))) #<representation binary64>) () ())
#s(alt (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))) (patch (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a)))) (patch (sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a)))) #<representation binary64>) () ())
#s(alt (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a))) (patch (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a))) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a)) (patch #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a)) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a) (patch (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a) #<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 a) (patch (/.f64 b 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 (* (/ 1 a) (sqrt (fabs (* (+ a b) (- a b))))) (taylor 0 b) (#s(alt (sqrt.f64 #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))) (patch (sqrt.f64 #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (/ 1 a) (sqrt (fabs (* (+ a b) (- a b))))) (taylor 0 b) (#s(alt (sqrt.f64 #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))) (patch (sqrt.f64 #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (/ 1 a) (sqrt (fabs (* (+ a b) (- a b))))) (taylor 0 b) (#s(alt (sqrt.f64 #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))) (patch (sqrt.f64 #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (/ 1 a) (sqrt (fabs (* (+ a b) (- a b))))) (taylor 0 b) (#s(alt (sqrt.f64 #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))) (patch (sqrt.f64 #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (/ (fabs (* (+ a b) (- a b))) (pow a 2)) (taylor 0 b) (#s(alt #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))) (patch #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (fabs (* (+ a b) (- a b))) (pow a 2)) (taylor 0 b) (#s(alt #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))) (patch #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (fabs (* (+ a b) (- a b))) (pow a 2)) (taylor 0 b) (#s(alt #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))) (patch #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (fabs (* (+ a b) (- a b))) (pow a 2)) (taylor 0 b) (#s(alt #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))) (patch #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (fabs (- (/ (pow b 2) (pow a 2)) 1)) (taylor 0 b) (#s(alt (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))) (patch (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (fabs (- (/ (pow b 2) (pow a 2)) 1)) (taylor 0 b) (#s(alt (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))) (patch (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (fabs (- (/ (pow b 2) (pow a 2)) 1)) (taylor 0 b) (#s(alt (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))) (patch (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (fabs (- (/ (pow b 2) (pow a 2)) 1)) (taylor 0 b) (#s(alt (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))) (patch (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 b) (#s(alt (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (/ (pow b 2) (pow a 2)) 1) (taylor 0 b) (#s(alt (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (/ (pow b 2) (pow a 2)) 1) (taylor 0 b) (#s(alt (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (/ (pow b 2) (pow a 2)) 1) (taylor 0 b) (#s(alt (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 b a) (/.f64 b 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)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a)))) (patch (sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) 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 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a)))) (patch (sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) 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 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a)))) (patch (sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) 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 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a)))) (patch (sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a)))) #<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)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a))) (patch (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a))) #<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)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a))) (patch (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a))) #<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)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a))) (patch (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a))) #<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)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a))) (patch (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 b) (#s(alt #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a)) (patch #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a)) #<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)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a)) (patch #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a)) #<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)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a)) (patch #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a)) #<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)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a)) (patch #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 b) (#s(alt (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a) (patch (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (pow b 2) (pow a 2)))) (taylor 0 b) (#s(alt (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a) (patch (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (pow b 2) (pow a 2)))) (taylor 0 b) (#s(alt (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a) (patch (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (pow b 2) (pow a 2)))) (taylor 0 b) (#s(alt (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a) (patch (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a) #<representation binary64>) () ())) ())
