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

start0.0ms (0%)

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

analyze136.0ms (3.3%)

Memory

26.5MiB live, 162.4MiB allocated; 16ms collecting garbage

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)

sample1.3s (32.1%)

Memory

38.2MiB live, 1 441.9MiB allocated; 267ms collecting garbage

Samples

682.0ms	8 256×	0	valid
174.0ms	2 476×	0	invalid

Precisions

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

ival-mult: 309.0ms (65.3% of total)

ival-sqrt: 88.0ms (18.6% of total)

ival-sub: 62.0ms (13.1% of total)

ival-true: 6.0ms (1.3% of total)

adjust: 4.0ms (0.8% of total)

ival-assert: 4.0ms (0.8% of total)

Bogosity

explain173.0ms (4.2%)

Memory

-9.4MiB live, 191.9MiB allocated; 58ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
142	-	4	(1.8041455220023238e+118 -4.5308735946552105e-159 3.364201565239741e-302)	`(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))`
17	-	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	119	0
↳	`(*.f64 y y)`	overflow	119
↳	`(-.f64 (.f64 y y) (.f64 z z))`	overflow	119
↳	`(*.f64 z z)`	overflow	17
`sqrt.f64`	`(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))`	uflow-rescue	19	0
↳	`(*.f64 y y)`	underflow	19
↳	`(-.f64 (.f64 y y) (.f64 z z))`	underflow	19
↳	`(*.f64 z z)`	underflow	104
`-.f64`	`(-.f64 (.f64 y y) (.f64 z z))`	nan-rescue	17	0
↳	`(*.f64 y y)`	overflow	119
↳	`(*.f64 z z)`	overflow	17

Confusion

	Predicted +	Predicted -
+	97	3
-	41	115

Precision

0.7028985507246377

Recall

0.97

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	97	0	3
-	41	0	115

Precision?

0.7028985507246377

Recall?

0.97

Freqs

test

number	freq
0	118
1	121
2	17

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

72.0ms

512×

valid

Compiler

Compiled 82 to 28 computations (65.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 56.0ms

ival-mult: 50.0ms (89% of total)

ival-sqrt: 3.0ms (5.3% of total)

ival-sub: 2.0ms (3.6% of total)

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

adjust: 0.0ms (0% of total)

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

preprocess124.0ms (3%)

Memory

21.3MiB live, 110.3MiB allocated; 13ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	93
1	101	93
2	364	93
3	641	93
4	1529	93
5	3400	93
6	5521	93
7	7433	93
0	8	10
0	13	10
1	27	10
2	87	10
3	229	10
4	407	10
5	840	10
6	1389	10
7	2073	10
8	2900	10
9	3210	10
10	3272	10
11	3272	10
12	3350	10
0	3350	10

Stop Event

1×	iter limit
1×	saturated
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: 0.2MiB live, 0.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 3 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	63.3%	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))

Compiler

Compiled 10 to 8 computations (20% saved)

simplify73.0ms (1.8%)

Memory

-7.9MiB live, 41.5MiB allocated; 11ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 y y)
cost-diff	0	(-.f64 (.f64 y y) (.f64 z z))
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))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	34
0	13	34
1	27	34
2	87	34
3	229	34
4	407	34
5	840	34
6	1389	34
7	2073	34
8	2900	34
9	3210	34
10	3272	34
11	3272	34
12	3350	34
0	3350	34

Stop Event

1×	iter limit
1×	saturated
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

localize48.0ms (1.2%)

Memory

-13.3MiB live, 32.3MiB allocated; 2ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 y y)
accuracy	0.0	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
accuracy	3.3867187500000004	(-.f64 (.f64 y y) (.f64 z z))
accuracy	32.48311354430071	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))

Samples

40.0ms

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 (64% of total)

ival-sqrt: 2.0ms (25.6% of total)

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

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

adjust: 0.0ms (0% of total)

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

series11.0ms (0.3%)

Memory

16.0MiB live, 16.0MiB allocated; 0ms collecting garbage

Counts

4 → 51

Calls

Call 1

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

Outputs
(* x (sqrt (- (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)))))))
(* -1 (pow z 2))
(- (pow y 2) (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) (+ 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))))))))
(+ (* -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 (* -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 y 2))
(* 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) (* 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))))))))
(* (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)))))))))

Calls

9 calls:

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

simplify199.0ms (4.9%)

Memory

-18.9MiB live, 251.9MiB allocated; 36ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	205	1144
1	708	1143
2	3083	1100
0	8534	1028

Stop Event

1×	iter limit
1×	node limit

Counts

51 → 50

Calls

Call 1

Inputs
(* x (sqrt (- (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)))))))
(* -1 (pow z 2))
(- (pow y 2) (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) (+ 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))))))))
(+ (* -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 (* -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 y 2))
(* 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) (* 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))))))))
(* (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)))))))))

Outputs
(* x (sqrt (- (pow y 2) (pow z 2))))
(.f64 (hypot.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) z) y) x)
(* x (* z (sqrt -1)))
(.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) z) x)
(+ (* 1/2 (/ (* x (pow y 2)) (* z (sqrt -1)))) (* x (* z (sqrt -1))))
(.f64 x (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) z)) y) y (.f64 (sqrt.f64 #s(literal -1 binary64)) z)))
(+ (* 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)))))))
(fma.f64 (.f64 z x) (sqrt.f64 #s(literal -1 binary64)) (.f64 (fma.f64 (.f64 (.f64 (/.f64 x (pow.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) z) #s(literal 3 binary64))) #s(literal -1/8 binary64)) y) y (.f64 (/.f64 x (.f64 (sqrt.f64 #s(literal -1 binary64)) z)) #s(literal 1/2 binary64))) (.f64 y y)))
(+ (* 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)))))))))
(fma.f64 x (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) z)) y) y (.f64 (sqrt.f64 #s(literal -1 binary64)) z)) (.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (/.f64 (.f64 (.f64 y y) x) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (pow.f64 z #s(literal 5 binary64)))) #s(literal 1/16 binary64) (.f64 (/.f64 x (pow.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) z) #s(literal 3 binary64))) #s(literal -1/8 binary64)))))
(* z (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) z)
(+ (* 1/2 (/ (pow y 2) (* z (sqrt -1)))) (* z (sqrt -1)))
(fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) z)) y) y (*.f64 (sqrt.f64 #s(literal -1 binary64)) z))
(+ (* z (sqrt -1)) (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (* (pow z 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* z (sqrt -1)))))))
(fma.f64 (fma.f64 (.f64 y (/.f64 y (pow.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) z) #s(literal 3 binary64)))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) z))) (.f64 y y) (*.f64 (sqrt.f64 #s(literal -1 binary64)) z))
(+ (* 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)))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (/.f64 y (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 y (pow.f64 z #s(literal 5 binary64)))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) z) #s(literal 3 binary64)))) (.f64 y y) (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) z))) (.f64 y y) (.f64 (sqrt.f64 #s(literal -1 binary64)) z))
(* -1 (pow z 2))
(*.f64 (neg.f64 z) z)
(- (pow y 2) (pow z 2))
(*.f64 (+.f64 y z) (-.f64 y z))
(pow y 2)
(*.f64 y y)
(* x y)
(*.f64 y x)
(* y (+ x (* -1/2 (/ (* x (pow z 2)) (pow y 2)))))
(.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) y) (/.f64 (.f64 (*.f64 z z) x) y) x) y)
(* y (+ x (+ (* -1/2 (/ (* x (pow z 2)) (pow y 2))) (* -1/8 (/ (* x (pow z 4)) (pow y 4))))))
(.f64 (fma.f64 x (fma.f64 (/.f64 #s(literal -1/2 binary64) y) (/.f64 (.f64 z z) y) (/.f64 (*.f64 (pow.f64 z #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 y #s(literal 4 binary64)))) x) y)
(* 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)))))))
(.f64 (fma.f64 (.f64 #s(literal -1/16 binary64) x) (/.f64 (pow.f64 z #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (fma.f64 x (fma.f64 (/.f64 #s(literal -1/2 binary64) y) (/.f64 (.f64 z z) y) (/.f64 (.f64 (pow.f64 z #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 y #s(literal 4 binary64)))) x)) y)
y
(* y (+ 1 (* -1/2 (/ (pow z 2) (pow y 2)))))
(fma.f64 (.f64 y #s(literal -1/2 binary64)) (.f64 (/.f64 z y) (/.f64 z y)) y)
(* y (+ 1 (+ (* -1/2 (/ (pow z 2) (pow y 2))) (* -1/8 (/ (pow z 4) (pow y 4))))))
(fma.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) y) (/.f64 (.f64 z z) y) (/.f64 (.f64 (pow.f64 z #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 y #s(literal 4 binary64)))) y y)
(* 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)))))))
(.f64 (fma.f64 (/.f64 (pow.f64 z #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal -1/16 binary64) (fma.f64 (/.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 #s(literal -1/2 binary64) y) (/.f64 (.f64 z z) y) #s(literal 1 binary64)))) y)
(* (pow y 2) (+ 1 (* -1 (/ (pow z 2) (pow y 2)))))
(.f64 (fma.f64 (neg.f64 z) (/.f64 z (.f64 y y)) #s(literal 1 binary64)) (*.f64 y y))
(* -1 (* x y))
(*.f64 (neg.f64 x) y)
(* -1 (* y (+ x (* -1/2 (/ (* x (pow z 2)) (pow y 2))))))
(.f64 (neg.f64 y) (fma.f64 (/.f64 #s(literal -1/2 binary64) y) (/.f64 (.f64 (*.f64 z z) x) y) x))
(* -1 (* y (+ x (+ (* -1/2 (/ (* x (pow z 2)) (pow y 2))) (* -1/8 (/ (* x (pow z 4)) (pow y 4)))))))
(.f64 (neg.f64 y) (fma.f64 x (fma.f64 (/.f64 #s(literal -1/2 binary64) y) (/.f64 (.f64 z z) y) (/.f64 (*.f64 (pow.f64 z #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 y #s(literal 4 binary64)))) x))
(* -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))))))))
(.f64 (neg.f64 y) (fma.f64 (.f64 #s(literal -1/16 binary64) x) (/.f64 (pow.f64 z #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (fma.f64 x (fma.f64 (/.f64 #s(literal -1/2 binary64) y) (/.f64 (.f64 z z) y) (/.f64 (.f64 (pow.f64 z #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 y #s(literal 4 binary64)))) x)))
(* -1 y)
(neg.f64 y)
(* -1 (* y (+ 1 (* -1/2 (/ (pow z 2) (pow y 2))))))
(.f64 (fma.f64 (.f64 (/.f64 z y) (/.f64 z y)) #s(literal 1/2 binary64) #s(literal -1 binary64)) y)
(* -1 (* y (+ 1 (+ (* -1/2 (/ (pow z 2) (pow y 2))) (* -1/8 (/ (pow z 4) (pow y 4)))))))
(.f64 (+.f64 (fma.f64 (.f64 (/.f64 z y) (/.f64 z y)) #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 z #s(literal 4 binary64))) (pow.f64 y #s(literal 4 binary64)))) #s(literal -1 binary64)) y)
(* -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))))))))
(.f64 (neg.f64 y) (fma.f64 (/.f64 (pow.f64 z #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal -1/16 binary64) (fma.f64 (/.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 #s(literal -1/2 binary64) y) (/.f64 (.f64 z z) y) #s(literal 1 binary64)))))
(+ (* -1/2 (/ (* x (pow z 2)) y)) (* x y))
(.f64 x (fma.f64 (/.f64 (.f64 z z) y) #s(literal -1/2 binary64) y))
(+ (* 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 x (pow.f64 y #s(literal 3 binary64))) #s(literal -1/8 binary64)) z) z (.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 (.f64 (.f64 z z) (/.f64 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))) (pow.f64 z #s(literal 4 binary64)) (.f64 x (fma.f64 (/.f64 (*.f64 z z) y) #s(literal -1/2 binary64) y)))
(+ y (* -1/2 (/ (pow z 2) y)))
(fma.f64 (/.f64 (*.f64 z z) y) #s(literal -1/2 binary64) y)
(+ y (* (pow z 2) (- (* -1/8 (/ (pow z 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(fma.f64 (fma.f64 (.f64 z (/.f64 z (pow.f64 y #s(literal 3 binary64)))) #s(literal -1/8 binary64) (/.f64 #s(literal -1/2 binary64) y)) (.f64 z z) 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)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 z (/.f64 z (pow.f64 y #s(literal 5 binary64)))) #s(literal -1/16 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 3 binary64)))) (.f64 z z) (/.f64 #s(literal -1/2 binary64) y)) (*.f64 z z) y)
(+ (* -1 (pow z 2)) (pow y 2))
(*.f64 (+.f64 y z) (-.f64 y z))
(* z (+ (* 1/2 (/ (* x (pow y 2)) (* (pow z 2) (sqrt -1)))) (* x (sqrt -1))))
(.f64 (.f64 x (fma.f64 (.f64 (/.f64 y (.f64 z z)) (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) z)
(* 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)))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 x (pow.f64 z #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (.f64 x (fma.f64 (.f64 (/.f64 y (*.f64 z z)) (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) z)
(* 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))))))
(.f64 (fma.f64 x (fma.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 z #s(literal 4 binary64))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1/16 binary64)) (.f64 (pow.f64 z #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))))) (.f64 x (fma.f64 (.f64 (/.f64 y (.f64 z z)) (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) z)
(* z (+ (sqrt -1) (* 1/2 (/ (pow y 2) (* (pow z 2) (sqrt -1))))))
(.f64 (fma.f64 (.f64 (/.f64 y (*.f64 z z)) (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) z)
(* 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)))))))
(.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 z z)) (*.f64 y (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 z #s(literal 4 binary64))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1 binary64)))) z)
(* 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))))))))
(.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 z z)) (*.f64 y (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 z #s(literal 6 binary64))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (fma.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 z #s(literal 4 binary64))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1 binary64))))) z)
(* (pow z 2) (- (/ (pow y 2) (pow z 2)) 1))
(.f64 (-.f64 (.f64 (/.f64 y z) (/.f64 y z)) #s(literal 1 binary64)) (*.f64 z z))
(* -1 (* x (* z (sqrt -1))))
(.f64 (.f64 (neg.f64 z) x) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* z (+ (* 1/2 (/ (* x (pow y 2)) (* (pow z 2) (sqrt -1)))) (* x (sqrt -1)))))
(.f64 (neg.f64 z) (.f64 x (fma.f64 (.f64 (/.f64 y (.f64 z z)) (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -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))))))
(.f64 (neg.f64 z) (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 x (pow.f64 z #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (.f64 x (fma.f64 (.f64 (/.f64 y (*.f64 z z)) (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))))
(* -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)))))))
(.f64 (neg.f64 z) (fma.f64 x (fma.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 z #s(literal 4 binary64))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1/16 binary64)) (.f64 (pow.f64 z #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))))) (.f64 x (fma.f64 (.f64 (/.f64 y (.f64 z z)) (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))))
(* -1 (* z (sqrt -1)))
(*.f64 (neg.f64 z) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* z (+ (sqrt -1) (* 1/2 (/ (pow y 2) (* (pow z 2) (sqrt -1)))))))
(.f64 (neg.f64 z) (fma.f64 (.f64 (/.f64 y (*.f64 z z)) (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* -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))))))))
(.f64 (neg.f64 z) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 z z)) (*.f64 y (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 z #s(literal 4 binary64))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1 binary64)))))
(* -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)))))))))
(.f64 (neg.f64 z) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 z z)) (*.f64 y (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 z #s(literal 6 binary64))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (fma.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 z #s(literal 4 binary64))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1 binary64))))))

