Metrics for Falkner and Boettcher, Appendix B, 2

analyze4.0ms (0%)

Memory

9.5MiB live, 9.6MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
0%	0%	50%	0%	0%	50%	0%	3
50%	25%	25%	0%	0%	50%	0%	4
75%	37.5%	12.5%	0%	0%	50%	0%	5
87.5%	43.7%	6.2%	0%	0%	50%	0%	6
93.8%	46.9%	3.1%	0%	0%	50%	0%	7
96.9%	48.4%	1.6%	0%	0%	50%	0%	8
98.4%	49.2%	0.8%	0%	0%	50%	0%	9
99.2%	49.6%	0.4%	0%	0%	50%	0%	10
99.6%	49.8%	0.2%	0%	0%	50%	0%	11
99.8%	49.9%	0.1%	0%	0%	50%	0%	12

Compiler

Compiled 21 to 16 computations (23.8% saved)

sample1.3s (12.6%)

Memory

43.3MiB live, 1 612.6MiB allocated

Samples

926.0ms	8 256×	0	valid
1.0ms	10×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 680.0ms

ival-mult: 272.0ms (40% of total)

ival-sqrt: 216.0ms (31.8% of total)

ival-sub: 107.0ms (15.7% of total)

ival-div: 60.0ms (8.8% of total)

exact: 15.0ms (2.2% of total)

ival-true: 6.0ms (0.9% of total)

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

Bogosity

preprocess357.0ms (3.4%)

Memory

9.3MiB live, 415.3MiB allocated

Algorithm

2×	egg-herbie

Rules

7 438×	`accelerator-lowering-fma.f32`
7 438×	`accelerator-lowering-fma.f64`
3 206×	`-lowering-.f32`
3 206×	`-lowering-.f64`
1 088×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	58
1	73	57
2	191	57
3	614	57
4	1678	57
5	2989	57
6	4018	57
7	4349	57
8	4401	57
9	4461	57
10	4557	57
11	5267	57
12	6053	57
13	7166	57
14	7517	57
0	14	19
1	36	19
2	88	19
3	219	19
4	646	19
5	1458	19
6	2003	19
7	3601	19
8	4895	19
9	6414	19
10	7378	19
0	8003	17

Stop Event

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

Calls

Call 1

Inputs
(* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v)))

Outputs

(* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v)))

(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 v v)))) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal 4 binary64)))))

Call 2

Inputs

(* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v)))

(* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (neg v) (neg v)))))) (- 1 (* (neg v) (neg v))))

(neg (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (neg v) (neg v)))))) (- 1 (* (neg v) (neg v)))))

Outputs
(* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v)))
(* (* (sqrt 2) 1/4) (* (sqrt (+ 1 (* v (* v -3)))) (- 1 (* v v))))
(* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (neg v) (neg v)))))) (- 1 (* (neg v) (neg v))))
(* (* (sqrt 2) 1/4) (* (sqrt (+ 1 (* v (* v -3)))) (- 1 (* v v))))
(neg (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* (neg v) (neg v)))))) (- 1 (* (neg v) (neg v)))))
(* (* (sqrt 2) 1/4) (* (sqrt (+ 1 (* v (* v -3)))) (+ (* v v) -1)))

Symmetry

(abs v)

explain217.0ms (2%)

Memory

0.3MiB live, 342.0MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))`
-	-	`(.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (*.f64 v v)))))`
-	-	`(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))`
-	-	`(*.f64 v v)`
-	-	`#s(literal 1 binary64)`
-	-	`#s(literal 3 binary64)`
-	-	`(/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64))`
-	-	`(sqrt.f64 #s(literal 2 binary64))`
-	-	`(-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v)))`
-	-	`#s(literal 4 binary64)`
-	-	`(.f64 #s(literal 3 binary64) (.f64 v v))`
-	-	`v`
-	-	`#s(literal 2 binary64)`
-	-	`(-.f64 #s(literal 1 binary64) (*.f64 v v))`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

80.0ms

512×

valid

Compiler

Compiled 186 to 60 computations (67.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 60.0ms

ival-sub: 27.0ms (45.1% of total)

ival-mult: 20.0ms (33.4% of total)

ival-sqrt: 8.0ms (13.4% of total)

ival-div: 4.0ms (6.7% of total)

ival-true: 1.0ms (1.7% of total)

exact: 1.0ms (1.7% of total)

