Metrics for Eccentricity of an ellipse

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze14.0ms (0.3%)

Memory

-3.6MiB live, 35.2MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 25 to 16 computations (36% saved)

sample1.3s (25%)

Memory

2.7MiB live, 1 506.7MiB allocated

Samples

862.0ms	8 256×	0	valid
72.0ms	836×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 669.0ms

ival-<=: 233.0ms (34.8% of total)

ival-mult: 147.0ms (22% of total)

ival-div: 75.0ms (11.2% of total)

ival-sqrt: 67.0ms (10% of total)

ival-sub: 64.0ms (9.6% of total)

ival-fabs: 49.0ms (7.3% of total)

ival-and: 19.0ms (2.8% of total)

exact: 12.0ms (1.8% of total)

ival-assert: 3.0ms (0.4% of total)

Bogosity

explain119.0ms (2.3%)

Memory

-4.7MiB live, 120.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
46	-	2	(7.919885202206345e-157 6.7805599968442926e-161)	`(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))`
0	-	0	-	`(*.f64 a a)`
0	-	0	-	`a`
0	-	0	-	`b`
0	-	0	-	`(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))`
0	-	0	-	`(fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a)))`
0	-	0	-	`(-.f64 (.f64 a a) (.f64 b b))`
0	-	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	44	0
↳	`(*.f64 b b)`	underflow	185
↳	`(-.f64 (.f64 a a) (.f64 b b))`	underflow	44
↳	`(*.f64 a a)`	underflow	44
↳	`(*.f64 a a)`	underflow	44

Confusion

	Predicted +	Predicted -
+	44	2
-	0	210

Precision

1.0

Recall

0.9565217391304348

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	44	0	2
-	0	0	210

Precision?

1.0

Recall?

0.9565217391304348

Freqs

test

number	freq
0	212
1	44

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

55.0ms

512×

valid

Compiler

Compiled 170 to 36 computations (78.8% saved)

Precisions

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

ival-mult: 7.0ms (36.1% of total)

ival-sub: 3.0ms (15.5% of total)

ival-div: 3.0ms (15.5% of total)

ival-fabs: 3.0ms (15.5% of total)

ival-sqrt: 3.0ms (15.5% of total)

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

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

preprocess218.0ms (4.1%)

Memory

-17.9MiB live, 72.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	67
1	85	57
2	338	57
3	2483	57
4	6466	57
0	8	13
0	14	13
1	30	11
2	75	11
3	199	11
4	484	11
5	1735	11
6	5661	11
0	8206	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

0.4MiB live, 0.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	82.6%	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

Compiler

Compiled 13 to 8 computations (38.5% saved)

simplify193.0ms (3.7%)

Memory

-13.8MiB live, 61.1MiB 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	484	45
5	1735	45
6	5661	45
0	8206	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

localize23.0ms (0.4%)

Memory

16.4MiB live, 16.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a)))
accuracy	0.0078125	(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	10.805401982722369	(/.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 (32.1% of total)

ival-div: 2.0ms (21.4% of total)

ival-sqrt: 2.0ms (21.4% of total)

ival-sub: 1.0ms (10.7% of total)

ival-fabs: 1.0ms (10.7% of total)

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

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

series6.0ms (0.1%)

Memory

4.3MiB live, 4.3MiB 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
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)))
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)))

simplify234.0ms (4.4%)

Memory

-6.6MiB live, 75.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	102
1	55	92
2	165	92
3	709	92
4	3817	92
0	8045	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)

rewrite183.0ms (3.5%)

Memory

20.2MiB live, 57.3MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	46
0	14	46
1	58	40
2	431	34
3	4348	34
0	8229	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))))

eval115.0ms (2.2%)

Memory: 6.6MiB live, 44.6MiB allocated
Compiler: Compiled 9 570 to 1 905 computations (80.1% saved)

prune50.0ms (0.9%)

Memory

-19.3MiB live, 18.8MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	445	5	450
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	446	5	451

Accuracy

100.0%

Counts

451 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	81.9%	(/.f64 (sqrt.f64 (fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a)))) a)
▶	99.9%	(sqrt.f64 (fabs.f64 (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)))
▶	81.6%	(sqrt.f64 (fabs.f64 (.f64 (-.f64 a b) (/.f64 (+.f64 b a) (.f64 a a)))))
▶	98.4%	(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 150 to 100 computations (33.3% saved)

simplify177.0ms (3.4%)

Memory

4.5MiB live, 49.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)
cost-diff	0	(sqrt.f64 (fabs.f64 (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)))
cost-diff	128	(fabs.f64 (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a))
cost-diff	192	(*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b))
cost-diff	0	(-.f64 a b)
cost-diff	0	(sqrt.f64 (fabs.f64 (.f64 (-.f64 a b) (/.f64 (+.f64 b a) (.f64 a a)))))
cost-diff	128	(fabs.f64 (.f64 (-.f64 a b) (/.f64 (+.f64 b a) (.f64 a a))))
cost-diff	192	(.f64 (-.f64 a b) (/.f64 (+.f64 b a) (.f64 a a)))
cost-diff	0	(*.f64 (-.f64 a b) (+.f64 b a))
cost-diff	0	(fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
cost-diff	0	(sqrt.f64 (fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a))))
cost-diff	0	(/.f64 (sqrt.f64 (fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a)))) a)
cost-diff	0	#s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))
cost-diff	0	(fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64)))
cost-diff	0	(sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))))
cost-diff	0	(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: 3 (0.0ms)