rewrite152.0ms (3.7%)

Memory

18.4MiB live, 127.4MiB allocated; 51ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	28
0	13	28
1	45	28
2	356	28
3	4776	28
0	8785	17

Stop Event

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

Counts

4 → 143

Calls

Call 1

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

Outputs
(.f64 (.f64 x (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 1/4 binary64))) (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 1/4 binary64)))
(.f64 (.f64 x (sqrt.f64 (+.f64 z y))) (sqrt.f64 (-.f64 y z)))
(.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 1/4 binary64)) (.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 1/4 binary64)) x))
(.f64 (sqrt.f64 (+.f64 z y)) (.f64 (sqrt.f64 (-.f64 y z)) x))
(*.f64 (hypot.f64 z y) x)
(*.f64 x (hypot.f64 z y))
(/.f64 (*.f64 (pow.f64 (hypot.f64 z y) #s(literal 2 binary64)) x) (hypot.f64 z y))
(/.f64 (.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))) x) (hypot.f64 (.f64 z (+.f64 z y)) (*.f64 y y)))
(/.f64 (*.f64 x (pow.f64 (hypot.f64 z y) #s(literal 2 binary64))) (hypot.f64 z y))
(/.f64 (.f64 x (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64)))) (hypot.f64 (.f64 z (+.f64 z y)) (*.f64 y y)))
(.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 z #s(literal 6 binary64))) (-.f64 (pow.f64 y #s(literal 8 binary64)) (-.f64 (pow.f64 z #s(literal 8 binary64)) (pow.f64 (.f64 z y) #s(literal 4 binary64))))) #s(literal 1/2 binary64)) (hypot.f64 (.f64 z (+.f64 z y)) (.f64 y y)))
(.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 z #s(literal 6 binary64))) (+.f64 (pow.f64 (pow.f64 (.f64 z (+.f64 z y)) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 y #s(literal 12 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (pow.f64 (.f64 z (+.f64 z y)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 z (+.f64 z y)) #s(literal 2 binary64)) (pow.f64 y #s(literal 4 binary64))) (pow.f64 y #s(literal 8 binary64)))))
(*.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 z #s(literal 4 binary64))) (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 z #s(literal 4 binary64)))) #s(literal 1/2 binary64)) (hypot.f64 z y))
(.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 z #s(literal 4 binary64))) (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 z #s(literal 6 binary64)))) #s(literal 1/2 binary64)) (hypot.f64 (.f64 z (+.f64 z y)) (*.f64 y y)))
(.f64 (pow.f64 (.f64 (fma.f64 z z (*.f64 y y)) (-.f64 y z)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 z y) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 (fma.f64 z z (*.f64 y y)) (+.f64 z y)) #s(literal 1/4 binary64)) (pow.f64 (-.f64 y z) #s(literal 1/4 binary64)))
(.f64 (neg.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 (fma.f64 z z (*.f64 y y)) #s(literal 1/4 binary64))))
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(exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 y) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 y) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 y) #s(literal 2 binary64))))

eval23.0ms (0.6%)

Memory: 15.5MiB live, 59.8MiB allocated; 4ms collecting garbage
Compiler: Compiled 4 447 to 826 computations (81.4% saved)

prune6.0ms (0.1%)

Memory

-28.7MiB live, 17.9MiB allocated; 2ms collecting garbage

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	187	5	192
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	188	5	193

Accuracy

100.0%

Counts

193 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.3%	(.f64 (.f64 x (sqrt.f64 (+.f64 z y))) (sqrt.f64 (-.f64 y z)))
▶	99.3%	(.f64 (sqrt.f64 (+.f64 z y)) (.f64 (sqrt.f64 (-.f64 y z)) x))
▶	65.5%	(.f64 x (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))))
▶	93.2%	(.f64 x #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (/.f64 (*.f64 z z) y) #s(literal -1/2 binary64) y)))
▶	99.4%	#s(approx (* x (sqrt (- (* y y) (* z z)))) (*.f64 y x))

Compiler

Compiled 130 to 98 computations (24.6% saved)

simplify130.0ms (3.2%)

Memory

-4.5MiB live, 94.4MiB allocated; 7ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	177
0	44	177
1	81	177
2	176	177
3	418	177
4	809	177
5	1420	177
6	1965	177
7	2654	177
8	3498	177
9	4206	177
10	4660	177
11	5153	177
12	5507	177
13	5609	177
14	5826	177
15	5863	177
16	5902	177
0	5902	177

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize75.0ms (1.8%)

Memory

10.1MiB live, 149.9MiB allocated; 16ms collecting garbage

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(sqrt.f64 (-.f64 y z))
accuracy	0.01171875	(sqrt.f64 (+.f64 z y))
accuracy	0.25	(*.f64 x (sqrt.f64 (+.f64 z y)))
accuracy	0.28515625	(.f64 (.f64 x (sqrt.f64 (+.f64 z y))) (sqrt.f64 (-.f64 y z)))
accuracy	0.01171875	(sqrt.f64 (-.f64 y z))
accuracy	0.01171875	(sqrt.f64 (+.f64 z y))
accuracy	0.25	(*.f64 (sqrt.f64 (-.f64 y z)) x)
accuracy	0.28353500976844204	(.f64 (sqrt.f64 (+.f64 z y)) (.f64 (sqrt.f64 (-.f64 y z)) x))
accuracy	0.0	(*.f64 z z)
accuracy	0.0	(.f64 x #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (/.f64 (*.f64 z z) y) #s(literal -1/2 binary64) y)))
accuracy	0.2305891678966206	#s(approx (sqrt (- (* y y) (* z z))) (fma.f64 (/.f64 (*.f64 z z) y) #s(literal -1/2 binary64) y))
accuracy	9.436146951246547	(/.f64 (*.f64 z z) y)
accuracy	0.0	(+.f64 z y)
accuracy	0.0	(*.f64 (-.f64 y z) (+.f64 z y))
accuracy	0.0	(.f64 x (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))))
accuracy	32.48311354430071	(sqrt.f64 (*.f64 (-.f64 y z) (+.f64 z y)))
accuracy	0.0	(*.f64 y x)
accuracy	0.3538286404803771	#s(approx (* x (sqrt (- (* y y) (* z z)))) (*.f64 y x))

