Metrics for Eccentricity of an ellipse

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze12.0ms (0.2%)

Memory

5.1MiB live, 5.1MiB 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)

sample1.2s (22.5%)

Memory

60.7MiB live, 701.7MiB allocated

Samples

757.0ms	8 256×	0	valid
56.0ms	832×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 473.0ms

ival-mult: 134.0ms (28.4% of total)

ival-<=: 86.0ms (18.2% of total)

ival-fabs: 66.0ms (14% of total)

ival-sqrt: 57.0ms (12.1% of total)

ival-div: 54.0ms (11.4% of total)

ival-sub: 42.0ms (8.9% of total)

ival-and: 18.0ms (3.8% of total)

exact: 11.0ms (2.3% of total)

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

Bogosity

explain109.0ms (2.1%)

Memory

-39.6MiB live, 153.5MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f64`	`(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))`	u/u	48	0
↳	`(*.f64 b b)`	underflow	186
↳	`(-.f64 (.f64 a a) (.f64 b b))`	underflow	48
↳	`(*.f64 a a)`	underflow	48
↳	`(*.f64 a a)`	underflow	48

Confusion

	Predicted +	Predicted -
+	48	0
-	0	208

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	48	0	0
-	0	0	208

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	208
1	48

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

32.0ms

512×

valid

Compiler

Compiled 119 to 28 computations (76.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-mult: 6.0ms (32.9% of total)

ival-sub: 3.0ms (16.5% of total)

ival-div: 3.0ms (16.5% of total)

ival-sqrt: 3.0ms (16.5% of total)

ival-fabs: 2.0ms (11% of total)

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

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

preprocess126.0ms (2.4%)

Memory

1.2MiB live, 162.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	67
1	88	57
2	586	57
3	3099	57
0	8	13
0	14	13
1	37	11
2	204	11
3	1434	11
0	8739	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

0.8MiB live, 0.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	81.2%	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

Compiler

Compiled 13 to 8 computations (38.5% saved)

simplify105.0ms (2%)

Memory

5.1MiB live, 145.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 (.f64 a a) (.f64 b b))
cost-diff	0	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
cost-diff	1	(fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a)))
cost-diff	2	(/.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	37	45
2	204	45
3	1434	45
0	8739	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))
(fma.f64 (/.f64 (/.f64 (neg.f64 b) a) a) b #s(literal 1 binary64))
(-.f64 (.f64 a a) (.f64 b b))
(*.f64 (-.f64 a b) (+.f64 b a))
(*.f64 a a)
a
(*.f64 b b)
b

localize32.0ms (0.6%)

Memory

3.0MiB live, 56.0MiB 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	0.00390625	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
accuracy	0.01953125	(-.f64 (.f64 a a) (.f64 b b))
accuracy	11.640757051003826	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))

Samples

17.0ms

256×

valid

Compiler

Compiled 53 to 10 computations (81.1% saved)

Precisions

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

ival-mult: 3.0ms (33.5% of total)

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

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

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

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

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

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

series5.0ms (0.1%)

Memory

11.6MiB live, 11.6MiB allocated

Counts

4 → 13

Calls

Call 1

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

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

Calls

6 calls:

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

simplify121.0ms (2.3%)

Memory

5.4MiB live, 144.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	117
1	58	104
2	194	104
3	1182	104
4	5531	104
0	8296	101

Stop Event

1×	iter limit
1×	node limit

Counts

13 → 13

Calls

Call 1

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

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

rewrite112.0ms (2.1%)

Memory

-3.3MiB live, 142.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	43
0	14	42
1	60	36
2	560	26
0	9127	25