#s(alt (* (/ 1 a) (sqrt (* (fabs (+ a b)) (fabs (- b a))))) (taylor 0 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 0 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 0 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 0 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 0 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 0 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 0 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 0 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 0 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 0 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 0 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 0 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 0 b) (#s(alt (fabs.f64 (-.f64 b a)) (patch (fabs.f64 (-.f64 b a)) #<representation binary64>) () ())) ())
#s(alt (fabs (- b a)) (taylor 0 b) (#s(alt (fabs.f64 (-.f64 b a)) (patch (fabs.f64 (-.f64 b a)) #<representation binary64>) () ())) ())
#s(alt (fabs (- b a)) (taylor 0 b) (#s(alt (fabs.f64 (-.f64 b a)) (patch (fabs.f64 (-.f64 b a)) #<representation binary64>) () ())) ())
#s(alt (fabs (- b a)) (taylor 0 b) (#s(alt (fabs.f64 (-.f64 b a)) (patch (fabs.f64 (-.f64 b a)) #<representation binary64>) () ())) ())
#s(alt (/ b a) (taylor 0 b) (#s(alt (/.f64 b a) (patch (/.f64 b a) #<representation binary64>) () ())) ())
#s(alt (/ b a) (taylor 0 b) (#s(alt (/.f64 b a) (patch (/.f64 b a) #<representation binary64>) () ())) ())
#s(alt (/ b a) (taylor 0 b) (#s(alt (/.f64 b a) (patch (/.f64 b a) #<representation binary64>) () ())) ())
#s(alt (/ b a) (taylor 0 b) (#s(alt (/.f64 b a) (patch (/.f64 b a) #<representation binary64>) () ())) ())
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#s(alt (sqrt (fabs (+ a b))) (taylor 0 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 0 b) (#s(alt (sqrt.f64 (fabs.f64 (+.f64 a b))) (patch (sqrt.f64 (fabs.f64 (+.f64 a b))) #<representation binary64>) () ())) ())
#s(alt (* (/ 1 a) (sqrt (fabs (* (+ a b) (- a b))))) (taylor inf b) (#s(alt (sqrt.f64 #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))) (patch (sqrt.f64 #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (/ 1 a) (sqrt (fabs (* (+ a b) (- a b))))) (taylor inf b) (#s(alt (sqrt.f64 #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))) (patch (sqrt.f64 #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (/ 1 a) (sqrt (fabs (* (+ a b) (- a b))))) (taylor inf b) (#s(alt (sqrt.f64 #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))) (patch (sqrt.f64 #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (/ 1 a) (sqrt (fabs (* (+ a b) (- a b))))) (taylor inf b) (#s(alt (sqrt.f64 #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))) (patch (sqrt.f64 #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (/ (fabs (* (+ a b) (- a b))) (pow a 2)) (taylor inf b) (#s(alt #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))) (patch #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (fabs (* (+ a b) (- a b))) (pow a 2)) (taylor inf b) (#s(alt #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))) (patch #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (fabs (* (+ a b) (- a b))) (pow a 2)) (taylor inf b) (#s(alt #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))) (patch #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (fabs (* (+ a b) (- a b))) (pow a 2)) (taylor inf b) (#s(alt #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))) (patch #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #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 a) (/.f64 b a) #s(literal -1 binary64))) (patch (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #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 a) (/.f64 b a) #s(literal -1 binary64))) (patch (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #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 a) (/.f64 b a) #s(literal -1 binary64))) (patch (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #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 a) (/.f64 b a) #s(literal -1 binary64))) (patch (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (pow b 2) (pow a 2)) (taylor inf b) (#s(alt (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 b a) (/.f64 b a) #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 a) (/.f64 b a) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 b a) (/.f64 b a) #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 a) (/.f64 b a) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 b a) (/.f64 b a) #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 a) (/.f64 b a) #s(literal -1 binary64)) (patch (fma.f64 (/.f64 b a) (/.f64 b a) #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 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a)))) (patch (sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) 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 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a)))) (patch (sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) 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 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a)))) (patch (sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) 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 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a)))) (patch (sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a)))) #<representation binary64>) () ())) ())
#s(alt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))) (taylor inf b) (#s(alt (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a))) (patch (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a))) #<representation binary64>) () ())) ())
#s(alt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))) (taylor inf b) (#s(alt (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a))) (patch (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a))) #<representation binary64>) () ())) ())
