Metrics for Eccentricity of an ellipse

analyze21.0ms (0.4%)

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%	81.3%	0%	0%	0%	2
0%	0%	9.4%	90.6%	0%	0%	0%	3
0%	0%	9.4%	90.6%	0%	0%	0%	4
0%	0%	7%	93%	0%	0%	0%	5
20%	1.2%	4.7%	94.1%	0%	0%	0%	6
25%	1.2%	3.5%	95.3%	0%	0%	0%	7
40%	1.8%	2.6%	95.6%	0%	0%	0%	8
51.9%	2%	1.9%	96%	0%	0%	0%	9
64.7%	2.4%	1.3%	96.3%	0%	0%	0%	10
72.9%	2.6%	1%	96.5%	0%	0%	0%	11
80.2%	2.7%	0.7%	96.6%	0%	0%	0%	12

Compiler

Compiled 26 to 15 computations (42.3% saved)

Precisions

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

ival-mult: 2.0ms (22.8% of total)

ival-<=: 2.0ms (22.8% of total)

ival-div: 1.0ms (11.4% of total)

ival-fabs: 1.0ms (11.4% of total)

ival-sub: 1.0ms (11.4% of total)

ival-sqrt: 1.0ms (11.4% of total)

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

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

sample1.9s (38.2%)

Results

1.1s	8256×	0	valid
87.0ms	803×	0	precondition

Precisions

Click to see histograms. Total time spent on operations: 786.0ms

ival-mult: 200.0ms (25.4% of total)

ival-<=: 192.0ms (24.4% of total)

ival-sqrt: 130.0ms (16.5% of total)

ival-fabs: 90.0ms (11.5% of total)

ival-div: 77.0ms (9.8% of total)

ival-sub: 54.0ms (6.9% of total)

ival-and: 27.0ms (3.4% of total)

const: 12.0ms (1.5% of total)

backward-pass: 4.0ms (0.5% of total)

Bogosity

preprocess230.0ms (4.7%)

Algorithm

2×	egg-herbie

Rules

2436×	`-lowering-.f32`
2436×	`-lowering-.f64`
1626×	`fmsub-define`
1568×	`fmm-def`
1520×	`fnmadd-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	26	62
1	95	56
2	289	50
3	1650	50
4	4880	50
0	8	10
1	25	9
2	59	8
3	137	8
4	298	8
5	837	8
6	3634	8
0	8269	8

Stop Event

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

Calls

Call 1

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

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

Call 2

Inputs
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
(sqrt (fabs (/ (- (* (neg a) (neg a)) (* b b)) (* (neg a) (neg a)))))
(sqrt (fabs (/ (- (* a a) (* (neg b) (neg b))) (* a a))))
(neg (sqrt (fabs (/ (- (* (neg a) (neg a)) (* b b)) (* (neg a) (neg a))))))
(neg (sqrt (fabs (/ (- (* a a) (* (neg b) (neg b))) (* a a)))))
(sqrt (fabs (/ (- (* b b) (* a a)) (* b b))))

Outputs
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
(sqrt (fabs (- 1 (square (/ b a)))))
(sqrt (fabs (/ (- (* (neg a) (neg a)) (* b b)) (* (neg a) (neg a)))))
(sqrt (fabs (- 1 (square (/ b a)))))
(sqrt (fabs (/ (- (* a a) (* (neg b) (neg b))) (* a a))))
(sqrt (fabs (- 1 (square (/ b a)))))
(neg (sqrt (fabs (/ (- (* (neg a) (neg a)) (* b b)) (* (neg a) (neg a))))))
(neg (sqrt (fabs (- 1 (square (/ b a))))))
(neg (sqrt (fabs (/ (- (* a a) (* (neg b) (neg b))) (* a a)))))
(neg (sqrt (fabs (- 1 (square (/ b a))))))
(sqrt (fabs (/ (- (* b b) (* a a)) (* b b))))
(sqrt (fabs (- 1 (square (/ a b)))))

Symmetry

(abs a)

(abs b)

explain106.0ms (2.2%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
66	-	-	`(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))`
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)`
0	-	-	`b`
0	-	-	`a`
0	-	-	`(*.f64 a a)`

Results

76.0ms

512×

valid

Compiler

Compiled 123 to 26 computations (78.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 39.0ms

ival-mult: 25.0ms (64.9% of total)

ival-sqrt: 4.0ms (10.4% of total)

ival-div: 3.0ms (7.8% of total)

ival-fabs: 3.0ms (7.8% of total)

ival-sub: 2.0ms (5.2% of total)

const: 1.0ms (2.6% of total)

backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 13 to 9 computations (30.8% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.2%	(sqrt.f64 (fabs.f64 (+.f64 (/.f64 (/.f64 (*.f64 b b) a) a) #s(literal -1 binary64))))