Stop Event

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

Counts

4 → 403

Calls

Call 1

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

Outputs
(.f64 (/.f64 (fma.f64 b b (.f64 a a)) (fma.f64 b b (*.f64 a a))) (pow.f64 (/.f64 (hypot.f64 b a) a) #s(literal 2 binary64)))
(*.f64 (/.f64 (fabs.f64 (+.f64 b a)) (neg.f64 a)) (/.f64 (fabs.f64 (-.f64 b a)) (neg.f64 a)))
(*.f64 (/.f64 (fabs.f64 (+.f64 b a)) a) (/.f64 (fabs.f64 (-.f64 b a)) a))
(.f64 (/.f64 (fma.f64 (fma.f64 b b (.f64 a a)) (.f64 b b) (pow.f64 a #s(literal 4 binary64))) (fma.f64 (fma.f64 b b (.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64)))) (pow.f64 (/.f64 (hypot.f64 b a) a) #s(literal 2 binary64)))
(*.f64 (/.f64 (+.f64 (neg.f64 b) a) (neg.f64 a)) (/.f64 (-.f64 (neg.f64 a) b) a))
(*.f64 (/.f64 (+.f64 (neg.f64 b) a) (neg.f64 a)) (/.f64 (-.f64 (neg.f64 a) b) (neg.f64 a)))
(*.f64 (/.f64 (+.f64 (neg.f64 b) a) a) (/.f64 (-.f64 (neg.f64 a) b) a))
(*.f64 (/.f64 (+.f64 (neg.f64 b) a) a) (/.f64 (-.f64 (neg.f64 a) b) (neg.f64 a)))
(*.f64 (neg.f64 (/.f64 (hypot.f64 b a) a)) (neg.f64 (/.f64 (hypot.f64 b a) a)))
(*.f64 (fabs.f64 (/.f64 (+.f64 b a) a)) (fabs.f64 (/.f64 (-.f64 a b) a)))
(*.f64 (/.f64 (/.f64 (-.f64 a b) a) a) (+.f64 b a))
(.f64 (+.f64 (neg.f64 b) a) (/.f64 (-.f64 (neg.f64 a) b) (.f64 a a)))
(.f64 (+.f64 (neg.f64 b) a) (/.f64 (-.f64 (neg.f64 a) b) (.f64 (neg.f64 a) a)))
(*.f64 (/.f64 (-.f64 a b) a) (/.f64 (+.f64 b a) a))
(*.f64 (/.f64 (+.f64 b a) a) (/.f64 (-.f64 a b) a))
(.f64 (fma.f64 (fma.f64 b b (.f64 a a)) (.f64 b b) (pow.f64 a #s(literal 4 binary64))) (/.f64 (fma.f64 b b (.f64 a a)) (.f64 (fma.f64 (fma.f64 b b (.f64 a a)) (.f64 b b) (pow.f64 a #s(literal 4 binary64))) (.f64 a a))))
(.f64 (fabs.f64 (+.f64 b a)) (/.f64 (fabs.f64 (-.f64 b a)) (.f64 a a)))
(*.f64 (fabs.f64 (+.f64 b a)) (fabs.f64 (/.f64 (/.f64 (-.f64 a b) a) a)))
(*.f64 (/.f64 (hypot.f64 b a) a) (/.f64 (hypot.f64 b a) a))
(.f64 (-.f64 a b) (/.f64 (+.f64 b a) (.f64 a a)))
(.f64 (-.f64 a b) (/.f64 (+.f64 b a) (.f64 (neg.f64 a) a)))
(*.f64 (+.f64 b a) (/.f64 (/.f64 (-.f64 a b) a) a))
(.f64 (fma.f64 b b (.f64 a a)) (/.f64 (fma.f64 b b (.f64 a a)) (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 (.f64 b a) #s(literal 2 binary64)))))
(pow.f64 (/.f64 (hypot.f64 b a) a) #s(literal 2 binary64))
(pow.f64 (pow.f64 (pow.f64 (/.f64 (hypot.f64 b a) a) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (/.f64 (hypot.f64 b a) a) #s(literal 2 binary64)) #s(literal 1 binary64))
(/.f64 (/.f64 (*.f64 (hypot.f64 b a) (hypot.f64 b a)) (neg.f64 a)) (neg.f64 a))
(/.f64 (/.f64 (*.f64 (hypot.f64 b a) (hypot.f64 b a)) (neg.f64 a)) a)
(/.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 (*.f64 b a) #s(literal 2 binary64))) (pow.f64 a #s(literal 3 binary64))) (neg.f64 a))
(/.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 (*.f64 b a) #s(literal 2 binary64))) (pow.f64 a #s(literal 3 binary64))) a)
(/.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 (.f64 b a) #s(literal 2 binary64))) (.f64 (neg.f64 a) a)) (*.f64 (neg.f64 a) a))
(/.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 (*.f64 b a) #s(literal 2 binary64))) (neg.f64 a)) (pow.f64 a #s(literal 3 binary64)))
(/.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 (.f64 b a) #s(literal 2 binary64))) (.f64 a a)) (*.f64 a a))
(/.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 (*.f64 b a) #s(literal 2 binary64))) a) (pow.f64 a #s(literal 3 binary64)))
(/.f64 (.f64 (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (/.f64 (/.f64 (-.f64 a b) a) a)) (fma.f64 b (-.f64 b a) (.f64 a a)))
(/.f64 (.f64 (fma.f64 b b (.f64 a a)) (/.f64 (/.f64 (-.f64 a b) a) a)) (-.f64 a b))
(/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) (neg.f64 a))
(/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64))) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (/.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 a #s(literal 4 binary64))) (*.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (fabs.f64 (/.f64 (fma.f64 b b (*.f64 a a)) a))) (neg.f64 a))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 a #s(literal 4 binary64))))) (neg.f64 (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 a #s(literal 4 binary64))))) (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 (pow.f64 b #s(literal 6 binary64)) (pow.f64 a #s(literal 6 binary64))))) (neg.f64 (fma.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 (pow.f64 b #s(literal 6 binary64)) (pow.f64 a #s(literal 6 binary64))))) (fma.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (neg.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 (*.f64 b a) #s(literal 2 binary64)))) (pow.f64 a #s(literal 4 binary64)))
(/.f64 (.f64 (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (-.f64 a b)) (.f64 (fma.f64 b (-.f64 b a) (.f64 a a)) (.f64 a a)))
(/.f64 (.f64 (fma.f64 b b (.f64 a a)) (-.f64 a b)) (.f64 (-.f64 a b) (.f64 a a)))
(/.f64 (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64))) (.f64 (+.f64 (-.f64 (pow.f64 b #s(literal 8 binary64)) (pow.f64 (.f64 b a) #s(literal 4 binary64))) (pow.f64 a #s(literal 8 binary64))) (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 (*.f64 b a) #s(literal 2 binary64)))))
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(+.f64 (.f64 (neg.f64 a) a) (.f64 b b))
(+.f64 (.f64 b b) (.f64 (neg.f64 a) a))
(+.f64 (.f64 b b) (.f64 a a))
(+.f64 (.f64 a a) (.f64 (neg.f64 b) b))
(+.f64 (.f64 a a) (.f64 b b))