Samples

47.0ms

256×

valid

Compiler

Compiled 158 to 26 computations (83.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 28.0ms

ival-mult: 16.0ms (57% of total)

ival-sqrt: 6.0ms (21.4% of total)

ival-div: 2.0ms (7.1% of total)

ival-add: 2.0ms (7.1% of total)

ival-sub: 2.0ms (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)

series46.0ms (1.1%)

Memory

-4.8MiB live, 84.1MiB allocated; 8ms collecting garbage

Counts

18 → 202

Calls

Call 1

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

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

Calls

9 calls:

Time	Variable		Point	Expression
9.0ms	y	@	-inf	((* x (sqrt (- (* y y) (* z z)))) (* y x) (* x (sqrt (* (- y z) (+ z y)))) (sqrt (* (- y z) (+ z y))) (* (- y z) (+ z y)) (- y z) (* x (sqrt (- (* y y) (* z z)))) (sqrt (- (* y y) (* z z))) (+ (* (/ (* z z) y) -1/2) y) (/ (* z z) y) (* (sqrt (+ z y)) (* (sqrt (- y z)) x)) (sqrt (+ z y)) (+ z y) (* (sqrt (- y z)) x) (* (* x (sqrt (+ z y))) (sqrt (- y z))) (* x (sqrt (+ z y))) (* z z) (sqrt (- y z)))
7.0ms	y	@	inf	((* x (sqrt (- (* y y) (* z z)))) (* y x) (* x (sqrt (* (- y z) (+ z y)))) (sqrt (* (- y z) (+ z y))) (* (- y z) (+ z y)) (- y z) (* x (sqrt (- (* y y) (* z z)))) (sqrt (- (* y y) (* z z))) (+ (* (/ (* z z) y) -1/2) y) (/ (* z z) y) (* (sqrt (+ z y)) (* (sqrt (- y z)) x)) (sqrt (+ z y)) (+ z y) (* (sqrt (- y z)) x) (* (* x (sqrt (+ z y))) (sqrt (- y z))) (* x (sqrt (+ z y))) (* z z) (sqrt (- y z)))
6.0ms	z	@	-inf	((* x (sqrt (- (* y y) (* z z)))) (* y x) (* x (sqrt (* (- y z) (+ z y)))) (sqrt (* (- y z) (+ z y))) (* (- y z) (+ z y)) (- y z) (* x (sqrt (- (* y y) (* z z)))) (sqrt (- (* y y) (* z z))) (+ (* (/ (* z z) y) -1/2) y) (/ (* z z) y) (* (sqrt (+ z y)) (* (sqrt (- y z)) x)) (sqrt (+ z y)) (+ z y) (* (sqrt (- y z)) x) (* (* x (sqrt (+ z y))) (sqrt (- y z))) (* x (sqrt (+ z y))) (* z z) (sqrt (- y z)))
5.0ms	z	@	inf	((* x (sqrt (- (* y y) (* z z)))) (* y x) (* x (sqrt (* (- y z) (+ z y)))) (sqrt (* (- y z) (+ z y))) (* (- y z) (+ z y)) (- y z) (* x (sqrt (- (* y y) (* z z)))) (sqrt (- (* y y) (* z z))) (+ (* (/ (* z z) y) -1/2) y) (/ (* z z) y) (* (sqrt (+ z y)) (* (sqrt (- y z)) x)) (sqrt (+ z y)) (+ z y) (* (sqrt (- y z)) x) (* (* x (sqrt (+ z y))) (sqrt (- y z))) (* x (sqrt (+ z y))) (* z z) (sqrt (- y z)))
5.0ms	y	@	0	((* x (sqrt (- (* y y) (* z z)))) (* y x) (* x (sqrt (* (- y z) (+ z y)))) (sqrt (* (- y z) (+ z y))) (* (- y z) (+ z y)) (- y z) (* x (sqrt (- (* y y) (* z z)))) (sqrt (- (* y y) (* z z))) (+ (* (/ (* z z) y) -1/2) y) (/ (* z z) y) (* (sqrt (+ z y)) (* (sqrt (- y z)) x)) (sqrt (+ z y)) (+ z y) (* (sqrt (- y z)) x) (* (* x (sqrt (+ z y))) (sqrt (- y z))) (* x (sqrt (+ z y))) (* z z) (sqrt (- y z)))

simplify212.0ms (5.2%)

Memory

48.2MiB live, 328.9MiB allocated; 63ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1006	5617
1	3824	5329
0	8651	5025