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

eval0.0ms (0%)

Memory: 1.4MiB live, 1.4MiB allocated
Compiler: Compiled 20 to 15 computations (25% saved)

prune1.0ms (0%)

Memory

3.4MiB live, 3.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v)))) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal 4 binary64)))))

Status

Accuracy

Program

▶

100.0%

(*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 v v)))) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal 4 binary64)))))

Compiler

Compiled 20 to 15 computations (25% saved)

simplify367.0ms (3.5%)

Memory

-43.0MiB live, 462.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))
✓	cost-diff	(.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v)))) (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal 4 binary64))))
✓	cost-diff	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v)))) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal 4 binary64)))))

Rules

6 656×	`accelerator-lowering-fma.f32`
6 656×	`accelerator-lowering-fma.f64`
2 184×	`-lowering-.f32`
2 184×	`-lowering-.f64`
1 984×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	78
1	34	78
2	84	78
3	200	78
4	471	78
5	838	78
6	1156	78
7	1487	78
8	2122	78
9	2608	78
10	3375	78
11	3625	78
12	3737	78
13	3818	78
14	3845	78
15	4378	78
16	4784	78
17	5104	78
18	6006	78
19	6104	78
20	6871	78
0	8248	71

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (sqrt 2) (* (sqrt (- 1 (* 3 (* v v)))) (- 1/4 (/ (* v v) 4))))
(sqrt 2)
2
(* (sqrt (- 1 (* 3 (* v v)))) (- 1/4 (/ (* v v) 4)))
(sqrt (- 1 (* 3 (* v v))))
(- 1 (* 3 (* v v)))
1
(* 3 (* v v))
3
(* v v)
v
(- 1/4 (/ (* v v) 4))
1/4
(/ (* v v) 4)
4

Outputs
(* (sqrt 2) (* (sqrt (- 1 (* 3 (* v v)))) (- 1/4 (/ (* v v) 4))))
(.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 v v) #s(literal -3 binary64)))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(* (sqrt (- 1 (* 3 (* v v)))) (- 1/4 (/ (* v v) 4)))
(/.f64 (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 v v) #s(literal -3 binary64)))) (+.f64 (.f64 v v) #s(literal -1 binary64))) #s(literal -4 binary64))
(sqrt (- 1 (* 3 (* v v))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 v v) #s(literal -3 binary64))))
(- 1 (* 3 (* v v)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 v v) #s(literal -3 binary64)))
1
#s(literal 1 binary64)
(* 3 (* v v))
(.f64 #s(literal 3 binary64) (.f64 v v))
3
#s(literal 3 binary64)
(* v v)
(*.f64 v v)
v
(- 1/4 (/ (* v v) 4))
(+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal -4 binary64)))
1/4
#s(literal 1/4 binary64)
(/ (* v v) 4)
(/.f64 (*.f64 v v) #s(literal 4 binary64))
4
#s(literal 4 binary64)

localize54.0ms (0.5%)

Memory

12.9MiB live, 90.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))
✓	accuracy	100.0%	(.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v)))) (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal 4 binary64))))
✓	accuracy	100.0%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v)))) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal 4 binary64)))))
✓	accuracy	99.7%	(.f64 #s(literal 3 binary64) (.f64 v v))

Samples

23.0ms

256×

valid

Compiler

Compiled 80 to 17 computations (78.8% saved)

Precisions

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

ival-mult: 6.0ms (41.8% of total)

ival-sqrt: 4.0ms (27.9% of total)

ival-div: 2.0ms (13.9% of total)

ival-sub: 2.0ms (13.9% of total)

exact: 1.0ms (7% of total)

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

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

series6.0ms (0.1%)

Memory

13.7MiB live, 13.7MiB allocated

Counts

5 → 48

Calls

Call 1

Inputs
#<alt (* (sqrt 2) (* (sqrt (- 1 (* 3 (* v v)))) (- 1/4 (/ (* v v) 4))))>
#<alt (sqrt 2)>
#<alt (* (sqrt (- 1 (* 3 (* v v)))) (- 1/4 (/ (* v v) 4)))>
#<alt (sqrt (- 1 (* 3 (* v v))))>
#<alt (* 3 (* v v))>

