Metrics for Eccentricity of an ellipse

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze13.0ms (0.3%)

Memory

18.9MiB live, 18.9MiB 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)

sample1.4s (29.2%)

Memory

31.3MiB live, 1 248.0MiB allocated

Samples

919.0ms	8 256×	0	valid
61.0ms	782×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 689.0ms

ival-mult: 193.0ms (28% of total)

ival-sub: 112.0ms (16.3% of total)

ival-div: 91.0ms (13.2% of total)

ival-fabs: 89.0ms (12.9% of total)

ival-sqrt: 85.0ms (12.3% of total)

ival-<=: 84.0ms (12.2% of total)

ival-and: 20.0ms (2.9% of total)

exact: 13.0ms (1.9% of total)

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

Bogosity

explain138.0ms (3%)

Memory

-1.5MiB live, 159.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
63	-	-	`(/.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	63	0
↳	`(*.f64 b b)`	underflow	183
↳	`(-.f64 (.f64 a a) (.f64 b b))`	underflow	63
↳	`(*.f64 a a)`	underflow	63
↳	`(*.f64 a a)`	underflow	63

Confusion

	Predicted +	Predicted -
+	63	0
-	0	193

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	63	0	0
-	0	0	193

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	193
1	63

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

38.0ms

512×

valid

Compiler

Compiled 170 to 36 computations (78.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-mult: 7.0ms (35.3% of total)

ival-div: 4.0ms (20.2% of total)

ival-fabs: 3.0ms (15.1% of total)

ival-sqrt: 3.0ms (15.1% of total)

ival-sub: 2.0ms (10.1% of total)

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

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

preprocess181.0ms (3.9%)

Memory

-0.1MiB live, 160.5MiB allocated

Algorithm

1×	egg-herbie

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: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	75.4%	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

Compiler

Compiled 13 to 8 computations (38.5% saved)

simplify140.0ms (3%)

Memory

-13.9MiB live, 144.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

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

localize24.0ms (0.5%)

Memory

18.1MiB live, 57.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a)))
accuracy	0.00390625	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
accuracy	0.01171875	(-.f64 (.f64 a a) (.f64 b b))
accuracy	15.277535814199423	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))

Samples

16.0ms

256×

valid

Compiler

Compiled 104 to 18 computations (82.7% saved)

Precisions

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

ival-mult: 3.0ms (32.5% of total)

ival-div: 2.0ms (21.7% of total)

ival-sqrt: 2.0ms (21.7% of total)

ival-sub: 1.0ms (10.8% of total)

ival-fabs: 1.0ms (10.8% of total)

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

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

series17.0ms (0.4%)

Memory

-16.8MiB live, 30.4MiB allocated

Counts

5 → 13

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

Calls

6 calls:

Time	Variable		Point	Expression
12.0ms	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	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	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)))

simplify154.0ms (3.3%)

Memory

18.5MiB live, 176.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	102
1	55	92
2	165	92
3	710	92
4	3810	92
0	8018	90

Stop Event

1×	iter limit
1×	node limit

Counts

13 → 13

Calls

Call 1

Inputs
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(* -1 (pow b 2))
(- (pow a 2) (pow b 2))
(sqrt (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)) (pow a 2))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
1
(+ 1 (* -1 (/ (pow b 2) (pow a 2))))
(+ (* -1 (pow b 2)) (pow a 2))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ 1 (pow b 2)) (/ 1 (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)))
(* -1 (pow b 2))
(*.f64 (neg.f64 b) b)
(- (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))))
(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)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(*.f64 (-.f64 a b) (+.f64 b 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 (pow b 2)) (pow a 2))
(*.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) (- (/ 1 (pow b 2)) (/ 1 (pow a 2))))
(/.f64 (fma.f64 (neg.f64 b) (/.f64 b a) a) a)

rewrite185.0ms (4%)