#s(alt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))) (taylor inf b) (#s(alt (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a))) (patch (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a))) #<representation binary64>) () ())) ())
#s(alt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))) (taylor inf b) (#s(alt (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a))) (patch (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (pow b 2) (pow a 2))) (taylor inf b) (#s(alt #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a)) (patch #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a)) #<representation binary64>) () ())) ())
#s(alt (* (pow b 2) (- (/ 1 (pow b 2)) (/ 1 (pow a 2)))) (taylor inf b) (#s(alt #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a)) (patch #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a)) #<representation binary64>) () ())) ())
#s(alt (* (pow b 2) (- (/ 1 (pow b 2)) (/ 1 (pow a 2)))) (taylor inf b) (#s(alt #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a)) (patch #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a)) #<representation binary64>) () ())) ())
#s(alt (* (pow b 2) (- (/ 1 (pow b 2)) (/ 1 (pow a 2)))) (taylor inf b) (#s(alt #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a)) (patch #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (pow b 2) (pow a 2))) (taylor inf b) (#s(alt (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a) (patch (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a) #<representation binary64>) () ())) ())
#s(alt (* (pow b 2) (- (/ 1 (pow b 2)) (/ 1 (pow a 2)))) (taylor inf b) (#s(alt (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a) (patch (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a) #<representation binary64>) () ())) ())
#s(alt (* (pow b 2) (- (/ 1 (pow b 2)) (/ 1 (pow a 2)))) (taylor inf b) (#s(alt (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a) (patch (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a) #<representation binary64>) () ())) ())
#s(alt (* (pow b 2) (- (/ 1 (pow b 2)) (/ 1 (pow a 2)))) (taylor inf b) (#s(alt (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a) (patch (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) 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 (* (/ 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 a) (taylor inf b) (#s(alt (/.f64 b a) (patch (/.f64 b a) #<representation binary64>) () ())) ())
#s(alt (/ b a) (taylor inf b) (#s(alt (/.f64 b a) (patch (/.f64 b a) #<representation binary64>) () ())) ())
#s(alt (/ b a) (taylor inf b) (#s(alt (/.f64 b a) (patch (/.f64 b a) #<representation binary64>) () ())) ())
#s(alt (/ b a) (taylor inf b) (#s(alt (/.f64 b a) (patch (/.f64 b 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 (* (/ 1 a) (sqrt (fabs (* (+ a (* -1 b)) (- a (* -1 b)))))) (taylor -inf b) (#s(alt (sqrt.f64 #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))) (patch (sqrt.f64 #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (/ 1 a) (sqrt (fabs (* (+ a (* -1 b)) (- a (* -1 b)))))) (taylor -inf b) (#s(alt (sqrt.f64 #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))) (patch (sqrt.f64 #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (/ 1 a) (sqrt (fabs (* (+ a (* -1 b)) (- a (* -1 b)))))) (taylor -inf b) (#s(alt (sqrt.f64 #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))) (patch (sqrt.f64 #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))) #<representation binary64>) () ())) ())
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#s(alt (+ 1 (* -1 (/ (pow b 2) (pow a 2)))) (taylor -inf a) (#s(alt (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a) (patch (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) 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 (* (/ 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 a) (taylor -inf a) (#s(alt (/.f64 b a) (patch (/.f64 b a) #<representation binary64>) () ())) ())
#s(alt (/ b a) (taylor -inf a) (#s(alt (/.f64 b a) (patch (/.f64 b a) #<representation binary64>) () ())) ())
#s(alt (/ b a) (taylor -inf a) (#s(alt (/.f64 b a) (patch (/.f64 b a) #<representation binary64>) () ())) ())
#s(alt (/ b a) (taylor -inf a) (#s(alt (/.f64 b a) (patch (/.f64 b 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
22.0ms	a	@	inf	((sqrt (/ (fabs (* (- a b) (+ b a))) (* a a))) (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs (+ (* (/ b a) (/ b a)) -1)) (+ (* (/ b a) (/ b a)) -1) (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (/ (- (* a a) (* b b)) (* a a)) (/ (+ (* (neg b) (/ b a)) a) 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) (sqrt (fabs (+ a b))))
3.0ms	b	@	inf	((sqrt (/ (fabs (* (- a b) (+ b a))) (* a a))) (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs (+ (* (/ b a) (/ b a)) -1)) (+ (* (/ b a) (/ b a)) -1) (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (/ (- (* a a) (* b b)) (* a a)) (/ (+ (* (neg b) (/ b a)) a) 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) (sqrt (fabs (+ a b))))
3.0ms	b	@	-inf	((sqrt (/ (fabs (* (- a b) (+ b a))) (* a a))) (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs (+ (* (/ b a) (/ b a)) -1)) (+ (* (/ b a) (/ b a)) -1) (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (/ (- (* a a) (* b b)) (* a a)) (/ (+ (* (neg b) (/ b a)) a) 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) (sqrt (fabs (+ a b))))
3.0ms	b	@	0	((sqrt (/ (fabs (* (- a b) (+ b a))) (* a a))) (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs (+ (* (/ b a) (/ b a)) -1)) (+ (* (/ b a) (/ b a)) -1) (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (/ (- (* a a) (* b b)) (* a a)) (/ (+ (* (neg b) (/ b a)) a) 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) (sqrt (fabs (+ a b))))
3.0ms	a	@	-inf	((sqrt (/ (fabs (* (- a b) (+ b a))) (* a a))) (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs (+ (* (/ b a) (/ b a)) -1)) (+ (* (/ b a) (/ b a)) -1) (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (/ (- (* a a) (* b b)) (* a a)) (/ (+ (* (neg b) (/ b a)) a) 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) (sqrt (fabs (+ a b))))