Outputs
#<alt (* 1/4 (sqrt 2))>
#<alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* -1/4 (sqrt 2)))))>
#<alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (+ (* -1/4 (sqrt 2)) (* (pow v 2) (+ (* -9/32 (sqrt 2)) (* 3/8 (sqrt 2))))))))>
#<alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (+ (* -1/4 (sqrt 2)) (* (pow v 2) (+ (* -9/32 (sqrt 2)) (+ (* 3/8 (sqrt 2)) (* (pow v 2) (+ (* -27/64 (sqrt 2)) (* 9/32 (sqrt 2)))))))))))>
#<alt (* -1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))>
#<alt (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* -1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (/ (* (sqrt -3) (sqrt 2)) (pow v 2))))))>
#<alt (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* -1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (+ (* 1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 4) (sqrt -3)))) (* 1/4 (/ (* (sqrt -3) (sqrt 2)) (pow v 2))))))))>
#<alt (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* -1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (+ (* -1/32 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 3)))) (+ (* -1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 4) (sqrt -3)))) (* 1/4 (/ (* (sqrt -3) (sqrt 2)) (pow v 2))))))))))>
#<alt (* 1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))>
#<alt (* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* -1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (/ (* (sqrt -3) (sqrt 2)) (pow v 2)))))))>
#<alt (* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* -1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (+ (* 1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 4) (sqrt -3)))) (* 1/4 (/ (* (sqrt -3) (sqrt 2)) (pow v 2)))))))))>
#<alt (* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* -1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (+ (* -1/32 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 3)))) (+ (* -1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 4) (sqrt -3)))) (* 1/4 (/ (* (sqrt -3) (sqrt 2)) (pow v 2)))))))))))>
#<alt 1/4>
#<alt (+ 1/4 (* -5/8 (pow v 2)))>
#<alt (+ 1/4 (* (pow v 2) (- (* 3/32 (pow v 2)) 5/8)))>
#<alt (+ 1/4 (* (pow v 2) (- (* (pow v 2) (+ 3/32 (* -9/64 (pow v 2)))) 5/8)))>
#<alt (* -1/4 (* (pow v 3) (sqrt -3)))>
#<alt (* (pow v 3) (- (+ (* -1/4 (sqrt -3)) (* 1/4 (/ (sqrt -3) (pow v 2)))) (/ 1/8 (* (pow v 2) (sqrt -3)))))>
#<alt (* (pow v 3) (- (+ (* -1/4 (sqrt -3)) (+ (* 1/4 (/ (sqrt -3) (pow v 2))) (+ (* 1/8 (/ 1 (* (pow v 4) (sqrt -3)))) (* 1/32 (/ 1 (* (pow v 4) (pow (sqrt -3) 3))))))) (/ 1/8 (* (pow v 2) (sqrt -3)))))>
#<alt (* (pow v 3) (- (+ (* -1 (/ (+ (* 1/64 (/ 1 (pow (sqrt -3) 5))) (* 1/32 (/ 1 (pow (sqrt -3) 3)))) (pow v 6))) (+ (* -1/4 (sqrt -3)) (+ (* 1/4 (/ (sqrt -3) (pow v 2))) (+ (* 1/8 (/ 1 (* (pow v 4) (sqrt -3)))) (* 1/32 (/ 1 (* (pow v 4) (pow (sqrt -3) 3)))))))) (/ 1/8 (* (pow v 2) (sqrt -3)))))>
#<alt (* 1/4 (* (pow v 3) (sqrt -3)))>
#<alt (* -1 (* (pow v 3) (- (+ (* -1/4 (sqrt -3)) (* 1/4 (/ (sqrt -3) (pow v 2)))) (/ 1/8 (* (pow v 2) (sqrt -3))))))>
#<alt (* -1 (* (pow v 3) (- (+ (* -1/4 (sqrt -3)) (+ (* 1/4 (/ (sqrt -3) (pow v 2))) (+ (* 1/8 (/ 1 (* (pow v 4) (sqrt -3)))) (* 1/32 (/ 1 (* (pow v 4) (pow (sqrt -3) 3))))))) (/ 1/8 (* (pow v 2) (sqrt -3))))))>
#<alt (* -1 (* (pow v 3) (- (+ (* -1 (/ (+ (* 1/64 (/ 1 (pow (sqrt -3) 5))) (* 1/32 (/ 1 (pow (sqrt -3) 3)))) (pow v 6))) (+ (* -1/4 (sqrt -3)) (+ (* 1/4 (/ (sqrt -3) (pow v 2))) (+ (* 1/8 (/ 1 (* (pow v 4) (sqrt -3)))) (* 1/32 (/ 1 (* (pow v 4) (pow (sqrt -3) 3)))))))) (/ 1/8 (* (pow v 2) (sqrt -3))))))>
#<alt 1>
#<alt (+ 1 (* -3/2 (pow v 2)))>
#<alt (+ 1 (* (pow v 2) (- (* -9/8 (pow v 2)) 3/2)))>
#<alt (+ 1 (* (pow v 2) (- (* (pow v 2) (- (* -27/16 (pow v 2)) 9/8)) 3/2)))>
#<alt (* v (sqrt -3))>
#<alt (* v (+ (sqrt -3) (* 1/2 (/ 1 (* (pow v 2) (sqrt -3))))))>
#<alt (* v (- (+ (sqrt -3) (/ 1/2 (* (pow v 2) (sqrt -3)))) (/ 1/8 (* (pow v 4) (pow (sqrt -3) 3)))))>
#<alt (* v (- (+ (sqrt -3) (+ (/ 1/2 (* (pow v 2) (sqrt -3))) (* 1/16 (/ 1 (* (pow v 6) (pow (sqrt -3) 5)))))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -3) 3))))))>
#<alt (* -1 (* v (sqrt -3)))>
#<alt (* -1 (* v (+ (sqrt -3) (* 1/2 (/ 1 (* (pow v 2) (sqrt -3)))))))>
#<alt (* -1 (* v (- (+ (sqrt -3) (/ 1/2 (* (pow v 2) (sqrt -3)))) (/ 1/8 (* (pow v 4) (pow (sqrt -3) 3))))))>
#<alt (* -1 (* v (- (+ (sqrt -3) (+ (/ 1/2 (* (pow v 2) (sqrt -3))) (* 1/16 (/ 1 (* (pow v 6) (pow (sqrt -3) 5)))))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -3) 3)))))))>
#<alt (* 3 (pow v 2))>
#<alt (* 3 (pow v 2))>
#<alt (* 3 (pow v 2))>
#<alt (* 3 (pow v 2))>
#<alt (* 3 (pow v 2))>
#<alt (* 3 (pow v 2))>
#<alt (* 3 (pow v 2))>
#<alt (* 3 (pow v 2))>
#<alt (* 3 (pow v 2))>
#<alt (* 3 (pow v 2))>
#<alt (* 3 (pow v 2))>
#<alt (* 3 (pow v 2))>