Compiler

Compiled 13 to 9 computations (30.8% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

14×	`-lowering-.f32`
14×	`-lowering-.f64`
12×	`/-lowering-/.f32`
12×	`/-lowering-/.f64`
8×	`fma-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	42
1	15	38
2	22	34
3	27	34
4	28	34
0	28	34

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize63.0ms (1.3%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 (/.f64 (/.f64 (*.f64 b b) a) a) #s(literal -1 binary64))
✓	accuracy	100.0%	(sqrt.f64 (fabs.f64 (+.f64 (/.f64 (/.f64 (*.f64 b b) a) a) #s(literal -1 binary64))))
✓	accuracy	80.8%	(/.f64 (/.f64 (*.f64 b b) a) a)
✓	accuracy	75.4%	(/.f64 (*.f64 b b) a)

Results

34.0ms

256×

valid

Compiler

Compiled 51 to 10 computations (80.4% saved)

Precisions

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

ival-sqrt: 7.0ms (44.5% of total)

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

ival-mult: 2.0ms (12.7% of total)

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

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

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series8.0ms (0.2%)

Counts

5 → 120

Calls

Call 1

Inputs
#<alt (sqrt (fabs (+ (/ (/ (* b b) a) a) -1)))>
#<alt (fabs (+ (/ (/ (* b b) a) a) -1))>
#<alt (+ (/ (/ (* b b) a) a) -1)>
#<alt (/ (/ (* b b) a) a)>
#<alt (/ (* b b) a)>

Outputs
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt -1>
#<alt (- (/ (pow b 2) (pow a 2)) 1)>
#<alt (- (/ (pow b 2) (pow a 2)) 1)>
#<alt (- (/ (pow b 2) (pow a 2)) 1)>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (* (pow b 2) (- (/ 1 (pow a 2)) (/ 1 (pow b 2))))>
#<alt (* (pow b 2) (- (/ 1 (pow a 2)) (/ 1 (pow b 2))))>
#<alt (* (pow b 2) (- (/ 1 (pow a 2)) (/ 1 (pow b 2))))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (* (pow b 2) (- (/ 1 (pow a 2)) (/ 1 (pow b 2))))>
#<alt (* (pow b 2) (- (/ 1 (pow a 2)) (/ 1 (pow b 2))))>
#<alt (* (pow b 2) (- (/ 1 (pow a 2)) (/ 1 (pow b 2))))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (+ (* -1 (pow a 2)) (pow b 2)) (pow a 2))>
#<alt (/ (+ (* -1 (pow a 2)) (pow b 2)) (pow a 2))>
#<alt (/ (+ (* -1 (pow a 2)) (pow b 2)) (pow a 2))>
#<alt -1>
#<alt (- (/ (pow b 2) (pow a 2)) 1)>
#<alt (- (/ (pow b 2) (pow a 2)) 1)>
#<alt (- (/ (pow b 2) (pow a 2)) 1)>
#<alt -1>
#<alt (- (/ (pow b 2) (pow a 2)) 1)>
#<alt (- (/ (pow b 2) (pow a 2)) 1)>
#<alt (- (/ (pow b 2) (pow a 2)) 1)>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>

Calls

30 calls:

Time	Variable		Point	Expression
1.0ms	b	@	inf	(/ (* b b) a)
1.0ms	b	@	inf	(+ (/ (/ (* b b) a) a) -1)
0.0ms	b	@	0	(+ (/ (/ (* b b) a) a) -1)
0.0ms	a	@	0	(+ (/ (/ (* b b) a) a) -1)
0.0ms	b	@	0	(sqrt (fabs (+ (/ (/ (* b b) a) a) -1)))

rewrite237.0ms (4.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1586×	`/-lowering-/.f32`
1586×	`/-lowering-/.f64`
1492×	`-lowering-.f32`
1492×	`-lowering-.f64`
1218×	`--lowering--.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	37
1	34	33
2	161	29
3	861	29
4	3950	29
0	8215	29

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 286

Calls

Call 1

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

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

simplify153.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

1910×	`-lowering-.f32`
1910×	`-lowering-.f64`
1890×	`sum3-define`
1582×	`fnmadd-define`
1156×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	978
1	36	768
2	81	675
3	183	675
4	453	675
5	1037	675
6	2945	675
7	7679	675
0	8096	675

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

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

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

eval65.0ms (1.3%)

Compiler: Compiled 7344 to 1456 computations (80.2% saved)

prune69.0ms (1.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	403	3	406
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	404	3	407

Accuracy

100.0%

Counts

407 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	4.7%	(sqrt.f64 (fabs.f64 (/.f64 (/.f64 (*.f64 b b) a) a)))
▶	100.0%	(sqrt.f64 (fabs.f64 (+.f64 (/.f64 (/.f64 b (/.f64 a b)) a) #s(literal -1 binary64))))
▶	97.5%	(sqrt.f64 (fabs.f64 #s(literal -1 binary64)))