Iter	Nodes	Cost
0	34	271
0	58	265
1	107	247
2	184	243
3	370	241
4	798	241
5	2654	241
6	7902	241
0	8224	241

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

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

localize102.0ms (1.9%)

Memory

3.0MiB live, 41.1MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(sqrt.f64 (fabs.f64 (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)))
accuracy	0.01171875	(/.f64 (+.f64 b a) a)
accuracy	0.01171875	(/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)
accuracy	0.06640625	(*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b))
accuracy	0.0	(fabs.f64 (.f64 (-.f64 a b) (/.f64 (+.f64 b a) (.f64 a a))))
accuracy	0.0078125	(sqrt.f64 (fabs.f64 (.f64 (-.f64 a b) (/.f64 (+.f64 b a) (.f64 a a)))))
accuracy	0.1796875	(.f64 (-.f64 a b) (/.f64 (+.f64 b a) (.f64 a a)))
accuracy	11.515804987165822	(/.f64 (+.f64 b a) (*.f64 a a))
accuracy	0.0	(*.f64 (-.f64 a b) (+.f64 b a))
accuracy	0.0	(fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
accuracy	0.01171875	(/.f64 (sqrt.f64 (fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a)))) a)
accuracy	11.294649182763997	(sqrt.f64 (fabs.f64 (*.f64 (-.f64 a b) (+.f64 b a))))
accuracy	0.0	(fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64)))
accuracy	0.0078125	(sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))))
accuracy	1.0530159979067961	#s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))
accuracy	0.0	(fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))
accuracy	0.0	#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64))))
accuracy	0.0078125	(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	0.26171875	(/.f64 (/.f64 b a) a)

Samples

80.0ms

256×

valid

Compiler

Compiled 520 to 66 computations (87.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 65.0ms

ival-fabs: 34.0ms (52.6% of total)

ival-div: 10.0ms (15.5% of total)

ival-mult: 9.0ms (13.9% of total)

ival-sqrt: 6.0ms (9.3% of total)

ival-add: 2.0ms (3.1% of total)

ival-sub: 2.0ms (3.1% of total)

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

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

exact: 0.0ms (0% of total)

series53.0ms (1%)

Memory

-21.0MiB live, 17.2MiB allocated

Counts

22 → 74

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

Calls

6 calls:

Time	Variable		Point	Expression
34.0ms	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) (sqrt (fabs (* (- a b) (+ b a)))) (fabs (* (- a b) (+ b a))) (* (- a b) (+ b a)) (* (- a b) (/ (+ b a) (* a a))) (fabs (* (- a b) (/ (+ b a) (* a a)))) (sqrt (fabs (* (- a b) (/ (+ b a) (* a a))))) (- a b) (* (/ (+ b a) a) (- a b)) (fabs (/ (* (/ (+ b a) a) (- a b)) a)) (sqrt (fabs (/ (* (/ (+ b a) a) (- a b)) a))) (/ (* (/ (+ b a) a) (- a b)) a) (/ (/ b a) a) (/ (+ b a) (* a a)) (/ (+ b 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) (sqrt (fabs (* (- a b) (+ b a)))) (fabs (* (- a b) (+ b a))) (* (- a b) (+ b a)) (* (- a b) (/ (+ b a) (* a a))) (fabs (* (- a b) (/ (+ b a) (* a a)))) (sqrt (fabs (* (- a b) (/ (+ b a) (* a a))))) (- a b) (* (/ (+ b a) a) (- a b)) (fabs (/ (* (/ (+ b a) a) (- a b)) a)) (sqrt (fabs (/ (* (/ (+ b a) a) (- a b)) a))) (/ (* (/ (+ b a) a) (- a b)) a) (/ (/ b a) a) (/ (+ b a) (* a a)) (/ (+ b 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) (sqrt (fabs (* (- a b) (+ b a)))) (fabs (* (- a b) (+ b a))) (* (- a b) (+ b a)) (* (- a b) (/ (+ b a) (* a a))) (fabs (* (- a b) (/ (+ b a) (* a a)))) (sqrt (fabs (* (- a b) (/ (+ b a) (* a a))))) (- a b) (* (/ (+ b a) a) (- a b)) (fabs (/ (* (/ (+ b a) a) (- a b)) a)) (sqrt (fabs (/ (* (/ (+ b a) a) (- a b)) a))) (/ (* (/ (+ b a) a) (- a b)) a) (/ (/ b a) a) (/ (+ b a) (* a a)) (/ (+ b a) a))
4.0ms	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) (sqrt (fabs (* (- a b) (+ b a)))) (fabs (* (- a b) (+ b a))) (* (- a b) (+ b a)) (* (- a b) (/ (+ b a) (* a a))) (fabs (* (- a b) (/ (+ b a) (* a a)))) (sqrt (fabs (* (- a b) (/ (+ b a) (* a a))))) (- a b) (* (/ (+ b a) a) (- a b)) (fabs (/ (* (/ (+ b a) a) (- a b)) a)) (sqrt (fabs (/ (* (/ (+ b a) a) (- a b)) a))) (/ (* (/ (+ b a) a) (- a b)) a) (/ (/ b a) a) (/ (+ b a) (* a a)) (/ (+ b a) a))
3.0ms	b	@	-inf	((sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs (+ (* (/ (/ b a) a) b) -1)) (+ (* (/ (/ b a) a) b) -1) (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (/ (- (* a a) (* b b)) (* a a)) (/ (sqrt (fabs (* (- a b) (+ b a)))) a) (sqrt (fabs (* (- a b) (+ b a)))) (fabs (* (- a b) (+ b a))) (* (- a b) (+ b a)) (* (- a b) (/ (+ b a) (* a a))) (fabs (* (- a b) (/ (+ b a) (* a a)))) (sqrt (fabs (* (- a b) (/ (+ b a) (* a a))))) (- a b) (* (/ (+ b a) a) (- a b)) (fabs (/ (* (/ (+ b a) a) (- a b)) a)) (sqrt (fabs (/ (* (/ (+ b a) a) (- a b)) a))) (/ (* (/ (+ b a) a) (- a b)) a) (/ (/ b a) a) (/ (+ b a) (* a a)) (/ (+ b a) a))