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	v	@	inf	(* (sqrt 2) (* (sqrt (- 1 (* 3 (* v v)))) (- 1/4 (/ (* v v) 4))))
1.0ms	v	@	0	(* (sqrt 2) (* (sqrt (- 1 (* 3 (* v v)))) (- 1/4 (/ (* v v) 4))))
1.0ms	v	@	0	(* 3 (* v v))
1.0ms	v	@	inf	(* (sqrt (- 1 (* 3 (* v v)))) (- 1/4 (/ (* v v) 4)))
0.0ms	v	@	inf	(sqrt (- 1 (* 3 (* v v))))

rewrite384.0ms (3.6%)

Memory

13.5MiB live, 486.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 048×	`accelerator-lowering-fma.f32`
4 048×	`accelerator-lowering-fma.f64`
4 018×	`-lowering-.f32`
4 018×	`-lowering-.f64`
2 540×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	50
1	72	49
2	509	49
3	6455	49
0	8146	44

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 191

Calls

Call 1

Inputs
(* (sqrt 2) (* (sqrt (- 1 (* 3 (* v v)))) (- 1/4 (/ (* v v) 4))))
(sqrt 2)
(* (sqrt (- 1 (* 3 (* v v)))) (- 1/4 (/ (* v v) 4)))
(sqrt (- 1 (* 3 (* v v))))
(* 3 (* v v))