Compiler

Compiled 29 to 21 computations (27.6% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 (*.f64 b b) a)
✓	cost-diff	0	(/.f64 (/.f64 (*.f64 b b) a) a)
✓	cost-diff	256	(sqrt.f64 (fabs.f64 (/.f64 (/.f64 (*.f64 b b) a) a)))
✓	cost-diff	6400	(fabs.f64 (/.f64 (/.f64 (*.f64 b b) a) a))
✓	cost-diff	0	(/.f64 (/.f64 b (/.f64 a b)) a)
✓	cost-diff	0	(+.f64 (/.f64 (/.f64 b (/.f64 a b)) a) #s(literal -1 binary64))
✓	cost-diff	0	(fabs.f64 (+.f64 (/.f64 (/.f64 b (/.f64 a b)) a) #s(literal -1 binary64)))
✓	cost-diff	0	(sqrt.f64 (fabs.f64 (+.f64 (/.f64 (/.f64 b (/.f64 a b)) a) #s(literal -1 binary64))))
✓	cost-diff	6400	(fabs.f64 #s(literal -1 binary64))
✓	cost-diff	6400	(sqrt.f64 (fabs.f64 #s(literal -1 binary64)))

Rules

62×	`/-lowering-/.f32`
62×	`/-lowering-/.f64`
56×	`-lowering-.f32`
56×	`-lowering-.f64`
50×	`fabs-mul`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	82
1	31	67
2	48	59
3	71	58
4	113	58
5	142	58
6	153	58
7	160	58
8	162	58
0	162	58

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize96.0ms (2%)

Localize:

Found 10 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fabs.f64 (/.f64 (/.f64 (*.f64 b b) a) a))
✓	accuracy	80.8%	(/.f64 (/.f64 (*.f64 b b) a) a)
✓	accuracy	78.7%	(sqrt.f64 (fabs.f64 (/.f64 (/.f64 (*.f64 b b) a) a)))
✓	accuracy	75.4%	(/.f64 (*.f64 b b) a)
✓	accuracy	100.0%	(+.f64 (/.f64 (/.f64 b (/.f64 a b)) a) #s(literal -1 binary64))
✓	accuracy	100.0%	(sqrt.f64 (fabs.f64 (+.f64 (/.f64 (/.f64 b (/.f64 a b)) a) #s(literal -1 binary64))))
✓	accuracy	99.8%	(/.f64 b (/.f64 a b))
✓	accuracy	80.8%	(/.f64 (/.f64 b (/.f64 a b)) a)
✓	accuracy	100.0%	(sqrt.f64 (fabs.f64 #s(literal -1 binary64)))
✓	accuracy	100.0%	(fabs.f64 #s(literal -1 binary64))

Results

75.0ms

256×

valid

Compiler

Compiled 91 to 17 computations (81.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 23.0ms

ival-div: 9.0ms (39.7% of total)

ival-fabs: 5.0ms (22% of total)

ival-sqrt: 5.0ms (22% of total)

ival-mult: 2.0ms (8.8% of total)

ival-add: 1.0ms (4.4% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series4.0ms (0.1%)

Counts

11 → 216

Calls

Call 1

Inputs
#<alt (sqrt (fabs -1))>
#<alt (fabs -1)>
#<alt (sqrt (fabs (+ (/ (/ b (/ a b)) a) -1)))>
#<alt (fabs (+ (/ (/ b (/ a b)) a) -1))>
#<alt (+ (/ (/ b (/ a b)) a) -1)>
#<alt (/ (/ b (/ a b)) a)>
#<alt (fabs (/ (/ (* b b) a) a))>
#<alt (sqrt (fabs (/ (/ (* b b) a) a)))>
#<alt (/ (/ (* b b) a) a)>
#<alt (/ (* b b) a)>
#<alt (/ b (/ a b))>