Stop Event

1×	iter limit
1×	node limit

Counts

202 → 200

Calls

Call 1

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

Outputs
(* x (sqrt (- (pow y 2) (pow z 2))))
(.f64 (hypot.f64 y (.f64 (sqrt.f64 #s(literal -1 binary64)) z)) x)
(* x y)
(*.f64 y x)
(* x (sqrt (* (+ y z) (- y z))))
(.f64 (hypot.f64 y (.f64 (sqrt.f64 #s(literal -1 binary64)) z)) x)
(* x (sqrt (- y z)))
(*.f64 (sqrt.f64 (-.f64 y z)) x)
(* x (sqrt (+ y z)))
(*.f64 (sqrt.f64 (+.f64 z y)) x)
(* x (* z (sqrt -1)))
(.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) z) x)
(+ (* 1/2 (/ (* x (pow y 2)) (* z (sqrt -1)))) (* x (* z (sqrt -1))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (.f64 (.f64 y y) x) z) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) z) x))
(+ (* 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)))))))
(fma.f64 (.f64 z x) (sqrt.f64 #s(literal -1 binary64)) (.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) z) (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 y y) x)) (pow.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) z) #s(literal 3 binary64)))) (*.f64 y y)))
(+ (* 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)))))))))
(fma.f64 (.f64 z x) (sqrt.f64 #s(literal -1 binary64)) (.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) z) (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (.f64 (fma.f64 (/.f64 (.f64 (.f64 y y) x) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (pow.f64 z #s(literal 5 binary64)))) #s(literal 1/16 binary64) (.f64 (/.f64 x (pow.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) z) #s(literal 3 binary64))) #s(literal -1/8 binary64))) (.f64 y y))) (.f64 y y)))
(+ (* 1/2 (/ (* x (* y (+ z (* -1 z)))) (* z (sqrt -1)))) (* x (* z (sqrt -1))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (.f64 (.f64 (.f64 #s(literal 0 binary64) z) y) x) z) (.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) z) x))
(+ (* x (* z (sqrt -1))) (* y (+ (* 1/2 (/ (* x (* y (- 1 (* 1/4 (/ (pow (+ z (* -1 z)) 2) (* (pow z 2) (pow (sqrt -1) 2))))))) (* z (sqrt -1)))) (* 1/2 (/ (* x (+ z (* -1 z))) (* z (sqrt -1)))))))
(fma.f64 (.f64 z x) (sqrt.f64 #s(literal -1 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (.f64 y x) (-.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 #s(literal 0 binary64) (.f64 z z)) (.f64 z z)) #s(literal -1/4 binary64))) (.f64 (.f64 #s(literal 0 binary64) z) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) z))) y))
(+ (* x (* z (sqrt -1))) (* y (+ (* 1/2 (/ (* x (+ z (* -1 z))) (* z (sqrt -1)))) (* y (+ (* -1/4 (/ (* x (* y (* (+ z (* -1 z)) (- 1 (* 1/4 (/ (pow (+ z (* -1 z)) 2) (* (pow z 2) (pow (sqrt -1) 2)))))))) (* (pow z 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (* x (- 1 (* 1/4 (/ (pow (+ z (* -1 z)) 2) (* (pow z 2) (pow (sqrt -1) 2)))))) (* z (sqrt -1)))))))))
(fma.f64 (fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) z) (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 #s(literal 0 binary64) (.f64 z z)) (.f64 z z)) #s(literal -1/4 binary64))) x) (sqrt.f64 #s(literal -1 binary64))) (.f64 (.f64 x (/.f64 (.f64 (.f64 (.f64 #s(literal 0 binary64) z) y) (-.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 #s(literal 0 binary64) (.f64 z z)) (.f64 z z)) #s(literal -1/4 binary64)))) (pow.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) z) #s(literal 3 binary64)))) #s(literal -1/4 binary64))) y (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (.f64 (.f64 #s(literal 0 binary64) z) x) z))) y (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) z) x))
(* z (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) z)
(+ (* 1/2 (/ (* y (+ z (* -1 z))) (* z (sqrt -1)))) (* z (sqrt -1)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (.f64 (.f64 #s(literal 0 binary64) z) y) z) (*.f64 (sqrt.f64 #s(literal -1 binary64)) z))
(+ (* y (+ (* 1/2 (/ (* y (- 1 (* 1/4 (/ (pow (+ z (* -1 z)) 2) (* (pow z 2) (pow (sqrt -1) 2)))))) (* z (sqrt -1)))) (* 1/2 (/ (+ z (* -1 z)) (* z (sqrt -1)))))) (* z (sqrt -1)))
(fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 #s(literal 0 binary64) (.f64 z z)) (.f64 z z)) #s(literal -1/4 binary64))) y (.f64 #s(literal 0 binary64) z)) (.f64 (sqrt.f64 #s(literal -1 binary64)) z))) y (.f64 (sqrt.f64 #s(literal -1 binary64)) z))
(+ (* y (+ (* 1/2 (/ (+ z (* -1 z)) (* z (sqrt -1)))) (* y (+ (* -1/4 (/ (* y (* (+ z (* -1 z)) (- 1 (* 1/4 (/ (pow (+ z (* -1 z)) 2) (* (pow z 2) (pow (sqrt -1) 2))))))) (* (pow z 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ z (* -1 z)) 2) (* (pow z 2) (pow (sqrt -1) 2))))) (* z (sqrt -1)))))))) (* z (sqrt -1)))
(fma.f64 (fma.f64 (fma.f64 (/.f64 (.f64 (.f64 (.f64 #s(literal 0 binary64) z) y) (-.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 #s(literal 0 binary64) (.f64 z z)) (.f64 z z)) #s(literal -1/4 binary64)))) (pow.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) z) #s(literal 3 binary64))) #s(literal -1/4 binary64) (.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 #s(literal 0 binary64) (.f64 z z)) (.f64 z z)) #s(literal -1/4 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) z)) #s(literal 1/2 binary64))) y (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (.f64 #s(literal 0 binary64) z) z))) y (*.f64 (sqrt.f64 #s(literal -1 binary64)) z))
(* -1 (pow z 2))
(*.f64 (neg.f64 z) z)
(+ (* -1 (pow z 2)) (* y (+ z (* -1 z))))
(*.f64 (fma.f64 #s(literal 0 binary64) y (neg.f64 z)) z)
(+ (* -1 (pow z 2)) (* y (+ y (+ z (* -1 z)))))
(fma.f64 (neg.f64 z) z (*.f64 (fma.f64 #s(literal 0 binary64) z y) y))
(* -1 z)
(neg.f64 z)
(- y z)
(-.f64 y z)
(+ (* 1/2 (/ (pow y 2) (* z (sqrt -1)))) (* z (sqrt -1)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (.f64 y y) z) (.f64 (sqrt.f64 #s(literal -1 binary64)) z))
(+ (* z (sqrt -1)) (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (* (pow z 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* z (sqrt -1)))))))
(fma.f64 (fma.f64 (/.f64 (.f64 y y) (pow.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) z) #s(literal 3 binary64))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) z))) (.f64 y y) (*.f64 (sqrt.f64 #s(literal -1 binary64)) z))
(+ (* 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)))))))
(fma.f64 (fma.f64 (-.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 y y)) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (pow.f64 z #s(literal 5 binary64)))) (/.f64 #s(literal 1/8 binary64) (pow.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) z) #s(literal 3 binary64)))) (.f64 y y) (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) z))) (.f64 y y) (.f64 (sqrt.f64 #s(literal -1 binary64)) z))
(* -1/2 (/ (pow z 2) y))
(.f64 (/.f64 (.f64 z z) y) #s(literal -1/2 binary64))
(/ (+ (* -1/2 (pow z 2)) (pow y 2)) y)
(/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 z z) (.f64 y y)) y)
(/ (pow z 2) y)
(/.f64 (*.f64 z z) y)
(sqrt z)
(sqrt.f64 z)
(+ (sqrt z) (* 1/2 (* y (sqrt (/ 1 z)))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (sqrt.f64 z))
(+ (sqrt z) (* y (+ (* -1/8 (* y (sqrt (/ 1 (pow z 3))))) (* 1/2 (sqrt (/ 1 z))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) #s(literal 1/2 binary64))) y (sqrt.f64 z))
(+ (sqrt z) (* y (+ (* 1/2 (sqrt (/ 1 z))) (* y (+ (* -1/8 (sqrt (/ 1 (pow z 3)))) (* 1/16 (* y (sqrt (/ 1 (pow z 5))))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 5 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64)))) #s(literal -1/8 binary64))) y (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) #s(literal 1/2 binary64))) y (sqrt.f64 z))
z
(+ y z)
(+.f64 z y)
(* (* x (sqrt -1)) (sqrt z))
(.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 z))
(+ (* 1/2 (* (/ (* x y) (sqrt -1)) (sqrt (/ 1 z)))) (* (* x (sqrt -1)) (sqrt z)))
(fma.f64 (.f64 (.f64 x (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) z))) #s(literal 1/2 binary64) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 z)))
(+ (* y (+ (* -1/8 (* (/ (* x y) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow z 3))))) (* 1/2 (* (/ x (sqrt -1)) (sqrt (/ 1 z)))))) (* (* x (sqrt -1)) (sqrt z)))
(fma.f64 (fma.f64 (.f64 (/.f64 (.f64 y x) #s(literal -1 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/8 binary64) (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)))) y (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 z)))
(+ (* 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)))
(fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 x (/.f64 y (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 5 binary64))))) #s(literal 1/16 binary64) (.f64 (.f64 #s(literal -1/8 binary64) (/.f64 x (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64)))))) y (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)))) y (.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 z)))
(* x (sqrt z))
(*.f64 (sqrt.f64 z) x)
(+ (* 1/2 (* (* x y) (sqrt (/ 1 z)))) (* x (sqrt z)))
(fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 y x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (*.f64 (sqrt.f64 z) x))
(+ (* x (sqrt z)) (* y (+ (* -1/8 (* (* x y) (sqrt (/ 1 (pow z 3))))) (* 1/2 (* x (sqrt (/ 1 z)))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 y x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64)))) (.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)))) y (*.f64 (sqrt.f64 z) x))
(+ (* x (sqrt z)) (* y (+ (* 1/2 (* x (sqrt (/ 1 z)))) (* y (+ (* -1/8 (* x (sqrt (/ 1 (pow z 3))))) (* 1/16 (* (* x y) (sqrt (/ 1 (pow z 5))))))))))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) (.f64 y x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 5 binary64)))) (.f64 (.f64 #s(literal -1/8 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64)))))) y)) y (*.f64 (sqrt.f64 z) x))
(* (sqrt z) (sqrt -1))
(*.f64 (sqrt.f64 z) (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (* (/ y (sqrt -1)) (sqrt (/ 1 z)))) (* (sqrt z) (sqrt -1)))
(fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (.f64 (sqrt.f64 z) (sqrt.f64 #s(literal -1 binary64))))
(+ (* y (+ (* -1/8 (* (/ y (pow (sqrt -1) 3)) (sqrt (/ 1 (pow z 3))))) (* 1/2 (* (sqrt (/ 1 z)) (/ 1 (sqrt -1)))))) (* (sqrt z) (sqrt -1)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 y (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64)))) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) z))) #s(literal 1/2 binary64))) y (*.f64 (sqrt.f64 z) (sqrt.f64 #s(literal -1 binary64))))
(+ (* y (+ (* 1/2 (* (sqrt (/ 1 z)) (/ 1 (sqrt -1)))) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow z 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (/ y (pow (sqrt -1) 5)) (sqrt (/ 1 (pow z 5))))))))) (* (sqrt z) (sqrt -1)))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) (/.f64 y (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 5 binary64)))) (.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1 binary64)) #s(literal -1/8 binary64))) y (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) z))) #s(literal 1/2 binary64))) y (.f64 (sqrt.f64 z) (sqrt.f64 #s(literal -1 binary64))))
(* y (+ x (* -1/2 (/ (* x (pow z 2)) (pow y 2)))))
(.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) y) (.f64 x (/.f64 (*.f64 z z) y)) x) y)
(* y (+ x (+ (* -1/2 (/ (* x (pow z 2)) (pow y 2))) (* -1/8 (/ (* x (pow z 4)) (pow y 4))))))
(.f64 (+.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) y) (.f64 x (/.f64 (.f64 z z) y)) (/.f64 (.f64 #s(literal -1/8 binary64) (*.f64 (pow.f64 z #s(literal 4 binary64)) x)) (pow.f64 y #s(literal 4 binary64)))) x) y)
(* 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)))))))
(.f64 (+.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) y) (.f64 x (/.f64 (.f64 z z) y)) x) (fma.f64 (/.f64 (.f64 (pow.f64 z #s(literal 6 binary64)) x) (pow.f64 y #s(literal 6 binary64))) #s(literal -1/16 binary64) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 (pow.f64 z #s(literal 4 binary64)) x)) (pow.f64 y #s(literal 4 binary64))))) y)
(* y (+ x (* 1/2 (/ (* x (+ z (* -1 z))) y))))
(.f64 (fma.f64 (/.f64 (.f64 (*.f64 #s(literal 0 binary64) z) x) y) #s(literal 1/2 binary64) x) y)
(* y (+ x (+ (* 1/2 (/ (* x (+ z (* -1 z))) y)) (* 1/2 (/ (* x (- (* -1 (pow z 2)) (* 1/4 (pow (+ z (* -1 z)) 2)))) (pow y 2))))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 x (/.f64 (.f64 #s(literal 0 binary64) z) y) (.f64 x (/.f64 (fma.f64 (neg.f64 z) z (.f64 #s(literal -1/4 binary64) (.f64 #s(literal 0 binary64) (.f64 z z)))) (*.f64 y y)))) x) y)
(* 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)))))))
(.f64 (+.f64 (fma.f64 (/.f64 (.f64 (.f64 (.f64 #s(literal 0 binary64) z) x) (fma.f64 (neg.f64 z) z (.f64 #s(literal -1/4 binary64) (.f64 #s(literal 0 binary64) (.f64 z z))))) (pow.f64 y #s(literal 3 binary64))) #s(literal -1/4 binary64) (.f64 #s(literal 1/2 binary64) (fma.f64 x (/.f64 (.f64 #s(literal 0 binary64) z) y) (.f64 x (/.f64 (fma.f64 (neg.f64 z) z (.f64 #s(literal -1/4 binary64) (.f64 #s(literal 0 binary64) (.f64 z z)))) (.f64 y y)))))) x) y)
y
(* y (+ 1 (* 1/2 (/ (+ z (* -1 z)) y))))
(.f64 (fma.f64 (/.f64 (.f64 #s(literal 0 binary64) z) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)
(* y (+ 1 (+ (* 1/2 (/ (+ z (* -1 z)) y)) (* 1/2 (/ (- (* -1 (pow z 2)) (* 1/4 (pow (+ z (* -1 z)) 2))) (pow y 2))))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 0 binary64) (/.f64 z y) (/.f64 (fma.f64 (neg.f64 z) z (.f64 #s(literal -1/4 binary64) (.f64 #s(literal 0 binary64) (.f64 z z)))) (*.f64 y y))) #s(literal 1 binary64)) y)
(* y (+ 1 (+ (* -1/4 (/ (* (+ z (* -1 z)) (- (* -1 (pow z 2)) (* 1/4 (pow (+ z (* -1 z)) 2)))) (pow y 3))) (+ (* 1/2 (/ (+ z (* -1 z)) y)) (* 1/2 (/ (- (* -1 (pow z 2)) (* 1/4 (pow (+ z (* -1 z)) 2))) (pow y 2)))))))
(.f64 (+.f64 (fma.f64 (/.f64 (.f64 (fma.f64 (neg.f64 z) z (.f64 #s(literal -1/4 binary64) (.f64 #s(literal 0 binary64) (.f64 z z)))) (.f64 #s(literal 0 binary64) z)) (pow.f64 y #s(literal 3 binary64))) #s(literal -1/4 binary64) (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 0 binary64) (/.f64 z y) (/.f64 (fma.f64 (neg.f64 z) z (.f64 #s(literal -1/4 binary64) (.f64 #s(literal 0 binary64) (.f64 z z)))) (*.f64 y y))))) #s(literal 1 binary64)) y)
(pow y 2)
(*.f64 y y)
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(.f64 (neg.f64 z) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) y) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64)))) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)))))
(* -1 (* z (+ (* -1/8 (* (* x (* (pow y 2) (sqrt -1))) (sqrt (/ 1 (pow z 5))))) (+ (* 1/2 (* (* x (* y (sqrt -1))) (sqrt (/ 1 (pow z 3))))) (* (* x (sqrt -1)) (sqrt (/ 1 z)))))))
(.f64 (neg.f64 z) (fma.f64 (.f64 (.f64 (.f64 (.f64 y y) x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 5 binary64))))) #s(literal -1/8 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) y) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64)))) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) z))))))
(* -1 (* z (+ (* -1/8 (* (* x (* (pow y 2) (sqrt -1))) (sqrt (/ 1 (pow z 5))))) (+ (* 1/16 (* (* x (* (pow y 3) (sqrt -1))) (sqrt (/ 1 (pow z 7))))) (+ (* 1/2 (* (* x (* y (sqrt -1))) (sqrt (/ 1 (pow z 3))))) (* (* x (sqrt -1)) (sqrt (/ 1 z))))))))
(.f64 (neg.f64 z) (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 (.f64 y y) x) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 5 binary64)))) (fma.f64 (.f64 (.f64 (.f64 (pow.f64 y #s(literal 3 binary64)) x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 7 binary64))))) #s(literal 1/16 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) y) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64)))) (.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)))))))
(* -1 (* (* x (pow (sqrt -1) 2)) (sqrt z)))
(.f64 x (.f64 (sqrt.f64 z) #s(literal 1 binary64)))
(* -1 (* z (+ (* 1/2 (* (* x y) (sqrt (/ 1 (pow z 3))))) (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))
(.f64 (neg.f64 z) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 y x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64)))) (.f64 (*.f64 #s(literal -1 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)))))
(* -1 (* z (+ (* -1/8 (* (/ (* x (pow y 2)) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow z 5))))) (+ (* 1/2 (* (* x y) (sqrt (/ 1 (pow z 3))))) (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 z)))))))
(.f64 (neg.f64 z) (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (.f64 (.f64 y y) x) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 5 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 y x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64)))) (.f64 (.f64 #s(literal -1 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) z))))))
(* -1 (* z (+ (* -1/8 (* (/ (* x (pow y 2)) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow z 5))))) (+ (* 1/16 (* (/ (* x (pow y 3)) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow z 7))))) (+ (* 1/2 (* (* x y) (sqrt (/ 1 (pow z 3))))) (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 z))))))))
(.f64 (neg.f64 z) (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (.f64 (.f64 y y) x) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 5 binary64)))) (fma.f64 (/.f64 (.f64 (.f64 (pow.f64 y #s(literal 3 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 7 binary64))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 y x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64)))) (.f64 (.f64 #s(literal -1 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) z)))))))
(* -1 (* (sqrt z) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 z)) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* z (+ (* 1/2 (* (* y (sqrt -1)) (sqrt (/ 1 (pow z 3))))) (* (sqrt (/ 1 z)) (sqrt -1)))))
(.f64 (neg.f64 z) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* z (+ (* -1/8 (* (* (pow y 2) (sqrt -1)) (sqrt (/ 1 (pow z 5))))) (+ (* 1/2 (* (* y (sqrt -1)) (sqrt (/ 1 (pow z 3))))) (* (sqrt (/ 1 z)) (sqrt -1))))))
(.f64 (neg.f64 z) (fma.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 y y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 5 binary64))))) #s(literal -1/8 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (sqrt.f64 #s(literal -1 binary64))))))
(* -1 (* z (+ (* -1/8 (* (* (pow y 2) (sqrt -1)) (sqrt (/ 1 (pow z 5))))) (+ (* 1/16 (* (* (pow y 3) (sqrt -1)) (sqrt (/ 1 (pow z 7))))) (+ (* 1/2 (* (* y (sqrt -1)) (sqrt (/ 1 (pow z 3))))) (* (sqrt (/ 1 z)) (sqrt -1)))))))
(.f64 (neg.f64 z) (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 y y))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 5 binary64)))) (fma.f64 (.f64 (.f64 (pow.f64 y #s(literal 3 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 7 binary64))))) #s(literal 1/16 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 z #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) z)) (sqrt.f64 #s(literal -1 binary64)))))))