simplify93.0ms (1.6%)

Memory

20.1MiB live, 93.3MiB allocated

Algorithm

1×	egg-herbie

Rules

3 586×	`lower-fma.f64`
3 586×	`lower-fma.f32`
2 500×	`lower-*.f64`
2 500×	`lower-*.f32`
1 612×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	3036
1	176	2704
2	402	2704
3	1456	2704
4	4462	2704
0	8279	2590

Stop Event

1×	iter limit
1×	node limit

Counts

336 → 336

Calls

Call 1

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

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

rewrite165.0ms (2.8%)

Memory

-8.2MiB live, 159.5MiB allocated

Rules

5 788×	`lower-/.f32`
5 782×	`lower-/.f64`
4 244×	`lower-fma.f32`
4 240×	`lower-fma.f64`
4 098×	`lower-*.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	31	178
0	50	170
1	206	158
2	1581	158
0	8359	158

Stop Event

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

Counts

14 → 311

Calls

Call 1

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

Outputs
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eval117.0ms (2%)

Memory: -3.0MiB live, 199.5MiB allocated
Compiler: Compiled 11 609 to 1 826 computations (84.3% saved)

prune40.0ms (0.7%)

Memory

-25.3MiB live, 56.6MiB allocated

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	754	1	755
Fresh	0	0	0
Picked	0	3	3
Done	2	3	5
Total	756	7	763

Accuracy

100.0%

Counts

763 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(/.f64 (*.f64 (sqrt.f64 (fabs.f64 (-.f64 b a))) (sqrt.f64 (fabs.f64 (+.f64 a b)))) a)
✓	72.6%	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
✓	72.2%	(sqrt.f64 (fabs.f64 (.f64 (-.f64 a b) (/.f64 (+.f64 b a) (.f64 a a)))))
✓	100.0%	(sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a))))
✓	98.0%	(sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))))
✓	100.0%	(sqrt.f64 #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))))
▶	73.5%	(sqrt.f64 #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) #s(literal -1 binary64)))))

Compiler

Compiled 77 to 59 computations (23.4% saved)

simplify137.0ms (2.3%)

Memory

11.7MiB live, 132.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

9 710×	`lower-fma.f32`
9 708×	`lower-fma.f64`
2 118×	`lower-*.f32`
2 116×	`lower-*.f64`
1 838×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	73
0	21	73
1	42	73
2	80	73
3	147	73
4	256	73
5	504	73
6	1069	73
7	2429	73
8	5962	73
9	7624	73
0	8034	73

Stop Event

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

Calls

Call 1

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

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

localize32.0ms (0.5%)

Memory

14.5MiB live, 53.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) #s(literal -1 binary64)))
accuracy	0	#s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) #s(literal -1 binary64))))
accuracy	0.015625	(sqrt.f64 #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) #s(literal -1 binary64)))))
accuracy	17.488907632422418	(/.f64 b (*.f64 a a))

Samples

24.0ms

256×

valid

Compiler

Compiled 57 to 16 computations (71.9% saved)