simplify204.0ms (3.9%)

Memory

3.1MiB live, 120.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	160	619
1	453	525
2	1303	505
3	6808	505
0	8542	491

Stop Event

1×	iter limit
1×	node limit

Counts

74 → 73

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

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

rewrite206.0ms (3.9%)

Memory

26.4MiB live, 271.2MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	34	240
0	58	230
1	209	214
2	1386	190
0	8695	190

Stop Event

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

Counts

22 → 1 791

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

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

eval307.0ms (5.8%)

Memory: -20.5MiB live, 407.3MiB allocated
Compiler: Compiled 40 014 to 6 645 computations (83.4% saved)

prune50.0ms (1%)

Memory

2.0MiB live, 95.5MiB allocated

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	1 477	3	1 480
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	1 478	7	1 485

Accuracy

100.0%

Counts

1 485 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	6.0%	(/.f64 (sqrt.f64 (fabs.f64 (*.f64 #s(approx (- a b) (neg.f64 b)) (+.f64 b a)))) a)
✓	99.9%	(sqrt.f64 (fabs.f64 (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)))
✓	81.6%	(sqrt.f64 (fabs.f64 (.f64 (-.f64 a b) (/.f64 (+.f64 b a) (.f64 a a)))))
▶	96.0%	(sqrt.f64 (fabs.f64 (.f64 (-.f64 a b) #s(approx (/ (+ b a) ( a a)) (/.f64 #s(literal 1 binary64) a)))))
✓	98.4%	(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)))))
▶	83.3%	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64)))))

Compiler

Compiled 118 to 78 computations (33.9% saved)

simplify167.0ms (3.2%)

Memory

11.8MiB live, 170.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	31	201
0	48	201
1	89	197
2	155	195
3	335	195
4	757	195
5	2218	195
6	6030	195
0	8114	195

Stop Event

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

Calls

Call 1

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

localize69.0ms (1.3%)

Memory

1.1MiB live, 117.8MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0.0	(fabs.f64 (*.f64 #s(approx (- a b) (neg.f64 b)) (+.f64 b a)))
accuracy	0.01171875	(/.f64 (sqrt.f64 (fabs.f64 (*.f64 #s(approx (- a b) (neg.f64 b)) (+.f64 b a)))) a)
accuracy	11.294649182763997	(sqrt.f64 (fabs.f64 (*.f64 #s(approx (- a b) (neg.f64 b)) (+.f64 b a))))
accuracy	61.90757020791876	#s(approx (- a b) (neg.f64 b))
accuracy	0.0	(fabs.f64 (.f64 (-.f64 a b) #s(approx (/ (+ b a) ( a a)) (/.f64 #s(literal 1 binary64) a))))
accuracy	0.0078125	(sqrt.f64 (fabs.f64 (.f64 (-.f64 a b) #s(approx (/ (+ b a) ( a a)) (/.f64 #s(literal 1 binary64) a)))))
accuracy	0.1796875	(.f64 (-.f64 a b) #s(approx (/ (+ b a) ( a a)) (/.f64 #s(literal 1 binary64) a)))
accuracy	2.505196058102495	#s(approx (/ (+ b a) (* a a)) (/.f64 #s(literal 1 binary64) a))
accuracy	0.0	(fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64)))
accuracy	0.0	#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64))))
accuracy	0.0078125	(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	11.602521989796166	(/.f64 b (*.f64 a a))

Samples

52.0ms

256×

valid

Compiler

Compiled 355 to 59 computations (83.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 38.0ms

ival-sqrt: 10.0ms (26.5% of total)

ival-mult: 9.0ms (23.8% of total)

ival-div: 8.0ms (21.2% of total)

ival-fabs: 5.0ms (13.2% of total)

ival-add: 2.0ms (5.3% of total)

ival-sub: 2.0ms (5.3% of total)

ival-neg: 1.0ms (2.6% of total)

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

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

exact: 0.0ms (0% of total)

series14.0ms (0.3%)