Memory

-32.4MiB live, 219.7MiB allocated

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
(.f64 (exp.f64 (log.f64 (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a))))) (pow.f64 a #s(literal -2 binary64)))
(.f64 (.f64 (fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a))) #s(literal 1 binary64)) (pow.f64 a #s(literal -2 binary64)))
(*.f64 (/.f64 (fabs.f64 (+.f64 b a)) a) (/.f64 (fabs.f64 (-.f64 b a)) a))
(*.f64 (fabs.f64 (/.f64 (+.f64 b a) a)) (fabs.f64 (/.f64 (-.f64 a b) a)))
(.f64 (neg.f64 (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a)))) (neg.f64 (pow.f64 a #s(literal -2 binary64))))
(.f64 (fabs.f64 (-.f64 (/.f64 (.f64 b b) a) a)) (fabs.f64 (pow.f64 a #s(literal -1 binary64))))
(.f64 (fabs.f64 (-.f64 (/.f64 (.f64 b b) a) a)) (pow.f64 a #s(literal -1 binary64)))
(.f64 (fabs.f64 (+.f64 b a)) (/.f64 (fabs.f64 (-.f64 b a)) (.f64 a a)))
(.f64 (fabs.f64 (+.f64 b a)) (.f64 (fabs.f64 (-.f64 b a)) (pow.f64 a #s(literal -2 binary64))))
(*.f64 (fabs.f64 (+.f64 b a)) (fabs.f64 (/.f64 (/.f64 (-.f64 a b) a) a)))
(.f64 (pow.f64 a #s(literal -2 binary64)) (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a))))
(*.f64 #s(literal 1 binary64) (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))))
(.f64 (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a))) (pow.f64 a #s(literal -2 binary64)))
(pow.f64 (/.f64 a (fabs.f64 (-.f64 (/.f64 (*.f64 b b) a) a))) #s(literal -1 binary64))
(pow.f64 (/.f64 (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)) #s(literal -1 binary64))
(pow.f64 (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))
(/.f64 (exp.f64 (log.f64 (neg.f64 (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a)))))) (exp.f64 (log.f64 (.f64 (neg.f64 a) a))))
(/.f64 (exp.f64 (log.f64 (fabs.f64 (-.f64 (/.f64 (*.f64 b b) a) a)))) a)
(/.f64 (exp.f64 (log.f64 (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a))))) (.f64 a a))
(/.f64 (/.f64 (neg.f64 (fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a)))) (neg.f64 a)) a)
(/.f64 (/.f64 (neg.f64 (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a)))) #s(literal -1 binary64)) (.f64 a a))
(/.f64 (/.f64 (neg.f64 (fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a)))) a) (neg.f64 a))
(/.f64 (.f64 (fabs.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64)))) (pow.f64 a #s(literal -2 binary64))) (fabs.f64 (fma.f64 b b (.f64 a a))))
(/.f64 (.f64 (fabs.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) (pow.f64 a #s(literal -2 binary64))) (fabs.f64 (fma.f64 (.f64 (fma.f64 b b (*.f64 a a)) a) a (pow.f64 b #s(literal 4 binary64)))))
(/.f64 (.f64 (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a))) (pow.f64 a #s(literal -1 binary64))) a)
(/.f64 (.f64 (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a))) #s(literal -1 binary64)) (*.f64 (neg.f64 a) a))
(/.f64 (.f64 (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a))) #s(literal 1 binary64)) (*.f64 a a))
(/.f64 (neg.f64 (neg.f64 (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a))))) (.f64 a a))
(/.f64 (neg.f64 (fabs.f64 (-.f64 (/.f64 (*.f64 b b) a) a))) (neg.f64 a))
(/.f64 (.f64 (fabs.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64)))) (pow.f64 a #s(literal -1 binary64))) (.f64 (fabs.f64 (fma.f64 b b (*.f64 a a))) a))
(/.f64 (.f64 (fabs.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64)))) #s(literal -1 binary64)) (.f64 (fabs.f64 (fma.f64 b b (.f64 a a))) (.f64 (neg.f64 a) a)))
(/.f64 (.f64 (fabs.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64)))) #s(literal 1 binary64)) (.f64 (fabs.f64 (fma.f64 b b (.f64 a a))) (.f64 a a)))
(/.f64 (.f64 (fabs.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) (pow.f64 a #s(literal -1 binary64))) (.f64 (fabs.f64 (fma.f64 (.f64 (fma.f64 b b (.f64 a a)) a) a (pow.f64 b #s(literal 4 binary64)))) a))
(/.f64 (.f64 (fabs.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) #s(literal -1 binary64)) (.f64 (fabs.f64 (fma.f64 (.f64 (fma.f64 b b (.f64 a a)) a) a (pow.f64 b #s(literal 4 binary64)))) (*.f64 (neg.f64 a) a)))
(/.f64 (.f64 (fabs.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) #s(literal 1 binary64)) (.f64 (fabs.f64 (fma.f64 (.f64 (fma.f64 b b (.f64 a a)) a) a (pow.f64 b #s(literal 4 binary64)))) (*.f64 a a)))
(/.f64 (fabs.f64 (.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (pow.f64 a #s(literal -2 binary64)))) (fabs.f64 (fma.f64 b b (.f64 a a))))
(/.f64 (fabs.f64 (.f64 (pow.f64 a #s(literal -2 binary64)) (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))))) (fabs.f64 (fma.f64 (.f64 (fma.f64 b b (*.f64 a a)) a) a (pow.f64 b #s(literal 4 binary64)))))
(/.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 4 binary64)))) (fabs.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))))
(/.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 6 binary64)))) (fabs.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 4 binary64))) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))))
(/.f64 (fabs.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 (*.f64 b a) #s(literal 2 binary64)))) (pow.f64 a #s(literal 4 binary64)))
(/.f64 (neg.f64 (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a)))) (.f64 (neg.f64 a) a))
(/.f64 (fabs.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64)))) (.f64 (.f64 a a) (fabs.f64 (fma.f64 b b (*.f64 a a)))))
(/.f64 (fabs.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64)))) (fabs.f64 (+.f64 (pow.f64 (*.f64 b a) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))))
(/.f64 (fabs.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) (.f64 (.f64 a a) (fabs.f64 (fma.f64 (.f64 (fma.f64 b b (.f64 a a)) a) a (pow.f64 b #s(literal 4 binary64))))))
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(/.f64 (neg.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) (.f64 (.f64 a a) (neg.f64 (fma.f64 (.f64 (fma.f64 b b (.f64 a a)) a) a (pow.f64 b #s(literal 4 binary64))))))
(/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 (*.f64 b a) #s(literal 2 binary64))) (pow.f64 a #s(literal 4 binary64)))
(/.f64 #s(literal -1 binary64) (.f64 (pow.f64 (.f64 (-.f64 a b) (+.f64 b a)) #s(literal -1 binary64)) (*.f64 (neg.f64 a) a)))
(/.f64 #s(literal -1 binary64) (pow.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) #s(literal -1 binary64)))
(/.f64 (-.f64 a (/.f64 (*.f64 b b) a)) (neg.f64 (neg.f64 a)))
(/.f64 (-.f64 a (/.f64 (*.f64 b b) a)) a)
(/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (.f64 (.f64 (neg.f64 a) a) (neg.f64 (fma.f64 b b (*.f64 a a)))))
(/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (.f64 (neg.f64 (fma.f64 b b (.f64 a a))) (*.f64 (neg.f64 a) a)))
(/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (+.f64 (pow.f64 (*.f64 b a) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))))
(/.f64 (pow.f64 a #s(literal -2 binary64)) (pow.f64 (*.f64 (-.f64 a b) (+.f64 b a)) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 b b (.f64 a a)) (.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (pow.f64 a #s(literal -2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (fma.f64 b b (.f64 a a)) a) a (pow.f64 b #s(literal 4 binary64))) (*.f64 (pow.f64 a #s(literal -2 binary64)) (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))))))
(/.f64 #s(literal 1 binary64) (/.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 4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 4 binary64))) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 6 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 a #s(literal 4 binary64)) (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 (*.f64 b a) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) #s(literal -1 binary64)))
(/.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (.f64 (.f64 (neg.f64 a) a) (neg.f64 (fma.f64 (.f64 (fma.f64 b b (.f64 a a)) a) a (pow.f64 b #s(literal 4 binary64))))))
(/.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 b b (.f64 a a)) a) a (pow.f64 b #s(literal 4 binary64)))) (.f64 (neg.f64 a) a)))
(/.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (fma.f64 (+.f64 (pow.f64 (.f64 b a) #s(literal 2 binary64)) (pow.f64 b #s(literal 4 binary64))) (.f64 a a) (pow.f64 a #s(literal 6 binary64))))
(/.f64 (.f64 (+.f64 b a) (-.f64 b a)) (.f64 (neg.f64 a) a))
(/.f64 (.f64 (-.f64 a b) (+.f64 b a)) (.f64 a a))
(neg.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))
(fma.f64 (neg.f64 (/.f64 b a)) (/.f64 b a) #s(literal 1 binary64))
(fma.f64 (/.f64 b a) (neg.f64 (/.f64 b a)) #s(literal 1 binary64))
(fma.f64 #s(literal -1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64))
(fma.f64 (neg.f64 b) (*.f64 b (pow.f64 a #s(literal -2 binary64))) #s(literal 1 binary64))
(fma.f64 (*.f64 (neg.f64 b) b) (pow.f64 a #s(literal -2 binary64)) #s(literal 1 binary64))
(fma.f64 (pow.f64 a #s(literal -2 binary64)) (*.f64 (neg.f64 b) b) #s(literal 1 binary64))
(fma.f64 (*.f64 b b) (neg.f64 (pow.f64 a #s(literal -2 binary64))) #s(literal 1 binary64))
(fma.f64 b (neg.f64 (*.f64 b (pow.f64 a #s(literal -2 binary64)))) #s(literal 1 binary64))
(-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) #s(literal -1 binary64)) (/.f64 (pow.f64 (/.f64 b a) #s(literal 4 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))))
(-.f64 (pow.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 4 binary64))) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) #s(literal -1 binary64)) (/.f64 (pow.f64 (/.f64 b a) #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 4 binary64))) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))))
(-.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (+.f64 (pow.f64 (.f64 b a) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) (/.f64 (pow.f64 b #s(literal 4 binary64)) (+.f64 (pow.f64 (.f64 b a) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))))
(-.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (fma.f64 (+.f64 (pow.f64 (.f64 b a) #s(literal 2 binary64)) (pow.f64 b #s(literal 4 binary64))) (.f64 a a) (pow.f64 a #s(literal 6 binary64)))) (/.f64 (pow.f64 b #s(literal 6 binary64)) (fma.f64 (+.f64 (pow.f64 (.f64 b a) #s(literal 2 binary64)) (pow.f64 b #s(literal 4 binary64))) (.f64 a a) (pow.f64 a #s(literal 6 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (*.f64 (neg.f64 a) a)) (+.f64 #s(literal -1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))
(-.f64 (/.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))) (.f64 a a)) (/.f64 (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))) (.f64 a a)))
(-.f64 (/.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (fma.f64 (.f64 (fma.f64 b b (.f64 a a)) a) a (pow.f64 b #s(literal 4 binary64)))) (.f64 a a)) (/.f64 (/.f64 (pow.f64 b #s(literal 6 binary64)) (fma.f64 (.f64 (fma.f64 b b (.f64 a a)) a) a (pow.f64 b #s(literal 4 binary64)))) (.f64 a a)))
(-.f64 #s(literal 0 binary64) (+.f64 #s(literal -1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))
(-.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (*.f64 b a) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))))
(-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))
(exp.f64 (*.f64 (neg.f64 (log1p.f64 (neg.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64))))) #s(literal -1 binary64)))
(+.f64 (.f64 (pow.f64 a #s(literal -2 binary64)) (.f64 (neg.f64 b) b)) #s(literal 1 binary64))
(+.f64 (neg.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64))) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64))) #s(literal 1 binary64)))
(+.f64 #s(literal 1 binary64) (.f64 (pow.f64 a #s(literal -2 binary64)) (.f64 (neg.f64 b) b)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)))))
(+.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64))))

eval90.0ms (1.9%)