Outputs
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (sqrt (fabs (- (/ (pow b 2) (pow a 2)) 1)))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt (fabs (- (/ (pow b 2) (pow a 2)) 1))>
#<alt -1>
#<alt (- (/ (pow b 2) (pow a 2)) 1)>
#<alt (- (/ (pow b 2) (pow a 2)) 1)>
#<alt (- (/ (pow b 2) (pow a 2)) 1)>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (* (pow b 2) (- (/ 1 (pow a 2)) (/ 1 (pow b 2))))>
#<alt (* (pow b 2) (- (/ 1 (pow a 2)) (/ 1 (pow b 2))))>
#<alt (* (pow b 2) (- (/ 1 (pow a 2)) (/ 1 (pow b 2))))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (* (pow b 2) (- (/ 1 (pow a 2)) (/ 1 (pow b 2))))>
#<alt (* (pow b 2) (- (/ 1 (pow a 2)) (/ 1 (pow b 2))))>
#<alt (* (pow b 2) (- (/ 1 (pow a 2)) (/ 1 (pow b 2))))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (+ (* -1 (pow a 2)) (pow b 2)) (pow a 2))>
#<alt (/ (+ (* -1 (pow a 2)) (pow b 2)) (pow a 2))>
#<alt (/ (+ (* -1 (pow a 2)) (pow b 2)) (pow a 2))>
#<alt -1>
#<alt (- (/ (pow b 2) (pow a 2)) 1)>
#<alt (- (/ (pow b 2) (pow a 2)) 1)>
#<alt (- (/ (pow b 2) (pow a 2)) 1)>
#<alt -1>
#<alt (- (/ (pow b 2) (pow a 2)) 1)>
#<alt (- (/ (pow b 2) (pow a 2)) 1)>
#<alt (- (/ (pow b 2) (pow a 2)) 1)>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (fabs (/ (pow b 2) (pow a 2)))>
#<alt (fabs (/ (pow b 2) (pow a 2)))>
#<alt (fabs (/ (pow b 2) (pow a 2)))>
#<alt (fabs (/ (pow b 2) (pow a 2)))>
#<alt (fabs (/ (pow b 2) (pow a 2)))>
#<alt (fabs (/ (pow b 2) (pow a 2)))>
#<alt (fabs (/ (pow b 2) (pow a 2)))>
#<alt (fabs (/ (pow b 2) (pow a 2)))>
#<alt (fabs (/ (pow b 2) (pow a 2)))>
#<alt (fabs (/ (pow b 2) (pow a 2)))>
#<alt (fabs (/ (pow b 2) (pow a 2)))>
#<alt (fabs (/ (pow b 2) (pow a 2)))>
#<alt (fabs (/ (pow b 2) (pow a 2)))>
#<alt (fabs (/ (pow b 2) (pow a 2)))>
#<alt (fabs (/ (pow b 2) (pow a 2)))>
#<alt (fabs (/ (pow b 2) (pow a 2)))>
#<alt (fabs (/ (pow b 2) (pow a 2)))>
#<alt (fabs (/ (pow b 2) (pow a 2)))>
#<alt (fabs (/ (pow b 2) (pow a 2)))>
#<alt (fabs (/ (pow b 2) (pow a 2)))>
#<alt (fabs (/ (pow b 2) (pow a 2)))>
#<alt (fabs (/ (pow b 2) (pow a 2)))>
#<alt (fabs (/ (pow b 2) (pow a 2)))>
#<alt (fabs (/ (pow b 2) (pow a 2)))>
#<alt (sqrt (fabs (/ (pow b 2) (pow a 2))))>
#<alt (sqrt (fabs (/ (pow b 2) (pow a 2))))>
#<alt (sqrt (fabs (/ (pow b 2) (pow a 2))))>
#<alt (sqrt (fabs (/ (pow b 2) (pow a 2))))>
#<alt (sqrt (fabs (/ (pow b 2) (pow a 2))))>
#<alt (sqrt (fabs (/ (pow b 2) (pow a 2))))>
#<alt (sqrt (fabs (/ (pow b 2) (pow a 2))))>
#<alt (sqrt (fabs (/ (pow b 2) (pow a 2))))>
#<alt (sqrt (fabs (/ (pow b 2) (pow a 2))))>
#<alt (sqrt (fabs (/ (pow b 2) (pow a 2))))>
#<alt (sqrt (fabs (/ (pow b 2) (pow a 2))))>
#<alt (sqrt (fabs (/ (pow b 2) (pow a 2))))>
#<alt (sqrt (fabs (/ (pow b 2) (pow a 2))))>
#<alt (sqrt (fabs (/ (pow b 2) (pow a 2))))>
#<alt (sqrt (fabs (/ (pow b 2) (pow a 2))))>
#<alt (sqrt (fabs (/ (pow b 2) (pow a 2))))>
#<alt (sqrt (fabs (/ (pow b 2) (pow a 2))))>
#<alt (sqrt (fabs (/ (pow b 2) (pow a 2))))>
#<alt (sqrt (fabs (/ (pow b 2) (pow a 2))))>
#<alt (sqrt (fabs (/ (pow b 2) (pow a 2))))>
#<alt (sqrt (fabs (/ (pow b 2) (pow a 2))))>
#<alt (sqrt (fabs (/ (pow b 2) (pow a 2))))>
#<alt (sqrt (fabs (/ (pow b 2) (pow a 2))))>
#<alt (sqrt (fabs (/ (pow b 2) (pow a 2))))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) (pow a 2))>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>
#<alt (/ (pow b 2) a)>