Memory

-23.1MiB live, 20.5MiB allocated

Counts

15 → 60

Calls

Call 1

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

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))
(sqrt (fabs (/ (* (+ a b) (- a b)) (pow a 2))))
(fabs (/ (* (+ a b) (- a b)) (pow a 2)))
(* -1 (/ (pow b 2) (pow a 2)))
(/ (+ (* -1 (pow b 2)) (* a (+ b (* -1 b)))) (pow a 2))
(/ (+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b))))) (pow a 2))
(* -1 b)
(- a b)
(* (/ 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))
(/ (+ a b) (pow a 2))
-1
(- (/ (pow b 2) (pow a 2)) 1)
1
(+ 1 (+ (* -1 (/ b a)) (/ b a)))
(+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a))))
a
(* a (+ 1 (* -1 (/ b a))))
(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)
(/ (+ 1 (/ b a)) a)
(sqrt (fabs (* -1 (/ (* (+ b (* -1 a)) (- b (* -1 a))) (pow a 2)))))
(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) (+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a))))
(* -1 (/ (- (* -1 (/ b a)) 1) a))
(+ 1 (* -1 (/ (pow b 2) (pow a 2))))
(+ a (* -1 b))
(+ (* b (+ a (* -1 a))) (pow a 2))
(+ (* b (+ a (+ (* -1 a) (* -1 b)))) (pow a 2))
(+ (/ 1 a) (/ b (pow a 2)))
(* (pow b 2) (- (/ 1 (pow a 2)) (/ 1 (pow b 2))))
(* (pow b 2) (- (/ 1 (pow b 2)) (/ 1 (pow a 2))))
(* b (- (/ a b) 1))
(* (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 (+ (/ 1 (* a b)) (/ 1 (pow a 2))))
(sqrt (fabs (/ (* (+ a (* -1 b)) (- a (* -1 b))) (pow a 2))))
(fabs (/ (* (+ a (* -1 b)) (- a (* -1 b))) (pow a 2)))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(* (/ 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
5.0ms	b	@	inf	((sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs (+ (* (/ b (* a a)) b) -1)) (+ (* (/ b (* a a)) b) -1) (sqrt (fabs (* (- a b) (/ (+ b a) (* a a))))) (fabs (* (- a b) (/ (+ b a) (* a a)))) (* (- a b) (/ (+ b a) (* a a))) (- a b) (/ (sqrt (fabs (* (- a b) (+ b a)))) a) (sqrt (fabs (* (- a b) (+ b a)))) (fabs (* (- a b) (+ b a))) (* (- a b) (+ b a)) (/ b (* a a)) (/ (+ b a) (* a a)) (- a b))
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 b) (/ (+ b a) (* a a))))) (fabs (* (- a b) (/ (+ b a) (* a a)))) (* (- a b) (/ (+ b a) (* a a))) (- a b) (/ (sqrt (fabs (* (- a b) (+ b a)))) a) (sqrt (fabs (* (- a b) (+ b a)))) (fabs (* (- a b) (+ b a))) (* (- a b) (+ b a)) (/ b (* a a)) (/ (+ b a) (* a a)) (- a b))
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 b) (/ (+ b a) (* a a))))) (fabs (* (- a b) (/ (+ b a) (* a a)))) (* (- a b) (/ (+ b a) (* a a))) (- a b) (/ (sqrt (fabs (* (- a b) (+ b a)))) a) (sqrt (fabs (* (- a b) (+ b a)))) (fabs (* (- a b) (+ b a))) (* (- a b) (+ b a)) (/ b (* a a)) (/ (+ b a) (* a a)) (- a b))
2.0ms	b	@	0	((sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs (+ (* (/ b (* a a)) b) -1)) (+ (* (/ b (* a a)) b) -1) (sqrt (fabs (* (- a b) (/ (+ b a) (* a a))))) (fabs (* (- a b) (/ (+ b a) (* a a)))) (* (- a b) (/ (+ b a) (* a a))) (- a b) (/ (sqrt (fabs (* (- a b) (+ b a)))) a) (sqrt (fabs (* (- a b) (+ b a)))) (fabs (* (- a b) (+ b a))) (* (- a b) (+ b a)) (/ b (* a a)) (/ (+ b a) (* a a)) (- a b))
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 b) (/ (+ b a) (* a a))))) (fabs (* (- a b) (/ (+ b a) (* a a)))) (* (- a b) (/ (+ b a) (* a a))) (- a b) (/ (sqrt (fabs (* (- a b) (+ b a)))) a) (sqrt (fabs (* (- a b) (+ b a)))) (fabs (* (- a b) (+ b a))) (* (- a b) (+ b a)) (/ b (* a a)) (/ (+ b a) (* a a)) (- a b))

simplify143.0ms (2.7%)

Memory

1.0MiB live, 198.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	133	496
1	379	407
2	1091	407
3	5263	407
0	8417	395

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 59

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

rewrite168.0ms (3.2%)

Memory

12.1MiB live, 244.7MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	31	182
0	48	182
1	174	176
2	1114	170
0	8879	170