Memory: 16.2MiB live, 96.8MiB allocated
Compiler: Compiled 9 570 to 1 905 computations (80.1% saved)

prune24.0ms (0.5%)

Memory

-14.5MiB live, 24.1MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	446	4	450
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	447	4	451

Accuracy

100.0%

Counts

451 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	75.6%	(/.f64 (sqrt.f64 (fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a)))) a)
▶	75.4%	(sqrt.f64 (/.f64 (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a))) (.f64 a a)))
▶	97.6%	(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 62 to 41 computations (33.9% saved)

simplify154.0ms (3.3%)

Memory

3.8MiB live, 159.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	27	210
0	44	207
1	81	195
2	149	192
3	313	192
4	656	192
5	2227	192
6	6766	192
0	8158	192

Stop Event

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

Calls

Call 1

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

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

localize60.0ms (1.3%)

Memory

8.5MiB live, 86.6MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0	(fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
accuracy	0.0078125	(*.f64 (-.f64 a b) (+.f64 b a))
accuracy	0.01171875	(/.f64 (sqrt.f64 (fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a)))) a)
accuracy	15.185959066536848	(sqrt.f64 (fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a))))
accuracy	0	(fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
accuracy	0.00390625	(sqrt.f64 (/.f64 (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a))) (.f64 a a)))
accuracy	0.0078125	(*.f64 (-.f64 a b) (+.f64 b a))
accuracy	15.277535814199423	(/.f64 (fabs.f64 (.f64 (-.f64 a b) (+.f64 b a))) (.f64 a a))
accuracy	0	(fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64)))
accuracy	0.00390625	(sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))))
accuracy	1.546476247944076	#s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))
accuracy	0	#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64))))
accuracy	0.00390625	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))))
accuracy	0.010097509768442016	(fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64))
accuracy	0.24609375	(/.f64 (/.f64 b a) a)

Samples

40.0ms

256×

valid

Compiler

Compiled 398 to 52 computations (86.9% saved)

Precisions

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

ival-div: 7.0ms (25.9% of total)

ival-mult: 6.0ms (22.2% of total)

ival-sqrt: 5.0ms (18.5% of total)

ival-fabs: 4.0ms (14.8% of total)

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

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

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

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

exact: 0.0ms (0% of total)

series20.0ms (0.4%)

Memory

-17.8MiB live, 28.4MiB allocated

Counts

15 → 48

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
6.0ms	b	@	inf	((sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs (+ (* (/ (/ b a) a) b) -1)) (+ (* (/ (/ b a) a) b) -1) (sqrt (fabs (/ (- (* a 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 a))) (fabs (* (- a b) (+ b a))) (* (- a b) (+ b a)) (- a b) (/ (sqrt (fabs (* (- a b) (+ b a)))) a) (sqrt (fabs (* (- a b) (+ b a)))) (/ (/ b a) a) (/ (fabs (* (- a b) (+ b a))) (* a a)))
4.0ms	a	@	-inf	((sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs (+ (* (/ (/ b a) a) b) -1)) (+ (* (/ (/ b a) a) b) -1) (sqrt (fabs (/ (- (* a 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 a))) (fabs (* (- a b) (+ b a))) (* (- a b) (+ b a)) (- a b) (/ (sqrt (fabs (* (- a b) (+ b a)))) a) (sqrt (fabs (* (- a b) (+ b a)))) (/ (/ b a) a) (/ (fabs (* (- a b) (+ b a))) (* a a)))
3.0ms	a	@	0	((sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs (+ (* (/ (/ b a) a) b) -1)) (+ (* (/ (/ b a) a) b) -1) (sqrt (fabs (/ (- (* a 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 a))) (fabs (* (- a b) (+ b a))) (* (- a b) (+ b a)) (- a b) (/ (sqrt (fabs (* (- a b) (+ b a)))) a) (sqrt (fabs (* (- a b) (+ b a)))) (/ (/ b a) a) (/ (fabs (* (- a b) (+ b a))) (* a a)))
2.0ms	b	@	-inf	((sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs (+ (* (/ (/ b a) a) b) -1)) (+ (* (/ (/ b a) a) b) -1) (sqrt (fabs (/ (- (* a 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 a))) (fabs (* (- a b) (+ b a))) (* (- a b) (+ b a)) (- a b) (/ (sqrt (fabs (* (- a b) (+ b a)))) a) (sqrt (fabs (* (- a b) (+ b a)))) (/ (/ b a) a) (/ (fabs (* (- a b) (+ b a))) (* a a)))
2.0ms	b	@	0	((sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs (+ (* (/ (/ b a) a) b) -1)) (+ (* (/ (/ b a) a) b) -1) (sqrt (fabs (/ (- (* a 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 a))) (fabs (* (- a b) (+ b a))) (* (- a b) (+ b a)) (- a b) (/ (sqrt (fabs (* (- a b) (+ b a)))) a) (sqrt (fabs (* (- a b) (+ b a)))) (/ (/ b a) a) (/ (fabs (* (- a b) (+ b a))) (* a a)))

simplify122.0ms (2.6%)

Memory

28.9MiB live, 103.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	116	380
1	332	321
2	998	321
3	4640	321
0	8379	312

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 47

Calls

Call 1

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

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

rewrite191.0ms (4.1%)

Memory

3.7MiB live, 156.8MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	27	172
0	44	171
1	170	153
2	1156	138
0	8575	138