eval47.0ms (0.9%)

Memory: -20.1MiB live, 76.4MiB allocated
Compiler: Compiled 6 154 to 1 251 computations (79.7% saved)

prune6.0ms (0.1%)

Memory

21.6MiB live, 21.6MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	284	5	289
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	285	5	290

Accuracy

100.0%

Counts

290 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	81.2%	(sqrt.f64 (fabs.f64 (/.f64 (fma.f64 (-.f64 a b) b (.f64 (-.f64 a b) a)) (.f64 a a))))
▶	81.2%	(sqrt.f64 (fabs.f64 (/.f64 (.f64 (-.f64 a b) (+.f64 b a)) (.f64 a a))))
▶	80.8%	(sqrt.f64 (fabs.f64 (.f64 (-.f64 a b) (/.f64 (+.f64 b a) (.f64 a a)))))
▶	97.8%	(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 160 to 102 computations (36.3% saved)

simplify165.0ms (3.1%)

Memory

-8.9MiB live, 180.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (fabs.f64 (/.f64 (fma.f64 (-.f64 a b) b (.f64 (-.f64 a b) a)) (.f64 a a))))
cost-diff	1	(fabs.f64 (/.f64 (fma.f64 (-.f64 a b) b (.f64 (-.f64 a b) a)) (.f64 a a)))
cost-diff	2	(/.f64 (fma.f64 (-.f64 a b) b (.f64 (-.f64 a b) a)) (.f64 a a))
cost-diff	3	(fma.f64 (-.f64 a b) b (*.f64 (-.f64 a b) a))
cost-diff	0	(*.f64 (-.f64 a b) (+.f64 b a))
cost-diff	0	(sqrt.f64 (fabs.f64 (/.f64 (.f64 (-.f64 a b) (+.f64 b a)) (.f64 a a))))
cost-diff	1	(fabs.f64 (/.f64 (.f64 (-.f64 a b) (+.f64 b a)) (.f64 a a)))
cost-diff	2	(/.f64 (.f64 (-.f64 a b) (+.f64 b a)) (.f64 a a))
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	1	(fabs.f64 (.f64 (-.f64 a b) (/.f64 (+.f64 b a) (.f64 a a))))
cost-diff	2	(.f64 (-.f64 a b) (/.f64 (+.f64 b a) (.f64 a a)))
cost-diff	0	#s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))
cost-diff	0	(fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64)))
cost-diff	0	(sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))))
cost-diff	0	(fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64))
cost-diff	0	(fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))
cost-diff	0	#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64))))
cost-diff	0	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	34	292
0	60	271
1	129	249
2	417	244
3	2766	244
0	8620	244

