Metrics for Diagrams.TwoD.Apollonian:initialConfig from diagrams-contrib-1.3.0.5, B

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze158.0ms (3.4%)

Memory

15.6MiB live, 208.6MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
0%	0%	99.9%	0.1%	0%	0%	0%	4
0%	0%	99.9%	0.1%	0%	0%	0%	5
0%	0%	99.9%	0.1%	0%	0%	0%	6
30.8%	25%	56.2%	0.1%	0%	18.7%	0%	7
30.8%	25%	56.2%	0.1%	0%	18.7%	0%	8
32%	25%	53%	0.1%	0%	21.8%	0%	9
55.8%	37.4%	29.6%	0.1%	0%	32.8%	0%	10
55.8%	37.4%	29.6%	0.1%	0%	32.8%	0%	11
57.8%	37.4%	27.3%	0.1%	0%	35.1%	0%	12

Compiler

Compiled 12 to 10 computations (16.7% saved)

sample1.4s (30.4%)

Memory

34.8MiB live, 2 031.1MiB allocated

Samples

807.0ms	8 256×	0	valid
227.0ms	2 486×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 646.0ms

ival-mult: 345.0ms (53.4% of total)

ival-sqrt: 211.0ms (32.6% of total)

ival-sub: 77.0ms (11.9% of total)

ival-true: 9.0ms (1.4% of total)

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

Bogosity

explain95.0ms (2%)

Memory

-6.4MiB live, 198.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
125	-	1	(2.1931456799435843e-119 6.838840922268816e-156 6.116829763791465e-168)	`(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))`
14	-	0	-	`(-.f64 (.f64 y y) (.f64 z z))`
0	-	0	-	`(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))`
0	-	0	-	`y`
0	-	0	-	`(*.f64 z z)`
0	-	0	-	`(*.f64 y y)`
0	-	0	-	`z`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))`	oflow-rescue	115	0
↳	`(*.f64 y y)`	overflow	115
↳	`(-.f64 (.f64 y y) (.f64 z z))`	overflow	115
↳	`(*.f64 z z)`	overflow	14
`-.f64`	`(-.f64 (.f64 y y) (.f64 z z))`	nan-rescue	14	0
↳	`(*.f64 y y)`	overflow	115
↳	`(*.f64 z z)`	overflow	14
`sqrt.f64`	`(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))`	uflow-rescue	9	0
↳	`(*.f64 y y)`	underflow	9
↳	`(-.f64 (.f64 y y) (.f64 z z))`	underflow	9
↳	`(*.f64 z z)`	underflow	107

Confusion

	Predicted +	Predicted -
+	84	1
-	40	131

Precision

0.6774193548387096

Recall

0.9882352941176471

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	84	0	1
-	40	0	131

Precision?

0.6774193548387096

Recall?

0.9882352941176471

Freqs

test

number	freq
0	132
1	110
2	14

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

36.0ms

512×

valid

Compiler

Compiled 82 to 28 computations (65.9% saved)

Precisions

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

ival-mult: 13.0ms (65.1% of total)

ival-sqrt: 4.0ms (20% of total)

ival-sub: 2.0ms (10% of total)

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

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

preprocess529.0ms (11.3%)

Memory

-12.0MiB live, 301.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	93
1	108	93
2	221	93
3	608	93
4	1655	93
5	2753	93
6	3995	93
7	4670	93
8	5262	93
9	5561	93
10	5651	93
11	5747	93
12	5811	93
13	6963	93
14	7539	93
15	7635	93
16	7731	93
17	7827	93
18	7827	93
0	8	10
0	13	10
1	22	10
2	33	10
3	59	10
4	123	10
5	324	10
6	579	10
7	1254	10
8	2514	10
9	4177	10
10	5039	10
11	5408	10
12	5638	10
13	5752	10
14	5752	10
15	6712	10
16	6872	10
17	7192	10
18	7192	10
19	7592	10
20	7752	10
21	7832	10
22	7832	10
23	7832	10
0	10485	10

Stop Event

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

Calls

Call 1

Inputs
(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))

Outputs
(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
(.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x)

Symmetry

(abs z)

(abs y)

(negabs x)

Compiler

Compiled 10 to 8 computations (20% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 0 to 3 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	68.5%	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))

Compiler

Compiled 10 to 8 computations (20% saved)

simplify341.0ms (7.3%)

Memory

0.2MiB live, 186.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 y y)
cost-diff	0	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))
cost-diff	0	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
cost-diff	128	(-.f64 (.f64 y y) (.f64 z z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	34
0	13	34
1	22	34
2	33	34
3	59	34
4	123	34
5	324	34
6	579	34
7	1254	34
8	2514	34
9	4177	34
10	5039	34
11	5408	34
12	5638	34
13	5752	34
14	5752	34
15	6712	34
16	6872	34
17	7192	34
18	7192	34
19	7592	34
20	7752	34
21	7832	34
22	7832	34
23	7832	34
0	10485	34

Stop Event

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

Calls

Call 1

Inputs
(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
x
(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))
(-.f64 (.f64 y y) (.f64 z z))
(*.f64 y y)
y
(*.f64 z z)
z

Outputs
(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
(.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x)
x
(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))
(sqrt.f64 (*.f64 (-.f64 y z) (+.f64 z y)))
(-.f64 (.f64 y y) (.f64 z z))
(*.f64 (-.f64 y z) (+.f64 z y))
(*.f64 y y)
y
(*.f64 z z)
z

localize21.0ms (0.4%)

Memory

27.0MiB live, 27.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 y y)
accuracy	0.00390625	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
accuracy	2.7929687500000004	(-.f64 (.f64 y y) (.f64 z z))
accuracy	28.89181931374142	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))

Samples

15.0ms

256×

valid

Compiler

Compiled 36 to 10 computations (72.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-mult: 5.0ms (63.8% of total)

ival-sqrt: 2.0ms (25.5% of total)

ival-sub: 1.0ms (12.8% of total)

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

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

series16.0ms (0.3%)

Memory

-16.1MiB live, 21.9MiB allocated

Counts

4 → 96

Calls

Call 1

Inputs
#s(alt (-.f64 (.f64 y y) (.f64 z z)) (patch (-.f64 (.f64 y y) (.f64 z z)) #<representation binary64>) () ())
#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) (patch (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) #<representation binary64>) () ())
#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())