Stop Event

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

Counts

15 → 832

Calls

Call 1

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

Outputs
(.f64 (pow.f64 #s(approx (fabs (/ (- ( a a) (* b b)) (* a a))) (fabs.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64)))) #s(literal 1/4 binary64)) (pow.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64)))) #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 (log.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64)))))) #s(literal 1/2 binary64))
(pow.f64 (.f64 #s(approx (fabs (/ (- ( a a) (* b b)) (* a a))) (fabs.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64)))) #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64))))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64)))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64)))) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(exp.f64 (.f64 (log.f64 #s(approx (fabs (/ (- ( a a) (* b b)) (* a a))) (fabs.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64))))) #s(literal 1/2 binary64)))
#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64))))
(.f64 (.f64 (fabs.f64 (/.f64 (fma.f64 (neg.f64 a) a (*.f64 b b)) a)) #s(literal 1 binary64)) (pow.f64 a #s(literal -1 binary64)))
(.f64 (.f64 (pow.f64 a #s(literal -2 binary64)) (fabs.f64 (+.f64 b a))) (fabs.f64 (-.f64 b a)))
(.f64 (.f64 (pow.f64 a #s(literal -2 binary64)) (fabs.f64 (-.f64 b a))) (fabs.f64 (+.f64 b a)))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 b a)) a)) (/.f64 (fabs.f64 (+.f64 b a)) a))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 (fabs.f64 (fma.f64 (neg.f64 a) a (*.f64 b b))))) (neg.f64 (pow.f64 a #s(literal -2 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (fabs.f64 (-.f64 b a))) (*.f64 (fabs.f64 (+.f64 b a)) (pow.f64 a #s(literal -2 binary64))))
(.f64 (/.f64 (neg.f64 (fabs.f64 (-.f64 b a))) #s(literal -1 binary64)) (.f64 (fabs.f64 (+.f64 b a)) (pow.f64 a #s(literal -2 binary64))))
(*.f64 (/.f64 (neg.f64 (fabs.f64 (-.f64 b a))) a) (/.f64 (fabs.f64 (+.f64 b a)) (neg.f64 a)))
(*.f64 (/.f64 (fabs.f64 (-.f64 b a)) (neg.f64 a)) (/.f64 (neg.f64 (fabs.f64 (+.f64 b a))) a))
(.f64 (/.f64 (fabs.f64 (-.f64 b a)) #s(literal -1 binary64)) (/.f64 (neg.f64 (fabs.f64 (+.f64 b a))) (.f64 a a)))
(*.f64 (fabs.f64 (/.f64 (-.f64 a b) a)) (fabs.f64 (/.f64 (+.f64 b a) a)))
(*.f64 (fabs.f64 (/.f64 (+.f64 b a) a)) (fabs.f64 (/.f64 (-.f64 a b) a)))
(*.f64 (pow.f64 (/.f64 a (fabs.f64 (-.f64 b a))) #s(literal -1 binary64)) (pow.f64 (/.f64 a (fabs.f64 (+.f64 b a))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) a) (/.f64 (fabs.f64 (fma.f64 (neg.f64 a) a (.f64 b b))) (neg.f64 a)))
(*.f64 (/.f64 (fabs.f64 (+.f64 b a)) a) (/.f64 (fabs.f64 (-.f64 b a)) a))
(*.f64 (/.f64 (fabs.f64 (-.f64 b a)) a) (/.f64 (fabs.f64 (+.f64 b a)) a))
(.f64 (/.f64 (fabs.f64 (fma.f64 (neg.f64 a) a (.f64 b b))) (neg.f64 a)) (/.f64 #s(literal -1 binary64) a))
(*.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (fabs.f64 (-.f64 #s(literal -1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))))
(*.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)))) (fabs.f64 (pow.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64))))
(*.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (fabs.f64 (+.f64 (+.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))))
(*.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64)))) (fabs.f64 (pow.f64 (+.f64 (+.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) #s(literal -1 binary64))))
(.f64 (fabs.f64 (/.f64 (fma.f64 (neg.f64 a) a (.f64 b b)) a)) (fabs.f64 (pow.f64 a #s(literal -1 binary64))))
(.f64 (fabs.f64 (/.f64 (fma.f64 (neg.f64 a) a (.f64 b b)) a)) (pow.f64 a #s(literal -1 binary64)))
(.f64 (pow.f64 a #s(literal -2 binary64)) (pow.f64 (pow.f64 (fabs.f64 (fma.f64 (neg.f64 a) a (.f64 b b))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 a #s(literal -2 binary64)) (fabs.f64 (fma.f64 (neg.f64 a) a (.f64 b b))))
(.f64 (pow.f64 a #s(literal -1 binary64)) (fabs.f64 (/.f64 (fma.f64 (neg.f64 a) a (.f64 b b)) a)))
(.f64 (neg.f64 (fabs.f64 (fma.f64 (neg.f64 a) a (.f64 b b)))) (neg.f64 (pow.f64 a #s(literal -2 binary64))))
(.f64 (fabs.f64 (+.f64 b a)) (fabs.f64 (.f64 (-.f64 a b) (pow.f64 a #s(literal -2 binary64)))))
(.f64 (fabs.f64 (-.f64 b a)) (.f64 (fabs.f64 (+.f64 b a)) (pow.f64 a #s(literal -2 binary64))))
(*.f64 (sqrt.f64 (fabs.f64 (-.f64 (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 (fabs.f64 (fma.f64 (neg.f64 a) a (.f64 b b))) (pow.f64 a #s(literal -2 binary64)))
(*.f64 #s(literal 1 binary64) (fabs.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64))))
(*.f64 #s(literal -1 binary64) (neg.f64 (fabs.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(pow.f64 (fabs.f64 (/.f64 #s(literal -1 binary64) (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64)))) #s(literal -1 binary64))
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(pow.f64 (/.f64 (*.f64 a a) b) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal -1 binary64) a) (/.f64 (neg.f64 a) b))
(/.f64 (pow.f64 a #s(literal -1 binary64)) (/.f64 a b))
(/.f64 (neg.f64 b) (*.f64 (neg.f64 a) a))
(/.f64 (/.f64 (neg.f64 b) a) (neg.f64 a))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 a a) b))
(/.f64 #s(literal -1 binary64) (*.f64 (/.f64 (neg.f64 a) b) a))
(/.f64 (/.f64 b a) a)
(/.f64 b (*.f64 a a))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (*.f64 a a) b)))
(neg.f64 (*.f64 (pow.f64 a #s(literal -1 binary64)) (/.f64 (neg.f64 b) a)))
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 (/.f64 (neg.f64 b) a) a)))
(neg.f64 (/.f64 (neg.f64 b) (*.f64 a a)))
(neg.f64 (/.f64 b (*.f64 (neg.f64 a) a)))
(neg.f64 (/.f64 (/.f64 (neg.f64 b) a) a))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 (neg.f64 a) a)) (/.f64 b (.f64 (neg.f64 a) a)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 a)) (/.f64 (/.f64 (neg.f64 b) a) a))
(-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (neg.f64 b) a) a))
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 a a) b)) #s(literal -1 binary64)))
(.f64 (.f64 (fabs.f64 (/.f64 (fma.f64 (neg.f64 a) a (*.f64 b b)) a)) #s(literal 1 binary64)) (pow.f64 a #s(literal -1 binary64)))
(.f64 (.f64 (pow.f64 a #s(literal -2 binary64)) (fabs.f64 (+.f64 b a))) (fabs.f64 (-.f64 b a)))
(.f64 (.f64 (pow.f64 a #s(literal -2 binary64)) (fabs.f64 (-.f64 b a))) (fabs.f64 (+.f64 b a)))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 b a)) a)) (/.f64 (fabs.f64 (+.f64 b a)) a))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 (fabs.f64 (fma.f64 (neg.f64 a) a (*.f64 b b))))) (neg.f64 (pow.f64 a #s(literal -2 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (fabs.f64 (-.f64 b a))) (*.f64 (fabs.f64 (+.f64 b a)) (pow.f64 a #s(literal -2 binary64))))
(.f64 (/.f64 (neg.f64 (fabs.f64 (-.f64 b a))) #s(literal -1 binary64)) (.f64 (fabs.f64 (+.f64 b a)) (pow.f64 a #s(literal -2 binary64))))
(*.f64 (/.f64 (neg.f64 (fabs.f64 (-.f64 b a))) a) (/.f64 (fabs.f64 (+.f64 b a)) (neg.f64 a)))