Outputs
(+.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64))))) (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64)))) (/.f64 #s(literal -4 binary64) (.f64 v v))))
(+.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64)))) (/.f64 #s(literal -4 binary64) (.f64 v v))) (.f64 #s(literal 1/4 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64))))))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 v v) #s(literal -3 binary64)))) #s(literal 1/4 binary64)) (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64)))) (/.f64 #s(literal -4 binary64) (*.f64 v v))))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 v v) #s(literal -3 binary64)))) (/.f64 #s(literal -4 binary64) (.f64 v v))) (.f64 #s(literal 1/4 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64))))))
(fma.f64 v (.f64 (/.f64 v #s(literal -4 binary64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64))))) (.f64 #s(literal 1/4 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64))))))
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(/.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (.f64 (.f64 v v) (.f64 (.f64 v v) #s(literal 9 binary64))))) (sqrt.f64 (+.f64 (.f64 (.f64 v v) #s(literal -3 binary64)) #s(literal -1 binary64))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 27 binary64) (.f64 v (.f64 v v))) (.f64 v (.f64 v v)))))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 v v) (+.f64 #s(literal 3 binary64) (.f64 (.f64 v v) #s(literal 9 binary64))))))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 v v) (.f64 (.f64 v v) #s(literal 9 binary64)))))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))))
(pow.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 v v) #s(literal -3 binary64))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 v v) #s(literal -3 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 v v) #s(literal -3 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 v v) #s(literal -3 binary64)))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log1p.f64 (.f64 (.f64 v v) #s(literal -3 binary64)))) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 v v) #s(literal -3 binary64))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 v v) (+.f64 #s(literal 3 binary64) (.f64 (.f64 v v) #s(literal 9 binary64)))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 27 binary64) (.f64 v (.f64 v v))) (.f64 v (.f64 v v)))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 v v) (.f64 (.f64 v v) #s(literal 9 binary64)))))) #s(literal -1 binary64))
(.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 27 binary64) (.f64 v (.f64 v v))) (.f64 v (.f64 v v))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 v v) (+.f64 #s(literal 3 binary64) (.f64 (*.f64 v v) #s(literal 9 binary64)))))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 27 binary64) (.f64 v (.f64 v v))) (.f64 v (.f64 v v))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 v v) (+.f64 #s(literal 3 binary64) (.f64 (*.f64 v v) #s(literal 9 binary64))))))))
(.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 27 binary64) (.f64 v (.f64 v v))) (.f64 v (.f64 v v))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 v v) (+.f64 #s(literal 3 binary64) (.f64 (*.f64 v v) #s(literal 9 binary64))))))))
(.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 v v) (.f64 (.f64 v v) #s(literal 9 binary64))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (*.f64 v v)))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 v v) (.f64 (.f64 v v) #s(literal 9 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (*.f64 v v))))))
(.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 v v) (.f64 (.f64 v v) #s(literal 9 binary64))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (*.f64 v v))))))
(.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 v v) #s(literal -3 binary64))) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (.f64 (*.f64 v v) #s(literal -3 binary64))) #s(literal 1/4 binary64)))
(.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (*.f64 v v)))
(.f64 #s(literal 3 binary64) (.f64 v v))
(.f64 v (.f64 #s(literal 3 binary64) v))
(.f64 (.f64 v v) #s(literal 3 binary64))
(.f64 (.f64 #s(literal 3 binary64) (*.f64 v v)) #s(literal 1 binary64))
(.f64 (.f64 #s(literal 3 binary64) v) v)
(.f64 (.f64 #s(literal 3 binary64) v) (*.f64 v #s(literal 1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) v) (*.f64 #s(literal 3 binary64) v))

simplify783.0ms (7.4%)

Memory

3.7MiB live, 1 117.5MiB allocated

Algorithm

1×	egg-herbie

Rules

22 876×	`accelerator-lowering-fma.f32`
22 876×	`accelerator-lowering-fma.f64`
6 326×	`-lowering-.f32`
6 326×	`-lowering-.f64`
4 592×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	182	1054
1	500	1032
2	1780	924
3	7807	924
0	8459	876