rewrite127.0ms (3.1%)

Memory

-24.1MiB live, 260.4MiB allocated; 21ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	142
0	44	140
1	132	140
2	884	126
0	9413	104

Stop Event

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

Counts

18 → 583

Calls

Call 1

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

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

eval96.0ms (2.3%)

Memory: 26.9MiB live, 211.4MiB allocated; 17ms collecting garbage
Compiler: Compiled 28 587 to 3 569 computations (87.5% saved)

prune27.0ms (0.6%)

Memory

5.7MiB live, 50.1MiB allocated; 3ms collecting garbage

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	923	2	925
Fresh	0	0	0
Picked	2	3	5
Done	0	0	0
Total	925	5	930

Accuracy

100.0%

Counts

930 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.3%	(.f64 (sqrt.f64 (+.f64 z y)) (.f64 (sqrt.f64 (-.f64 y z)) x))
✓	65.5%	(.f64 x (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))))
▶	99.9%	(.f64 x #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (*.f64 (/.f64 z y) z) #s(literal -1/2 binary64) y)))
▶	63.3%	(.f64 x #s(approx (sqrt (- ( y y) (* z z))) #s(approx (+ (* (/ (* z z) y) -1/2) y) (/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 z z) (.f64 y y)) y))))
✓	99.4%	#s(approx (* x (sqrt (- (* y y) (* z z)))) (*.f64 y x))

Compiler

Compiled 85 to 59 computations (30.6% saved)

simplify107.0ms (2.6%)

Memory

-11.0MiB live, 91.5MiB allocated; 7ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	23	164
0	34	163
1	67	163
2	184	163
3	488	153
4	960	153
5	3341	153
6	5262	153
7	6992	153
0	8468	153

Stop Event

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

Calls

Call 1

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

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

localize98.0ms (2.4%)

Memory

-29.3MiB live, 61.1MiB allocated; 8ms collecting garbage

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.0	(/.f64 z y)
accuracy	0.0	(.f64 x #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (*.f64 (/.f64 z y) z) #s(literal -1/2 binary64) y)))
accuracy	0.13671875	(*.f64 (/.f64 z y) z)
accuracy	0.2305891678966206	#s(approx (sqrt (- (* y y) (* z z))) (fma.f64 (*.f64 (/.f64 z y) z) #s(literal -1/2 binary64) y))
accuracy	0.0	#s(approx (+ (* (/ (* z z) y) -1/2) y) (/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 z z) (.f64 y y)) y))
accuracy	0.2305891678966206	#s(approx (sqrt (- (* y y) (* z z))) #s(approx (+ (* (/ (* z z) y) -1/2) y) (/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 z z) (.f64 y y)) y)))
accuracy	3.3867187500000004	(fma.f64 #s(literal -1/2 binary64) (.f64 z z) (.f64 y y))
accuracy	32.53774910208077	(/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 z z) (.f64 y y)) y)

Samples

65.0ms

256×

valid

Compiler

Compiled 98 to 21 computations (78.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-mult: 10.0ms (46.4% of total)

ival-div: 5.0ms (23.2% of total)

ival-add: 3.0ms (13.9% of total)

ival-sqrt: 2.0ms (9.3% of total)

ival-sub: 1.0ms (4.6% 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)

series13.0ms (0.3%)

Memory

19.6MiB live, 19.6MiB allocated; 0ms collecting garbage

Counts

10 → 56

Calls

Call 1

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

Outputs
(* x (sqrt (- (pow y 2) (pow z 2))))
(* -1/2 (/ (pow z 2) y))
(/ (+ (* -1/2 (pow z 2)) (pow y 2)) y)
(* 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 z 2) y)
(* -1/2 (pow z 2))
(+ (* -1/2 (pow z 2)) (pow y 2))
(/ z y)
y
(* y (+ 1 (* -1/2 (/ (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 (+ 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) (+ 1 (* -1/2 (/ (pow z 2) (pow y 2)))))
(* -1 (* y (- (* 1/2 (/ (pow z 2) (pow y 2))) 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))))))))
(* -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 (* -1/2 (/ (pow z 2) 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 (* (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)))))
(* (pow z 2) (- (/ y (pow z 2)) (* 1/2 (/ 1 y))))
(* 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) (* 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))))))))
(* (pow z 2) (- (/ (pow y 2) (pow z 2)) 1/2))
(* -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)))))))))

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	z	@	inf	((/ (+ (* -1/2 (* z z)) (* y y)) y) (* x (sqrt (- (* y y) (* z z)))) (sqrt (- (* y y) (* z z))) (+ (* (/ (* z z) y) -1/2) y) (* x (sqrt (- (* y y) (* z z)))) (sqrt (- (* y y) (* z z))) (+ (* (* (/ z y) z) -1/2) y) (* (/ z y) z) (+ (* -1/2 (* z z)) (* y y)) (/ z y))
2.0ms	y	@	-inf	((/ (+ (* -1/2 (* z z)) (* y y)) y) (* x (sqrt (- (* y y) (* z z)))) (sqrt (- (* y y) (* z z))) (+ (* (/ (* z z) y) -1/2) y) (* x (sqrt (- (* y y) (* z z)))) (sqrt (- (* y y) (* z z))) (+ (* (* (/ z y) z) -1/2) y) (* (/ z y) z) (+ (* -1/2 (* z z)) (* y y)) (/ z y))
2.0ms	z	@	-inf	((/ (+ (* -1/2 (* z z)) (* y y)) y) (* x (sqrt (- (* y y) (* z z)))) (sqrt (- (* y y) (* z z))) (+ (* (/ (* z z) y) -1/2) y) (* x (sqrt (- (* y y) (* z z)))) (sqrt (- (* y y) (* z z))) (+ (* (* (/ z y) z) -1/2) y) (* (/ z y) z) (+ (* -1/2 (* z z)) (* y y)) (/ z y))
1.0ms	y	@	inf	((/ (+ (* -1/2 (* z z)) (* y y)) y) (* x (sqrt (- (* y y) (* z z)))) (sqrt (- (* y y) (* z z))) (+ (* (/ (* z z) y) -1/2) y) (* x (sqrt (- (* y y) (* z z)))) (sqrt (- (* y y) (* z z))) (+ (* (* (/ z y) z) -1/2) y) (* (/ z y) z) (+ (* -1/2 (* z z)) (* y y)) (/ z y))
1.0ms	y	@	0	((/ (+ (* -1/2 (* z z)) (* y y)) y) (* x (sqrt (- (* y y) (* z z)))) (sqrt (- (* y y) (* z z))) (+ (* (/ (* z z) y) -1/2) y) (* x (sqrt (- (* y y) (* z z)))) (sqrt (- (* y y) (* z z))) (+ (* (* (/ z y) z) -1/2) y) (* (/ z y) z) (+ (* -1/2 (* z z)) (* y y)) (/ z y))

simplify238.0ms (5.8%)

Memory

-38.3MiB live, 142.0MiB allocated; 98ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	212	1196
1	717	1196
2	3095	1149
0	8436	1076