(*.f64 (/.f64 (fabs.f64 (-.f64 b a)) (neg.f64 a)) (/.f64 (neg.f64 (fabs.f64 (+.f64 b a))) a))
(.f64 (/.f64 (fabs.f64 (-.f64 b a)) #s(literal -1 binary64)) (/.f64 (neg.f64 (fabs.f64 (+.f64 b a))) (.f64 a a)))
(*.f64 (fabs.f64 (/.f64 (-.f64 a b) a)) (fabs.f64 (/.f64 (+.f64 b a) a)))
(*.f64 (fabs.f64 (/.f64 (+.f64 b a) a)) (fabs.f64 (/.f64 (-.f64 a b) a)))
(*.f64 (pow.f64 (/.f64 a (fabs.f64 (-.f64 b a))) #s(literal -1 binary64)) (pow.f64 (/.f64 a (fabs.f64 (+.f64 b a))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) a) (/.f64 (fabs.f64 (fma.f64 (neg.f64 a) a (.f64 b b))) (neg.f64 a)))
(*.f64 (/.f64 (fabs.f64 (+.f64 b a)) a) (/.f64 (fabs.f64 (-.f64 b a)) a))
(*.f64 (/.f64 (fabs.f64 (-.f64 b a)) a) (/.f64 (fabs.f64 (+.f64 b a)) a))
(.f64 (/.f64 (fabs.f64 (fma.f64 (neg.f64 a) a (.f64 b b))) (neg.f64 a)) (/.f64 #s(literal -1 binary64) a))
(*.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (fabs.f64 (-.f64 #s(literal -1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))))
(*.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)))) (fabs.f64 (pow.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64))))
(*.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (fabs.f64 (+.f64 (+.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))))
(*.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64)))) (fabs.f64 (pow.f64 (+.f64 (+.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) #s(literal -1 binary64))))
(.f64 (fabs.f64 (/.f64 (fma.f64 (neg.f64 a) a (.f64 b b)) a)) (fabs.f64 (pow.f64 a #s(literal -1 binary64))))
(.f64 (fabs.f64 (/.f64 (fma.f64 (neg.f64 a) a (.f64 b b)) a)) (pow.f64 a #s(literal -1 binary64)))
(.f64 (pow.f64 a #s(literal -2 binary64)) (pow.f64 (pow.f64 (fabs.f64 (fma.f64 (neg.f64 a) a (.f64 b b))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 a #s(literal -2 binary64)) (fabs.f64 (fma.f64 (neg.f64 a) a (.f64 b b))))
(.f64 (pow.f64 a #s(literal -1 binary64)) (fabs.f64 (/.f64 (fma.f64 (neg.f64 a) a (.f64 b b)) a)))
(.f64 (neg.f64 (fabs.f64 (fma.f64 (neg.f64 a) a (.f64 b b)))) (neg.f64 (pow.f64 a #s(literal -2 binary64))))
(.f64 (fabs.f64 (+.f64 b a)) (fabs.f64 (.f64 (-.f64 a b) (pow.f64 a #s(literal -2 binary64)))))
(.f64 (fabs.f64 (-.f64 b a)) (.f64 (fabs.f64 (+.f64 b a)) (pow.f64 a #s(literal -2 binary64))))
(*.f64 (sqrt.f64 (fabs.f64 (-.f64 (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 (fabs.f64 (fma.f64 (neg.f64 a) a (.f64 b b))) (pow.f64 a #s(literal -2 binary64)))
(*.f64 #s(literal 1 binary64) (fabs.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64))))
(*.f64 #s(literal -1 binary64) (neg.f64 (fabs.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(pow.f64 (fabs.f64 (/.f64 #s(literal -1 binary64) (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64)))) #s(literal -1 binary64))
(/.f64 (neg.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64))))) (neg.f64 (fabs.f64 (-.f64 #s(literal -1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))))
(/.f64 (neg.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64))))) (neg.f64 (fabs.f64 (+.f64 (+.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))))
(/.f64 (fabs.f64 (.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (pow.f64 a #s(literal -2 binary64)))) (fabs.f64 (fma.f64 b b (.f64 a a))))
(/.f64 (fabs.f64 (.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (pow.f64 a #s(literal -2 binary64)))) (fabs.f64 (fma.f64 (.f64 b b) (fma.f64 b b (*.f64 a a)) (pow.f64 a #s(literal 4 binary64)))))
(/.f64 (fabs.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 (*.f64 b a) #s(literal 2 binary64)))) (pow.f64 a #s(literal 4 binary64)))
(/.f64 (/.f64 (fabs.f64 (fma.f64 (neg.f64 a) a (*.f64 b b))) (neg.f64 a)) (neg.f64 a))
(/.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)))) (fabs.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))))
(/.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)))) (fabs.f64 (-.f64 #s(literal -1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))))
(/.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64)))) (fabs.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))))
(/.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64)))) (fabs.f64 (+.f64 (+.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))))
(/.f64 (fabs.f64 (-.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 a #s(literal 4 binary64)))) (fabs.f64 (.f64 (.f64 (fma.f64 b b (*.f64 a a)) a) a)))
(/.f64 (fabs.f64 (-.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 a #s(literal 4 binary64)))) (fabs.f64 (+.f64 (pow.f64 (*.f64 b a) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))))
(/.f64 (fabs.f64 (-.f64 (pow.f64 b #s(literal 6 binary64)) (pow.f64 a #s(literal 6 binary64)))) (fabs.f64 (.f64 (fma.f64 (.f64 b b) (fma.f64 b b (.f64 a a)) (pow.f64 a #s(literal 4 binary64))) (.f64 a a))))
(/.f64 (fabs.f64 (-.f64 (pow.f64 b #s(literal 6 binary64)) (pow.f64 a #s(literal 6 binary64)))) (fabs.f64 (fma.f64 (+.f64 (pow.f64 (.f64 b a) #s(literal 2 binary64)) (pow.f64 b #s(literal 4 binary64))) (.f64 a a) (pow.f64 a #s(literal 6 binary64)))))
(/.f64 (fabs.f64 (/.f64 (fma.f64 (neg.f64 a) a (*.f64 b b)) a)) a)
(/.f64 (neg.f64 (fabs.f64 (fma.f64 (neg.f64 a) a (.f64 b b)))) (.f64 (neg.f64 a) a))
(/.f64 (fabs.f64 (fma.f64 (neg.f64 a) a (.f64 b b))) (.f64 a a))
(/.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 #s(literal -1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))) (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (+.f64 (+.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))) (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (fabs.f64 (/.f64 #s(literal -1 binary64) (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (fabs.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(neg.f64 (/.f64 (/.f64 (fabs.f64 (fma.f64 (neg.f64 a) a (*.f64 b b))) (neg.f64 a)) a))
(neg.f64 (/.f64 #s(literal -1 binary64) (fabs.f64 (/.f64 #s(literal -1 binary64) (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64))))))
(neg.f64 (/.f64 (fabs.f64 (/.f64 (fma.f64 (neg.f64 a) a (*.f64 b b)) a)) (neg.f64 a)))
(neg.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (fabs.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64))))))
(neg.f64 (neg.f64 (fabs.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (*.f64 (neg.f64 a) a)) (neg.f64 (fabs.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(-.f64 #s(literal 0 binary64) (neg.f64 (fabs.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(fabs.f64 (-.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) #s(literal 0 binary64)))
(fabs.f64 (-.f64 (pow.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)))))
(fabs.f64 (-.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal 0 binary64)))
(fabs.f64 (-.f64 (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))))
(exp.f64 (*.f64 (log.f64 (fabs.f64 (/.f64 #s(literal -1 binary64) (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64))))) #s(literal -1 binary64)))