Stop Event

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

Counts

15 → 541

Calls

Call 1

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

Outputs
(.f64 (pow.f64 #s(approx (fabs (/ (- ( a a) (* b b)) (* a a))) (fabs.f64 (-.f64 #s(literal 1 binary64) (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 (-.f64 #s(literal 1 binary64) (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 (-.f64 #s(literal 1 binary64) (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 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))) #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (-.f64 #s(literal 1 binary64) (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 (-.f64 #s(literal 1 binary64) (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 (-.f64 #s(literal 1 binary64) (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 (-.f64 #s(literal 1 binary64) (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 (-.f64 #s(literal 1 binary64) (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 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))))
(.f64 (.f64 (fabs.f64 (fma.f64 (neg.f64 a) a (*.f64 b b))) #s(literal 1 binary64)) (pow.f64 a #s(literal -2 binary64)))
(*.f64 (/.f64 (fabs.f64 (+.f64 b a)) (fabs.f64 a)) (/.f64 (fabs.f64 (-.f64 b a)) (fabs.f64 a)))
(*.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 (fma.f64 (neg.f64 a) a (.f64 b b)))) (neg.f64 (pow.f64 a #s(literal -2 binary64))))
(.f64 (fabs.f64 (-.f64 (.f64 b (/.f64 b a)) a)) (/.f64 #s(literal 1 binary64) (fabs.f64 a)))
(.f64 (fabs.f64 (-.f64 (.f64 b (/.f64 b a)) a)) (fabs.f64 (pow.f64 a #s(literal -1 binary64))))
(*.f64 (fabs.f64 (-.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) #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)))))
(*.f64 (fabs.f64 (-.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 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 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fabs.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64))))))
(*.f64 (fabs.f64 (+.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64)) #s(literal -1 binary64))) (fabs.f64 (pow.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 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 (fabs.f64 (fma.f64 (neg.f64 a) a (.f64 b 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 (fabs.f64 (+.f64 b a)) (fabs.f64 (.f64 (-.f64 a b) (pow.f64 a #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)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))) #s(literal -1 binary64))
(/.f64 (neg.f64 (neg.f64 (fabs.f64 (fma.f64 (neg.f64 a) a (.f64 b b))))) (.f64 a a))
(/.f64 (neg.f64 (fabs.f64 (-.f64 (*.f64 b (/.f64 b a)) a))) (neg.f64 (fabs.f64 a)))
(/.f64 (neg.f64 (fabs.f64 (-.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)))) (neg.f64 (fabs.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)))))
(/.f64 (neg.f64 (fabs.f64 (+.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64)) #s(literal -1 binary64)))) (neg.f64 (fabs.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #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 (neg.f64 (fabs.f64 (fma.f64 (neg.f64 a) a (.f64 b b)))) (.f64 (neg.f64 a) a))
(/.f64 (fabs.f64 (-.f64 (*.f64 b (/.f64 b a)) a)) (fabs.f64 a))
(/.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 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64))) (fabs.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))))
(/.f64 (fabs.f64 (-.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64))) (fabs.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64))))
(/.f64 (fabs.f64 (+.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64)) #s(literal -1 binary64))) (fabs.f64 (+.f64 #s(literal 1 binary64) (*.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 (fabs.f64 (+.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64)) #s(literal -1 binary64))) (fabs.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)))))
(/.f64 (fabs.f64 (fma.f64 (neg.f64 a) a (.f64 b b))) (.f64 a a))
(/.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 a) (fabs.f64 (-.f64 (*.f64 b (/.f64 b a)) a))))
(/.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64))) (fabs.f64 (-.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)))) (fabs.f64 (+.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64)) #s(literal -1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))))))
(neg.f64 (/.f64 (neg.f64 (fabs.f64 (fma.f64 (neg.f64 a) a (.f64 b b)))) (.f64 a a)))
(neg.f64 (/.f64 (fabs.f64 (fma.f64 (neg.f64 a) a (.f64 b b))) (.f64 (neg.f64 a) a)))
(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 (expm1.f64 (log.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)))) #s(literal 0 binary64)))
(fabs.f64 (expm1.f64 (log.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)))))
(fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))
(*.f64 (+.f64 (/.f64 b a) #s(literal 1 binary64)) (-.f64 (/.f64 b a) #s(literal 1 binary64)))
(.f64 (/.f64 (.f64 (+.f64 b a) (-.f64 a b)) #s(literal -1 binary64)) (pow.f64 a #s(literal -2 binary64)))
(*.f64 (/.f64 (-.f64 (neg.f64 b) a) (fabs.f64 a)) (/.f64 (-.f64 a b) (fabs.f64 a)))
(.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (neg.f64 a)) (/.f64 (pow.f64 (fma.f64 b b (.f64 a a)) #s(literal -1 binary64)) a))
(.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) #s(literal -1 binary64)) (/.f64 (pow.f64 (fma.f64 b b (.f64 a a)) #s(literal -1 binary64)) (*.f64 a a)))
(.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (neg.f64 a)) (/.f64 (pow.f64 (fma.f64 (.f64 b b) (fma.f64 b b (*.f64 a a)) (pow.f64 a #s(literal 4 binary64))) #s(literal -1 binary64)) a))
(.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) #s(literal -1 binary64)) (/.f64 (pow.f64 (fma.f64 (.f64 b b) (fma.f64 b b (.f64 a a)) (pow.f64 a #s(literal 4 binary64))) #s(literal -1 binary64)) (.f64 a a)))
(.f64 (/.f64 (-.f64 a b) #s(literal -1 binary64)) (.f64 (pow.f64 a #s(literal -2 binary64)) (+.f64 b a)))
(*.f64 (/.f64 (-.f64 a b) (neg.f64 a)) (/.f64 (+.f64 b a) a))
(.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) a) (/.f64 (pow.f64 (fma.f64 b b (.f64 a a)) #s(literal -1 binary64)) (neg.f64 a)))