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

Inputs
(* 1/4 (sqrt 2))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* -1/4 (sqrt 2)))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (+ (* -1/4 (sqrt 2)) (* (pow v 2) (+ (* -9/32 (sqrt 2)) (* 3/8 (sqrt 2))))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (+ (* -1/4 (sqrt 2)) (* (pow v 2) (+ (* -9/32 (sqrt 2)) (+ (* 3/8 (sqrt 2)) (* (pow v 2) (+ (* -27/64 (sqrt 2)) (* 9/32 (sqrt 2)))))))))))
(* -1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* -1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (/ (* (sqrt -3) (sqrt 2)) (pow v 2))))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* -1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (+ (* 1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 4) (sqrt -3)))) (* 1/4 (/ (* (sqrt -3) (sqrt 2)) (pow v 2))))))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* -1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (+ (* -1/32 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 3)))) (+ (* -1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 4) (sqrt -3)))) (* 1/4 (/ (* (sqrt -3) (sqrt 2)) (pow v 2))))))))))
(* 1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* -1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (/ (* (sqrt -3) (sqrt 2)) (pow v 2)))))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* -1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (+ (* 1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 4) (sqrt -3)))) (* 1/4 (/ (* (sqrt -3) (sqrt 2)) (pow v 2)))))))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* -1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (+ (* -1/32 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 3)))) (+ (* -1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 4) (sqrt -3)))) (* 1/4 (/ (* (sqrt -3) (sqrt 2)) (pow v 2)))))))))))
1/4
(+ 1/4 (* -5/8 (pow v 2)))
(+ 1/4 (* (pow v 2) (- (* 3/32 (pow v 2)) 5/8)))
(+ 1/4 (* (pow v 2) (- (* (pow v 2) (+ 3/32 (* -9/64 (pow v 2)))) 5/8)))
(* -1/4 (* (pow v 3) (sqrt -3)))
(* (pow v 3) (- (+ (* -1/4 (sqrt -3)) (* 1/4 (/ (sqrt -3) (pow v 2)))) (/ 1/8 (* (pow v 2) (sqrt -3)))))
(* (pow v 3) (- (+ (* -1/4 (sqrt -3)) (+ (* 1/4 (/ (sqrt -3) (pow v 2))) (+ (* 1/8 (/ 1 (* (pow v 4) (sqrt -3)))) (* 1/32 (/ 1 (* (pow v 4) (pow (sqrt -3) 3))))))) (/ 1/8 (* (pow v 2) (sqrt -3)))))
(* (pow v 3) (- (+ (* -1 (/ (+ (* 1/64 (/ 1 (pow (sqrt -3) 5))) (* 1/32 (/ 1 (pow (sqrt -3) 3)))) (pow v 6))) (+ (* -1/4 (sqrt -3)) (+ (* 1/4 (/ (sqrt -3) (pow v 2))) (+ (* 1/8 (/ 1 (* (pow v 4) (sqrt -3)))) (* 1/32 (/ 1 (* (pow v 4) (pow (sqrt -3) 3)))))))) (/ 1/8 (* (pow v 2) (sqrt -3)))))
(* 1/4 (* (pow v 3) (sqrt -3)))
(* -1 (* (pow v 3) (- (+ (* -1/4 (sqrt -3)) (* 1/4 (/ (sqrt -3) (pow v 2)))) (/ 1/8 (* (pow v 2) (sqrt -3))))))
(* -1 (* (pow v 3) (- (+ (* -1/4 (sqrt -3)) (+ (* 1/4 (/ (sqrt -3) (pow v 2))) (+ (* 1/8 (/ 1 (* (pow v 4) (sqrt -3)))) (* 1/32 (/ 1 (* (pow v 4) (pow (sqrt -3) 3))))))) (/ 1/8 (* (pow v 2) (sqrt -3))))))
(* -1 (* (pow v 3) (- (+ (* -1 (/ (+ (* 1/64 (/ 1 (pow (sqrt -3) 5))) (* 1/32 (/ 1 (pow (sqrt -3) 3)))) (pow v 6))) (+ (* -1/4 (sqrt -3)) (+ (* 1/4 (/ (sqrt -3) (pow v 2))) (+ (* 1/8 (/ 1 (* (pow v 4) (sqrt -3)))) (* 1/32 (/ 1 (* (pow v 4) (pow (sqrt -3) 3)))))))) (/ 1/8 (* (pow v 2) (sqrt -3))))))
1
(+ 1 (* -3/2 (pow v 2)))
(+ 1 (* (pow v 2) (- (* -9/8 (pow v 2)) 3/2)))
(+ 1 (* (pow v 2) (- (* (pow v 2) (- (* -27/16 (pow v 2)) 9/8)) 3/2)))
(* v (sqrt -3))
(* v (+ (sqrt -3) (* 1/2 (/ 1 (* (pow v 2) (sqrt -3))))))
(* v (- (+ (sqrt -3) (/ 1/2 (* (pow v 2) (sqrt -3)))) (/ 1/8 (* (pow v 4) (pow (sqrt -3) 3)))))
(* v (- (+ (sqrt -3) (+ (/ 1/2 (* (pow v 2) (sqrt -3))) (* 1/16 (/ 1 (* (pow v 6) (pow (sqrt -3) 5)))))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -3) 3))))))
(* -1 (* v (sqrt -3)))
(* -1 (* v (+ (sqrt -3) (* 1/2 (/ 1 (* (pow v 2) (sqrt -3)))))))
(* -1 (* v (- (+ (sqrt -3) (/ 1/2 (* (pow v 2) (sqrt -3)))) (/ 1/8 (* (pow v 4) (pow (sqrt -3) 3))))))
(* -1 (* v (- (+ (sqrt -3) (+ (/ 1/2 (* (pow v 2) (sqrt -3))) (* 1/16 (/ 1 (* (pow v 6) (pow (sqrt -3) 5)))))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -3) 3)))))))
(* 3 (pow v 2))
(* 3 (pow v 2))
(* 3 (pow v 2))
(* 3 (pow v 2))
(* 3 (pow v 2))
(* 3 (pow v 2))
(* 3 (pow v 2))
(* 3 (pow v 2))
(* 3 (pow v 2))
(* 3 (pow v 2))
(* 3 (pow v 2))
(* 3 (pow v 2))