eval200.0ms (4.3%)

Memory: -2.0MiB live, 276.3MiB allocated
Compiler: Compiled 33 145 to 4 260 computations (87.1% saved)

prune36.0ms (0.8%)

Memory

11.6MiB live, 48.6MiB allocated

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	1 119	3	1 122
Fresh	0	0	0
Picked	2	2	4
Done	0	0	0
Total	1 121	5	1 126

Accuracy

100.0%

Counts

1 126 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	4.7%	(/.f64 (sqrt.f64 (fabs.f64 #s(approx (* (- a b) (+ b a)) (*.f64 (neg.f64 b) b)))) a)
✓	97.6%	(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)))))
▶	76.2%	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64)))))
▶	6.5%	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 #s(approx (+ (* (/ (/ b a) a) b) -1) (*.f64 (/.f64 b a) (/.f64 b a))))))

Compiler

Compiled 109 to 67 computations (38.5% saved)

simplify142.0ms (3%)

Memory

-27.8MiB live, 93.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	33	246
0	48	242
1	83	234
2	156	230
3	354	230
4	742	230
5	2326	230
6	6986	230
0	8147	230

Stop Event

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

Calls

Call 1

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

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

localize63.0ms (1.3%)

Memory

23.3MiB live, 61.8MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0	(fabs.f64 #s(approx (* (- a b) (+ b a)) (*.f64 (neg.f64 b) b)))
accuracy	0.01171875	(/.f64 (sqrt.f64 (fabs.f64 #s(approx (* (- a b) (+ b a)) (*.f64 (neg.f64 b) b)))) a)
accuracy	15.185959066536848	(sqrt.f64 (fabs.f64 #s(approx (* (- a b) (+ b a)) (*.f64 (neg.f64 b) b))))
accuracy	45.352232854355684	#s(approx (* (- a b) (+ b a)) (*.f64 (neg.f64 b) b))
accuracy	0	#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64))))
accuracy	0.00390625	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64)))))
accuracy	0.010097509768442016	(fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64))
accuracy	15.499391310841308	(/.f64 b (*.f64 a a))
accuracy	0	#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 #s(approx (+ (* (/ (/ b a) a) b) -1) (*.f64 (/.f64 b a) (/.f64 b a)))))
accuracy	0.00390625	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 #s(approx (+ (* (/ (/ b a) a) b) -1) (*.f64 (/.f64 b a) (/.f64 b a))))))
accuracy	0.38900375976844204	(*.f64 (/.f64 b a) (/.f64 b a))
accuracy	62.47462786026734	#s(approx (+ (* (/ (/ b a) a) b) -1) (*.f64 (/.f64 b a) (/.f64 b a)))

Samples

47.0ms

256×

valid

Compiler

Compiled 402 to 63 computations (84.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 34.0ms

ival-mult: 10.0ms (29% of total)

ival-div: 9.0ms (26.1% of total)

ival-fabs: 5.0ms (14.5% of total)

ival-add: 3.0ms (8.7% of total)

ival-sqrt: 3.0ms (8.7% of total)

ival-sub: 2.0ms (5.8% of total)

ival-neg: 1.0ms (2.9% of total)

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

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

exact: 0.0ms (0% of total)

series12.0ms (0.3%)

Memory

-25.8MiB live, 12.7MiB allocated

Counts

14 → 31

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	b	@	-inf	((sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs (+ (* (/ (/ b a) a) b) -1)) (+ (* (/ (/ b a) a) b) -1) (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs (+ (* (/ b (* a a)) b) -1)) (+ (* (/ b (* a a)) b) -1) (/ (sqrt (fabs (* (- a b) (+ b a)))) a) (sqrt (fabs (* (- a b) (+ b a)))) (fabs (* (- a b) (+ b a))) (* (- a b) (+ b a)) (* (/ b a) (/ b a)) (/ b (* a a)))
2.0ms	b	@	inf	((sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs (+ (* (/ (/ b a) a) b) -1)) (+ (* (/ (/ b a) a) b) -1) (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs (+ (* (/ b (* a a)) b) -1)) (+ (* (/ b (* a a)) b) -1) (/ (sqrt (fabs (* (- a b) (+ b a)))) a) (sqrt (fabs (* (- a b) (+ b a)))) (fabs (* (- a b) (+ b a))) (* (- a b) (+ b a)) (* (/ b a) (/ b a)) (/ b (* a a)))
2.0ms	a	@	0	((sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs (+ (* (/ (/ b a) a) b) -1)) (+ (* (/ (/ b a) a) b) -1) (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs (+ (* (/ b (* a a)) b) -1)) (+ (* (/ b (* a a)) b) -1) (/ (sqrt (fabs (* (- a b) (+ b a)))) a) (sqrt (fabs (* (- a b) (+ b a)))) (fabs (* (- a b) (+ b a))) (* (- a b) (+ b a)) (* (/ b a) (/ b a)) (/ b (* a a)))
1.0ms	a	@	-inf	((sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs (+ (* (/ (/ b a) a) b) -1)) (+ (* (/ (/ b a) a) b) -1) (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs (+ (* (/ b (* a a)) b) -1)) (+ (* (/ b (* a a)) b) -1) (/ (sqrt (fabs (* (- a b) (+ b a)))) a) (sqrt (fabs (* (- a b) (+ b a)))) (fabs (* (- a b) (+ b a))) (* (- a b) (+ b a)) (* (/ b a) (/ b a)) (/ b (* a a)))
1.0ms	b	@	0	((sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs (+ (* (/ (/ b a) a) b) -1)) (+ (* (/ (/ b a) a) b) -1) (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs (+ (* (/ b (* a a)) b) -1)) (+ (* (/ b (* a a)) b) -1) (/ (sqrt (fabs (* (- a b) (+ b a)))) a) (sqrt (fabs (* (- a b) (+ b a)))) (fabs (* (- a b) (+ b a))) (* (- a b) (+ b a)) (* (/ b a) (/ b a)) (/ b (* a a)))

simplify148.0ms (3.2%)

Memory

16.5MiB live, 106.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	97	300
1	283	250
2	818	244
3	3886	238
0	8754	230

Stop Event

1×	iter limit
1×	node limit

Counts

31 → 31

Calls

Call 1

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

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

rewrite172.0ms (3.7%)

Memory

4.0MiB live, 123.4MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	33	227
0	48	205
1	180	189
2	1176	189
0	8482	189

Stop Event

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

Counts

14 → 359

Calls

Call 1

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

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

eval52.0ms (1.1%)

Memory: -13.8MiB live, 62.7MiB allocated
Compiler: Compiled 11 133 to 1 715 computations (84.6% saved)

prune6.0ms (0.1%)

Memory

17.2MiB live, 17.2MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	372	1	373
Fresh	0	0	0
Picked	0	3	3
Done	0	2	2
Total	372	6	378

Accuracy

100.0%

Counts

378 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	4.7%	(/.f64 (sqrt.f64 (fabs.f64 #s(approx (* (- a b) (+ b a)) (*.f64 (neg.f64 b) b)))) a)
✓	97.6%	(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)))))
✓	76.2%	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64)))))
▶	3.9%	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 #s(approx (+ (* (/ (/ b a) a) b) -1) (/.f64 (.f64 b b) (.f64 a a))))))
✓	6.5%	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 #s(approx (+ (* (/ (/ b a) a) b) -1) (*.f64 (/.f64 b a) (/.f64 b a))))))

Compiler

Compiled 141 to 86 computations (39% saved)

simplify138.0ms (3%)

Memory

3.7MiB live, 84.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	113
0	24	113
1	49	109
2	100	109
3	229	109
4	526	109
5	1822	109
6	5835	109
0	8521	103

Stop Event

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

Calls

Call 1

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

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

localize53.0ms (1.1%)

Memory

-5.8MiB live, 32.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 #s(approx (+ (* (/ (/ b a) a) b) -1) (/.f64 (.f64 b b) (.f64 a a)))))
accuracy	0.00390625	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 #s(approx (+ (* (/ (/ b a) a) b) -1) (/.f64 (.f64 b b) (.f64 a a))))))
accuracy	30.738067898752526	(/.f64 (.f64 b b) (.f64 a a))
accuracy	62.47462786026734	#s(approx (+ (* (/ (/ b a) a) b) -1) (/.f64 (.f64 b b) (.f64 a a)))