Stop Event

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

Calls

Call 1

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

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

localize112.0ms (2.1%)

Memory

-14.9MiB live, 128.5MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(sqrt.f64 (fabs.f64 (/.f64 (fma.f64 (-.f64 a b) b (.f64 (-.f64 a b) a)) (.f64 a a))))
accuracy	0.015625	(fma.f64 (-.f64 a b) b (*.f64 (-.f64 a b) a))
accuracy	0.01953125	(*.f64 (-.f64 a b) a)
accuracy	11.640757051003826	(/.f64 (fma.f64 (-.f64 a b) b (.f64 (-.f64 a b) a)) (.f64 a a))
accuracy	0.0	(*.f64 a a)
accuracy	0.0	(fabs.f64 (/.f64 (.f64 (-.f64 a b) (+.f64 b a)) (.f64 a a)))
accuracy	0.00390625	(sqrt.f64 (fabs.f64 (/.f64 (.f64 (-.f64 a b) (+.f64 b a)) (.f64 a a))))
accuracy	11.640757051003826	(/.f64 (.f64 (-.f64 a b) (+.f64 b a)) (.f64 a a))
accuracy	0.0	(fabs.f64 (.f64 (-.f64 a b) (/.f64 (+.f64 b a) (.f64 a a))))
accuracy	0.00390625	(sqrt.f64 (fabs.f64 (.f64 (-.f64 a b) (/.f64 (+.f64 b a) (.f64 a a)))))
accuracy	0.140625	(.f64 (-.f64 a b) (/.f64 (+.f64 b a) (.f64 a a)))
accuracy	11.973814015952184	(/.f64 (+.f64 b a) (*.f64 a a))
accuracy	0.0	(fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64)))
accuracy	0.00390625	(sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))))
accuracy	1.4415602757521204	#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	0.00390625	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))))
accuracy	0.28515625	(/.f64 (/.f64 b a) a)

Samples

79.0ms

256×

valid

Compiler

Compiled 274 to 33 computations (88% saved)

Precisions

Click to see histograms. Total time spent on operations: 63.0ms

ival-mult: 32.0ms (50.5% of total)

ival-sqrt: 11.0ms (17.4% of total)

ival-div: 9.0ms (14.2% of total)

ival-fabs: 5.0ms (7.9% of total)

ival-add: 3.0ms (4.7% of total)

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

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

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

exact: 0.0ms (0% of total)

series28.0ms (0.5%)

Memory

-2.2MiB live, 48.7MiB allocated

Counts

23 → 73

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

Calls

6 calls:

Time	Variable		Point	Expression
7.0ms	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)) (* (- a b) (/ (+ b a) (* a a))) (fabs (* (- a b) (/ (+ b a) (* a a)))) (sqrt (fabs (* (- a b) (/ (+ b a) (* a a))))) (- a b) (/ (* (- 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 b) b) (* (- a b) a)) (/ (+ (* (- a b) b) (* (- a b) a)) (* a a)) (fabs (/ (+ (* (- a b) b) (* (- a b) a)) (* a a))) (sqrt (fabs (/ (+ (* (- a b) b) (* (- a b) a)) (* a a)))) (/ (/ b a) a) (/ (+ b a) (* a a)) (* a a) (* (- a b) a))
6.0ms	b	@	-inf	((sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs (+ (* (/ (/ b a) a) b) -1)) (+ (* (/ (/ b a) a) b) -1) (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (/ (- (* a a) (* b b)) (* a a)) (* (- a b) (/ (+ b a) (* a a))) (fabs (* (- a b) (/ (+ b a) (* a a)))) (sqrt (fabs (* (- a b) (/ (+ b a) (* a a))))) (- a b) (/ (* (- 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 b) b) (* (- a b) a)) (/ (+ (* (- a b) b) (* (- a b) a)) (* a a)) (fabs (/ (+ (* (- a b) b) (* (- a b) a)) (* a a))) (sqrt (fabs (/ (+ (* (- a b) b) (* (- a b) a)) (* a a)))) (/ (/ b a) a) (/ (+ b a) (* a a)) (* a a) (* (- a b) 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)) (* (- a b) (/ (+ b a) (* a a))) (fabs (* (- a b) (/ (+ b a) (* a a)))) (sqrt (fabs (* (- a b) (/ (+ b a) (* a a))))) (- a b) (/ (* (- 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 b) b) (* (- a b) a)) (/ (+ (* (- a b) b) (* (- a b) a)) (* a a)) (fabs (/ (+ (* (- a b) b) (* (- a b) a)) (* a a))) (sqrt (fabs (/ (+ (* (- a b) b) (* (- a b) a)) (* a a)))) (/ (/ b a) a) (/ (+ b a) (* a a)) (* a a) (* (- a b) a))
3.0ms	a	@	0	((sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs (+ (* (/ (/ b a) a) b) -1)) (+ (* (/ (/ b a) a) b) -1) (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (/ (- (* a a) (* b b)) (* a a)) (* (- a b) (/ (+ b a) (* a a))) (fabs (* (- a b) (/ (+ b a) (* a a)))) (sqrt (fabs (* (- a b) (/ (+ b a) (* a a))))) (- a b) (/ (* (- 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 b) b) (* (- a b) a)) (/ (+ (* (- a b) b) (* (- a b) a)) (* a a)) (fabs (/ (+ (* (- a b) b) (* (- a b) a)) (* a a))) (sqrt (fabs (/ (+ (* (- a b) b) (* (- a b) a)) (* a a)))) (/ (/ b a) a) (/ (+ b a) (* a a)) (* a a) (* (- a b) a))
3.0ms	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)) (* (- a b) (/ (+ b a) (* a a))) (fabs (* (- a b) (/ (+ b a) (* a a)))) (sqrt (fabs (* (- a b) (/ (+ b a) (* a a))))) (- a b) (/ (* (- 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 b) b) (* (- a b) a)) (/ (+ (* (- a b) b) (* (- a b) a)) (* a a)) (fabs (/ (+ (* (- a b) b) (* (- a b) a)) (* a a))) (sqrt (fabs (/ (+ (* (- a b) b) (* (- a b) a)) (* a a)))) (/ (/ b a) a) (/ (+ b a) (* a a)) (* a a) (* (- a b) a))

simplify87.0ms (1.7%)

Memory

17.7MiB live, 157.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	173	651
1	580	549
2	2132	544
0	8693	521

Stop Event

1×	iter limit
1×	node limit

Counts

73 → 72

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

rewrite538.0ms (10.2%)

Memory

120.2MiB live, 460.5MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	34	261
0	60	244
1	217	216
2	1555	163
0	8950	163

Stop Event

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

Counts

23 → 3 431

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

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

eval238.0ms (4.5%)

Memory: -4.8MiB live, 318.3MiB allocated
Compiler: Compiled 40 307 to 6 207 computations (84.6% saved)

prune847.0ms (16.1%)

Memory

-180.5MiB live, 71.7MiB allocated

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	1 383	2	1 385
Fresh	0	0	0
Picked	3	2	5
Done	0	0	0
Total	1 386	4	1 390

Accuracy

100.0%

Counts

1 390 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	81.2%	(sqrt.f64 (fabs.f64 (/.f64 (fma.f64 (-.f64 a b) b (.f64 (-.f64 a b) a)) (.f64 a a))))
✓	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)))))
▶	81.8%	(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)))))
▶	97.8%	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64)))

Compiler

Compiled 77 to 47 computations (39% saved)

simplify127.0ms (2.4%)

Memory

25.6MiB live, 166.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	103
0	24	103
1	56	95
2	244	91
3	1624	91
0	9083	91

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

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

localize32.0ms (0.6%)

Memory

0.1MiB live, 46.9MiB allocated

Localize:

Found 6 expressions of interest:

New	Metric	Score
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	0.00390625	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64)))))
accuracy	12.089892818980406	(/.f64 b (*.f64 a a))
accuracy	0.00390625	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64)))
accuracy	1.4415602757521204	#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64))