Calls

54 calls:

Time	Variable		Point	Expression
0.0ms	b	@	inf	(sqrt (fabs (/ (/ (* b b) a) a)))
0.0ms	b	@	0	(sqrt (fabs (/ (/ (* b b) a) a)))
0.0ms	a	@	inf	(sqrt (fabs (/ (/ (* b b) a) a)))
0.0ms	a	@	0	(sqrt (fabs (/ (/ (* b b) a) a)))
0.0ms	b	@	0	(sqrt (fabs (+ (/ (/ b (/ a b)) a) -1)))

rewrite216.0ms (4.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1086×	`-lowering-.f32`
1086×	`-lowering-.f64`
912×	`sum5-define`
800×	`/-lowering-/.f32`
800×	`/-lowering-/.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	69
1	68	56
2	362	48
3	2024	46
4	7062	46
0	8109	46

Stop Event

1×	iter limit
1×	node limit

Counts

11 → 758

Calls

Call 1

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

Outputs
#s(literal 1 binary64)
#s(literal 1 binary64)
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (fabs.f64 (+.f64 #s(literal -1 binary64) (/.f64 b (.f64 a (/.f64 a b))))))))
(sqrt.f64 (fabs.f64 (+.f64 #s(literal -1 binary64) (/.f64 b (*.f64 a (/.f64 a b))))))
(pow.f64 (fabs.f64 (+.f64 #s(literal -1 binary64) (/.f64 b (*.f64 a (/.f64 a b))))) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (fabs.f64 (+.f64 #s(literal -1 binary64) (/.f64 b (*.f64 a (/.f64 a b)))))))
(.f64 #s(literal 1 binary64) (sqrt.f64 (fabs.f64 (+.f64 #s(literal -1 binary64) (/.f64 b (.f64 a (/.f64 a b)))))))
(.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (fabs.f64 (+.f64 #s(literal -1 binary64) (/.f64 b (.f64 a (/.f64 a b)))))))
(exp.f64 (log.f64 (fabs.f64 (+.f64 #s(literal -1 binary64) (/.f64 b (*.f64 a (/.f64 a b)))))))
(fabs.f64 (+.f64 #s(literal -1 binary64) (/.f64 b (*.f64 a (/.f64 a b)))))
(fabs.f64 (+.f64 #s(literal 1 binary64) (/.f64 b (*.f64 a (/.f64 a b)))))
(fabs.f64 (-.f64 (+.f64 #s(literal 1 binary64) (/.f64 b (*.f64 a (/.f64 a b)))) #s(literal 0 binary64)))
(.f64 #s(literal 1 binary64) (fabs.f64 (+.f64 #s(literal -1 binary64) (/.f64 b (.f64 a (/.f64 a b))))))
(.f64 (fabs.f64 (+.f64 #s(literal -1 binary64) (/.f64 b (.f64 a (/.f64 a b))))) #s(literal 1 binary64))
(+.f64 #s(literal -1 binary64) (/.f64 b (*.f64 a (/.f64 a b))))
(+.f64 (+.f64 #s(literal -1 binary64) (/.f64 b (*.f64 a (/.f64 a b)))) #s(literal 0 binary64))
(+.f64 (/.f64 b (*.f64 a (/.f64 a b))) #s(literal -1 binary64))
(+.f64 #s(literal 0 binary64) (+.f64 #s(literal -1 binary64) (/.f64 b (*.f64 a (/.f64 a b)))))
(-.f64 #s(literal -1 binary64) (/.f64 b (*.f64 a (/.f64 a b))))
(-.f64 (+.f64 #s(literal -1 binary64) (/.f64 b (*.f64 a (/.f64 a b)))) #s(literal 0 binary64))
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(/.f64 a (/.f64 (*.f64 a (/.f64 a b)) b))
(/.f64 (/.f64 a b) (.f64 (/.f64 a b) (/.f64 a (.f64 b b))))
(/.f64 (*.f64 b b) a)
(/.f64 (*.f64 b b) (-.f64 #s(literal 0 binary64) a))
(/.f64 (/.f64 b (/.f64 a b)) #s(literal -1 binary64))
(/.f64 (/.f64 b (/.f64 a b)) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) b) (/.f64 a b))
(/.f64 (-.f64 #s(literal 0 binary64) a) (/.f64 (*.f64 a (/.f64 a b)) b))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 b b)) a)
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 b b)) (-.f64 #s(literal 0 binary64) a))
(/.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) (*.f64 b b)))
(/.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal -1 binary64) (*.f64 b b)))
(/.f64 (/.f64 b a) (/.f64 #s(literal 1 binary64) b))
(/.f64 (/.f64 b a) (/.f64 #s(literal -1 binary64) b))
(/.f64 (/.f64 #s(literal -1 binary64) a) (/.f64 #s(literal 1 binary64) (*.f64 b b)))
(/.f64 (/.f64 #s(literal -1 binary64) a) (/.f64 #s(literal -1 binary64) (*.f64 b b)))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 a b)) (.f64 (/.f64 a b) b)) (/.f64 (*.f64 a (/.f64 a b)) b))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) a) (.f64 (/.f64 a b) (.f64 b b))) (.f64 a (/.f64 a b)))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 a b) (/.f64 b (/.f64 a b)))) (/.f64 a b))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 a b)) (.f64 (/.f64 a b) (-.f64 #s(literal 0 binary64) b))) (/.f64 (*.f64 a (/.f64 a b)) b))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) a)) (.f64 (/.f64 a b) (-.f64 #s(literal 0 binary64) (.f64 b b)))) (.f64 a (/.f64 a b)))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (.f64 b b))) (.f64 (/.f64 a b) (/.f64 #s(literal 1 binary64) a))) (.f64 (/.f64 a b) (/.f64 #s(literal 1 binary64) (*.f64 b b))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 a b)) (.f64 a b)) (*.f64 a (/.f64 a b)))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) a) (.f64 a (.f64 b b))) (.f64 a a))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 a (/.f64 b (/.f64 a b)))) a)