Precisions

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

ival-mult: 4.0ms (24.3% of total)

ival-div: 3.0ms (18.2% of total)

ival-add: 3.0ms (18.2% of total)

ival-fabs: 2.0ms (12.2% of total)

ival-sqrt: 2.0ms (12.2% of total)

ival-sub: 1.0ms (6.1% of total)

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

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

exact: 0.0ms (0% of total)

series12.0ms (0.2%)

Memory

-21.2MiB live, 17.4MiB allocated

Counts

5 → 120

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	b	@	inf	((sqrt (/ (fabs (* (- a b) (+ b a))) (* a a))) (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs (+ (* b (/ b (* a a))) -1)) (+ (* b (/ b (* a a))) -1) (/ b (* a a)))
1.0ms	b	@	-inf	((sqrt (/ (fabs (* (- a b) (+ b a))) (* a a))) (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs (+ (* b (/ b (* a a))) -1)) (+ (* b (/ b (* a a))) -1) (/ b (* a a)))
1.0ms	b	@	0	((sqrt (/ (fabs (* (- a b) (+ b a))) (* a a))) (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs (+ (* b (/ b (* a a))) -1)) (+ (* b (/ b (* a a))) -1) (/ b (* a a)))
1.0ms	a	@	0	((sqrt (/ (fabs (* (- a b) (+ b a))) (* a a))) (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs (+ (* b (/ b (* a a))) -1)) (+ (* b (/ b (* a a))) -1) (/ b (* a a)))
1.0ms	a	@	inf	((sqrt (/ (fabs (* (- a b) (+ b a))) (* a a))) (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs (+ (* b (/ b (* a a))) -1)) (+ (* b (/ b (* a a))) -1) (/ b (* a a)))

simplify108.0ms (1.8%)

Memory

-1.7MiB live, 121.9MiB allocated

Algorithm

1×	egg-herbie

Rules

4 642×	`lower-fma.f64`
4 642×	`lower-fma.f32`
2 070×	`lower-*.f64`
2 070×	`lower-*.f32`
1 382×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	1210
1	107	1150
2	297	1150
3	929	1150
4	3433	1150
5	6106	1054
0	8042	988

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

Inputs
(* (/ 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)))))
(/ (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))
(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)
(/ b (pow a 2))
(/ b (pow a 2))
(/ b (pow a 2))
(/ 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)))))
(/ (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))
(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))))
(/ b (pow a 2))
(/ b (pow a 2))
(/ b (pow a 2))
(/ b (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))))))
(/ (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))
(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))))
(/ b (pow a 2))
(/ b (pow a 2))
(/ b (pow a 2))
(/ 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)))))
(/ (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))
(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))
(/ b (pow a 2))
(/ b (pow a 2))
(/ b (pow a 2))
(/ 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)))))
(/ (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))
(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)
(/ b (pow a 2))
(/ b (pow a 2))
(/ b (pow a 2))
(/ b (pow a 2))
(* -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))))))))
(/ (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))
(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)
(/ b (pow a 2))
(/ b (pow a 2))
(/ b (pow a 2))
(/ b (pow a 2))

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

rewrite126.0ms (2.1%)

Memory

24.5MiB live, 143.7MiB allocated

Rules

4 998×	`lower-fma.f32`
4 996×	`lower-fma.f64`
4 532×	`lower-*.f32`
4 530×	`lower-*.f64`
3 812×	`lower-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	67
0	21	67
1	93	67
2	683	63
0	8132	63

Stop Event

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

Counts

5 → 144

Calls

Call 1

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

Outputs
#<batchref>
#<batchref>
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#<batchref>
#<batchref>
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#<batchref>

eval52.0ms (0.9%)

Memory: -11.9MiB live, 65.7MiB allocated
Compiler: Compiled 4 503 to 759 computations (83.1% saved)

prune27.0ms (0.5%)

Memory

-16.5MiB live, 23.0MiB allocated

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	264	0	264
Fresh	0	0	0
Picked	0	1	1
Done	0	6	6
Total	264	7	271