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(.f64 (/.f64 #s(literal -1 binary64) (fabs.f64 a)) (/.f64 (.f64 (+.f64 b a) (-.f64 a b)) (fabs.f64 a)))
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(/.f64 (neg.f64 (.f64 (.f64 (+.f64 b a) #s(approx (- a b) (neg.f64 b))) (-.f64 b a))) (-.f64 a b))
(/.f64 (neg.f64 (.f64 #s(approx (- a b) (neg.f64 b)) (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))))) (neg.f64 (fma.f64 b b (.f64 a (-.f64 a b)))))
(/.f64 (neg.f64 (.f64 (.f64 (+.f64 b a) #s(approx (- a b) (neg.f64 b))) (.f64 #s(approx (- a b) (neg.f64 b)) (-.f64 b a)))) (neg.f64 (.f64 #s(approx (- a b) (neg.f64 b)) (-.f64 b a))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 #s(approx (- a b) (neg.f64 b)) b) #s(literal 3 binary64)) (pow.f64 (.f64 #s(approx (- a b) (neg.f64 b)) a) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (.f64 #s(approx (- a b) (neg.f64 b)) b) #s(literal 2 binary64)) (.f64 (.f64 #s(approx (- a b) (neg.f64 b)) a) (-.f64 (.f64 #s(approx (- a b) (neg.f64 b)) a) (*.f64 #s(approx (- a b) (neg.f64 b)) b))))))
(/.f64 (.f64 (fma.f64 (neg.f64 a) a (.f64 b b)) #s(approx (- a b) (neg.f64 b))) (-.f64 b a))
(/.f64 (.f64 (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) #s(approx (- a b) (neg.f64 b))) (fma.f64 b b (.f64 a (-.f64 a b))))
(/.f64 (.f64 (.f64 (+.f64 b a) #s(approx (- a b) (neg.f64 b))) (-.f64 b a)) (-.f64 b a))
(/.f64 (.f64 #s(approx (- a b) (neg.f64 b)) (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (fma.f64 b b (.f64 a (-.f64 a b))))
(/.f64 (.f64 (.f64 (+.f64 b a) #s(approx (- a b) (neg.f64 b))) (.f64 #s(approx (- a b) (neg.f64 b)) (-.f64 b a))) (.f64 #s(approx (- a b) (neg.f64 b)) (-.f64 b a)))
(/.f64 (+.f64 (pow.f64 (.f64 #s(approx (- a b) (neg.f64 b)) b) #s(literal 3 binary64)) (pow.f64 (.f64 #s(approx (- a b) (neg.f64 b)) a) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 #s(approx (- a b) (neg.f64 b)) b) #s(literal 2 binary64)) (.f64 (.f64 #s(approx (- a b) (neg.f64 b)) a) (-.f64 (.f64 #s(approx (- a b) (neg.f64 b)) a) (*.f64 #s(approx (- a b) (neg.f64 b)) b)))))
(/.f64 #s(approx (- a b) (neg.f64 b)) (pow.f64 (+.f64 b a) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 b a) (.f64 (fma.f64 (neg.f64 a) a (.f64 b b)) #s(approx (- a b) (neg.f64 b)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 b b (.f64 a (-.f64 a b))) (.f64 (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) #s(approx (- a b) (neg.f64 b)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 b a) (.f64 (.f64 (+.f64 b a) #s(approx (- a b) (neg.f64 b))) (-.f64 b a))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 b b (.f64 a (-.f64 a b))) (.f64 #s(approx (- a b) (neg.f64 b)) (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(approx (- a b) (neg.f64 b)) (-.f64 b a)) (.f64 (.f64 (+.f64 b a) #s(approx (- a b) (neg.f64 b))) (.f64 #s(approx (- a b) (neg.f64 b)) (-.f64 b a)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (.f64 #s(approx (- a b) (neg.f64 b)) b) #s(literal 2 binary64)) (.f64 (.f64 #s(approx (- a b) (neg.f64 b)) a) (-.f64 (.f64 #s(approx (- a b) (neg.f64 b)) a) (.f64 #s(approx (- a b) (neg.f64 b)) b)))) (+.f64 (pow.f64 (.f64 #s(approx (- a b) (neg.f64 b)) b) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(approx (- a b) (neg.f64 b)) a) #s(literal 3 binary64)))))
(neg.f64 (*.f64 (-.f64 (neg.f64 b) a) #s(approx (- a b) (neg.f64 b))))
(fma.f64 (.f64 #s(approx (- a b) (neg.f64 b)) a) #s(literal 1 binary64) (.f64 #s(approx (- a b) (neg.f64 b)) b))
(fma.f64 #s(approx (- a b) (neg.f64 b)) b (*.f64 #s(approx (- a b) (neg.f64 b)) a))
(fma.f64 #s(approx (- a b) (neg.f64 b)) a (*.f64 #s(approx (- a b) (neg.f64 b)) b))
(fma.f64 b #s(approx (- a b) (neg.f64 b)) (*.f64 #s(approx (- a b) (neg.f64 b)) a))
(fma.f64 a (.f64 #s(literal 1 binary64) #s(approx (- a b) (neg.f64 b))) (.f64 #s(approx (- a b) (neg.f64 b)) b))
(fma.f64 a #s(approx (- a b) (neg.f64 b)) (*.f64 #s(approx (- a b) (neg.f64 b)) b))
(-.f64 (/.f64 (pow.f64 (.f64 #s(approx (- a b) (neg.f64 b)) b) #s(literal 2 binary64)) (.f64 #s(approx (- a b) (neg.f64 b)) (-.f64 b a))) (/.f64 (pow.f64 (.f64 #s(approx (- a b) (neg.f64 b)) a) #s(literal 2 binary64)) (.f64 #s(approx (- a b) (neg.f64 b)) (-.f64 b a))))
(-.f64 #s(literal 0 binary64) (*.f64 (-.f64 (neg.f64 b) a) #s(approx (- a b) (neg.f64 b))))
(+.f64 (neg.f64 (.f64 #s(approx (- a b) (neg.f64 b)) (neg.f64 b))) (neg.f64 (.f64 (neg.f64 a) #s(approx (- a b) (neg.f64 b)))))
(+.f64 (.f64 #s(approx (- a b) (neg.f64 b)) b) (.f64 #s(approx (- a b) (neg.f64 b)) a))
(+.f64 (.f64 #s(approx (- a b) (neg.f64 b)) a) (.f64 #s(approx (- a b) (neg.f64 b)) b))
(.f64 (.f64 (/.f64 b a) (pow.f64 a #s(literal -1/2 binary64))) (pow.f64 a #s(literal -1/2 binary64)))
(.f64 (.f64 (/.f64 b a) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) a))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 b)) (neg.f64 (pow.f64 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 #s(literal -1 binary64)) (neg.f64 (pow.f64 a #s(literal -2 binary64))))
(*.f64 (/.f64 b (fabs.f64 a)) (/.f64 #s(literal 1 binary64) (fabs.f64 a)))
(*.f64 (/.f64 #s(literal -1 binary64) a) (/.f64 (neg.f64 b) a))
(*.f64 (/.f64 (neg.f64 b) a) (/.f64 #s(literal -1 binary64) a))
(*.f64 (/.f64 b a) (/.f64 (pow.f64 a #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 b a) (pow.f64 a #s(literal -1 binary64)))
(*.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 (neg.f64 b) (neg.f64 (pow.f64 a #s(literal -2 binary64))))
(*.f64 (pow.f64 a #s(literal -1 binary64)) (/.f64 b a))
(.f64 #s(literal 1 binary64) (/.f64 b (.f64 a a)))
(*.f64 #s(literal -1 binary64) (/.f64 (/.f64 (neg.f64 b) a) a))
(.f64 (/.f64 b (.f64 a a)) #s(literal 1 binary64))
(*.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 (neg.f64 b) a) (neg.f64 a))
(/.f64 (/.f64 b a) a)
(/.f64 (neg.f64 b) (*.f64 (neg.f64 a) a))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 a a) b))
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 a) (/.f64 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 b (*.f64 a a)))
#s(approx (/ (+ b a) (* a a)) (pow.f64 a #s(literal -1 binary64)))
#s(approx (- a b) (neg.f64 b))