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 a b)) (.f64 a (-.f64 #s(literal 0 binary64) b))) (*.f64 a (/.f64 a b)))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) a)) (.f64 a (-.f64 #s(literal 0 binary64) (.f64 b b)))) (-.f64 #s(literal 0 binary64) (.f64 a a)))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (.f64 b b))) (.f64 a (/.f64 #s(literal 1 binary64) a))) (/.f64 a (.f64 b b)))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 a (/.f64 b a))) (/.f64 a b))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 a b)) (.f64 (-.f64 #s(literal 0 binary64) a) b)) (*.f64 a (/.f64 a b)))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) a)) (.f64 (-.f64 #s(literal 0 binary64) a) (.f64 b b))) (.f64 a a))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 a b)) (.f64 (-.f64 #s(literal 0 binary64) a) (-.f64 #s(literal 0 binary64) b))) (*.f64 a (/.f64 a b)))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) a) (.f64 (-.f64 #s(literal 0 binary64) a) (-.f64 #s(literal 0 binary64) (.f64 b b)))) (-.f64 #s(literal 0 binary64) (.f64 a a)))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (-.f64 #s(literal 0 binary64) a) (/.f64 b a))) (/.f64 a b))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (.f64 b b))) (.f64 (-.f64 #s(literal 0 binary64) a) (/.f64 #s(literal -1 binary64) a))) (/.f64 a (.f64 b b)))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) a)) (.f64 (/.f64 a b) (.f64 b b))) (.f64 a (/.f64 a b)))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) a) (.f64 (/.f64 a b) (-.f64 #s(literal 0 binary64) (.f64 b b)))) (.f64 a (/.f64 a b)))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (/.f64 a b) (/.f64 b a))) (/.f64 a (.f64 b b)))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (.f64 b b))) (.f64 (/.f64 a b) (/.f64 #s(literal -1 binary64) a))) (.f64 (/.f64 a b) (/.f64 #s(literal 1 binary64) (*.f64 b b))))
(pow.f64 (/.f64 b (/.f64 a b)) #s(literal 1 binary64))
(pow.f64 (/.f64 a (*.f64 b b)) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 b (/.f64 a b)))
(*.f64 #s(literal 1 binary64) (/.f64 b (/.f64 a b)))
(*.f64 b (/.f64 b a))
(.f64 (.f64 b b) (/.f64 #s(literal 1 binary64) a))
(.f64 (.f64 b b) (/.f64 #s(literal -1 binary64) a))
(*.f64 (/.f64 b (/.f64 a b)) #s(literal -1 binary64))
(*.f64 (/.f64 b (/.f64 a b)) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) b) (/.f64 b a))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 b b)) (/.f64 #s(literal 1 binary64) a))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 b b)) (/.f64 #s(literal -1 binary64) a))
(.f64 (/.f64 #s(literal 1 binary64) a) (.f64 b b))
(.f64 (/.f64 #s(literal 1 binary64) a) (-.f64 #s(literal 0 binary64) (.f64 b b)))
(.f64 (/.f64 #s(literal 1 binary64) a) (pow.f64 (/.f64 #s(literal -1 binary64) (.f64 b b)) #s(literal -1 binary64)))
(*.f64 (/.f64 b a) b)
(*.f64 (/.f64 b a) (-.f64 #s(literal 0 binary64) b))
(.f64 (/.f64 #s(literal -1 binary64) a) (.f64 b b))
(.f64 (/.f64 #s(literal -1 binary64) a) (-.f64 #s(literal 0 binary64) (.f64 b b)))
(.f64 (/.f64 #s(literal -1 binary64) a) (pow.f64 (/.f64 #s(literal -1 binary64) (.f64 b b)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (.f64 b b)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) a))

simplify201.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

1800×	`-lowering-.f32`
1800×	`-lowering-.f64`
1718×	`/-lowering-/.f32`
1718×	`/-lowering-/.f64`
1226×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	1650
1	41	1248
2	91	1059
3	253	1059
4	834	1059
5	2173	1059
6	5602	1059
0	8219	1059