Samples

44.0ms

256×

valid

Compiler

Compiled 174 to 36 computations (79.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-div: 24.0ms (67.4% of total)

ival-mult: 5.0ms (14% of total)

ival-fabs: 2.0ms (5.6% of total)

ival-sqrt: 2.0ms (5.6% of total)

ival-add: 1.0ms (2.8% of total)

ival-sub: 1.0ms (2.8% of total)

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

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

exact: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory

4.7MiB live, 4.7MiB allocated

Counts

5 → 8

Calls

Call 1

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

Outputs
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(fabs (- (/ (pow b 2) (pow a 2)) 1))
(/ (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) (- (/ 1 (pow a 2)) (/ 1 (pow b 2))))

Calls

6 calls:

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

simplify100.0ms (2.1%)

Memory

-10.7MiB live, 65.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	72
1	42	66
2	107	66
3	256	66
4	703	66
5	2612	66
6	6932	66
0	8089	60

Stop Event

1×	iter limit
1×	node limit

Counts

8 → 8

Calls

Call 1

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

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

rewrite133.0ms (2.9%)

Memory

-16.9MiB live, 103.2MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	105
0	24	105
1	106	79
2	850	79
0	9071	79

Stop Event

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

Counts

5 → 86

Calls

Call 1

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

Outputs
(.f64 (pow.f64 #s(approx (fabs (/ (- ( a a) (* b b)) (* a a))) (fabs.f64 #s(approx (+ (* (/ (/ b a) a) b) -1) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))) #s(literal 1/4 binary64)) (pow.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 #s(approx (+ (* (/ (/ b a) a) b) -1) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))) #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 (log.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 #s(approx (+ (* (/ (/ b a) a) b) -1) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))))) #s(literal 1/2 binary64))
(pow.f64 (.f64 #s(approx (fabs (/ (- ( a a) (* b b)) (* a a))) (fabs.f64 #s(approx (+ (* (/ (/ b a) a) b) -1) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))) #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 #s(approx (+ (* (/ (/ b a) a) b) -1) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 #s(approx (+ (* (/ (/ b a) a) b) -1) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 #s(approx (+ (* (/ (/ b a) a) b) -1) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 #s(approx (+ (* (/ (/ b a) a) b) -1) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))))
(exp.f64 (.f64 (log.f64 #s(approx (fabs (/ (- ( a a) (* b b)) (* a a))) (fabs.f64 #s(approx (+ (* (/ (/ b a) a) b) -1) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))))) #s(literal 1/2 binary64)))
#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 #s(approx (+ (* (/ (/ b a) a) b) -1) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))))
(.f64 #s(literal 1 binary64) (fabs.f64 #s(approx (+ ( (/ (/ b a) a) b) -1) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))))
(fabs.f64 (-.f64 #s(approx (+ (* (/ (/ b a) a) b) -1) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) #s(literal 0 binary64)))
(fabs.f64 (neg.f64 #s(approx (+ (* (/ (/ b a) a) b) -1) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))))
(fabs.f64 #s(approx (+ (* (/ (/ b a) a) b) -1) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))
(.f64 #s(literal 1 binary64) #s(approx (+ ( (/ (/ b a) a) b) -1) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))
(.f64 #s(literal -1 binary64) (neg.f64 #s(approx (+ ( (/ (/ b a) a) b) -1) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))))
#s(approx (+ (* (/ (/ b a) a) b) -1) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))
(neg.f64 (neg.f64 #s(approx (+ (* (/ (/ b a) a) b) -1) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))))
(-.f64 #s(literal 0 binary64) (neg.f64 #s(approx (+ (* (/ (/ b a) a) b) -1) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))))
(*.f64 (pow.f64 (pow.f64 (/.f64 a b) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (/.f64 a b) #s(literal 2 binary64)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 b a) #s(literal 1 binary64)) (pow.f64 (/.f64 b a) #s(literal 1 binary64)))
(*.f64 (/.f64 (/.f64 (neg.f64 b) a) #s(literal -1 binary64)) (/.f64 b a))
(*.f64 (/.f64 (/.f64 b a) #s(literal -1 binary64)) (/.f64 (neg.f64 b) a))
(*.f64 (/.f64 b (fabs.f64 a)) (/.f64 b (fabs.f64 a)))
(*.f64 (/.f64 (neg.f64 b) #s(literal -1 binary64)) (/.f64 (/.f64 b a) a))
(.f64 (/.f64 b #s(literal -1 binary64)) (/.f64 b (.f64 (neg.f64 a) a)))
(.f64 (/.f64 (.f64 b b) (fabs.f64 a)) (/.f64 #s(literal 1 binary64) (fabs.f64 a)))
(.f64 (/.f64 b (.f64 (neg.f64 a) a)) (*.f64 b #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) a) (/.f64 (.f64 (neg.f64 b) b) a))
(.f64 (/.f64 (.f64 (neg.f64 b) b) a) (/.f64 #s(literal -1 binary64) a))
(.f64 (.f64 (/.f64 b a) b) (*.f64 (pow.f64 a #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 (/.f64 b a) b) (pow.f64 a #s(literal -1 binary64)))
(*.f64 (pow.f64 a #s(literal -2 binary64)) (/.f64 b (pow.f64 b #s(literal -1 binary64))))
(*.f64 (pow.f64 a #s(literal -2 binary64)) (pow.f64 (pow.f64 b #s(literal -2 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 a #s(literal -2 binary64)) (.f64 b b))
(*.f64 (pow.f64 a #s(literal -1 binary64)) (/.f64 (/.f64 b a) (pow.f64 b #s(literal -1 binary64))))
(.f64 (pow.f64 a #s(literal -1 binary64)) (.f64 (/.f64 b a) b))
(*.f64 (neg.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)))
(.f64 (.f64 (neg.f64 b) b) (*.f64 (neg.f64 (pow.f64 a #s(literal -2 binary64))) #s(literal 1 binary64)))
(.f64 (.f64 (neg.f64 b) b) (*.f64 (pow.f64 a #s(literal -2 binary64)) #s(literal -1 binary64)))
(.f64 (.f64 (neg.f64 b) b) (neg.f64 (pow.f64 a #s(literal -2 binary64))))
(.f64 (neg.f64 b) (.f64 (/.f64 (/.f64 b a) a) #s(literal -1 binary64)))
(.f64 (neg.f64 b) (/.f64 b (.f64 (neg.f64 a) a)))
(*.f64 (/.f64 (neg.f64 b) a) (/.f64 (/.f64 #s(literal -1 binary64) a) (pow.f64 b #s(literal -1 binary64))))
(.f64 (/.f64 (neg.f64 b) a) (.f64 (/.f64 b a) #s(literal -1 binary64)))
(*.f64 (/.f64 (neg.f64 b) a) (/.f64 (neg.f64 b) a))
(.f64 (.f64 b b) (*.f64 (pow.f64 a #s(literal -2 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 b b) (neg.f64 (*.f64 (pow.f64 a #s(literal -2 binary64)) #s(literal -1 binary64))))
(.f64 (.f64 b b) (*.f64 (/.f64 #s(literal -1 binary64) a) (/.f64 #s(literal -1 binary64) a)))
(.f64 (.f64 b b) (pow.f64 (/.f64 #s(literal -1 binary64) a) #s(literal 2 binary64)))
(.f64 (.f64 b b) (pow.f64 a #s(literal -2 binary64)))
(*.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64))))
(*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64))
(.f64 (/.f64 (/.f64 b a) a) (neg.f64 (.f64 b #s(literal -1 binary64))))
(*.f64 (/.f64 (/.f64 b a) a) (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal -1 binary64))))
(*.f64 (/.f64 (/.f64 b a) a) b)
(.f64 (/.f64 b a) (neg.f64 (.f64 (/.f64 b a) #s(literal -1 binary64))))
(*.f64 (/.f64 b a) (/.f64 (pow.f64 a #s(literal -1 binary64)) (pow.f64 b #s(literal -1 binary64))))
(*.f64 (/.f64 b a) (/.f64 b a))
(.f64 b (.f64 (/.f64 (/.f64 b a) a) #s(literal 1 binary64)))
(.f64 b (neg.f64 (.f64 (/.f64 (/.f64 b a) a) #s(literal -1 binary64))))
(*.f64 b (/.f64 (/.f64 b a) a))
(pow.f64 (pow.f64 (/.f64 a b) #s(literal 2 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 a b) #s(literal -2 binary64))
(pow.f64 (/.f64 b a) #s(literal 2 binary64))
(/.f64 (neg.f64 (.f64 (.f64 (/.f64 b a) b) #s(literal -1 binary64))) a)
(/.f64 (neg.f64 (.f64 (.f64 (neg.f64 b) b) #s(literal -1 binary64))) (*.f64 (neg.f64 a) a))
(/.f64 (.f64 (.f64 (/.f64 b a) b) #s(literal -1 binary64)) (neg.f64 a))
(/.f64 (.f64 (.f64 (neg.f64 b) b) #s(literal -1 binary64)) (*.f64 a a))
(/.f64 (.f64 (.f64 b b) #s(literal -1 binary64)) (*.f64 (neg.f64 a) a))
(/.f64 (/.f64 (*.f64 (neg.f64 b) b) a) (neg.f64 a))
(/.f64 (*.f64 (/.f64 b a) b) a)
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 a b) #s(literal 2 binary64)))
(/.f64 (.f64 (neg.f64 b) b) (.f64 (neg.f64 a) a))
(/.f64 (neg.f64 b) (*.f64 (/.f64 (neg.f64 a) b) a))
(/.f64 (/.f64 (neg.f64 b) a) (/.f64 (neg.f64 a) b))
(/.f64 (.f64 b b) (.f64 a a))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (/.f64 a b) #s(literal 2 binary64))))
(/.f64 (/.f64 b a) (/.f64 a b))
(/.f64 b (/.f64 (*.f64 a a) b))
(neg.f64 (*.f64 (neg.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64))) #s(literal 1 binary64)))
(neg.f64 (neg.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (*.f64 (neg.f64 a) a)) (neg.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64))))
(-.f64 #s(literal 0 binary64) (neg.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 a b) #s(literal 2 binary64))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 b a)) #s(literal 2 binary64)))
(exp.f64 (log.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64))))

