Metrics for Eccentricity of an ellipse

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze12.0ms (0.3%)

Memory

15.5MiB live, 15.5MiB allocated; 0ms collecting garbage

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 (27.8%)

Memory

23.4MiB live, 1 093.7MiB allocated; 164ms collecting garbage

Samples

716.0ms	8 256×	0	valid
66.0ms	779×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 498.0ms

ival-mult: 119.0ms (23.9% of total)

ival-<=: 113.0ms (22.7% of total)

ival-fabs: 71.0ms (14.2% of total)

ival-sub: 56.0ms (11.2% of total)

ival-sqrt: 54.0ms (10.8% of total)

ival-div: 50.0ms (10% of total)

ival-and: 18.0ms (3.6% of total)

exact: 11.0ms (2.2% of total)

adjust: 3.0ms (0.6% of total)

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

Bogosity

explain188.0ms (4.5%)

Memory

10.1MiB live, 186.0MiB allocated; 57ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
50	-	-	`(/.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	50	0
↳	`(*.f64 b b)`	underflow	179
↳	`(-.f64 (.f64 a a) (.f64 b b))`	underflow	50
↳	`(*.f64 a a)`	underflow	50
↳	`(*.f64 a a)`	underflow	50

Confusion

	Predicted +	Predicted -
+	50	0
-	0	206

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	50	0	0
-	0	0	206

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	206
1	50

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

62.0ms

512×

valid

Compiler

Compiled 119 to 28 computations (76.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 49.0ms

ival-sub: 33.0ms (67.7% of total)

ival-mult: 7.0ms (14.4% of total)

ival-div: 3.0ms (6.2% of total)

ival-sqrt: 3.0ms (6.2% of total)

ival-fabs: 2.0ms (4.1% of total)

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

adjust: 0.0ms (0% of total)

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

preprocess180.0ms (4.3%)

Memory

-0.1MiB live, 102.9MiB allocated; 41ms collecting garbage

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; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	80.5%	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

Compiler

Compiled 13 to 8 computations (38.5% saved)

simplify119.0ms (2.9%)

Memory

10.0MiB live, 101.4MiB allocated; 9ms collecting garbage

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

localize21.0ms (0.5%)

Memory

25.7MiB live, 25.7MiB allocated; 0ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a)))
accuracy	0.0078125	(-.f64 (.f64 a a) (.f64 b b))
accuracy	0.01171875	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
accuracy	12.121231304049802	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))

Samples

15.0ms

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 (34.2% of total)

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

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

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

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

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

adjust: 0.0ms (0% of total)

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

series50.0ms (1.2%)

Memory

-32.1MiB live, 21.0MiB allocated; 5ms collecting garbage

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
46.0ms	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	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	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	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)))

simplify118.0ms (2.8%)

Memory

21.7MiB live, 112.0MiB allocated; 9ms collecting garbage

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)

rewrite101.0ms (2.4%)

Memory

-7.5MiB live, 88.7MiB allocated; 10ms collecting garbage

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)))
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(+.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (fma.f64 (fma.f64 b b (.f64 a a)) (.f64 b b) (pow.f64 a #s(literal 4 binary64)))) (/.f64 (pow.f64 b #s(literal 6 binary64)) (fma.f64 (fma.f64 b b (.f64 a a)) (.f64 b b) (pow.f64 a #s(literal 4 binary64)))))
(+.f64 (.f64 (neg.f64 b) b) (.f64 (neg.f64 a) a))
(+.f64 (.f64 (neg.f64 b) b) (.f64 a a))
(+.f64 (.f64 (neg.f64 a) a) (.f64 (neg.f64 b) b))
(+.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))

eval59.0ms (1.4%)

Memory: -1.3MiB live, 44.7MiB allocated; 3ms collecting garbage
Compiler: Compiled 6 154 to 1 251 computations (79.7% saved)

prune6.0ms (0.1%)

Memory

17.0MiB live, 17.0MiB allocated; 0ms collecting garbage

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
▶	100.0%	(sqrt.f64 (fabs.f64 (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)))
▶	80.5%	(sqrt.f64 (fabs.f64 (/.f64 (.f64 (-.f64 a b) (+.f64 b a)) (.f64 a a))))
▶	80.0%	(sqrt.f64 (fabs.f64 (.f64 (-.f64 a b) (/.f64 (+.f64 b a) (.f64 a a)))))
▶	98.8%	(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 154 to 102 computations (33.8% saved)

simplify82.0ms (2%)

Memory

6.5MiB live, 93.9MiB allocated; 9ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b))
cost-diff	0	(sqrt.f64 (fabs.f64 (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)))
cost-diff	1	(fabs.f64 (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a))
cost-diff	2	(/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.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	282
0	59	273
1	128	251
2	403	246
3	2558	246
0	8435	246

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

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

localize160.0ms (3.8%)