Outputs
#s(alt (pow y 2) (taylor 0 z) (#s(alt (-.f64 (.f64 y y) (.f64 z z)) (patch (-.f64 (.f64 y y) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow z 2)) (pow y 2)) (taylor 0 z) (#s(alt (-.f64 (.f64 y y) (.f64 z z)) (patch (-.f64 (.f64 y y) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow z 2)) (pow y 2)) (taylor 0 z) (#s(alt (-.f64 (.f64 y y) (.f64 z z)) (patch (-.f64 (.f64 y y) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow z 2)) (pow y 2)) (taylor 0 z) (#s(alt (-.f64 (.f64 y y) (.f64 z z)) (patch (-.f64 (.f64 y y) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 z) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (/ (* x (pow z 2)) y)) (* x y)) (taylor 0 z) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (+ (* x y) (* (pow z 2) (+ (* -1/2 (/ x y)) (* -1/8 (/ (* x (pow z 2)) (pow y 3)))))) (taylor 0 z) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (+ (* x y) (* (pow z 2) (+ (* -1/2 (/ x y)) (* (pow z 2) (+ (* -1/8 (/ x (pow y 3))) (* -1/16 (/ (* x (pow z 2)) (pow y 5)))))))) (taylor 0 z) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt y (taylor 0 z) (#s(alt (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) (patch (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) #<representation binary64>) () ())) ())
#s(alt (+ y (* -1/2 (/ (pow z 2) y))) (taylor 0 z) (#s(alt (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) (patch (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) #<representation binary64>) () ())) ())
#s(alt (+ y (* (pow z 2) (- (* -1/8 (/ (pow z 2) (pow y 3))) (* 1/2 (/ 1 y))))) (taylor 0 z) (#s(alt (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) (patch (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) #<representation binary64>) () ())) ())
#s(alt (+ y (* (pow z 2) (- (* (pow z 2) (- (* -1/16 (/ (pow z 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y))))) (taylor 0 z) (#s(alt (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) (patch (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow z 2)) (taylor inf z) (#s(alt (-.f64 (.f64 y y) (.f64 z z)) (patch (-.f64 (.f64 y y) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow z 2) (- (/ (pow y 2) (pow z 2)) 1)) (taylor inf z) (#s(alt (-.f64 (.f64 y y) (.f64 z z)) (patch (-.f64 (.f64 y y) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow z 2) (- (/ (pow y 2) (pow z 2)) 1)) (taylor inf z) (#s(alt (-.f64 (.f64 y y) (.f64 z z)) (patch (-.f64 (.f64 y y) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow z 2) (- (/ (pow y 2) (pow z 2)) 1)) (taylor inf z) (#s(alt (-.f64 (.f64 y y) (.f64 z z)) (patch (-.f64 (.f64 y y) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* x (* z (sqrt -1))) (taylor inf z) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (* z (+ (* 1/2 (/ (* x (pow y 2)) (* (pow z 2) (sqrt -1)))) (* x (sqrt -1)))) (taylor inf z) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (* z (+ (* -1/8 (/ (* x (pow y 4)) (* (pow z 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (* x (pow y 2)) (* (pow z 2) (sqrt -1)))) (* x (sqrt -1))))) (taylor inf z) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (* z (+ (* -1/8 (/ (* x (pow y 4)) (* (pow z 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (* x (pow y 6)) (* (pow z 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (/ (* x (pow y 2)) (* (pow z 2) (sqrt -1)))) (* x (sqrt -1)))))) (taylor inf z) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (* z (sqrt -1)) (taylor inf z) (#s(alt (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) (patch (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) #<representation binary64>) () ())) ())
#s(alt (* z (+ (sqrt -1) (* 1/2 (/ (pow y 2) (* (pow z 2) (sqrt -1)))))) (taylor inf z) (#s(alt (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) (patch (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) #<representation binary64>) () ())) ())
#s(alt (* z (+ (sqrt -1) (+ (* -1/8 (/ (pow y 4) (* (pow z 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow y 2) (* (pow z 2) (sqrt -1))))))) (taylor inf z) (#s(alt (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) (patch (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) #<representation binary64>) () ())) ())
#s(alt (* z (+ (sqrt -1) (+ (* -1/8 (/ (pow y 4) (* (pow z 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow y 6) (* (pow z 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow y 2) (* (pow z 2) (sqrt -1)))))))) (taylor inf z) (#s(alt (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) (patch (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow z 2)) (taylor -inf z) (#s(alt (-.f64 (.f64 y y) (.f64 z z)) (patch (-.f64 (.f64 y y) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow z 2) (- (/ (pow y 2) (pow z 2)) 1)) (taylor -inf z) (#s(alt (-.f64 (.f64 y y) (.f64 z z)) (patch (-.f64 (.f64 y y) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow z 2) (- (/ (pow y 2) (pow z 2)) 1)) (taylor -inf z) (#s(alt (-.f64 (.f64 y y) (.f64 z z)) (patch (-.f64 (.f64 y y) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow z 2) (- (/ (pow y 2) (pow z 2)) 1)) (taylor -inf z) (#s(alt (-.f64 (.f64 y y) (.f64 z z)) (patch (-.f64 (.f64 y y) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (* z (sqrt -1)))) (taylor -inf z) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (+ (* 1/2 (/ (* x (pow y 2)) (* (pow z 2) (sqrt -1)))) (* x (sqrt -1))))) (taylor -inf z) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (+ (* -1/8 (/ (* x (pow y 4)) (* (pow z 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (* x (pow y 2)) (* (pow z 2) (sqrt -1)))) (* x (sqrt -1)))))) (taylor -inf z) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (+ (* -1/8 (/ (* x (pow y 4)) (* (pow z 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (* x (pow y 6)) (* (pow z 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (/ (* x (pow y 2)) (* (pow z 2) (sqrt -1)))) (* x (sqrt -1))))))) (taylor -inf z) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (sqrt -1))) (taylor -inf z) (#s(alt (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) (patch (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (+ (sqrt -1) (* 1/2 (/ (pow y 2) (* (pow z 2) (sqrt -1))))))) (taylor -inf z) (#s(alt (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) (patch (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (+ (sqrt -1) (+ (* -1/8 (/ (pow y 4) (* (pow z 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow y 2) (* (pow z 2) (sqrt -1)))))))) (taylor -inf z) (#s(alt (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) (patch (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (+ (sqrt -1) (+ (* -1/8 (/ (pow y 4) (* (pow z 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow y 6) (* (pow z 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow y 2) (* (pow z 2) (sqrt -1))))))))) (taylor -inf z) (#s(alt (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) (patch (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow z 2)) (taylor 0 y) (#s(alt (-.f64 (.f64 y y) (.f64 z z)) (patch (-.f64 (.f64 y y) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (- (pow y 2) (pow z 2)) (taylor 0 y) (#s(alt (-.f64 (.f64 y y) (.f64 z z)) (patch (-.f64 (.f64 y y) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (- (pow y 2) (pow z 2)) (taylor 0 y) (#s(alt (-.f64 (.f64 y y) (.f64 z z)) (patch (-.f64 (.f64 y y) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (- (pow y 2) (pow z 2)) (taylor 0 y) (#s(alt (-.f64 (.f64 y y) (.f64 z z)) (patch (-.f64 (.f64 y y) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* x (* z (sqrt -1))) (taylor 0 y) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (/ (* x (pow y 2)) (* z (sqrt -1)))) (* x (* z (sqrt -1)))) (taylor 0 y) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (+ (* x (* z (sqrt -1))) (* (pow y 2) (+ (* -1/8 (/ (* x (pow y 2)) (* (pow z 3) (pow (sqrt -1) 3)))) (* 1/2 (/ x (* z (sqrt -1))))))) (taylor 0 y) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (+ (* x (* z (sqrt -1))) (* (pow y 2) (+ (* 1/2 (/ x (* z (sqrt -1)))) (* (pow y 2) (+ (* -1/8 (/ x (* (pow z 3) (pow (sqrt -1) 3)))) (* 1/16 (/ (* x (pow y 2)) (* (pow z 5) (pow (sqrt -1) 5))))))))) (taylor 0 y) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (* z (sqrt -1)) (taylor 0 y) (#s(alt (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) (patch (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (/ (pow y 2) (* z (sqrt -1)))) (* z (sqrt -1))) (taylor 0 y) (#s(alt (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) (patch (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) #<representation binary64>) () ())) ())
#s(alt (+ (* z (sqrt -1)) (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (* (pow z 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* z (sqrt -1))))))) (taylor 0 y) (#s(alt (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) (patch (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) #<representation binary64>) () ())) ())
#s(alt (+ (* z (sqrt -1)) (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (* (pow z 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow z 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* z (sqrt -1))))))) (taylor 0 y) (#s(alt (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) (patch (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (-.f64 (.f64 y y) (.f64 z z)) (patch (-.f64 (.f64 y y) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (* -1 (/ (pow z 2) (pow y 2))))) (taylor inf y) (#s(alt (-.f64 (.f64 y y) (.f64 z z)) (patch (-.f64 (.f64 y y) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (* -1 (/ (pow z 2) (pow y 2))))) (taylor inf y) (#s(alt (-.f64 (.f64 y y) (.f64 z z)) (patch (-.f64 (.f64 y y) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (* -1 (/ (pow z 2) (pow y 2))))) (taylor inf y) (#s(alt (-.f64 (.f64 y y) (.f64 z z)) (patch (-.f64 (.f64 y y) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf y) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (* y (+ x (* -1/2 (/ (* x (pow z 2)) (pow y 2))))) (taylor inf y) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (* y (+ x (+ (* -1/2 (/ (* x (pow z 2)) (pow y 2))) (* -1/8 (/ (* x (pow z 4)) (pow y 4)))))) (taylor inf y) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (* y (+ x (+ (* -1/2 (/ (* x (pow z 2)) (pow y 2))) (+ (* -1/8 (/ (* x (pow z 4)) (pow y 4))) (* -1/16 (/ (* x (pow z 6)) (pow y 6))))))) (taylor inf y) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) (patch (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* -1/2 (/ (pow z 2) (pow y 2))))) (taylor inf y) (#s(alt (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) (patch (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (+ (* -1/2 (/ (pow z 2) (pow y 2))) (* -1/8 (/ (pow z 4) (pow y 4)))))) (taylor inf y) (#s(alt (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) (patch (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (+ (* -1/2 (/ (pow z 2) (pow y 2))) (+ (* -1/8 (/ (pow z 4) (pow y 4))) (* -1/16 (/ (pow z 6) (pow y 6))))))) (taylor inf y) (#s(alt (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) (patch (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (-.f64 (.f64 y y) (.f64 z z)) (patch (-.f64 (.f64 y y) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (* -1 (/ (pow z 2) (pow y 2))))) (taylor -inf y) (#s(alt (-.f64 (.f64 y y) (.f64 z z)) (patch (-.f64 (.f64 y y) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (* -1 (/ (pow z 2) (pow y 2))))) (taylor -inf y) (#s(alt (-.f64 (.f64 y y) (.f64 z z)) (patch (-.f64 (.f64 y y) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (* -1 (/ (pow z 2) (pow y 2))))) (taylor -inf y) (#s(alt (-.f64 (.f64 y y) (.f64 z z)) (patch (-.f64 (.f64 y y) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x y)) (taylor -inf y) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ x (* -1/2 (/ (* x (pow z 2)) (pow y 2)))))) (taylor -inf y) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ x (+ (* -1/2 (/ (* x (pow z 2)) (pow y 2))) (* -1/8 (/ (* x (pow z 4)) (pow y 4))))))) (taylor -inf y) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ x (+ (* -1/2 (/ (* x (pow z 2)) (pow y 2))) (+ (* -1/8 (/ (* x (pow z 4)) (pow y 4))) (* -1/16 (/ (* x (pow z 6)) (pow y 6)))))))) (taylor -inf y) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (* -1 y) (taylor -inf y) (#s(alt (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) (patch (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1 (* -1/2 (/ (pow z 2) (pow y 2)))))) (taylor -inf y) (#s(alt (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) (patch (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1 (+ (* -1/2 (/ (pow z 2) (pow y 2))) (* -1/8 (/ (pow z 4) (pow y 4))))))) (taylor -inf y) (#s(alt (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) (patch (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1 (+ (* -1/2 (/ (pow z 2) (pow y 2))) (+ (* -1/8 (/ (pow z 4) (pow y 4))) (* -1/16 (/ (pow z 6) (pow y 6)))))))) (taylor -inf y) (#s(alt (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) (patch (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (- (pow y 2) (pow z 2)))) (taylor 0 x) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (- (pow y 2) (pow z 2)))) (taylor 0 x) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (- (pow y 2) (pow z 2)))) (taylor 0 x) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (- (pow y 2) (pow z 2)))) (taylor 0 x) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (- (pow y 2) (pow z 2)))) (taylor inf x) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (- (pow y 2) (pow z 2)))) (taylor inf x) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (- (pow y 2) (pow z 2)))) (taylor inf x) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (- (pow y 2) (pow z 2)))) (taylor inf x) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (- (pow y 2) (pow z 2)))) (taylor -inf x) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (- (pow y 2) (pow z 2)))) (taylor -inf x) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (- (pow y 2) (pow z 2)))) (taylor -inf x) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (- (pow y 2) (pow z 2)))) (taylor -inf x) (#s(alt (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) (patch (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))) #<representation binary64>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
5.0ms	z	@	inf	((- (* y y) (* z z)) (* x (sqrt (- (* y y) (* z z)))) (sqrt (- (* y y) (* z z))) (* y y))
2.0ms	y	@	inf	((- (* y y) (* z z)) (* x (sqrt (- (* y y) (* z z)))) (sqrt (- (* y y) (* z z))) (* y y))
2.0ms	y	@	0	((- (* y y) (* z z)) (* x (sqrt (- (* y y) (* z z)))) (sqrt (- (* y y) (* z z))) (* y y))
1.0ms	z	@	0	((- (* y y) (* z z)) (* x (sqrt (- (* y y) (* z z)))) (sqrt (- (* y y) (* z z))) (* y y))
1.0ms	x	@	0	((- (* y y) (* z z)) (* x (sqrt (- (* y y) (* z z)))) (sqrt (- (* y y) (* z z))) (* y y))

simplify197.0ms (4.2%)

Memory

-4.1MiB live, 239.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	205	1489
1	648	1483
2	2455	1426
3	7928	1426
0	8162	1349