Samples

24.0ms

256×

valid

Compiler

Compiled 83 to 16 computations (80.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-mult: 5.0ms (34% of total)

ival-div: 3.0ms (20.4% of total)

ival-fabs: 2.0ms (13.6% of total)

ival-sqrt: 2.0ms (13.6% of total)

ival-add: 1.0ms (6.8% of total)

ival-sub: 1.0ms (6.8% of total)

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

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

exact: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory

7.8MiB live, 7.8MiB allocated

Counts

7 → 9

Calls

Call 1

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

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))
(/ b (pow a 2))
-1
(- (/ (pow b 2) (pow a 2)) 1)
(* (pow b 2) (- (/ 1 (pow a 2)) (/ 1 (pow b 2))))

Calls

6 calls:

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

simplify100.0ms (1.9%)

Memory

-33.6MiB live, 114.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	83
1	44	77
2	127	77
3	496	77
4	4747	77
0	8170	72

Stop Event

1×	iter limit
1×	node limit

Counts

9 → 9

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))
(/ b (pow a 2))
-1
(- (/ (pow b 2) (pow a 2)) 1)
(* (pow b 2) (- (/ 1 (pow a 2)) (/ 1 (pow b 2))))

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

rewrite106.0ms (2%)

Memory

32.7MiB live, 126.5MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	96
0	24	95
1	96	87
2	769	69
0	9594	69

Stop Event

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

Counts

7 → 410

Calls

Call 1

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

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

eval42.0ms (0.8%)

Memory: -3.1MiB live, 43.3MiB allocated
Compiler: Compiled 7 797 to 941 computations (87.9% saved)

prune4.0ms (0.1%)

Memory

12.5MiB live, 12.5MiB allocated

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	227	1	228
Fresh	0	0	0
Picked	0	2	2
Done	1	1	2
Total	228	4	232

Accuracy

100.0%

Counts

232 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)))
✓	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)))))
✓	81.8%	(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)))))
✓	97.8%	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64)))

Compiler

Compiled 86 to 52 computations (39.5% saved)

simplify140.0ms (2.7%)

Memory

0.6MiB live, 144.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)
cost-diff	0	#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a))
cost-diff	0	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)))
cost-diff	2	(*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	82
0	20	82
1	51	72
2	238	72
3	1611	70
0	9810	68

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

localize59.0ms (1.1%)

Memory

5.5MiB live, 92.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)))
accuracy	0.0234375	(/.f64 (+.f64 b a) a)
accuracy	0.0234375	(/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)
accuracy	0.046875	(*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b))

Samples

32.0ms

256×

valid

Compiler

Compiled 60 to 15 computations (75% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-add: 10.0ms (40.1% of total)

ival-div: 5.0ms (20% of total)

ival-mult: 4.0ms (16% of total)

ival-sub: 2.0ms (8% of total)

ival-sqrt: 2.0ms (8% of total)

ival-fabs: 1.0ms (4% of total)

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

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

series6.0ms (0.1%)

Memory

10.6MiB live, 10.6MiB allocated

Counts

5 → 25

Calls

Call 1

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

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

Calls

6 calls:

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

simplify220.0ms (4.2%)

Memory

14.4MiB live, 235.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	224
1	220	164
2	787	164
3	4029	164
0	8478	162

Stop Event

1×	iter limit
1×	node limit

Counts

25 → 24

Calls

Call 1

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

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

rewrite88.0ms (1.7%)

Memory

-16.8MiB live, 74.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	74
0	20	74
1	95	64
2	883	52
0	9981	51

Stop Event

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

Counts

5 → 282

Calls

Call 1

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

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

eval92.0ms (1.7%)

Memory: 9.7MiB live, 61.0MiB allocated
Compiler: Compiled 10 352 to 1 411 computations (86.4% saved)

prune30.0ms (0.6%)

Memory

-35.3MiB live, 15.4MiB allocated

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	294	0	294
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	294	4	298

Accuracy

100.0%

Counts

298 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)))
✓	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)))))
✓	81.8%	(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)))))
✓	97.8%	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64)))

Compiler

Compiled 242 to 103 computations (57.4% saved)

regimes17.0ms (0.3%)

Memory

23.3MiB live, 23.4MiB allocated

Counts

9 → 1

Calls

Call 1

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

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

Calls

7 calls:

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

Results

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

Compiler

Compiled 44 to 31 computations (29.5% saved)

regimes12.0ms (0.2%)

Memory

15.7MiB live, 15.6MiB allocated

Counts

5 → 2

Calls

Call 1

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

Outputs

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

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

Calls

7 calls:

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

Results

Accuracy	Segments	Branch
99.4%	2	`(*.f64 b b)`
99.4%	2	`(*.f64 a a)`
99.4%	2	`(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))`
99.4%	2	`(fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a)))`
99.4%	2	`(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))`
99.4%	2	`a`
99.4%	2	`b`

Compiler

Compiled 44 to 31 computations (29.5% saved)

regimes18.0ms (0.3%)

Memory

-34.8MiB live, 12.5MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

7 calls:

12.0ms	(*.f64 a a)
1.0ms	a
1.0ms	b
1.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
1.0ms	(fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a)))

Results

Accuracy	Segments	Branch
97.8%	1	`(*.f64 b b)`
97.8%	1	`(*.f64 a a)`
97.8%	1	`(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))`
97.8%	1	`(fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a)))`
97.8%	1	`(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))`
97.8%	1	`a`
97.8%	1	`b`

Compiler

Compiled 44 to 31 computations (29.5% saved)

bsearch5.0ms (0.1%)

Memory

5.8MiB live, 5.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
4.0ms	1.2755831525145756e-179	1.7123234091827364e-179

Samples

3.0ms

48×

valid

Compiler

Compiled 130 to 91 computations (30% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-mult: 1.0ms (60.3% of total)

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

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

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

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

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

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

simplify35.0ms (0.7%)

Memory

32.7MiB live, 32.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	26	80
1	55	72
2	232	72
3	1475	72

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)))))

(if (<=.f64 b #s(literal 1240983847993237/72999049881955123498258745691204661198291656115976958889267080286388402675338838184094604981077942396458276953177510516971019275542007007972042581115555427012031914789764239201325987075945660416 binary64)) (sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64))) (sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64))))))

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

Outputs

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

(if (<=.f64 b #s(literal 1240983847993237/72999049881955123498258745691204661198291656115976958889267080286388402675338838184094604981077942396458276953177510516971019275542007007972042581115555427012031914789764239201325987075945660416 binary64)) (sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64))) (sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64))))))

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

derivations238.0ms (4.5%)

Memory

-37.0MiB live, 105.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	117
1	58	104
2	194	104
3	1182	104
4	5531	104
0	8296	101
0	34	261
0	60	244
1	217	216
2	1555	163
0	8950	163

Stop Event

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

Compiler

Compiled 80 to 26 computations (67.5% saved)

preprocess24.0ms (0.5%)

Memory

26.7MiB live, 26.7MiB allocated

Remove

(abs a)

(abs b)

Compiler

Compiled 278 to 124 computations (55.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze12.0ms (0.2%)

sample1.2s (22.5%)

explain109.0ms (2.1%)

preprocess126.0ms (2.4%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify105.0ms (2%)

localize32.0ms (0.6%)

series5.0ms (0.1%)

simplify121.0ms (2.3%)

rewrite112.0ms (2.1%)

eval47.0ms (0.9%)

prune6.0ms (0.1%)

simplify165.0ms (3.1%)

localize112.0ms (2.1%)

series28.0ms (0.5%)

simplify87.0ms (1.7%)

rewrite538.0ms (10.2%)

eval238.0ms (4.5%)

prune847.0ms (16.1%)

simplify127.0ms (2.4%)

localize32.0ms (0.6%)

series5.0ms (0.1%)

simplify100.0ms (1.9%)

rewrite106.0ms (2%)

eval42.0ms (0.8%)

prune4.0ms (0.1%)

simplify140.0ms (2.7%)

localize59.0ms (1.1%)

series6.0ms (0.1%)

simplify220.0ms (4.2%)

rewrite88.0ms (1.7%)

eval92.0ms (1.7%)

prune30.0ms (0.6%)

regimes17.0ms (0.3%)

regimes12.0ms (0.2%)

regimes18.0ms (0.3%)

bsearch5.0ms (0.1%)

simplify35.0ms (0.7%)

derivations238.0ms (4.5%)

preprocess24.0ms (0.5%)

end0.0ms (0%)

Profiling