Stop Event

1×	iter limit
1×	node limit

Counts

56 → 55

Calls

Call 1

Inputs
(* x (sqrt (- (pow y 2) (pow z 2))))
(* -1/2 (/ (pow z 2) y))
(/ (+ (* -1/2 (pow z 2)) (pow y 2)) y)
(* 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 z 2) y)
(* -1/2 (pow z 2))
(+ (* -1/2 (pow z 2)) (pow y 2))
(/ z y)
y
(* y (+ 1 (* -1/2 (/ (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 (+ 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) (+ 1 (* -1/2 (/ (pow z 2) (pow y 2)))))
(* -1 (* y (- (* 1/2 (/ (pow z 2) (pow y 2))) 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))))))))
(* -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 (* -1/2 (/ (pow z 2) 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 (* (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)))))
(* (pow z 2) (- (/ y (pow z 2)) (* 1/2 (/ 1 y))))
(* 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) (* 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))))))))
(* (pow z 2) (- (/ (pow y 2) (pow z 2)) 1/2))
(* -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)))))))))

Outputs
(* x (sqrt (- (pow y 2) (pow z 2))))
(.f64 (sqrt.f64 (.f64 (+.f64 y z) (-.f64 y z))) x)
(* -1/2 (/ (pow z 2) y))
(.f64 (/.f64 (.f64 z z) y) #s(literal -1/2 binary64))
(/ (+ (* -1/2 (pow z 2)) (pow y 2)) y)
(fma.f64 (/.f64 (*.f64 z z) y) #s(literal -1/2 binary64) y)
(* x (* z (sqrt -1)))
(.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) z) x)
(+ (* 1/2 (/ (* x (pow y 2)) (* z (sqrt -1)))) (* x (* z (sqrt -1))))
(.f64 x (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) z)) y) y (.f64 (sqrt.f64 #s(literal -1 binary64)) z)))
(+ (* 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)))))))
(fma.f64 (.f64 x z) (sqrt.f64 #s(literal -1 binary64)) (.f64 (fma.f64 (.f64 (.f64 (/.f64 x (pow.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) z) #s(literal 3 binary64))) #s(literal -1/8 binary64)) y) y (.f64 (/.f64 x (.f64 (sqrt.f64 #s(literal -1 binary64)) z)) #s(literal 1/2 binary64))) (.f64 y y)))
(+ (* 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)))))))))
(fma.f64 x (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) z)) y) y (.f64 (sqrt.f64 #s(literal -1 binary64)) z)) (.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (/.f64 (.f64 (.f64 y y) x) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (pow.f64 z #s(literal 5 binary64)))) #s(literal 1/16 binary64) (.f64 (/.f64 x (pow.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) z) #s(literal 3 binary64))) #s(literal -1/8 binary64)))))
(* z (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) z)
(+ (* 1/2 (/ (pow y 2) (* z (sqrt -1)))) (* z (sqrt -1)))
(fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) z)) y) y (*.f64 (sqrt.f64 #s(literal -1 binary64)) z))
(+ (* z (sqrt -1)) (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (* (pow z 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* z (sqrt -1)))))))
(fma.f64 (fma.f64 (.f64 y (/.f64 y (pow.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) z) #s(literal 3 binary64)))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) z))) (.f64 y y) (*.f64 (sqrt.f64 #s(literal -1 binary64)) z))
(+ (* 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)))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (/.f64 y (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 y (pow.f64 z #s(literal 5 binary64)))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) z) #s(literal 3 binary64)))) (.f64 y y) (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) z))) (.f64 y y) (.f64 (sqrt.f64 #s(literal -1 binary64)) z))
(/ (pow z 2) y)
(/.f64 (*.f64 z z) y)
(* -1/2 (pow z 2))
(.f64 (.f64 z z) #s(literal -1/2 binary64))
(+ (* -1/2 (pow z 2)) (pow y 2))
(fma.f64 (.f64 z z) #s(literal -1/2 binary64) (.f64 y y))
(/ z y)
(/.f64 z y)
y
(* y (+ 1 (* -1/2 (/ (pow z 2) (pow y 2)))))
(.f64 (fma.f64 (/.f64 (/.f64 (.f64 z z) y) y) #s(literal -1/2 binary64) #s(literal 1 binary64)) y)
(* x y)
(*.f64 x y)
(* y (+ x (* -1/2 (/ (* x (pow z 2)) (pow y 2)))))
(.f64 (fma.f64 (.f64 (/.f64 (/.f64 (*.f64 z z) y) y) x) #s(literal -1/2 binary64) x) y)
(* y (+ x (+ (* -1/2 (/ (* x (pow z 2)) (pow y 2))) (* -1/8 (/ (* x (pow z 4)) (pow y 4))))))
(.f64 (fma.f64 x (fma.f64 (/.f64 #s(literal -1/2 binary64) y) (/.f64 (.f64 z z) y) (/.f64 (*.f64 (pow.f64 z #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 y #s(literal 4 binary64)))) x) y)
(* 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)))))))
(.f64 (fma.f64 (.f64 #s(literal -1/16 binary64) x) (/.f64 (pow.f64 z #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (fma.f64 x (fma.f64 (/.f64 #s(literal -1/2 binary64) y) (/.f64 (.f64 z z) y) (/.f64 (.f64 (pow.f64 z #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 y #s(literal 4 binary64)))) x)) y)
(* y (+ 1 (+ (* -1/2 (/ (pow z 2) (pow y 2))) (* -1/8 (/ (pow z 4) (pow y 4))))))
(.f64 (fma.f64 (/.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 (.f64 z z) y) y) #s(literal -1/2 binary64) #s(literal 1 binary64))) y)
(* 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)))))))
(.f64 (fma.f64 (/.f64 (pow.f64 z #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal -1/16 binary64) (fma.f64 (/.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 (.f64 z z) y) y) #s(literal -1/2 binary64) #s(literal 1 binary64)))) y)
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (* -1/2 (/ (pow z 2) (pow y 2)))))
(.f64 (.f64 (fma.f64 (/.f64 (/.f64 (*.f64 z z) y) y) #s(literal -1/2 binary64) #s(literal 1 binary64)) y) y)
(* -1 (* y (- (* 1/2 (/ (pow z 2) (pow y 2))) 1)))
(.f64 (neg.f64 y) (-.f64 (.f64 (/.f64 (/.f64 (*.f64 z z) y) y) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(* -1 (* x y))
(*.f64 (neg.f64 x) y)
(* -1 (* y (+ x (* -1/2 (/ (* x (pow z 2)) (pow y 2))))))
(.f64 (fma.f64 (.f64 (/.f64 (/.f64 (*.f64 z z) y) y) x) #s(literal 1/2 binary64) (neg.f64 x)) y)
(* -1 (* y (+ x (+ (* -1/2 (/ (* x (pow z 2)) (pow y 2))) (* -1/8 (/ (* x (pow z 4)) (pow y 4)))))))
(.f64 (neg.f64 y) (fma.f64 x (fma.f64 (/.f64 #s(literal -1/2 binary64) y) (/.f64 (.f64 z z) y) (/.f64 (*.f64 (pow.f64 z #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 y #s(literal 4 binary64)))) x))
(* -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))))))))
(.f64 (neg.f64 y) (fma.f64 (.f64 #s(literal -1/16 binary64) x) (/.f64 (pow.f64 z #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (fma.f64 x (fma.f64 (/.f64 #s(literal -1/2 binary64) y) (/.f64 (.f64 z z) y) (/.f64 (.f64 (pow.f64 z #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 y #s(literal 4 binary64)))) x)))
(* -1 y)
(neg.f64 y)
(* -1 (* y (+ 1 (* -1/2 (/ (pow z 2) (pow y 2))))))
(.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 z z) y) #s(literal -1 binary64)) y)
(* -1 (* y (+ 1 (+ (* -1/2 (/ (pow z 2) (pow y 2))) (* -1/8 (/ (pow z 4) (pow y 4)))))))
(.f64 (neg.f64 y) (fma.f64 (/.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 (.f64 z z) y) y) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(* -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))))))))
(.f64 (neg.f64 y) (fma.f64 (/.f64 (pow.f64 z #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal -1/16 binary64) (fma.f64 (/.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 (.f64 z z) y) y) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
(+ y (* -1/2 (/ (pow z 2) y)))
(fma.f64 (/.f64 (*.f64 z z) y) #s(literal -1/2 binary64) y)
(+ (* -1/2 (/ (* x (pow z 2)) y)) (* x y))
(.f64 x (fma.f64 (/.f64 (.f64 z z) y) #s(literal -1/2 binary64) y))
(+ (* 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 x (pow.f64 y #s(literal 3 binary64))) #s(literal -1/8 binary64)) z) z (.f64 (/.f64 x y) #s(literal -1/2 binary64))) (.f64 z z) (*.f64 x y))
(+ (* 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 (.f64 (.f64 z z) (/.f64 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))) (pow.f64 z #s(literal 4 binary64)) (.f64 x (fma.f64 (/.f64 (*.f64 z z) y) #s(literal -1/2 binary64) y)))
(+ y (* (pow z 2) (- (* -1/8 (/ (pow z 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(fma.f64 (fma.f64 (.f64 z (/.f64 z (pow.f64 y #s(literal 3 binary64)))) #s(literal -1/8 binary64) (/.f64 #s(literal -1/2 binary64) y)) (.f64 z z) 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)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 z (/.f64 z (pow.f64 y #s(literal 5 binary64)))) #s(literal -1/16 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 3 binary64)))) (.f64 z z) (/.f64 #s(literal -1/2 binary64) y)) (*.f64 z z) y)
(* (pow z 2) (- (/ y (pow z 2)) (* 1/2 (/ 1 y))))
(.f64 (-.f64 (/.f64 y (.f64 z z)) (/.f64 #s(literal 1/2 binary64) y)) (*.f64 z z))
(* z (+ (* 1/2 (/ (* x (pow y 2)) (* (pow z 2) (sqrt -1)))) (* x (sqrt -1))))
(.f64 (.f64 x (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (.f64 y (/.f64 y (.f64 z z))) (sqrt.f64 #s(literal -1 binary64)))) z)
(* 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)))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 x (pow.f64 z #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (.f64 x (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (.f64 y (/.f64 y (*.f64 z z))) (sqrt.f64 #s(literal -1 binary64))))) z)
(* 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))))))
(.f64 (fma.f64 x (fma.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 z #s(literal 4 binary64))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1/16 binary64)) (.f64 (pow.f64 z #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))))) (.f64 x (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (.f64 y (/.f64 y (.f64 z z))) (sqrt.f64 #s(literal -1 binary64))))) z)
(* z (+ (sqrt -1) (* 1/2 (/ (pow y 2) (* (pow z 2) (sqrt -1))))))
(.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (.f64 y (/.f64 y (*.f64 z z))) (sqrt.f64 #s(literal -1 binary64))) z)
(* 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)))))))
(.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 z z)) (*.f64 y (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 z #s(literal 4 binary64))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1 binary64)))) z)
(* 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))))))))
(.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 z z)) (*.f64 y (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 z #s(literal 6 binary64))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (fma.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 z #s(literal 4 binary64))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1 binary64))))) z)
(* (pow z 2) (- (/ (pow y 2) (pow z 2)) 1/2))
(.f64 (.f64 (-.f64 (.f64 y (/.f64 y (.f64 z z))) #s(literal 1/2 binary64)) z) z)
(* -1 (* x (* z (sqrt -1))))
(.f64 (.f64 (neg.f64 z) x) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* z (+ (* 1/2 (/ (* x (pow y 2)) (* (pow z 2) (sqrt -1)))) (* x (sqrt -1)))))
(.f64 (neg.f64 z) (.f64 x (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (.f64 y (/.f64 y (.f64 z z))) (sqrt.f64 #s(literal -1 binary64)))))
(* -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))))))
(.f64 (neg.f64 z) (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 x (pow.f64 z #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (.f64 x (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (.f64 y (/.f64 y (*.f64 z z))) (sqrt.f64 #s(literal -1 binary64))))))
(* -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)))))))
(.f64 (neg.f64 z) (fma.f64 x (fma.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 z #s(literal 4 binary64))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1/16 binary64)) (.f64 (pow.f64 z #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))))) (.f64 x (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (.f64 y (/.f64 y (.f64 z z))) (sqrt.f64 #s(literal -1 binary64))))))
(* -1 (* z (sqrt -1)))
(*.f64 (neg.f64 z) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* z (+ (sqrt -1) (* 1/2 (/ (pow y 2) (* (pow z 2) (sqrt -1)))))))
(.f64 (neg.f64 z) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (.f64 y (/.f64 y (*.f64 z z))) (sqrt.f64 #s(literal -1 binary64))))
(* -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))))))))
(.f64 (neg.f64 z) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 z z)) (*.f64 y (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 z #s(literal 4 binary64))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1 binary64)))))
(* -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)))))))))
(.f64 (neg.f64 z) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 z z)) (*.f64 y (/.f64 y (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 z #s(literal 6 binary64))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (fma.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 z #s(literal 4 binary64))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1 binary64))))))