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 94

Calls

Call 1

Inputs
(pow y 2)
(+ (* -1 (pow z 2)) (pow y 2))
(+ (* -1 (pow z 2)) (pow y 2))
(+ (* -1 (pow z 2)) (pow y 2))
(* x y)
(+ (* -1/2 (/ (* x (pow z 2)) y)) (* x y))
(+ (* x y) (* (pow z 2) (+ (* -1/2 (/ x y)) (* -1/8 (/ (* x (pow z 2)) (pow y 3))))))
(+ (* x y) (* (pow z 2) (+ (* -1/2 (/ x y)) (* (pow z 2) (+ (* -1/8 (/ x (pow y 3))) (* -1/16 (/ (* x (pow z 2)) (pow y 5))))))))
y
(+ y (* -1/2 (/ (pow z 2) y)))
(+ y (* (pow z 2) (- (* -1/8 (/ (pow z 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(+ y (* (pow z 2) (- (* (pow z 2) (- (* -1/16 (/ (pow z 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(* -1 (pow z 2))
(* (pow z 2) (- (/ (pow y 2) (pow z 2)) 1))
(* (pow z 2) (- (/ (pow y 2) (pow z 2)) 1))
(* (pow z 2) (- (/ (pow y 2) (pow z 2)) 1))
(* x (* z (sqrt -1)))
(* z (+ (* 1/2 (/ (* x (pow y 2)) (* (pow z 2) (sqrt -1)))) (* x (sqrt -1))))
(* z (+ (* -1/8 (/ (* x (pow y 4)) (* (pow z 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (* x (pow y 2)) (* (pow z 2) (sqrt -1)))) (* x (sqrt -1)))))
(* z (+ (* -1/8 (/ (* x (pow y 4)) (* (pow z 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (* x (pow y 6)) (* (pow z 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (/ (* x (pow y 2)) (* (pow z 2) (sqrt -1)))) (* x (sqrt -1))))))
(* z (sqrt -1))
(* z (+ (sqrt -1) (* 1/2 (/ (pow y 2) (* (pow z 2) (sqrt -1))))))
(* z (+ (sqrt -1) (+ (* -1/8 (/ (pow y 4) (* (pow z 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow y 2) (* (pow z 2) (sqrt -1)))))))
(* z (+ (sqrt -1) (+ (* -1/8 (/ (pow y 4) (* (pow z 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow y 6) (* (pow z 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow y 2) (* (pow z 2) (sqrt -1))))))))
(* -1 (pow z 2))
(* (pow z 2) (- (/ (pow y 2) (pow z 2)) 1))
(* (pow z 2) (- (/ (pow y 2) (pow z 2)) 1))
(* (pow z 2) (- (/ (pow y 2) (pow z 2)) 1))
(* -1 (* x (* z (sqrt -1))))
(* -1 (* z (+ (* 1/2 (/ (* x (pow y 2)) (* (pow z 2) (sqrt -1)))) (* x (sqrt -1)))))
(* -1 (* z (+ (* -1/8 (/ (* x (pow y 4)) (* (pow z 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (* x (pow y 2)) (* (pow z 2) (sqrt -1)))) (* x (sqrt -1))))))
(* -1 (* z (+ (* -1/8 (/ (* x (pow y 4)) (* (pow z 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (* x (pow y 6)) (* (pow z 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (/ (* x (pow y 2)) (* (pow z 2) (sqrt -1)))) (* x (sqrt -1)))))))
(* -1 (* z (sqrt -1)))
(* -1 (* z (+ (sqrt -1) (* 1/2 (/ (pow y 2) (* (pow z 2) (sqrt -1)))))))
(* -1 (* z (+ (sqrt -1) (+ (* -1/8 (/ (pow y 4) (* (pow z 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow y 2) (* (pow z 2) (sqrt -1))))))))
(* -1 (* z (+ (sqrt -1) (+ (* -1/8 (/ (pow y 4) (* (pow z 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow y 6) (* (pow z 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow y 2) (* (pow z 2) (sqrt -1)))))))))
(* -1 (pow z 2))
(- (pow y 2) (pow z 2))
(- (pow y 2) (pow z 2))
(- (pow y 2) (pow z 2))
(* x (* z (sqrt -1)))
(+ (* 1/2 (/ (* x (pow y 2)) (* z (sqrt -1)))) (* x (* z (sqrt -1))))
(+ (* x (* z (sqrt -1))) (* (pow y 2) (+ (* -1/8 (/ (* x (pow y 2)) (* (pow z 3) (pow (sqrt -1) 3)))) (* 1/2 (/ x (* z (sqrt -1)))))))
(+ (* x (* z (sqrt -1))) (* (pow y 2) (+ (* 1/2 (/ x (* z (sqrt -1)))) (* (pow y 2) (+ (* -1/8 (/ x (* (pow z 3) (pow (sqrt -1) 3)))) (* 1/16 (/ (* x (pow y 2)) (* (pow z 5) (pow (sqrt -1) 5)))))))))
(* z (sqrt -1))
(+ (* 1/2 (/ (pow y 2) (* z (sqrt -1)))) (* z (sqrt -1)))
(+ (* z (sqrt -1)) (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (* (pow z 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* z (sqrt -1)))))))
(+ (* z (sqrt -1)) (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (* (pow z 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow z 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* z (sqrt -1)))))))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* (pow y 2) (+ 1 (* -1 (/ (pow z 2) (pow y 2)))))
(* (pow y 2) (+ 1 (* -1 (/ (pow z 2) (pow y 2)))))
(* (pow y 2) (+ 1 (* -1 (/ (pow z 2) (pow y 2)))))
(* x y)
(* y (+ x (* -1/2 (/ (* x (pow z 2)) (pow y 2)))))
(* y (+ x (+ (* -1/2 (/ (* x (pow z 2)) (pow y 2))) (* -1/8 (/ (* x (pow z 4)) (pow y 4))))))
(* y (+ x (+ (* -1/2 (/ (* x (pow z 2)) (pow y 2))) (+ (* -1/8 (/ (* x (pow z 4)) (pow y 4))) (* -1/16 (/ (* x (pow z 6)) (pow y 6)))))))
y
(* y (+ 1 (* -1/2 (/ (pow z 2) (pow y 2)))))
(* y (+ 1 (+ (* -1/2 (/ (pow z 2) (pow y 2))) (* -1/8 (/ (pow z 4) (pow y 4))))))
(* y (+ 1 (+ (* -1/2 (/ (pow z 2) (pow y 2))) (+ (* -1/8 (/ (pow z 4) (pow y 4))) (* -1/16 (/ (pow z 6) (pow y 6)))))))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* (pow y 2) (+ 1 (* -1 (/ (pow z 2) (pow y 2)))))
(* (pow y 2) (+ 1 (* -1 (/ (pow z 2) (pow y 2)))))
(* (pow y 2) (+ 1 (* -1 (/ (pow z 2) (pow y 2)))))
(* -1 (* x y))
(* -1 (* y (+ x (* -1/2 (/ (* x (pow z 2)) (pow y 2))))))
(* -1 (* y (+ x (+ (* -1/2 (/ (* x (pow z 2)) (pow y 2))) (* -1/8 (/ (* x (pow z 4)) (pow y 4)))))))
(* -1 (* y (+ x (+ (* -1/2 (/ (* x (pow z 2)) (pow y 2))) (+ (* -1/8 (/ (* x (pow z 4)) (pow y 4))) (* -1/16 (/ (* x (pow z 6)) (pow y 6))))))))
(* -1 y)
(* -1 (* y (+ 1 (* -1/2 (/ (pow z 2) (pow y 2))))))
(* -1 (* y (+ 1 (+ (* -1/2 (/ (pow z 2) (pow y 2))) (* -1/8 (/ (pow z 4) (pow y 4)))))))
(* -1 (* y (+ 1 (+ (* -1/2 (/ (pow z 2) (pow y 2))) (+ (* -1/8 (/ (pow z 4) (pow y 4))) (* -1/16 (/ (pow z 6) (pow y 6))))))))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* x (sqrt (- (pow y 2) (pow z 2))))
(* x (sqrt (- (pow y 2) (pow z 2))))
(* x (sqrt (- (pow y 2) (pow z 2))))
(* x (sqrt (- (pow y 2) (pow z 2))))
(* x (sqrt (- (pow y 2) (pow z 2))))
(* x (sqrt (- (pow y 2) (pow z 2))))
(* x (sqrt (- (pow y 2) (pow z 2))))
(* x (sqrt (- (pow y 2) (pow z 2))))
(* x (sqrt (- (pow y 2) (pow z 2))))
(* x (sqrt (- (pow y 2) (pow z 2))))
(* x (sqrt (- (pow y 2) (pow z 2))))
(* x (sqrt (- (pow y 2) (pow z 2))))

Outputs
(pow y 2)
(*.f64 y y)
(+ (* -1 (pow z 2)) (pow y 2))
(*.f64 (+.f64 z y) (-.f64 y z))
(+ (* -1 (pow z 2)) (pow y 2))
(*.f64 (+.f64 z y) (-.f64 y z))
(+ (* -1 (pow z 2)) (pow y 2))
(*.f64 (+.f64 z y) (-.f64 y z))
(* x y)
(*.f64 x y)
(+ (* -1/2 (/ (* x (pow z 2)) y)) (* x y))
(.f64 x (fma.f64 (.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y))
(+ (* x y) (* (pow z 2) (+ (* -1/2 (/ x y)) (* -1/8 (/ (* x (pow z 2)) (pow y 3))))))
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(* x (sqrt (- (pow y 2) (pow z 2))))
(.f64 (sqrt.f64 (.f64 (+.f64 z y) (-.f64 y z))) x)

rewrite161.0ms (3.4%)

Memory

29.1MiB live, 219.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	28
0	13	28
1	40	28
2	243	28
3	2153	28
0	9394	28

Stop Event

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

Counts

4 → 332

Calls

Call 1

Inputs
(-.f64 (.f64 y y) (.f64 z z))
(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))
(*.f64 y y)

Outputs
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eval58.0ms (1.2%)

Memory: -9.8MiB live, 108.2MiB allocated
Compiler: Compiled 12 357 to 1 728 computations (86% saved)

prune11.0ms (0.2%)

Memory

-11.8MiB live, 26.8MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	421	5	426
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	422	5	427

Accuracy

100.0%

Counts

427 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.4%	(.f64 (sqrt.f64 (+.f64 z y)) (.f64 (sqrt.f64 (-.f64 y z)) x))
▶	71.4%	(.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x)
▶	99.4%	(.f64 x (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y))))
▶	99.4%	(.f64 x #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y)))
▶	99.0%	#s(approx (* x (sqrt (- (* y y) (* z z)))) (*.f64 x y))

Compiler

Compiled 94 to 80 computations (14.9% saved)

simplify172.0ms (3.7%)