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 216

Calls

Call 1

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

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

eval147.0ms (3%)

Compiler: Compiled 13743 to 2128 computations (84.5% saved)

prune118.0ms (2.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	972	2	974
Fresh	0	0	0
Picked	2	1	3
Done	0	0	0
Total	974	3	977

Accuracy

100.0%

Counts

977 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	6.8%	(/.f64 b a)
✓	100.0%	(sqrt.f64 (fabs.f64 (+.f64 (/.f64 (/.f64 b (/.f64 a b)) a) #s(literal -1 binary64))))
▶	97.5%	#s(literal 1 binary64)

Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 b a)

Rules

2×	`/-lowering-/.f32`
2×	`/-lowering-/.f64`
2×	`1-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	6	6
0	6	6

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
1
(/ b a)
b
a

Outputs
1
#s(literal 1 binary64)
(/ b a)
(/.f64 b a)
b
a

localize21.0ms (0.4%)

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 b a)

Results

16.0ms

256×

valid

Compiler

Compiled 9 to 5 computations (44.4% saved)

Precisions

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

ival-div: 3.0ms (97.2% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series2.0ms (0%)

Counts

1 → 24

Calls

Call 1

Inputs
#<alt (/ b a)>

Outputs
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	b	@	inf	(/ b a)
0.0ms	b	@	-inf	(/ b a)
0.0ms	a	@	-inf	(/ b a)
0.0ms	a	@	inf	(/ b a)
0.0ms	a	@	0	(/ b a)

rewrite96.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

578×	`/-lowering-/.f32`
578×	`/-lowering-/.f64`
552×	`-lowering-.f32`
552×	`-lowering-.f64`
412×	`frac-times`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3
1	11	3
2	48	3
3	190	3
4	585	3
0	2286	3

Stop Event

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

Counts

1 → 47

Calls

Call 1

Inputs
(/ b a)

Outputs
(+.f64 (/.f64 b a) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (/.f64 b a))
(exp.f64 (log.f64 (/.f64 b a)))
(exp.f64 (*.f64 (log.f64 (/.f64 b a)) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 0 binary64) b) a))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 a (/.f64 #s(literal -1 binary64) a))) (/.f64 (-.f64 #s(literal 0 binary64) b) a))
(-.f64 (/.f64 #s(literal 0 binary64) (*.f64 a a)) (/.f64 (-.f64 #s(literal 0 binary64) b) a))
(fma.f64 (/.f64 #s(literal -1 binary64) a) #s(literal 0 binary64) (/.f64 b a))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) b) a))
(/.f64 b a)
(/.f64 a (*.f64 a (/.f64 a b)))
(/.f64 (/.f64 b a) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) b) (-.f64 #s(literal 0 binary64) a))
(/.f64 (-.f64 #s(literal 0 binary64) a) (/.f64 a (/.f64 (-.f64 #s(literal 0 binary64) b) a)))
(/.f64 #s(literal 1 binary64) (/.f64 a b))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 a (/.f64 a b)) a))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 a a) (.f64 b a)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 a (/.f64 #s(literal -1 binary64) a)) (/.f64 a (/.f64 #s(literal -1 binary64) b))))
(/.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 a b)))
(/.f64 (/.f64 #s(literal -1 binary64) a) (/.f64 #s(literal -1 binary64) b))
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) b) a) #s(literal -1 binary64))
(/.f64 (/.f64 a (/.f64 #s(literal -1 binary64) b)) (/.f64 a (/.f64 #s(literal -1 binary64) a)))
(/.f64 (.f64 b a) (.f64 a a))
(/.f64 (/.f64 a (-.f64 #s(literal 0 binary64) a)) (-.f64 #s(literal 0 binary64) (/.f64 a b)))
(/.f64 (/.f64 (*.f64 b a) (-.f64 #s(literal 0 binary64) a)) (-.f64 #s(literal 0 binary64) a))
(/.f64 (/.f64 (/.f64 a (/.f64 #s(literal -1 binary64) b)) (-.f64 #s(literal 0 binary64) a)) a)
(pow.f64 (/.f64 b a) #s(literal 1 binary64))
(pow.f64 (/.f64 a b) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (/.f64 a b)))
(*.f64 b (/.f64 #s(literal 1 binary64) a))
(.f64 a (/.f64 #s(literal 1 binary64) (.f64 a (/.f64 a b))))
(*.f64 (/.f64 b a) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) b) (/.f64 #s(literal -1 binary64) a))
(*.f64 (-.f64 #s(literal 0 binary64) b) (pow.f64 (/.f64 #s(literal -1 binary64) a) #s(literal 1 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 b a))
(*.f64 (/.f64 #s(literal 1 binary64) a) b)
(*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) b) a))
(*.f64 (/.f64 #s(literal -1 binary64) a) (-.f64 #s(literal 0 binary64) b))
(*.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 b (/.f64 a b)))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) b) a) #s(literal -1 binary64))
(.f64 (/.f64 #s(literal -1 binary64) b) (.f64 b (/.f64 (-.f64 #s(literal 0 binary64) b) a)))
(*.f64 (/.f64 a (/.f64 #s(literal -1 binary64) b)) (/.f64 #s(literal 1 binary64) (/.f64 a (/.f64 #s(literal -1 binary64) a))))
(.f64 (.f64 b a) (/.f64 #s(literal 1 binary64) (*.f64 a a)))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) a) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) b))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 b a)) (*.f64 b b))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 a (/.f64 #s(literal -1 binary64) b))) (/.f64 b (/.f64 #s(literal -1 binary64) b)))