Memory

-39.7MiB live, 107.5MiB allocated; 54ms collecting garbage

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(sqrt.f64 (fabs.f64 (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)))
accuracy	0.015625	(/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)
accuracy	0.01953125	(/.f64 (+.f64 b a) a)
accuracy	0.05078125	(*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b))
accuracy	0.0	(*.f64 a a)
accuracy	0.0	(fabs.f64 (/.f64 (.f64 (-.f64 a b) (+.f64 b a)) (.f64 a a)))
accuracy	0.01171875	(sqrt.f64 (fabs.f64 (/.f64 (.f64 (-.f64 a b) (+.f64 b a)) (.f64 a a))))
accuracy	12.121231304049802	(/.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	0.01171875	(sqrt.f64 (fabs.f64 (.f64 (-.f64 a b) (/.f64 (+.f64 b a) (.f64 a a)))))
accuracy	0.22265625	(.f64 (-.f64 a b) (/.f64 (+.f64 b a) (.f64 a a)))
accuracy	12.438063300317515	(/.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	0.01171875	(sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))))
accuracy	0.8444330107362881	#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	0.01171875	(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	0.296875	(/.f64 (/.f64 b a) a)

Samples

66.0ms

256×

valid

Compiler

Compiled 260 to 32 computations (87.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 51.0ms

ival-mult: 22.0ms (43.2% of total)

ival-div: 10.0ms (19.6% of total)

ival-fabs: 8.0ms (15.7% of total)

ival-sqrt: 6.0ms (11.8% of total)

ival-add: 2.0ms (3.9% of total)

ival-sub: 2.0ms (3.9% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series19.0ms (0.5%)

Memory

31.1MiB live, 31.1MiB allocated; 0ms collecting garbage

Counts

23 → 65

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

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

Calls

6 calls:

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

simplify141.0ms (3.4%)

Memory

-10.7MiB live, 82.6MiB allocated; 10ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	150	548
1	473	449
2	1676	437
0	8556	424

Stop Event

1×	iter limit
1×	node limit

Counts

65 → 64

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

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

rewrite218.0ms (5.2%)

Memory

23.8MiB live, 254.8MiB allocated; 29ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	34	251
0	59	246
1	205	218
2	1457	169
0	9095	169

Stop Event

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

Counts

23 → 2 386

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

eval205.0ms (4.9%)

Memory: -4.6MiB live, 263.7MiB allocated; 33ms collecting garbage
Compiler: Compiled 30 391 to 5 020 computations (83.5% saved)

prune98.0ms (2.4%)

Memory

-8.7MiB live, 63.9MiB allocated; 110ms collecting garbage

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	1 091	2	1 093
Fresh	0	0	0
Picked	2	3	5
Done	0	0	0
Total	1 093	5	1 098

Accuracy

100.0%

Counts

1 098 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (fabs.f64 (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)))
✓	80.0%	(sqrt.f64 (fabs.f64 (.f64 (-.f64 a b) (/.f64 (+.f64 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)))))
▶	81.1%	(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)))))
▶	98.8%	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64)))

Compiler

Compiled 87 to 56 computations (35.6% saved)

simplify126.0ms (3%)

Memory

-3.2MiB live, 93.5MiB allocated; 11ms collecting garbage

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)

localize48.0ms (1.2%)

Memory

-17.0MiB live, 29.3MiB allocated; 2ms collecting garbage

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	0.01171875	(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	12.533943798548414	(/.f64 b (*.f64 a a))
accuracy	0.01171875	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64)))
accuracy	0.8444330107362881	#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64))

Samples

22.0ms

256×

valid

Compiler

Compiled 83 to 16 computations (80.7% saved)

Precisions

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

ival-mult: 5.0ms (35.3% of total)

ival-div: 3.0ms (21.2% of total)

ival-fabs: 2.0ms (14.1% of total)

ival-sqrt: 2.0ms (14.1% of total)

ival-add: 1.0ms (7.1% of total)

ival-sub: 1.0ms (7.1% of total)

adjust: 0.0ms (0% 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

9.7MiB live, 9.7MiB allocated; 0ms collecting garbage

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)))

simplify105.0ms (2.5%)

Memory

1.0MiB live, 96.8MiB allocated; 7ms collecting garbage

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 (2.5%)

Memory

2.8MiB live, 94.9MiB allocated; 3ms collecting garbage

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))))
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(+.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)))) #s(literal -1 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)))) #s(literal -1 binary64)))
(+.f64 (.f64 #s(literal -1 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 #s(literal -1 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 (/.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 (1%)

Memory: 0.6MiB live, 51.8MiB allocated; 5ms collecting garbage
Compiler: Compiled 7 797 to 941 computations (87.9% saved)

prune5.0ms (0.1%)

Memory

13.8MiB live, 13.8MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	227	1	228
Fresh	0	0	0
Picked	0	2	2
Done	1	2	3
Total	228	5	233

Accuracy

100.0%

Counts

233 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	80.0%	(sqrt.f64 (fabs.f64 (.f64 (-.f64 a b) (/.f64 (+.f64 b a) (.f64 a a)))))
▶	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)))))
✓	81.1%	(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)))))
✓	98.8%	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64)))