Memory

-4.1MiB live, 206.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 (sqrt.f64 (-.f64 y z)) x)
cost-diff	0	(+.f64 z y)
cost-diff	0	(sqrt.f64 (+.f64 z y))
cost-diff	0	(.f64 (sqrt.f64 (+.f64 z y)) (.f64 (sqrt.f64 (-.f64 y z)) x))
cost-diff	0	(*.f64 #s(literal -1/2 binary64) z)
cost-diff	0	(fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y)
cost-diff	0	#s(approx (sqrt (- (* y y) (* z z))) (fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y))
cost-diff	0	(.f64 x #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y)))
cost-diff	0	(-.f64 y z)
cost-diff	0	(*.f64 (-.f64 y z) (+.f64 z y))
cost-diff	0	(sqrt.f64 (*.f64 (-.f64 y z) (+.f64 z y)))
cost-diff	0	(.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x)
cost-diff	0	(*.f64 x y)
cost-diff	0	#s(approx (* x (sqrt (- (* y y) (* z z)))) (*.f64 x y))
cost-diff	0	(-.f64 y z)
cost-diff	0	(sqrt.f64 (-.f64 y z))
cost-diff	0	(*.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y)))
cost-diff	0	(.f64 x (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	178
0	44	178
1	77	178
2	118	178
3	181	178
4	305	178
5	658	178
6	1596	178
7	3356	178
8	6210	178
0	8346	178

Stop Event

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

Calls

Call 1

Inputs
(.f64 x (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y))))
x
(*.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y)))
(sqrt.f64 (-.f64 y z))
(-.f64 y z)
y
z
(sqrt.f64 (+.f64 z y))
(+.f64 z y)
#s(approx (* x (sqrt (- (* y y) (* z z)))) (*.f64 x y))
(*.f64 x y)
x
y
(.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x)
(sqrt.f64 (*.f64 (-.f64 y z) (+.f64 z y)))
(*.f64 (-.f64 y z) (+.f64 z y))
(-.f64 y z)
y
z
(+.f64 z y)
x
(.f64 x #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y)))
x
#s(approx (sqrt (- (* y y) (* z z))) (fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y))
(fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y)
(*.f64 #s(literal -1/2 binary64) z)
#s(literal -1/2 binary64)
z
(/.f64 z y)
y
(.f64 (sqrt.f64 (+.f64 z y)) (.f64 (sqrt.f64 (-.f64 y z)) x))
(sqrt.f64 (+.f64 z y))
(+.f64 z y)
z
y
(*.f64 (sqrt.f64 (-.f64 y z)) x)
(sqrt.f64 (-.f64 y z))
(-.f64 y z)
x

Outputs
(.f64 x (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y))))
(.f64 (.f64 (sqrt.f64 (-.f64 y z)) x) (sqrt.f64 (+.f64 z y)))
x
(*.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y)))
(*.f64 (sqrt.f64 (+.f64 z y)) (sqrt.f64 (-.f64 y z)))
(sqrt.f64 (-.f64 y z))
(-.f64 y z)
y
z
(sqrt.f64 (+.f64 z y))
(+.f64 z y)
#s(approx (* x (sqrt (- (* y y) (* z z)))) (*.f64 x y))
#s(approx (* x (sqrt (- (* y y) (* z z)))) (*.f64 y x))
(*.f64 x y)
(*.f64 y x)
x
y
(.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x)
(.f64 (sqrt.f64 (.f64 (+.f64 z y) (-.f64 y z))) x)
(sqrt.f64 (*.f64 (-.f64 y z) (+.f64 z y)))
(sqrt.f64 (*.f64 (+.f64 z y) (-.f64 y z)))
(*.f64 (-.f64 y z) (+.f64 z y))
(*.f64 (+.f64 z y) (-.f64 y z))
(-.f64 y z)
y
z
(+.f64 z y)
x
(.f64 x #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y)))
(.f64 #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (/.f64 z y) (*.f64 #s(literal -1/2 binary64) z) y)) x)
x
#s(approx (sqrt (- (* y y) (* z z))) (fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y))
#s(approx (sqrt (- (* y y) (* z z))) (fma.f64 (/.f64 z y) (*.f64 #s(literal -1/2 binary64) z) y))
(fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y)
(fma.f64 (/.f64 z y) (*.f64 #s(literal -1/2 binary64) z) y)
(*.f64 #s(literal -1/2 binary64) z)
#s(literal -1/2 binary64)
z
(/.f64 z y)
y
(.f64 (sqrt.f64 (+.f64 z y)) (.f64 (sqrt.f64 (-.f64 y z)) x))
(.f64 (.f64 (sqrt.f64 (-.f64 y z)) x) (sqrt.f64 (+.f64 z y)))
(sqrt.f64 (+.f64 z y))
(+.f64 z y)
z
y
(*.f64 (sqrt.f64 (-.f64 y z)) x)
(sqrt.f64 (-.f64 y z))
(-.f64 y z)
x

localize94.0ms (2%)

Memory

17.4MiB live, 101.1MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(sqrt.f64 (+.f64 z y))
accuracy	0.0078125	(sqrt.f64 (-.f64 y z))
accuracy	0.21484375	(*.f64 (sqrt.f64 (-.f64 y z)) x)
accuracy	0.25619125976844204	(.f64 (sqrt.f64 (+.f64 z y)) (.f64 (sqrt.f64 (-.f64 y z)) x))
accuracy	0	(/.f64 z y)
accuracy	0	(*.f64 #s(literal -1/2 binary64) z)
accuracy	0.00390625	(.f64 x #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y)))
accuracy	0.5003489090102228	#s(approx (sqrt (- (* y y) (* z z))) (fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y))
accuracy	0	(+.f64 z y)
accuracy	0	(*.f64 (-.f64 y z) (+.f64 z y))
accuracy	0.00390625	(.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x)
accuracy	28.89181931374142	(sqrt.f64 (*.f64 (-.f64 y z) (+.f64 z y)))
accuracy	0	(*.f64 x y)
accuracy	0.6203625571885782	#s(approx (* x (sqrt (- (* y y) (* z z)))) (*.f64 x y))
accuracy	0.00390625	(.f64 x (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y))))
accuracy	0.00390625	(sqrt.f64 (+.f64 z y))
accuracy	0.0078125	(sqrt.f64 (-.f64 y z))
accuracy	0.53515625	(*.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y)))

Samples

78.0ms

256×

valid

Compiler

Compiled 159 to 27 computations (83% saved)

Precisions

Click to see histograms. Total time spent on operations: 47.0ms

ival-mult: 33.0ms (70.5% of total)

ival-sqrt: 6.0ms (12.8% of total)

ival-sub: 3.0ms (6.4% of total)

ival-div: 2.0ms (4.3% of total)

ival-add: 2.0ms (4.3% of total)

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

exact: 0.0ms (0% of total)

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

series82.0ms (1.7%)

Memory

-29.4MiB live, 87.1MiB allocated

Counts

18 → 492

Calls

Call 1

Inputs
#s(alt (.f64 x (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y)))) (patch (.f64 x (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y)))) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y))) (patch (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (-.f64 y z)) (patch (sqrt.f64 (-.f64 y z)) #<representation binary64>) () ())
#s(alt (-.f64 y z) (patch (-.f64 y z) #<representation binary64>) () ())
#s(alt #s(approx (* x (sqrt (- (* y y) (* z z)))) (.f64 x y)) (patch #s(approx ( x (sqrt (- (* y y) (* z z)))) (*.f64 x y)) #<representation binary64>) () ())
#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x) (patch (.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) (patch (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) #<representation binary64>) () ())
#s(alt (.f64 (-.f64 y z) (+.f64 z y)) (patch (.f64 (-.f64 y z) (+.f64 z y)) #<representation binary64>) () ())
#s(alt (.f64 x #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y))) (patch (.f64 x #s(approx (sqrt (- (* y y) (* z z))) (fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (- (* y y) (* z z))) (fma.f64 (.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y)) (patch #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y) (patch (fma.f64 (.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y) #<representation binary64>) () ())
#s(alt (.f64 #s(literal -1/2 binary64) z) (patch (.f64 #s(literal -1/2 binary64) z) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 (+.f64 z y)) (.f64 (sqrt.f64 (-.f64 y z)) x)) (patch (.f64 (sqrt.f64 (+.f64 z y)) (.f64 (sqrt.f64 (-.f64 y z)) x)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (+.f64 z y)) (patch (sqrt.f64 (+.f64 z y)) #<representation binary64>) () ())
#s(alt (+.f64 z y) (patch (+.f64 z y) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 (-.f64 y z)) x) (patch (.f64 (sqrt.f64 (-.f64 y z)) x) #<representation binary64>) () ())
#s(alt (/.f64 z y) (patch (/.f64 z y) #<representation binary64>) () ())