rewrite183.0ms (4.4%)

Memory

27.9MiB live, 166.7MiB allocated; 18ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	150
0	34	147
1	124	147
2	816	147
0	9425	127

Stop Event

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

Counts

10 → 202

Calls

Call 1

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

Outputs
(.f64 (/.f64 (fma.f64 (.f64 z #s(literal -1/2 binary64)) z (.f64 y y)) (fma.f64 (.f64 z #s(literal -1/2 binary64)) z (.f64 (neg.f64 y) y))) (fma.f64 (.f64 (/.f64 z y) z) #s(literal -1/2 binary64) (*.f64 y #s(literal 1 binary64))))
(.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 z #s(literal 4 binary64)) (-.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (pow.f64 (.f64 z y) #s(literal 2 binary64)) #s(literal -1/2 binary64)))) (fma.f64 #s(literal 1/4 binary64) (pow.f64 z #s(literal 4 binary64)) (-.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (pow.f64 (.f64 z y) #s(literal 2 binary64)) #s(literal -1/2 binary64))))) (fma.f64 (.f64 (/.f64 z y) z) #s(literal -1/2 binary64) (*.f64 y #s(literal 1 binary64))))
(/.f64 (-.f64 (.f64 (.f64 y y) #s(literal 1 binary64)) (.f64 (/.f64 #s(literal 1/4 binary64) y) (/.f64 (pow.f64 z #s(literal 4 binary64)) y))) (-.f64 (.f64 y #s(literal 1 binary64)) (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z)))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 (/.f64 z y) z) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (pow.f64 (neg.f64 (.f64 y #s(literal 1 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 #s(literal 1/4 binary64) y) (/.f64 (pow.f64 z #s(literal 4 binary64)) y) (fma.f64 (.f64 y y) #s(literal 1 binary64) (.f64 (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z) (neg.f64 (.f64 y #s(literal 1 binary64)))))))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 (/.f64 z y) z) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal -1 binary64))) (fma.f64 (/.f64 #s(literal 1/4 binary64) y) (/.f64 (pow.f64 z #s(literal 4 binary64)) y) (fma.f64 (.f64 y y) #s(literal 1 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (/.f64 z y)) (.f64 z (.f64 y #s(literal 1 binary64)))))))
(/.f64 (fma.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal -1 binary64) (.f64 (pow.f64 (.f64 (/.f64 z y) z) #s(literal 3 binary64)) #s(literal -1/8 binary64))) (fma.f64 (.f64 y y) #s(literal 1 binary64) (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) y) (/.f64 (pow.f64 z #s(literal 4 binary64)) y)) (.f64 (.f64 y #s(literal 1 binary64)) (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z)))))
(/.f64 (neg.f64 (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) y) (/.f64 (pow.f64 z #s(literal 4 binary64)) y)) (.f64 (.f64 y y) #s(literal 1 binary64)))) (/.f64 (fma.f64 (.f64 z #s(literal -1/2 binary64)) z (*.f64 y y)) (neg.f64 y)))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 (/.f64 z y) z) #s(literal 3 binary64)) #s(literal -1/8 binary64) (.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal -1 binary64)))) (neg.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) y) (/.f64 (pow.f64 z #s(literal 4 binary64)) y) (.f64 (.f64 y #s(literal 1 binary64)) (-.f64 (.f64 y #s(literal 1 binary64)) (.f64 (*.f64 (/.f64 z y) #s(literal -1/2 binary64)) z))))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 z z) #s(literal -1/2 binary64)) y (pow.f64 y #s(literal 3 binary64)))) (*.f64 (neg.f64 y) y))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 z z)) (neg.f64 y)) (pow.f64 y #s(literal 3 binary64))) (.f64 y y))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 z z)) y) (pow.f64 y #s(literal 3 binary64))) (.f64 (neg.f64 y) y))
(/.f64 (-.f64 (.f64 (.f64 z #s(literal -1/2 binary64)) (.f64 z (neg.f64 y))) (pow.f64 y #s(literal 3 binary64))) (.f64 (neg.f64 y) y))
(/.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (.f64 (neg.f64 y) (.f64 #s(literal 1/2 binary64) (.f64 z z)))) (.f64 y y))
(/.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (.f64 (neg.f64 y) (.f64 (.f64 z z) #s(literal -1/2 binary64)))) (.f64 (neg.f64 y) y))
(/.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (.f64 y (.f64 #s(literal 1/2 binary64) (.f64 z z)))) (.f64 (neg.f64 y) y))
(/.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (.f64 y (.f64 (.f64 z z) #s(literal -1/2 binary64)))) (.f64 y y))
(/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 z z)) (neg.f64 y) (pow.f64 y #s(literal 3 binary64))) (*.f64 y y))
(/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 z z)) y (pow.f64 y #s(literal 3 binary64))) (*.f64 (neg.f64 y) y))
(/.f64 (fma.f64 (.f64 z #s(literal -1/2 binary64)) (.f64 z (neg.f64 y)) (pow.f64 y #s(literal 3 binary64))) (*.f64 (neg.f64 y) y))
(/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 z z)) (*.f64 (neg.f64 y) y)) (neg.f64 y))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) y) (/.f64 (pow.f64 z #s(literal 4 binary64)) y)) (.f64 (.f64 y y) #s(literal 1 binary64))) (fma.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z (neg.f64 (*.f64 y #s(literal 1 binary64)))))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) y) (/.f64 (pow.f64 z #s(literal 4 binary64)) y)) (.f64 (.f64 y y) #s(literal 1 binary64))) (fma.f64 (.f64 (/.f64 z y) z) #s(literal -1/2 binary64) (*.f64 y #s(literal 1 binary64))))
(/.f64 (fma.f64 (pow.f64 (.f64 (/.f64 z y) z) #s(literal 3 binary64)) #s(literal -1/8 binary64) (.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal -1 binary64))) (fma.f64 (/.f64 #s(literal 1/4 binary64) y) (/.f64 (pow.f64 z #s(literal 4 binary64)) y) (.f64 (.f64 y #s(literal 1 binary64)) (-.f64 (.f64 y #s(literal 1 binary64)) (.f64 (*.f64 (/.f64 z y) #s(literal -1/2 binary64)) z)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 z #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (neg.f64 (.f64 (fma.f64 (.f64 z #s(literal -1/2 binary64)) z (*.f64 (neg.f64 y) y)) y)))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 z #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) (neg.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 z #s(literal 4 binary64)) (-.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (pow.f64 (*.f64 z y) #s(literal 2 binary64)) #s(literal -1/2 binary64)))) y)))
(/.f64 (fma.f64 (.f64 (.f64 z z) #s(literal -1/2 binary64)) y (pow.f64 y #s(literal 3 binary64))) (*.f64 y y))
(/.f64 (fma.f64 (.f64 z #s(literal -1/2 binary64)) z (.f64 (neg.f64 y) y)) y)
(/.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 z #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (.f64 (fma.f64 (.f64 z #s(literal -1/2 binary64)) z (*.f64 (neg.f64 y) y)) y))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 z #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 z #s(literal 4 binary64)) (-.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (pow.f64 (*.f64 z y) #s(literal 2 binary64)) #s(literal -1/2 binary64)))) y))
(/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) z) z (.f64 (neg.f64 y) y)) (neg.f64 y))
(/.f64 (fma.f64 (.f64 z #s(literal -1/2 binary64)) z (.f64 y y)) y)
(neg.f64 (/.f64 (fma.f64 (.f64 (.f64 z z) #s(literal -1/2 binary64)) y (pow.f64 y #s(literal 3 binary64))) (*.f64 (neg.f64 y) y)))
(neg.f64 (/.f64 (fma.f64 (.f64 z #s(literal -1/2 binary64)) z (.f64 y y)) (neg.f64 y)))
(fma.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z (.f64 y #s(literal -1 binary64)))
(fma.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z (.f64 (neg.f64 y) #s(literal 1 binary64)))
(fma.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z (.f64 y #s(literal 1 binary64)))
(fma.f64 (.f64 #s(literal 1/2 binary64) z) (/.f64 (neg.f64 z) y) (.f64 y #s(literal -1 binary64)))
(fma.f64 (.f64 #s(literal 1/2 binary64) z) (/.f64 (neg.f64 z) y) (.f64 (neg.f64 y) #s(literal 1 binary64)))
(fma.f64 (.f64 #s(literal 1/2 binary64) z) (/.f64 (neg.f64 z) y) (.f64 y #s(literal 1 binary64)))
(fma.f64 (.f64 #s(literal -1/2 binary64) (/.f64 z y)) z (.f64 y #s(literal -1 binary64)))
(fma.f64 (.f64 #s(literal -1/2 binary64) (/.f64 z y)) z (.f64 (neg.f64 y) #s(literal 1 binary64)))
(fma.f64 (.f64 #s(literal -1/2 binary64) (/.f64 z y)) z (.f64 y #s(literal 1 binary64)))
(fma.f64 (.f64 z #s(literal -1/2 binary64)) (/.f64 z y) (.f64 y #s(literal -1 binary64)))
(fma.f64 (.f64 z #s(literal -1/2 binary64)) (/.f64 z y) (.f64 (neg.f64 y) #s(literal 1 binary64)))
(fma.f64 (.f64 z #s(literal -1/2 binary64)) (/.f64 z y) (.f64 y #s(literal 1 binary64)))
(fma.f64 (neg.f64 z) (.f64 (neg.f64 z) (/.f64 #s(literal -1/2 binary64) y)) (.f64 y #s(literal -1 binary64)))
(fma.f64 (neg.f64 z) (.f64 (neg.f64 z) (/.f64 #s(literal -1/2 binary64) y)) (.f64 (neg.f64 y) #s(literal 1 binary64)))
(fma.f64 (neg.f64 z) (.f64 (neg.f64 z) (/.f64 #s(literal -1/2 binary64) y)) (.f64 y #s(literal 1 binary64)))
(fma.f64 (neg.f64 z) (.f64 (/.f64 (neg.f64 z) y) #s(literal -1/2 binary64)) (.f64 y #s(literal -1 binary64)))
(fma.f64 (neg.f64 z) (.f64 (/.f64 (neg.f64 z) y) #s(literal -1/2 binary64)) (.f64 (neg.f64 y) #s(literal 1 binary64)))
(fma.f64 (neg.f64 z) (.f64 (/.f64 (neg.f64 z) y) #s(literal -1/2 binary64)) (.f64 y #s(literal 1 binary64)))
(fma.f64 (neg.f64 y) #s(literal -1 binary64) (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z))
(fma.f64 (.f64 (/.f64 z y) z) #s(literal -1/2 binary64) (.f64 y #s(literal -1 binary64)))
(fma.f64 (.f64 (/.f64 z y) z) #s(literal -1/2 binary64) (.f64 (neg.f64 y) #s(literal 1 binary64)))
(fma.f64 (.f64 (/.f64 z y) z) #s(literal -1/2 binary64) (.f64 y #s(literal 1 binary64)))
(fma.f64 (/.f64 z y) (.f64 z #s(literal -1/2 binary64)) (.f64 y #s(literal -1 binary64)))
(fma.f64 (/.f64 z y) (.f64 z #s(literal -1/2 binary64)) (.f64 (neg.f64 y) #s(literal 1 binary64)))
(fma.f64 (/.f64 z y) (.f64 z #s(literal -1/2 binary64)) (.f64 y #s(literal 1 binary64)))
(fma.f64 (.f64 z z) (/.f64 #s(literal -1/2 binary64) y) (.f64 y #s(literal -1 binary64)))
(fma.f64 (.f64 z z) (/.f64 #s(literal -1/2 binary64) y) (.f64 (neg.f64 y) #s(literal 1 binary64)))
(fma.f64 (.f64 z z) (/.f64 #s(literal -1/2 binary64) y) (.f64 y #s(literal 1 binary64)))
(fma.f64 y #s(literal 1 binary64) (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z))
(fma.f64 z (.f64 z (/.f64 #s(literal -1/2 binary64) y)) (.f64 y #s(literal -1 binary64)))
(fma.f64 z (.f64 z (/.f64 #s(literal -1/2 binary64) y)) (.f64 (neg.f64 y) #s(literal 1 binary64)))
(fma.f64 z (.f64 z (/.f64 #s(literal -1/2 binary64) y)) (.f64 y #s(literal 1 binary64)))
(fma.f64 z (.f64 (/.f64 z y) #s(literal -1/2 binary64)) (.f64 y #s(literal -1 binary64)))
(fma.f64 z (.f64 (/.f64 z y) #s(literal -1/2 binary64)) (.f64 (neg.f64 y) #s(literal 1 binary64)))
(fma.f64 z (.f64 (/.f64 z y) #s(literal -1/2 binary64)) (.f64 y #s(literal 1 binary64)))
(fma.f64 z (.f64 #s(literal -1/2 binary64) (/.f64 z y)) (.f64 y #s(literal -1 binary64)))
(fma.f64 z (.f64 #s(literal -1/2 binary64) (/.f64 z y)) (.f64 (neg.f64 y) #s(literal 1 binary64)))
(fma.f64 z (.f64 #s(literal -1/2 binary64) (/.f64 z y)) (.f64 y #s(literal 1 binary64)))
(fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 z y) z) (.f64 y #s(literal -1 binary64)))
(fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 z y) z) (.f64 (neg.f64 y) #s(literal 1 binary64)))
(fma.f64 #s(literal -1/2 binary64) (.f64 (/.f64 z y) z) (.f64 y #s(literal 1 binary64)))
(-.f64 (/.f64 (.f64 (/.f64 #s(literal 1/4 binary64) y) (/.f64 (pow.f64 z #s(literal 4 binary64)) y)) (fma.f64 (.f64 (/.f64 z y) z) #s(literal -1/2 binary64) (.f64 y #s(literal 1 binary64)))) (/.f64 (.f64 (.f64 y y) #s(literal 1 binary64)) (fma.f64 (.f64 (/.f64 z y) z) #s(literal -1/2 binary64) (*.f64 y #s(literal 1 binary64)))))
(-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (pow.f64 z #s(literal 4 binary64))) (.f64 (fma.f64 (.f64 z #s(literal -1/2 binary64)) z (.f64 (neg.f64 y) y)) y)) (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (fma.f64 (.f64 z #s(literal -1/2 binary64)) z (*.f64 (neg.f64 y) y)) y)))
(-.f64 (/.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (pow.f64 z #s(literal 4 binary64))) (fma.f64 (.f64 z #s(literal -1/2 binary64)) z (.f64 (neg.f64 y) y))) y) (/.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 z z) (*.f64 y y))) y))
(-.f64 (.f64 y #s(literal 1 binary64)) (.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 z y) z)))
(-.f64 (.f64 (.f64 (/.f64 z y) #s(literal -1/2 binary64)) z) (*.f64 y #s(literal -1 binary64)))
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eval42.0ms (1%)