eval104.0ms (2%)

Memory: 9.6MiB live, 172.5MiB allocated
Compiler: Compiled 17 040 to 2 545 computations (85.1% saved)

prune10.0ms (0.2%)

Memory

-7.2MiB live, 35.1MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	561	1	562
Fresh	0	0	0
Picked	2	1	3
Done	0	4	4
Total	563	6	569

Accuracy

100.0%

Counts

569 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(sqrt.f64 (fabs.f64 (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)))
✓	81.6%	(sqrt.f64 (fabs.f64 (.f64 (-.f64 a b) (/.f64 (+.f64 b a) (.f64 a a)))))
▶	8.0%	(sqrt.f64 (fabs.f64 (.f64 #s(approx (- a b) (neg.f64 b)) #s(approx (/ (+ b a) ( a a)) (/.f64 #s(literal 1 binary64) a)))))
✓	98.4%	(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)))))
✓	83.3%	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64)))))

Compiler

Compiled 107 to 70 computations (34.6% saved)

simplify252.0ms (4.8%)

Memory

11.6MiB live, 202.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	82
0	19	82
1	32	82
2	38	82
3	45	82
4	66	82
5	85	82
6	112	82
7	176	82
8	446	82
9	1065	82
10	1454	82
11	2235	82
12	2695	82
13	3390	82
14	4374	82
15	5303	82
16	5959	82
0	8500	82

Stop Event

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

Calls

Call 1

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

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

localize32.0ms (0.6%)

Memory

3.4MiB live, 41.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(sqrt.f64 (fabs.f64 (.f64 #s(approx (- a b) (neg.f64 b)) #s(approx (/ (+ b a) ( a a)) (/.f64 #s(literal 1 binary64) a)))))
accuracy	0.1796875	(.f64 #s(approx (- a b) (neg.f64 b)) #s(approx (/ (+ b a) ( a a)) (/.f64 #s(literal 1 binary64) a)))
accuracy	2.505196058102495	#s(approx (/ (+ b a) (* a a)) (/.f64 #s(literal 1 binary64) a))
accuracy	61.90757020791876	#s(approx (- a b) (neg.f64 b))