Outputs
#s(alt (* x y) (taylor 0 z) (#s(alt (.f64 x (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y)))) (patch (.f64 x (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (/ (* x (* z (+ y (* -1 y)))) y)) (* x y)) (taylor 0 z) (#s(alt (.f64 x (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y)))) (patch (.f64 x (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y)))) #<representation binary64>) () ())) ())
#s(alt (+ (* x y) (* z (+ (* -1/2 (/ (* x (* z (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2)))))) y)) (* 1/2 (/ (* x (+ y (* -1 y))) y))))) (taylor 0 z) (#s(alt (.f64 x (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y)))) (patch (.f64 x (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y)))) #<representation binary64>) () ())) ())
#s(alt (+ (* x y) (* z (+ (* 1/2 (/ (* x (+ y (* -1 y))) y)) (* z (+ (* -1/2 (/ (* x (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2))))) y)) (* 1/4 (/ (* x (* z (* (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2)))) (+ y (* -1 y))))) (pow y 3)))))))) (taylor 0 z) (#s(alt (.f64 x (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y)))) (patch (.f64 x (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y)))) #<representation binary64>) () ())) ())
#s(alt y (taylor 0 z) (#s(alt (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y))) (patch (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y))) #<representation binary64>) () ())) ())
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#s(alt (* x y) (taylor inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (* (+ y z) (- y z)))) (taylor inf x) (#s(alt (.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x) (patch (.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (* (+ y z) (- y z)))) (taylor inf x) (#s(alt (.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x) (patch (.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (* (+ y z) (- y z)))) (taylor inf x) (#s(alt (.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x) (patch (.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (* (+ y z) (- y z)))) (taylor inf x) (#s(alt (.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x) (patch (.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (- (pow y 2) (pow z 2)))) (taylor inf x) (#s(alt (.f64 x #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y))) (patch (.f64 x #s(approx (sqrt (- (* y y) (* z z))) (fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (- (pow y 2) (pow z 2)))) (taylor inf x) (#s(alt (.f64 x #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y))) (patch (.f64 x #s(approx (sqrt (- (* y y) (* z z))) (fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (- (pow y 2) (pow z 2)))) (taylor inf x) (#s(alt (.f64 x #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y))) (patch (.f64 x #s(approx (sqrt (- (* y y) (* z z))) (fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (- (pow y 2) (pow z 2)))) (taylor inf x) (#s(alt (.f64 x #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y))) (patch (.f64 x #s(approx (sqrt (- (* y y) (* z z))) (fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (* (+ y z) (- y z)))) (taylor inf x) (#s(alt (.f64 (sqrt.f64 (+.f64 z y)) (.f64 (sqrt.f64 (-.f64 y z)) x)) (patch (.f64 (sqrt.f64 (+.f64 z y)) (.f64 (sqrt.f64 (-.f64 y z)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (* (+ y z) (- y z)))) (taylor inf x) (#s(alt (.f64 (sqrt.f64 (+.f64 z y)) (.f64 (sqrt.f64 (-.f64 y z)) x)) (patch (.f64 (sqrt.f64 (+.f64 z y)) (.f64 (sqrt.f64 (-.f64 y z)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (* (+ y z) (- y z)))) (taylor inf x) (#s(alt (.f64 (sqrt.f64 (+.f64 z y)) (.f64 (sqrt.f64 (-.f64 y z)) x)) (patch (.f64 (sqrt.f64 (+.f64 z y)) (.f64 (sqrt.f64 (-.f64 y z)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (* (+ y z) (- y z)))) (taylor inf x) (#s(alt (.f64 (sqrt.f64 (+.f64 z y)) (.f64 (sqrt.f64 (-.f64 y z)) x)) (patch (.f64 (sqrt.f64 (+.f64 z y)) (.f64 (sqrt.f64 (-.f64 y z)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (- y z))) (taylor inf x) (#s(alt (.f64 (sqrt.f64 (-.f64 y z)) x) (patch (.f64 (sqrt.f64 (-.f64 y z)) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (- y z))) (taylor inf x) (#s(alt (.f64 (sqrt.f64 (-.f64 y z)) x) (patch (.f64 (sqrt.f64 (-.f64 y z)) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (- y z))) (taylor inf x) (#s(alt (.f64 (sqrt.f64 (-.f64 y z)) x) (patch (.f64 (sqrt.f64 (-.f64 y z)) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (- y z))) (taylor inf x) (#s(alt (.f64 (sqrt.f64 (-.f64 y z)) x) (patch (.f64 (sqrt.f64 (-.f64 y z)) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (* (+ y z) (- y z)))) (taylor -inf x) (#s(alt (.f64 x (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y)))) (patch (.f64 x (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (* (+ y z) (- y z)))) (taylor -inf x) (#s(alt (.f64 x (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y)))) (patch (.f64 x (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (* (+ y z) (- y z)))) (taylor -inf x) (#s(alt (.f64 x (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y)))) (patch (.f64 x (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (* (+ y z) (- y z)))) (taylor -inf x) (#s(alt (.f64 x (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y)))) (patch (.f64 x (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (- (pow y 2) (pow z 2)))) (taylor -inf x) (#s(alt #s(approx (* x (sqrt (- (* y y) (* z z)))) (.f64 x y)) (patch #s(approx ( x (sqrt (- (* y y) (* z z)))) (*.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (- (pow y 2) (pow z 2)))) (taylor -inf x) (#s(alt #s(approx (* x (sqrt (- (* y y) (* z z)))) (.f64 x y)) (patch #s(approx ( x (sqrt (- (* y y) (* z z)))) (*.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (- (pow y 2) (pow z 2)))) (taylor -inf x) (#s(alt #s(approx (* x (sqrt (- (* y y) (* z z)))) (.f64 x y)) (patch #s(approx ( x (sqrt (- (* y y) (* z z)))) (*.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (- (pow y 2) (pow z 2)))) (taylor -inf x) (#s(alt #s(approx (* x (sqrt (- (* y y) (* z z)))) (.f64 x y)) (patch #s(approx ( x (sqrt (- (* y y) (* z z)))) (*.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (* (+ y z) (- y z)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x) (patch (.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (* (+ y z) (- y z)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x) (patch (.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (* (+ y z) (- y z)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x) (patch (.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (* (+ y z) (- y z)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x) (patch (.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (- (pow y 2) (pow z 2)))) (taylor -inf x) (#s(alt (.f64 x #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y))) (patch (.f64 x #s(approx (sqrt (- (* y y) (* z z))) (fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (- (pow y 2) (pow z 2)))) (taylor -inf x) (#s(alt (.f64 x #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y))) (patch (.f64 x #s(approx (sqrt (- (* y y) (* z z))) (fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (- (pow y 2) (pow z 2)))) (taylor -inf x) (#s(alt (.f64 x #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y))) (patch (.f64 x #s(approx (sqrt (- (* y y) (* z z))) (fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (- (pow y 2) (pow z 2)))) (taylor -inf x) (#s(alt (.f64 x #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y))) (patch (.f64 x #s(approx (sqrt (- (* y y) (* z z))) (fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (* (+ y z) (- y z)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (+.f64 z y)) (.f64 (sqrt.f64 (-.f64 y z)) x)) (patch (.f64 (sqrt.f64 (+.f64 z y)) (.f64 (sqrt.f64 (-.f64 y z)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (* (+ y z) (- y z)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (+.f64 z y)) (.f64 (sqrt.f64 (-.f64 y z)) x)) (patch (.f64 (sqrt.f64 (+.f64 z y)) (.f64 (sqrt.f64 (-.f64 y z)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (* (+ y z) (- y z)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (+.f64 z y)) (.f64 (sqrt.f64 (-.f64 y z)) x)) (patch (.f64 (sqrt.f64 (+.f64 z y)) (.f64 (sqrt.f64 (-.f64 y z)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (* (+ y z) (- y z)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (+.f64 z y)) (.f64 (sqrt.f64 (-.f64 y z)) x)) (patch (.f64 (sqrt.f64 (+.f64 z y)) (.f64 (sqrt.f64 (-.f64 y z)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (- y z))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (-.f64 y z)) x) (patch (.f64 (sqrt.f64 (-.f64 y z)) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (- y z))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (-.f64 y z)) x) (patch (.f64 (sqrt.f64 (-.f64 y z)) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (- y z))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (-.f64 y z)) x) (patch (.f64 (sqrt.f64 (-.f64 y z)) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt (- y z))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (-.f64 y z)) x) (patch (.f64 (sqrt.f64 (-.f64 y z)) x) #<representation binary64>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
21.0ms	z	@	0	((* x (* (sqrt (- y z)) (sqrt (+ z y)))) (* (sqrt (- y z)) (sqrt (+ z y))) (sqrt (- y z)) (- y z) (* x (sqrt (- (* y y) (* z z)))) (* x y) (* (sqrt (* (- y z) (+ z y))) x) (sqrt (* (- y z) (+ z y))) (* (- y z) (+ z y)) (* x (sqrt (- (* y y) (* z z)))) (sqrt (- (* y y) (* z z))) (+ (* (* -1/2 z) (/ z y)) y) (* -1/2 z) (* (sqrt (+ z y)) (* (sqrt (- y z)) x)) (sqrt (+ z y)) (+ z y) (* (sqrt (- y z)) x) (/ z y))
10.0ms	x	@	inf	((* x (* (sqrt (- y z)) (sqrt (+ z y)))) (* (sqrt (- y z)) (sqrt (+ z y))) (sqrt (- y z)) (- y z) (* x (sqrt (- (* y y) (* z z)))) (* x y) (* (sqrt (* (- y z) (+ z y))) x) (sqrt (* (- y z) (+ z y))) (* (- y z) (+ z y)) (* x (sqrt (- (* y y) (* z z)))) (sqrt (- (* y y) (* z z))) (+ (* (* -1/2 z) (/ z y)) y) (* -1/2 z) (* (sqrt (+ z y)) (* (sqrt (- y z)) x)) (sqrt (+ z y)) (+ z y) (* (sqrt (- y z)) x) (/ z y))
6.0ms	y	@	0	((* x (* (sqrt (- y z)) (sqrt (+ z y)))) (* (sqrt (- y z)) (sqrt (+ z y))) (sqrt (- y z)) (- y z) (* x (sqrt (- (* y y) (* z z)))) (* x y) (* (sqrt (* (- y z) (+ z y))) x) (sqrt (* (- y z) (+ z y))) (* (- y z) (+ z y)) (* x (sqrt (- (* y y) (* z z)))) (sqrt (- (* y y) (* z z))) (+ (* (* -1/2 z) (/ z y)) y) (* -1/2 z) (* (sqrt (+ z y)) (* (sqrt (- y z)) x)) (sqrt (+ z y)) (+ z y) (* (sqrt (- y z)) x) (/ z y))
5.0ms	y	@	-inf	((* x (* (sqrt (- y z)) (sqrt (+ z y)))) (* (sqrt (- y z)) (sqrt (+ z y))) (sqrt (- y z)) (- y z) (* x (sqrt (- (* y y) (* z z)))) (* x y) (* (sqrt (* (- y z) (+ z y))) x) (sqrt (* (- y z) (+ z y))) (* (- y z) (+ z y)) (* x (sqrt (- (* y y) (* z z)))) (sqrt (- (* y y) (* z z))) (+ (* (* -1/2 z) (/ z y)) y) (* -1/2 z) (* (sqrt (+ z y)) (* (sqrt (- y z)) x)) (sqrt (+ z y)) (+ z y) (* (sqrt (- y z)) x) (/ z y))
5.0ms	z	@	inf	((* x (* (sqrt (- y z)) (sqrt (+ z y)))) (* (sqrt (- y z)) (sqrt (+ z y))) (sqrt (- y z)) (- y z) (* x (sqrt (- (* y y) (* z z)))) (* x y) (* (sqrt (* (- y z) (+ z y))) x) (sqrt (* (- y z) (+ z y))) (* (- y z) (+ z y)) (* x (sqrt (- (* y y) (* z z)))) (sqrt (- (* y y) (* z z))) (+ (* (* -1/2 z) (/ z y)) y) (* -1/2 z) (* (sqrt (+ z y)) (* (sqrt (- y z)) x)) (sqrt (+ z y)) (+ z y) (* (sqrt (- y z)) x) (/ z y))

simplify195.0ms (4.1%)

Memory

37.0MiB live, 229.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	917	9170
1	3138	7060
0	9525	6572