simplify27.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

2×	`/-lowering-/.f32`
2×	`/-lowering-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	72
0	3	72

Stop Event

1×	iter limit
1×	saturated

Counts

24 → 24

Calls

Call 1

Inputs
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)

Outputs
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)

eval12.0ms (0.2%)

Compiler: Compiled 445 to 89 computations (80% saved)

prune8.0ms (0.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	71	3	74

Accuracy

100.0%

Counts

74 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	6.8%	(/.f64 b a)
✓	100.0%	(sqrt.f64 (fabs.f64 (+.f64 (/.f64 (/.f64 b (/.f64 a b)) a) #s(literal -1 binary64))))
✓	97.5%	#s(literal 1 binary64)

Compiler

Compiled 74 to 41 computations (44.6% saved)

regimes33.0ms (0.7%)

Counts

7 → 1

Calls

Call 1

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

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

Calls

7 calls:

18.0ms	(*.f64 b b)
3.0ms	a
3.0ms	b
2.0ms	(*.f64 a a)
2.0ms	(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 58 to 31 computations (46.6% saved)

regimes7.0ms (0.1%)

Accuracy

Total -59.3b remaining (-3649.3%)

Threshold costs -59.3b (-3649.3%)

Counts

4 → 1

Calls

Call 1

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

Outputs
#s(literal 1 binary64)

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.5%	1	`a`
97.5%	1	`b`
97.5%	1	`(*.f64 b b)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	12
1	14	12

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.0s (21%)

Rules

2436×	`-lowering-.f32`
2436×	`-lowering-.f64`
1910×	`-lowering-.f32`
1910×	`-lowering-.f64`
1890×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	37
1	34	33
2	161	29
3	861	29
4	3950	29
0	8215	29
0	17	69
1	68	56
2	362	48
3	2024	46
4	7062	46
0	8109	46
0	19	978
1	36	768
2	81	675
3	183	675
4	453	675
5	1037	675
6	2945	675
7	7679	675
0	8096	675
0	8	10
1	25	9
2	59	8
3	137	8
4	298	8
5	837	8
6	3634	8
0	8269	8

Stop Event

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

Compiler

Compiled 61 to 45 computations (26.2% saved)

preprocess22.0ms (0.4%)

Remove

(abs b)

(abs a)

Compiler

Compiled 110 to 72 computations (34.5% saved)

Eccentricity of an ellipse

analyze21.0ms (0.4%)

sample1.9s (38.2%)

preprocess230.0ms (4.7%)

explain106.0ms (2.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify6.0ms (0.1%)

localize63.0ms (1.3%)

series8.0ms (0.2%)

rewrite237.0ms (4.9%)

simplify153.0ms (3.1%)

eval65.0ms (1.3%)

prune69.0ms (1.4%)

simplify10.0ms (0.2%)

localize96.0ms (2%)

series4.0ms (0.1%)

rewrite216.0ms (4.4%)

simplify201.0ms (4.1%)

eval147.0ms (3%)

prune118.0ms (2.4%)

simplify4.0ms (0.1%)

localize21.0ms (0.4%)

series2.0ms (0%)

rewrite96.0ms (2%)

simplify27.0ms (0.6%)

eval12.0ms (0.2%)

prune8.0ms (0.2%)

regimes33.0ms (0.7%)

regimes7.0ms (0.1%)

simplify7.0ms (0.1%)

soundness1.0s (21%)

preprocess22.0ms (0.4%)

end0.0ms (0%)

Profiling