Samples

24.0ms

256×

valid

Compiler

Compiled 138 to 28 computations (79.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-div: 3.0ms (21.9% of total)

ival-mult: 3.0ms (21.9% of total)

ival-sub: 2.0ms (14.6% of total)

ival-sqrt: 2.0ms (14.6% of total)

ival-add: 1.0ms (7.3% of total)

ival-fabs: 1.0ms (7.3% of total)

ival-neg: 1.0ms (7.3% 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

4.5MiB live, 4.5MiB allocated

Counts

5 → 30

Calls

Call 1

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

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

Calls

6 calls:

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

simplify182.0ms (3.4%)

Memory

4.7MiB live, 121.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	82	237
1	225	222
2	623	212
3	2234	190
4	6689	190
0	8057	184

Stop Event

1×	iter limit
1×	node limit

Counts

30 → 29

Calls

Call 1

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

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

rewrite139.0ms (2.6%)

Memory

-19.8MiB live, 142.4MiB allocated

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	74
0	19	74
1	72	74
2	405	74
3	4557	70
0	8997	70

Stop Event

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

Counts

5 → 39

Calls

Call 1

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

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

eval6.0ms (0.1%)

Memory: 9.7MiB live, 9.7MiB allocated
Compiler: Compiled 1 091 to 167 computations (84.7% saved)

prune5.0ms (0.1%)

Memory

10.9MiB live, 10.9MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	48	1	49
Fresh	0	0	0
Picked	1	0	1
Done	0	5	5
Total	49	6	55

Accuracy

100.0%

Counts

55 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(sqrt.f64 (fabs.f64 (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)))
✓	81.6%	(sqrt.f64 (fabs.f64 (.f64 (-.f64 a b) (/.f64 (+.f64 b a) (.f64 a a)))))
	8.0%	(sqrt.f64 (fabs.f64 (.f64 #s(approx (- a b) b) #s(approx (/ (+ b a) ( a a)) (/.f64 #s(literal 1 binary64) a)))))
✓	98.4%	(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)))))
✓	83.3%	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64)))))

Compiler

Compiled 287 to 134 computations (53.3% saved)

regimes25.0ms (0.5%)

Memory

-25.8MiB live, 52.0MiB allocated

Counts

11 → 1

Calls

Call 1

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

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

Calls

7 calls:

6.0ms	a
5.0ms	(*.f64 a a)
3.0ms	b
3.0ms	(*.f64 b b)
3.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

Results

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

Compiler

Compiled 44 to 31 computations (29.5% saved)

regimes17.0ms (0.3%)

Memory

37.4MiB live, 37.5MiB allocated

Accuracy

Total -59.1b remaining (-5827.3%)

Threshold costs -59.1b (-5827.3%)

Counts

8 → 1

Calls

Call 1

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

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

Calls

7 calls:

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

Results

Accuracy	Segments	Branch
98.4%	1	`a`
98.4%	1	`b`
98.4%	1	`(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))`
98.4%	1	`(fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a)))`
98.4%	1	`(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))`
98.4%	1	`(*.f64 a a)`
98.4%	1	`(*.f64 b b)`

Compiler

Compiled 44 to 31 computations (29.5% saved)

simplify66.0ms (1.2%)

Memory

-35.1MiB live, 51.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	38
1	40	34
2	93	34
3	238	34
4	572	34
5	1990	34
6	6345	34

Stop Event

1×	node 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)))))

(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)))))

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

soundness280.0ms (5.3%)

Memory

-4.4MiB live, 114.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	102
1	55	92
2	165	92
3	709	92
4	3817	92
0	8045	90

Stop Event

1×	fuel
1×	iter limit
1×	node limit

Compiler

Compiled 51 to 31 computations (39.2% saved)

preprocess20.0ms (0.4%)

Memory

29.5MiB live, 29.5MiB allocated

Remove

(abs a)

(abs b)

Compiler

Compiled 194 to 108 computations (44.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze14.0ms (0.3%)

sample1.3s (25%)

explain119.0ms (2.3%)

preprocess218.0ms (4.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify193.0ms (3.7%)

localize23.0ms (0.4%)

series6.0ms (0.1%)

simplify234.0ms (4.4%)

rewrite183.0ms (3.5%)

eval115.0ms (2.2%)

prune50.0ms (0.9%)

simplify177.0ms (3.4%)

localize102.0ms (1.9%)

series53.0ms (1%)

simplify204.0ms (3.9%)

rewrite206.0ms (3.9%)

eval307.0ms (5.8%)

prune50.0ms (1%)

simplify167.0ms (3.2%)

localize69.0ms (1.3%)

series14.0ms (0.3%)

simplify143.0ms (2.7%)

rewrite168.0ms (3.2%)

eval104.0ms (2%)

prune10.0ms (0.2%)

simplify252.0ms (4.8%)

localize32.0ms (0.6%)

series4.0ms (0.1%)

simplify182.0ms (3.4%)

rewrite139.0ms (2.6%)

eval6.0ms (0.1%)

prune5.0ms (0.1%)

regimes25.0ms (0.5%)

regimes17.0ms (0.3%)

simplify66.0ms (1.2%)

soundness280.0ms (5.3%)

preprocess20.0ms (0.4%)

end0.0ms (0%)

Profiling