Stop Event

1×	iter limit
1×	node limit

Counts

492 → 474

Calls

Call 1

Inputs
(* x y)
(+ (* 1/2 (/ (* x (* z (+ y (* -1 y)))) y)) (* x y))
(+ (* x y) (* z (+ (* -1/2 (/ (* x (* z (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2)))))) y)) (* 1/2 (/ (* x (+ y (* -1 y))) y)))))
(+ (* x y) (* z (+ (* 1/2 (/ (* x (+ y (* -1 y))) y)) (* z (+ (* -1/2 (/ (* x (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2))))) y)) (* 1/4 (/ (* x (* z (* (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2)))) (+ y (* -1 y))))) (pow y 3))))))))
y
(+ y (* 1/2 (/ (* z (+ y (* -1 y))) y)))
(+ y (* z (+ (* -1/2 (/ (* z (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2))))) y)) (* 1/2 (/ (+ y (* -1 y)) y)))))
(+ y (* z (+ (* 1/2 (/ (+ y (* -1 y)) y)) (* z (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2)))) y)) (* 1/4 (/ (* z (* (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2)))) (+ y (* -1 y)))) (pow y 3))))))))
(sqrt y)
(+ (sqrt y) (* -1/2 (* (sqrt (/ 1 y)) z)))
(+ (sqrt y) (* z (+ (* -1/2 (sqrt (/ 1 y))) (* -1/8 (* (sqrt (/ 1 (pow y 3))) z)))))
(+ (sqrt y) (* z (+ (* -1/2 (sqrt (/ 1 y))) (* z (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* -1/16 (* (sqrt (/ 1 (pow y 5))) z)))))))
y
(+ y (* -1 z))
(+ y (* -1 z))
(+ y (* -1 z))
(* x y)
(+ (* -1/2 (/ (* x (pow z 2)) y)) (* x y))
(+ (* x y) (* (pow z 2) (+ (* -1/2 (/ x y)) (* -1/8 (/ (* x (pow z 2)) (pow y 3))))))
(+ (* x y) (* (pow z 2) (+ (* -1/2 (/ x y)) (* (pow z 2) (+ (* -1/8 (/ x (pow y 3))) (* -1/16 (/ (* x (pow z 2)) (pow y 5))))))))
(* x y)
(+ (* 1/2 (/ (* x (* z (+ y (* -1 y)))) y)) (* x y))
(+ (* x y) (* z (+ (* -1/2 (/ (* x (* z (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2)))))) y)) (* 1/2 (/ (* x (+ y (* -1 y))) y)))))
(+ (* x y) (* z (+ (* 1/2 (/ (* x (+ y (* -1 y))) y)) (* z (+ (* -1/2 (/ (* x (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2))))) y)) (* 1/4 (/ (* x (* z (* (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2)))) (+ y (* -1 y))))) (pow y 3))))))))
y
(+ y (* 1/2 (/ (* z (+ y (* -1 y))) y)))
(+ y (* z (+ (* -1/2 (/ (* z (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2))))) y)) (* 1/2 (/ (+ y (* -1 y)) y)))))
(+ y (* z (+ (* 1/2 (/ (+ y (* -1 y)) y)) (* z (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2)))) y)) (* 1/4 (/ (* z (* (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2)))) (+ y (* -1 y)))) (pow y 3))))))))
(pow y 2)
(+ (* z (+ y (* -1 y))) (pow y 2))
(+ (* z (+ y (+ (* -1 y) (* -1 z)))) (pow y 2))
(+ (* z (+ y (+ (* -1 y) (* -1 z)))) (pow y 2))
(* x y)
(+ (* -1/2 (/ (* x (pow z 2)) y)) (* x y))
(+ (* x y) (* (pow z 2) (+ (* -1/2 (/ x y)) (* -1/8 (/ (* x (pow z 2)) (pow y 3))))))
(+ (* x y) (* (pow z 2) (+ (* -1/2 (/ x y)) (* (pow z 2) (+ (* -1/8 (/ x (pow y 3))) (* -1/16 (/ (* x (pow z 2)) (pow y 5))))))))
y
(+ y (* -1/2 (/ (pow z 2) y)))
(+ y (* (pow z 2) (- (* -1/8 (/ (pow z 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(+ y (* (pow z 2) (- (* (pow z 2) (- (* -1/16 (/ (pow z 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
y
(+ y (* -1/2 (/ (pow z 2) y)))
(+ y (* -1/2 (/ (pow z 2) y)))
(+ y (* -1/2 (/ (pow z 2) y)))
(* -1/2 z)
(* -1/2 z)
(* -1/2 z)
(* -1/2 z)
(* x y)
(+ (* 1/2 (/ (* x (* z (+ y (* -1 y)))) y)) (* x y))
(+ (* x y) (* z (+ (* -1/2 (/ (* x (* z (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2)))))) y)) (* 1/2 (/ (* x (+ y (* -1 y))) y)))))
(+ (* x y) (* z (+ (* 1/2 (/ (* x (+ y (* -1 y))) y)) (* z (+ (* -1/2 (/ (* x (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2))))) y)) (* 1/4 (/ (* x (* z (* (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2)))) (+ y (* -1 y))))) (pow y 3))))))))
(sqrt y)
(+ (sqrt y) (* 1/2 (* (sqrt (/ 1 y)) z)))
(+ (sqrt y) (* z (+ (* -1/8 (* (sqrt (/ 1 (pow y 3))) z)) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* z (+ (* 1/2 (sqrt (/ 1 y))) (* z (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (sqrt (/ 1 (pow y 5))) z)))))))
y
(+ y z)
(+ y z)
(+ y z)
(* x (sqrt y))
(+ (* -1/2 (* (* x z) (sqrt (/ 1 y)))) (* x (sqrt y)))
(+ (* x (sqrt y)) (* z (+ (* -1/2 (* x (sqrt (/ 1 y)))) (* -1/8 (* (* x z) (sqrt (/ 1 (pow y 3))))))))
(+ (* x (sqrt y)) (* z (+ (* -1/2 (* x (sqrt (/ 1 y)))) (* z (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* -1/16 (* (* x z) (sqrt (/ 1 (pow y 5))))))))))
(/ z y)
(/ z y)
(/ z y)
(/ z y)
(* x (* z (sqrt -1)))
(* z (+ (* 1/2 (/ (* x (+ y (* -1 y))) (* z (sqrt -1)))) (* x (sqrt -1))))
(* z (+ (* 1/2 (/ (* x (+ y (* -1 y))) (* z (sqrt -1)))) (+ (* 1/2 (/ (* x (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))))) (* (pow z 2) (sqrt -1)))) (* x (sqrt -1)))))
(* z (+ (* -1/4 (/ (* x (* (+ y (* -1 y)) (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))))) (* (pow z 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (* x (+ y (* -1 y))) (* z (sqrt -1)))) (+ (* 1/2 (/ (* x (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))))) (* (pow z 2) (sqrt -1)))) (* x (sqrt -1))))))
(* z (sqrt -1))
(* z (+ (sqrt -1) (* 1/2 (/ (+ y (* -1 y)) (* z (sqrt -1))))))
(* z (+ (sqrt -1) (+ (* 1/2 (/ (+ y (* -1 y)) (* z (sqrt -1)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* (pow z 2) (sqrt -1)))))))
(* z (+ (sqrt -1) (+ (* -1/4 (/ (* (+ y (* -1 y)) (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2))))) (* (pow z 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ y (* -1 y)) (* z (sqrt -1)))) (* 1/2 (/ (- (pow y 2) (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow (sqrt -1) 2)))) (* (pow z 2) (sqrt -1))))))))
(* (sqrt z) (sqrt -1))
(* z (+ (* 1/2 (* (/ y (sqrt -1)) (sqrt (/ 1 (pow z 3))))) (* (sqrt (/ 1 z)) (sqrt -1))))
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z
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z
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(+ (* 1/2 (* (/ (* x y) (sqrt -1)) (sqrt (/ 1 z)))) (* (* x (sqrt -1)) (sqrt z)))
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(+ (* y (+ (* 1/2 (* (/ x (sqrt -1)) (sqrt (/ 1 z)))) (* y (+ (* -1/8 (* (/ x (pow (sqrt -1) 3)) (sqrt (/ 1 (pow z 3))))) (* 1/16 (* (/ (* x y) (pow (sqrt -1) 5)) (sqrt (/ 1 (pow z 5))))))))) (* (* x (sqrt -1)) (sqrt z)))
(/ z y)
(/ z y)
(/ z y)
(/ z y)
(* x y)
(* y (+ x (* 1/2 (/ (* x (+ z (* -1 z))) y))))
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y
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(* y (+ x (+ (* -1/2 (/ (* x (pow z 2)) (pow y 2))) (* -1/8 (/ (* x (pow z 4)) (pow y 4))))))
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(* x y)
(* x y)
(* x y)
(* x y)
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(* y (+ x (+ (* -1/4 (/ (* x (* (+ z (* -1 z)) (- (* -1 (pow z 2)) (* 1/4 (pow (+ z (* -1 z)) 2))))) (pow y 3))) (+ (* 1/2 (/ (* x (+ z (* -1 z))) y)) (* 1/2 (/ (* x (- (* -1 (pow z 2)) (* 1/4 (pow (+ z (* -1 z)) 2)))) (pow y 2)))))))
y
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(pow y 2)
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(* x y)
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y
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y
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(sqrt y)
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(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (sqrt (/ 1 (pow y 5))) (pow z 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow y 7))) (pow z 3))) (* 1/2 (* (sqrt (/ 1 (pow y 3))) z))))))
y
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(* x (sqrt y))
(* y (+ (* -1/2 (* (* x z) (sqrt (/ 1 (pow y 3))))) (* x (sqrt (/ 1 y)))))
(* y (+ (* -1/2 (* (* x z) (sqrt (/ 1 (pow y 3))))) (+ (* -1/8 (* (* x (pow z 2)) (sqrt (/ 1 (pow y 5))))) (* x (sqrt (/ 1 y))))))
(* y (+ (* -1/2 (* (* x z) (sqrt (/ 1 (pow y 3))))) (+ (* -1/8 (* (* x (pow z 2)) (sqrt (/ 1 (pow y 5))))) (+ (* -1/16 (* (* x (pow z 3)) (sqrt (/ 1 (pow y 7))))) (* x (sqrt (/ 1 y)))))))
(/ z y)
(/ z y)
(/ z y)
(/ z y)
(* -1 (* x (* y (pow (sqrt -1) 2))))
(* -1 (* y (+ (* -1/2 (/ (* x (+ z (* -1 z))) y)) (* x (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1 (/ (+ (* -1/2 (/ (* x (- (pow z 2) (* 1/4 (/ (pow (+ z (* -1 z)) 2) (pow (sqrt -1) 2))))) y)) (* 1/2 (* x (+ z (* -1 z))))) y)) (* x (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* x (* (+ z (* -1 z)) (- (pow z 2) (* 1/4 (/ (pow (+ z (* -1 z)) 2) (pow (sqrt -1) 2)))))) (* y (pow (sqrt -1) 2)))) (* 1/2 (* x (- (pow z 2) (* 1/4 (/ (pow (+ z (* -1 z)) 2) (pow (sqrt -1) 2))))))) y)) (* 1/2 (* x (+ z (* -1 z))))) y)) (* x (pow (sqrt -1) 2)))))
(* -1 (* y (pow (sqrt -1) 2)))
(* -1 (* y (+ (* -1/2 (/ (+ z (* -1 z)) y)) (pow (sqrt -1) 2))))
(* -1 (* y (+ (* -1 (/ (+ (* -1/2 (/ (- (pow z 2) (* 1/4 (/ (pow (+ z (* -1 z)) 2) (pow (sqrt -1) 2)))) y)) (* 1/2 (+ z (* -1 z)))) y)) (pow (sqrt -1) 2))))
(* -1 (* y (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ z (* -1 z)) (- (pow z 2) (* 1/4 (/ (pow (+ z (* -1 z)) 2) (pow (sqrt -1) 2))))) (* y (pow (sqrt -1) 2)))) (* 1/2 (- (pow z 2) (* 1/4 (/ (pow (+ z (* -1 z)) 2) (pow (sqrt -1) 2)))))) y)) (* 1/2 (+ z (* -1 z)))) y)) (pow (sqrt -1) 2))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (sqrt (/ 1 (pow y 3))) (* z (pow (sqrt -1) 2)))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (sqrt (/ 1 (pow y 5))) (* (pow z 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow y 3))) (* z (pow (sqrt -1) 2)))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (sqrt (/ 1 (pow y 5))) (* (pow z 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow y 7))) (* (pow z 3) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow y 3))) (* z (pow (sqrt -1) 2)))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
y
(* -1 (* y (- (/ z y) 1)))
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(* -1 (* y (- (/ z y) 1)))
(* -1 (* x y))
(* -1 (* y (+ x (* -1/2 (/ (* x (pow z 2)) (pow y 2))))))
(* -1 (* y (+ x (+ (* -1/2 (/ (* x (pow z 2)) (pow y 2))) (* -1/8 (/ (* x (pow z 4)) (pow y 4)))))))
(* -1 (* y (+ x (+ (* -1/2 (/ (* x (pow z 2)) (pow y 2))) (+ (* -1/8 (/ (* x (pow z 4)) (pow y 4))) (* -1/16 (/ (* x (pow z 6)) (pow y 6))))))))
(* x y)
(* x y)
(* x y)
(* x y)
(* -1 (* x (* y (pow (sqrt -1) 2))))
(* -1 (* y (+ (* -1/2 (/ (* x (+ z (* -1 z))) y)) (* x (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1 (/ (+ (* -1/2 (/ (* x (- (pow z 2) (* 1/4 (/ (pow (+ z (* -1 z)) 2) (pow (sqrt -1) 2))))) y)) (* 1/2 (* x (+ z (* -1 z))))) y)) (* x (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* x (* (+ z (* -1 z)) (- (pow z 2) (* 1/4 (/ (pow (+ z (* -1 z)) 2) (pow (sqrt -1) 2)))))) (* y (pow (sqrt -1) 2)))) (* 1/2 (* x (- (pow z 2) (* 1/4 (/ (pow (+ z (* -1 z)) 2) (pow (sqrt -1) 2))))))) y)) (* 1/2 (* x (+ z (* -1 z))))) y)) (* x (pow (sqrt -1) 2)))))
(* -1 (* y (pow (sqrt -1) 2)))
(* -1 (* y (+ (* -1/2 (/ (+ z (* -1 z)) y)) (pow (sqrt -1) 2))))
(* -1 (* y (+ (* -1 (/ (+ (* -1/2 (/ (- (pow z 2) (* 1/4 (/ (pow (+ z (* -1 z)) 2) (pow (sqrt -1) 2)))) y)) (* 1/2 (+ z (* -1 z)))) y)) (pow (sqrt -1) 2))))
(* -1 (* y (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ z (* -1 z)) (- (pow z 2) (* 1/4 (/ (pow (+ z (* -1 z)) 2) (pow (sqrt -1) 2))))) (* y (pow (sqrt -1) 2)))) (* 1/2 (- (pow z 2) (* 1/4 (/ (pow (+ z (* -1 z)) 2) (pow (sqrt -1) 2)))))) y)) (* 1/2 (+ z (* -1 z)))) y)) (pow (sqrt -1) 2))))
(pow y 2)
(* (pow y 2) (+ 1 (+ (* -1 (/ z y)) (/ z y))))
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -1 (+ z (* -1 z))) (/ (pow z 2) y)) y))))
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -1 (+ z (* -1 z))) (/ (pow z 2) y)) y))))
(* -1 (* x y))
(* -1 (* y (+ x (* -1/2 (/ (* x (pow z 2)) (pow y 2))))))
(* -1 (* y (+ x (+ (* -1/2 (/ (* x (pow z 2)) (pow y 2))) (* -1/8 (/ (* x (pow z 4)) (pow y 4)))))))
(* -1 (* y (+ x (+ (* -1/2 (/ (* x (pow z 2)) (pow y 2))) (+ (* -1/8 (/ (* x (pow z 4)) (pow y 4))) (* -1/16 (/ (* x (pow z 6)) (pow y 6))))))))
(* -1 y)
(* -1 (* y (+ 1 (* -1/2 (/ (pow z 2) (pow y 2))))))
(* -1 (* y (+ 1 (+ (* -1/2 (/ (pow z 2) (pow y 2))) (* -1/8 (/ (pow z 4) (pow y 4)))))))
(* -1 (* y (+ 1 (+ (* -1/2 (/ (pow z 2) (pow y 2))) (+ (* -1/8 (/ (pow z 4) (pow y 4))) (* -1/16 (/ (pow z 6) (pow y 6))))))))
y
(* -1 (* y (- (* 1/2 (/ (pow z 2) (pow y 2))) 1)))
(* -1 (* y (- (* 1/2 (/ (pow z 2) (pow y 2))) 1)))
(* -1 (* y (- (* 1/2 (/ (pow z 2) (pow y 2))) 1)))
(* -1 (* x (* y (pow (sqrt -1) 2))))
(* -1 (* y (+ (* -1/2 (/ (* x (+ z (* -1 z))) y)) (* x (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1 (/ (+ (* -1/2 (/ (* x (- (pow z 2) (* 1/4 (/ (pow (+ z (* -1 z)) 2) (pow (sqrt -1) 2))))) y)) (* 1/2 (* x (+ z (* -1 z))))) y)) (* x (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* x (* (+ z (* -1 z)) (- (pow z 2) (* 1/4 (/ (pow (+ z (* -1 z)) 2) (pow (sqrt -1) 2)))))) (* y (pow (sqrt -1) 2)))) (* 1/2 (* x (- (pow z 2) (* 1/4 (/ (pow (+ z (* -1 z)) 2) (pow (sqrt -1) 2))))))) y)) (* 1/2 (* x (+ z (* -1 z))))) y)) (* x (pow (sqrt -1) 2)))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (sqrt (/ 1 (pow y 3))) z)) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (sqrt (/ 1 (pow y 5))) (/ (pow z 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow y 3))) z)) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (sqrt (/ 1 (pow y 5))) (/ (pow z 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow y 7))) (/ (pow z 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow y 3))) z)) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
y
(* -1 (* y (- (* -1 (/ z y)) 1)))
(* -1 (* y (- (* -1 (/ z y)) 1)))
(* -1 (* y (- (* -1 (/ z y)) 1)))
(* -1 (* (* x (pow (sqrt -1) 2)) (sqrt y)))
(* -1 (* y (+ (* 1/2 (* (* x (* z (pow (sqrt -1) 2))) (sqrt (/ 1 (pow y 3))))) (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 y))))))
(* -1 (* y (+ (* -1/8 (* (* x (* (pow z 2) (pow (sqrt -1) 2))) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (* x (* z (pow (sqrt -1) 2))) (sqrt (/ 1 (pow y 3))))) (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 y)))))))
(* -1 (* y (+ (* -1/8 (* (* x (* (pow z 2) (pow (sqrt -1) 2))) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (* x (* (pow z 3) (pow (sqrt -1) 2))) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (* x (* z (pow (sqrt -1) 2))) (sqrt (/ 1 (pow y 3))))) (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 y))))))))
(/ z y)
(/ z y)
(/ z y)
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(* x (sqrt (* (+ y z) (- y z))))
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(* x y)
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(* x y)
(* x y)
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(* x (sqrt (* (+ y z) (- y z))))
(* x (sqrt (* (+ y z) (- y z))))
(* x (sqrt (* (+ y z) (- y z))))
(* x (sqrt (- (pow y 2) (pow z 2))))
(* x (sqrt (- (pow y 2) (pow z 2))))
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(* x (sqrt (* (+ y z) (- y z))))
(* x (sqrt (* (+ y z) (- y z))))
(* x (sqrt (* (+ y z) (- y z))))
(* x (sqrt (* (+ y z) (- y z))))
(* x (sqrt (- y z)))
(* x (sqrt (- y z)))
(* x (sqrt (- y z)))
(* x (sqrt (- y z)))
(* x (sqrt (* (+ y z) (- y z))))
(* x (sqrt (* (+ y z) (- y z))))
(* x (sqrt (* (+ y z) (- y z))))
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(* x y)
(* x y)
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(* x (sqrt (- (pow y 2) (pow z 2))))
(* x (sqrt (- (pow y 2) (pow z 2))))
(* x (sqrt (* (+ y z) (- y z))))
(* x (sqrt (* (+ y z) (- y z))))
(* x (sqrt (* (+ y z) (- y z))))
(* x (sqrt (* (+ y z) (- y z))))
(* x (sqrt (- y z)))
(* x (sqrt (- y z)))
(* x (sqrt (- y z)))
(* x (sqrt (- y z)))
(* x (sqrt (* (+ y z) (- y z))))
(* x (sqrt (* (+ y z) (- y z))))
(* x (sqrt (* (+ y z) (- y z))))
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(* x y)
(* x y)
(* x y)
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(* x (sqrt (* (+ y z) (- y z))))
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(* x (sqrt (- (pow y 2) (pow z 2))))
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(* x (sqrt (* (+ y z) (- y z))))
(* x (sqrt (* (+ y z) (- y z))))
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(* x (sqrt (- y z)))
(* x (sqrt (- y z)))
(* x (sqrt (- y z)))
(* x (sqrt (- y z)))