Memory: -8.0MiB live, 37.8MiB allocated; 3ms collecting garbage
Compiler: Compiled 10 563 to 1 312 computations (87.6% saved)

prune7.0ms (0.2%)

Memory

12.2MiB live, 12.2MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	256	0	256
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	256	5	261

Accuracy

100.0%

Counts

261 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.3%	(.f64 (sqrt.f64 (+.f64 z y)) (.f64 (sqrt.f64 (-.f64 y z)) x))
✓	65.5%	(.f64 x (sqrt.f64 (.f64 (-.f64 y z) (+.f64 z y))))
✓	99.9%	(.f64 x #s(approx (sqrt (- ( y y) (* z z))) (fma.f64 (*.f64 (/.f64 z y) z) #s(literal -1/2 binary64) y)))
✓	63.3%	(.f64 x #s(approx (sqrt (- ( y y) (* z z))) #s(approx (+ (* (/ (* z z) y) -1/2) y) (/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 z z) (.f64 y y)) y))))
✓	99.4%	#s(approx (* x (sqrt (- (* y y) (* z z)))) (*.f64 y x))

Compiler

Compiled 210 to 104 computations (50.5% saved)

regimes35.0ms (0.8%)

Memory

-11.5MiB live, 36.0MiB allocated; 1ms collecting garbage

Counts

8 → 1

Calls

Call 1

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

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

Calls

8 calls:

18.0ms	y
3.0ms	x
3.0ms	z
2.0ms	(-.f64 (.f64 y y) (.f64 z z))
2.0ms	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))

Results

Accuracy	Segments	Branch
99.9%	1	`(*.f64 z z)`
99.9%	1	`(*.f64 y y)`
99.9%	1	`(-.f64 (.f64 y y) (.f64 z z))`
99.9%	1	`(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))`
99.9%	1	`(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))`
99.9%	1	`x`
99.9%	1	`y`
99.9%	1	`z`

Compiler

Compiled 34 to 38 computations (-11.8% saved)

regimes40.0ms (1%)

Memory

-35.5MiB live, 22.4MiB allocated; 7ms collecting garbage

Accuracy

Total -21.9b remaining (-6188.3%)

Threshold costs -21.9b (-6188.3%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

8 calls:

31.0ms	(-.f64 (.f64 y y) (.f64 z z))
1.0ms	(*.f64 y y)
1.0ms	y
1.0ms	z
1.0ms	x

Results

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

Compiler

Compiled 34 to 38 computations (-11.8% saved)

simplify68.0ms (1.7%)

Memory

3.2MiB live, 49.8MiB allocated; 2ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	33
1	30	33
2	90	33
3	232	33
4	412	33
5	847	33
6	1398	33
7	2082	33
8	2911	33
9	3221	33
10	3283	33
11	3283	33
12	3361	33

Stop Event

1×

saturated

Calls

Call 1

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

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

derivations258.0ms (6.3%)

Memory

18.5MiB live, 206.2MiB allocated; 18ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	142
0	44	140
1	132	140
2	884	126
0	9413	104
0	205	1144
1	708	1143
2	3083	1100
0	8534	1028

Stop Event

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

Compiler

Compiled 33 to 16 computations (51.5% saved)

preprocess42.0ms (1%)

Memory

-14.4MiB live, 77.3MiB allocated; 7ms collecting garbage

Remove

(negabs x)

(abs z)

Compiler

Compiled 276 to 180 computations (34.8% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze136.0ms (3.3%)

sample1.3s (32.1%)

explain173.0ms (4.2%)

preprocess124.0ms (3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify73.0ms (1.8%)

localize48.0ms (1.2%)

series11.0ms (0.3%)

simplify199.0ms (4.9%)

rewrite152.0ms (3.7%)

eval23.0ms (0.6%)

prune6.0ms (0.1%)

simplify130.0ms (3.2%)

localize75.0ms (1.8%)

series46.0ms (1.1%)

simplify212.0ms (5.2%)

rewrite127.0ms (3.1%)

eval96.0ms (2.3%)

prune27.0ms (0.6%)

simplify107.0ms (2.6%)

localize98.0ms (2.4%)

series13.0ms (0.3%)

simplify238.0ms (5.8%)

rewrite183.0ms (4.4%)

eval42.0ms (1%)

prune7.0ms (0.2%)

regimes35.0ms (0.8%)

regimes40.0ms (1%)

simplify68.0ms (1.7%)

derivations258.0ms (6.3%)

preprocess42.0ms (1%)

end0.0ms (0%)

Profiling