Compiler

Compiled 99 to 61 computations (38.4% saved)

simplify107.0ms (2.6%)

Memory

14.2MiB live, 105.3MiB allocated; 6ms collecting garbage

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)

localize31.0ms (0.8%)

Memory

-8.7MiB live, 37.8MiB allocated; 2ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)))
accuracy	0.015625	(/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)
accuracy	0.01953125	(/.f64 (+.f64 b a) a)
accuracy	0.05078125	(*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b))

Samples

24.0ms

256×

valid

Compiler

Compiled 60 to 15 computations (75% saved)

Precisions

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

ival-mult: 6.0ms (36.7% of total)

ival-div: 4.0ms (24.5% of total)

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

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

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

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

adjust: 0.0ms (0% of total)

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

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

series4.0ms (0.1%)

Memory

4.3MiB live, 4.3MiB allocated; 0ms collecting garbage

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	@	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))

simplify147.0ms (3.5%)

Memory

4.9MiB live, 101.8MiB allocated; 12ms collecting garbage

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)

rewrite94.0ms (2.3%)

Memory

-16.5MiB live, 75.3MiB allocated; 6ms collecting garbage

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

eval55.0ms (1.3%)

Memory: 3.3MiB live, 57.4MiB allocated; 10ms collecting garbage
Compiler: Compiled 10 352 to 1 411 computations (86.4% saved)

prune6.0ms (0.2%)

Memory

15.3MiB live, 15.3MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	294	0	294
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	294	5	299

Accuracy

100.0%

Counts

299 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	80.0%	(sqrt.f64 (fabs.f64 (.f64 (-.f64 a b) (/.f64 (+.f64 b a) (.f64 a a)))))
✓	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)))))
✓	81.1%	(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)))))
✓	98.8%	(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64)))

Compiler

Compiled 252 to 109 computations (56.7% saved)

regimes26.0ms (0.6%)

Memory

-27.7MiB live, 18.9MiB allocated; 3ms collecting garbage

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

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

Calls

7 calls:

11.0ms	a
3.0ms	b
2.0ms	(*.f64 a a)
2.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
2.0ms	(*.f64 b b)

Results

Accuracy	Segments	Branch
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 (0.3%)

Memory

13.1MiB live, 13.1MiB allocated; 0ms collecting garbage

Accuracy

Total -12.6b remaining (-1589.7%)

Threshold costs -12.6b (-1589.7%)

Counts

5 → 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))))

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

Results

Accuracy	Segments	Branch
98.8%	1	`(*.f64 b b)`
98.8%	1	`(*.f64 a a)`
98.8%	1	`(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))`
98.8%	1	`(fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a)))`
98.8%	1	`(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))`
98.8%	1	`a`
98.8%	1	`b`

Compiler

Compiled 44 to 31 computations (29.5% saved)

simplify35.0ms (0.8%)

Memory

19.1MiB live, 19.1MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	38
1	44	34
2	216	34
3	1452	34

Stop Event

1×	node limit

Calls

Call 1

Inputs

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

(sqrt.f64 #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)))))

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

derivations256.0ms (6.1%)

Memory

-39.2MiB live, 54.1MiB allocated; 3ms collecting garbage

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	251
0	59	246
1	205	218
2	1457	169
0	9095	169

Stop Event

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

Compiler

Compiled 38 to 17 computations (55.3% saved)

preprocess19.0ms (0.5%)

Memory

16.1MiB live, 16.1MiB allocated; 0ms collecting garbage

Remove

(abs a)

(abs b)

Compiler

Compiled 194 to 106 computations (45.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze12.0ms (0.3%)

sample1.2s (27.8%)

explain188.0ms (4.5%)

preprocess180.0ms (4.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify119.0ms (2.9%)

localize21.0ms (0.5%)

series50.0ms (1.2%)

simplify118.0ms (2.8%)

rewrite101.0ms (2.4%)

eval59.0ms (1.4%)

prune6.0ms (0.1%)

simplify82.0ms (2%)

localize160.0ms (3.8%)

series19.0ms (0.5%)

simplify141.0ms (3.4%)

rewrite218.0ms (5.2%)

eval205.0ms (4.9%)

prune98.0ms (2.4%)

simplify126.0ms (3%)

localize48.0ms (1.2%)

series5.0ms (0.1%)

simplify105.0ms (2.5%)

rewrite106.0ms (2.5%)

eval42.0ms (1%)

prune5.0ms (0.1%)

simplify107.0ms (2.6%)

localize31.0ms (0.8%)

series4.0ms (0.1%)

simplify147.0ms (3.5%)

rewrite94.0ms (2.3%)

eval55.0ms (1.3%)

prune6.0ms (0.2%)

regimes26.0ms (0.6%)

regimes12.0ms (0.3%)

simplify35.0ms (0.8%)

derivations256.0ms (6.1%)

preprocess19.0ms (0.5%)

end0.0ms (0%)

Profiling