Outputs
(* x y)
(*.f64 y x)
(+ (* 1/2 (/ (* x (* z (+ y (* -1 y)))) y)) (* x y))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 0 binary64) (.f64 y x))
(+ (* x y) (* z (+ (* -1/2 (/ (* x (* z (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2)))))) y)) (* 1/2 (/ (* x (+ y (* -1 y))) y)))))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 0 binary64) (/.f64 (.f64 (.f64 z x) #s(literal -1/2 binary64)) y)) z (.f64 y x))
(+ (* x y) (* z (+ (* 1/2 (/ (* x (+ y (* -1 y))) y)) (* z (+ (* -1/2 (/ (* x (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2))))) y)) (* 1/4 (/ (* x (* z (* (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2)))) (+ y (* -1 y))))) (pow y 3))))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 #s(literal 0 binary64) x) (.f64 (/.f64 x y) #s(literal -1/2 binary64))) z (.f64 (.f64 #s(literal 0 binary64) x) #s(literal 1/2 binary64))) z (*.f64 y x))
y
(+ y (* 1/2 (/ (* z (+ y (* -1 y))) y)))
y
(+ y (* z (+ (* -1/2 (/ (* z (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2))))) y)) (* 1/2 (/ (+ y (* -1 y)) y)))))
(fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) y) z) z y)
(+ y (* z (+ (* 1/2 (/ (+ y (* -1 y)) y)) (* z (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2)))) y)) (* 1/4 (/ (* z (* (+ 1 (* 1/4 (/ (pow (+ y (* -1 y)) 2) (pow y 2)))) (+ y (* -1 y)))) (pow y 3))))))))
(fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) y) z) z y)
(sqrt y)
(sqrt.f64 y)
(+ (sqrt y) (* -1/2 (* (sqrt (/ 1 y)) z)))
(fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal -1/2 binary64)) z (sqrt.f64 y))
(+ (sqrt y) (* z (+ (* -1/2 (sqrt (/ 1 y))) (* -1/8 (* (sqrt (/ 1 (pow y 3))) z)))))
(fma.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) #s(literal -1/8 binary64)) z (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal -1/2 binary64))) z (sqrt.f64 y))
(+ (sqrt y) (* z (+ (* -1/2 (sqrt (/ 1 y))) (* z (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* -1/16 (* (sqrt (/ 1 (pow y 5))) z)))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64))))) z (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) #s(literal -1/8 binary64))) z (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal -1/2 binary64))) z (sqrt.f64 y))
y
(+ y (* -1 z))
(-.f64 y z)
(+ y (* -1 z))
(-.f64 y z)
(+ y (* -1 z))
(-.f64 y z)
(* x y)
(*.f64 y x)
(+ (* -1/2 (/ (* x (pow z 2)) y)) (* x y))
(fma.f64 (/.f64 (.f64 (.f64 z z) x) y) #s(literal -1/2 binary64) (*.f64 y x))
(+ (* x y) (* (pow z 2) (+ (* -1/2 (/ x y)) (* -1/8 (/ (* x (pow z 2)) (pow y 3))))))
(fma.f64 (fma.f64 (/.f64 (.f64 (.f64 z z) x) (pow.f64 y #s(literal 3 binary64))) #s(literal -1/8 binary64) (.f64 (/.f64 x y) #s(literal -1/2 binary64))) (.f64 z z) (*.f64 y x))
(+ (* x y) (* (pow z 2) (+ (* -1/2 (/ x y)) (* (pow z 2) (+ (* -1/8 (/ x (pow y 3))) (* -1/16 (/ (* x (pow z 2)) (pow y 5))))))))
(fma.f64 (fma.f64 (fma.f64 (/.f64 (.f64 (.f64 z z) x) (pow.f64 y #s(literal 5 binary64))) #s(literal -1/16 binary64) (.f64 (/.f64 x (pow.f64 y #s(literal 3 binary64))) #s(literal -1/8 binary64))) (.f64 z z) (.f64 (/.f64 x y) #s(literal -1/2 binary64))) (.f64 z z) (*.f64 y x))
(* x y)
(*.f64 y x)
(+ (* 1/2 (/ (* x (* z (+ y (* -1 y)))) y)) (* x y))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 0 binary64) (.f64 y x))
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rewrite204.0ms (4.3%)