Accuracy

100.0%

Counts

271 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(/.f64 (*.f64 (sqrt.f64 (fabs.f64 (-.f64 b a))) (sqrt.f64 (fabs.f64 (+.f64 a b)))) a)
✓	72.6%	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
✓	72.2%	(sqrt.f64 (fabs.f64 (.f64 (-.f64 a b) (/.f64 (+.f64 b a) (.f64 a a)))))
✓	100.0%	(sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) (/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a))))
✓	98.0%	(sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))))
✓	100.0%	(sqrt.f64 #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))))
✓	73.5%	(sqrt.f64 #s(approx (/ (fabs (* (- a b) (+ b a))) (* a a)) (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) #s(literal -1 binary64)))))

Compiler

Compiled 202 to 120 computations (40.6% saved)

regimes40.0ms (0.7%)

Memory

-2.6MiB live, 40.3MiB allocated

Counts

11 → 1

Calls

Call 1

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

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

Calls

7 calls:

21.0ms	a
4.0ms	b
3.0ms	(*.f64 a a)
3.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
3.0ms	(*.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)

regimes25.0ms (0.4%)

Memory

2.7MiB live, 42.3MiB allocated

Counts

10 → 1

Calls

Call 1

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

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

Calls

7 calls:

7.0ms	b
3.0ms	a
3.0ms	(*.f64 a a)
3.0ms	(*.f64 b b)
3.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

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)

regimes19.0ms (0.3%)

Memory

0.2MiB live, 39.6MiB allocated

Counts

8 → 1

Calls

Call 1

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

4.0ms	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	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

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)

regimes14.0ms (0.2%)

Memory

29.0MiB live, 29.0MiB allocated

Accuracy

Total -17.7b remaining (-1385.3%)

Threshold costs -17.7b (-1385.3%)

Counts

5 → 1

Calls

Call 1

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

Calls

7 calls:

2.0ms	a
2.0ms	b
2.0ms	(*.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
98.0%	1	`a`
98.0%	1	`b`
98.0%	1	`(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))`
98.0%	1	`(fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a)))`
98.0%	1	`(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))`
98.0%	1	`(*.f64 a a)`
98.0%	1	`(*.f64 b b)`

Compiler

Compiled 44 to 31 computations (29.5% saved)

simplify44.0ms (0.7%)

Memory

-27.2MiB live, 53.4MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	74
1	40	74
2	47	74
3	53	74
4	59	74

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness536.0ms (9.1%)

Memory

-6.6MiB live, 276.1MiB allocated

Rules

17 628×	`lower-fma.f64`
17 628×	`lower-fma.f32`
5 538×	`lower-*.f64`
5 538×	`lower-*.f32`
3 746×	`lower-fma.f64`

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	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

Compiler

Compiled 94 to 60 computations (36.2% saved)

preprocess83.0ms (1.4%)

Memory

26.6MiB live, 107.0MiB allocated

Remove

(abs a)

(abs b)

Compiler

Compiled 210 to 164 computations (21.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze12.0ms (0.2%)

sample1.3s (22.6%)

explain109.0ms (1.9%)

preprocess172.0ms (2.9%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify117.0ms (2%)

localize29.0ms (0.5%)

series8.0ms (0.1%)

simplify177.0ms (3%)

rewrite204.0ms (3.4%)

eval115.0ms (1.9%)

prune28.0ms (0.5%)

simplify186.0ms (3.1%)

localize198.0ms (3.3%)

series43.0ms (0.7%)

simplify253.0ms (4.3%)

rewrite353.0ms (6%)

eval560.0ms (9.5%)

prune60.0ms (1%)

simplify131.0ms (2.2%)

localize110.0ms (1.9%)

series46.0ms (0.8%)

simplify93.0ms (1.6%)

rewrite165.0ms (2.8%)

eval117.0ms (2%)

prune40.0ms (0.7%)

simplify137.0ms (2.3%)

localize32.0ms (0.5%)

series12.0ms (0.2%)

simplify108.0ms (1.8%)

rewrite126.0ms (2.1%)

eval52.0ms (0.9%)

prune27.0ms (0.5%)

regimes40.0ms (0.7%)

regimes25.0ms (0.4%)

regimes19.0ms (0.3%)

regimes14.0ms (0.2%)

simplify44.0ms (0.7%)

soundness536.0ms (9.1%)

preprocess83.0ms (1.4%)

end0.0ms (0%)

Profiling