eval11.0ms (0.2%)

Memory: 16.1MiB live, 16.1MiB allocated
Compiler: Compiled 3 123 to 489 computations (84.3% saved)

prune5.0ms (0.1%)

Memory

9.1MiB live, 9.1MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	92	6	98

Accuracy

100.0%

Counts

98 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	4.7%	(/.f64 (sqrt.f64 (fabs.f64 #s(approx (* (- a b) (+ b a)) (*.f64 (neg.f64 b) b)))) a)
✓	97.6%	(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)))))
✓	76.2%	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64)))))
✓	3.9%	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 #s(approx (+ (* (/ (/ b a) a) b) -1) (/.f64 (.f64 b b) (.f64 a a))))))
✓	6.5%	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 #s(approx (+ (* (/ (/ b a) a) b) -1) (*.f64 (/.f64 b a) (/.f64 b a))))))

Compiler

Compiled 319 to 147 computations (53.9% saved)

regimes41.0ms (0.9%)

Memory

-15.1MiB live, 24.1MiB allocated

Counts

9 → 1

Calls

Call 1

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

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:

23.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
3.0ms	b
3.0ms	a
3.0ms	(*.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)

regimes17.0ms (0.4%)

Memory

22.7MiB live, 22.7MiB allocated

Counts

7 → 2

Calls

Call 1

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

Outputs

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

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

Calls

7 calls:

3.0ms	a
3.0ms	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
99.3%	2	`a`
99.3%	2	`b`
99.3%	2	`(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))`
99.3%	2	`(fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a)))`
99.3%	2	`(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))`
99.3%	2	`(*.f64 a a)`
99.3%	2	`(*.f64 b b)`

Compiler

Compiled 44 to 31 computations (29.5% saved)

regimes47.0ms (1%)

Memory

-23.5MiB live, 19.8MiB allocated

Accuracy

Total -60.0b remaining (-3990%)

Threshold costs -60b (-3990%)

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

7 calls:

37.0ms	(*.f64 b b)
2.0ms	b
2.0ms	a
2.0ms	(*.f64 a a)
1.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

Results

Accuracy	Segments	Branch
97.6%	1	`a`
97.6%	1	`b`
97.6%	1	`(*.f64 a a)`
97.6%	1	`(*.f64 b b)`
97.6%	1	`(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))`
97.6%	1	`(fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a)))`
97.6%	1	`(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))`

Compiler

Compiled 44 to 31 computations (29.5% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.9985529502280344	1.0

Compiler

Compiled 16 to 13 computations (18.8% saved)

simplify23.0ms (0.5%)

Memory

-7.4MiB live, 32.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	90
1	38	90
2	44	90
3	48	90
4	50	90

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

(if (<=.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a)) #s(literal 4497082694556685/4503599627370496 binary64)) (sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64))))) (sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64)))))

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

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)))))

(if (<=.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a)) #s(literal 4497082694556685/4503599627370496 binary64)) (sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64))))) (sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64)))))

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

soundness358.0ms (7.7%)

Memory

4.3MiB live, 158.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	102
1	55	92
2	165	92
3	710	92
4	3810	92
0	8018	90
0	27	172
0	44	171
1	170	153
2	1156	138
0	8575	138

Stop Event

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

Compiler

Compiled 139 to 70 computations (49.6% saved)

preprocess25.0ms (0.5%)

Memory

32.1MiB live, 32.1MiB allocated

Remove

(abs a)

(abs b)

Compiler

Compiled 298 to 132 computations (55.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze13.0ms (0.3%)

sample1.4s (29.2%)

explain138.0ms (3%)

preprocess181.0ms (3.9%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify140.0ms (3%)

localize24.0ms (0.5%)

series17.0ms (0.4%)

simplify154.0ms (3.3%)

rewrite185.0ms (4%)

eval90.0ms (1.9%)

prune24.0ms (0.5%)

simplify154.0ms (3.3%)

localize60.0ms (1.3%)

series20.0ms (0.4%)

simplify122.0ms (2.6%)

rewrite191.0ms (4.1%)

eval200.0ms (4.3%)

prune36.0ms (0.8%)

simplify142.0ms (3%)

localize63.0ms (1.3%)

series12.0ms (0.3%)

simplify148.0ms (3.2%)

rewrite172.0ms (3.7%)

eval52.0ms (1.1%)

prune6.0ms (0.1%)

simplify138.0ms (3%)

localize53.0ms (1.1%)

series4.0ms (0.1%)

simplify100.0ms (2.1%)

rewrite133.0ms (2.9%)

eval11.0ms (0.2%)

prune5.0ms (0.1%)

regimes41.0ms (0.9%)

regimes17.0ms (0.4%)

regimes47.0ms (1%)

bsearch0.0ms (0%)

simplify23.0ms (0.5%)

soundness358.0ms (7.7%)

preprocess25.0ms (0.5%)

end0.0ms (0%)

Profiling