Memory

-10.7MiB live, 234.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	143
0	44	140
1	132	140
2	805	140
0	8603	140

Stop Event

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

Counts

18 → 849

Calls

Call 1

Inputs
(.f64 x (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y))))
(*.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y)))
(sqrt.f64 (-.f64 y z))
(-.f64 y z)
#s(approx (* x (sqrt (- (* y y) (* z z)))) (*.f64 x y))
(*.f64 x y)
(.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x)
(sqrt.f64 (*.f64 (-.f64 y z) (+.f64 z y)))
(*.f64 (-.f64 y z) (+.f64 z y))
(.f64 x #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y)))
#s(approx (sqrt (- (* y y) (* z z))) (fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y))
(fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y)
(*.f64 #s(literal -1/2 binary64) z)
(.f64 (sqrt.f64 (+.f64 z y)) (.f64 (sqrt.f64 (-.f64 y z)) x))
(sqrt.f64 (+.f64 z y))
(+.f64 z y)
(*.f64 (sqrt.f64 (-.f64 y z)) x)
(/.f64 z y)

Outputs
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eval262.0ms (5.6%)

Memory: 32.9MiB live, 485.0MiB allocated
Compiler: Compiled 46 247 to 5 369 computations (88.4% saved)

prune118.0ms (2.5%)

Memory

-11.8MiB live, 125.2MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	1 918	0	1 918
Fresh	0	0	0
Picked	0	5	5
Done	0	0	0
Total	1 918	5	1 923

Accuracy

100.0%

Counts

1 923 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.4%	(.f64 (sqrt.f64 (+.f64 z y)) (.f64 (sqrt.f64 (-.f64 y z)) x))
✓	71.4%	(.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x)
✓	99.4%	(.f64 x (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y))))
✓	99.4%	(.f64 x #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y)))
✓	99.0%	#s(approx (* x (sqrt (- (* y y) (* z z)))) (*.f64 x y))

Compiler

Compiled 104 to 67 computations (35.6% saved)

regimes23.0ms (0.5%)

Memory

3.3MiB live, 40.9MiB allocated

Counts

6 → 1

Calls

Call 1

Inputs
#s(approx (* x (sqrt (- (* y y) (* z z)))) (*.f64 x y))
(.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x)
(.f64 x #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y)))
(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
(.f64 x (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y))))
(.f64 (sqrt.f64 (+.f64 z y)) (.f64 (sqrt.f64 (-.f64 y z)) x))

Outputs
(.f64 x (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y))))

Calls

8 calls:

4.0ms	(*.f64 z z)
3.0ms	x
3.0ms	y
3.0ms	z
2.0ms	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))

Results

Accuracy	Segments	Branch
99.4%	1	`x`
99.4%	1	`y`
99.4%	1	`z`
99.4%	1	`(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))`
99.4%	1	`(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))`
99.4%	1	`(-.f64 (.f64 y y) (.f64 z z))`
99.4%	1	`(*.f64 y y)`
99.4%	1	`(*.f64 z z)`

Compiler

Compiled 34 to 38 computations (-11.8% saved)

regimes22.0ms (0.5%)

Memory

-4.4MiB live, 33.6MiB allocated

Counts

4 → 1

Calls

Call 1

Inputs
#s(approx (* x (sqrt (- (* y y) (* z z)))) (*.f64 x y))
(.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x)
(.f64 x #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y)))
(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))

Outputs
(.f64 x #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y)))

Calls

8 calls:

7.0ms	(*.f64 z z)
2.0ms	y
2.0ms	x
2.0ms	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
2.0ms	z

Results

Accuracy	Segments	Branch
99.4%	1	`x`
99.4%	1	`y`
99.4%	1	`z`
99.4%	1	`(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))`
99.4%	1	`(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))`
99.4%	1	`(-.f64 (.f64 y y) (.f64 z z))`
99.4%	1	`(*.f64 y y)`
99.4%	1	`(*.f64 z z)`

Compiler

Compiled 34 to 38 computations (-11.8% saved)

regimes15.0ms (0.3%)

Memory

-5.4MiB live, 30.5MiB allocated

Accuracy

Total -17.9b remaining (-2877.5%)

Threshold costs -17.9b (-2877.5%)

Counts

2 → 1

Calls

Call 1

Inputs
#s(approx (* x (sqrt (- (* y y) (* z z)))) (*.f64 x y))
(.f64 (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))) x)

Outputs
#s(approx (* x (sqrt (- (* y y) (* z z)))) (*.f64 x y))

Calls

8 calls:

4.0ms	(-.f64 (.f64 y y) (.f64 z z))
2.0ms	y
2.0ms	x
1.0ms	z
1.0ms	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))

Results

Accuracy	Segments	Branch
99.0%	1	`x`
99.0%	1	`y`
99.0%	1	`z`
99.0%	1	`(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))`
99.0%	1	`(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))`
99.0%	1	`(-.f64 (.f64 y y) (.f64 z z))`
99.0%	1	`(*.f64 y y)`
99.0%	1	`(*.f64 z z)`

Compiler

Compiled 34 to 38 computations (-11.8% saved)

simplify23.0ms (0.5%)

Memory

8.4MiB live, 47.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	44
1	30	44
2	35	44
3	37	44
4	38	44

Stop Event

1×

saturated

Calls

Call 1

Inputs

(*.f64 x (*.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y))))

(*.f64 x #s(approx (sqrt (- (* y y) (* z z))) (fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y)))

#s(approx (* x (sqrt (- (* y y) (* z z)))) (*.f64 x y))

Outputs
(.f64 x (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (+.f64 z y))))
(.f64 (.f64 (sqrt.f64 (+.f64 z y)) (sqrt.f64 (-.f64 y z))) x)
(.f64 x #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y)))
(.f64 #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (*.f64 #s(literal -1/2 binary64) z) (/.f64 z y) y)) x)
#s(approx (* x (sqrt (- (* y y) (* z z)))) (*.f64 x y))
#s(approx (* x (sqrt (- (* y y) (* z z)))) (*.f64 y x))

soundness286.0ms (6.1%)

Memory

15.3MiB live, 210.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	28
0	13	28
1	40	28
2	243	28
3	2153	28
0	9394	28
0	205	1489
1	648	1483
2	2455	1426
3	7928	1426
0	8162	1349

Stop Event

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

Compiler

Compiled 60 to 43 computations (28.3% saved)

preprocess190.0ms (4%)

Memory

-36.0MiB live, 213.6MiB allocated

Remove

(negabs x)

(abs z)

Compiler

Compiled 462 to 366 computations (20.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze158.0ms (3.4%)

sample1.4s (30.4%)

explain95.0ms (2%)

preprocess529.0ms (11.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify341.0ms (7.3%)

localize21.0ms (0.4%)

series16.0ms (0.3%)

simplify197.0ms (4.2%)

rewrite161.0ms (3.4%)

eval58.0ms (1.2%)

prune11.0ms (0.2%)

simplify172.0ms (3.7%)

localize94.0ms (2%)

series82.0ms (1.7%)

simplify195.0ms (4.1%)

rewrite204.0ms (4.3%)

eval262.0ms (5.6%)

prune118.0ms (2.5%)

regimes23.0ms (0.5%)

regimes22.0ms (0.5%)

regimes15.0ms (0.3%)

simplify23.0ms (0.5%)

soundness286.0ms (6.1%)

preprocess190.0ms (4%)

end0.0ms (0%)

Profiling