Outputs
(* 1/4 (sqrt 2))
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* -1/4 (sqrt 2)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 v (*.f64 v #s(literal -5/8 binary64)))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (+ (* -1/4 (sqrt 2)) (* (pow v 2) (+ (* -9/32 (sqrt 2)) (* 3/8 (sqrt 2))))))))
(+.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 v v) (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal -5/8 binary64) (.f64 (.f64 v v) #s(literal 3/32 binary64))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (+ (* -1/4 (sqrt 2)) (* (pow v 2) (+ (* -9/32 (sqrt 2)) (+ (* 3/8 (sqrt 2)) (* (pow v 2) (+ (* -27/64 (sqrt 2)) (* 9/32 (sqrt 2)))))))))))
(+.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 v (.f64 v #s(literal -5/8 binary64))))) (.f64 (.f64 v v) (.f64 (.f64 v v) (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 3/32 binary64) (.f64 (.f64 v v) #s(literal -9/64 binary64)))))))
(* -1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 v v) (.f64 v (*.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -3 binary64))))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* -1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (/ (* (sqrt -3) (sqrt 2)) (pow v 2))))))
(.f64 (.f64 v (.f64 v v)) (+.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -3 binary64)))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v v)) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -3 binary64)))))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* -1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (+ (* 1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 4) (sqrt -3)))) (* 1/4 (/ (* (sqrt -3) (sqrt 2)) (pow v 2))))))))
(.f64 (.f64 v (.f64 v v)) (+.f64 (+.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -3 binary64)))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v (.f64 v (.f64 v v)))) (+.f64 (/.f64 #s(literal -1/96 binary64) (sqrt.f64 #s(literal -3 binary64))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -3 binary64)))))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v v)) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -3 binary64)))))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* -1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (+ (* -1/32 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 3)))) (+ (* -1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 4) (sqrt -3)))) (* 1/4 (/ (* (sqrt -3) (sqrt 2)) (pow v 2))))))))))
(.f64 (.f64 v (.f64 v v)) (+.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -3 binary64)))) (+.f64 (+.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v v)) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -3 binary64))))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v (.f64 v (.f64 v v)))) (+.f64 (/.f64 #s(literal -1/96 binary64) (sqrt.f64 #s(literal -3 binary64))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -3 binary64)))))) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 v #s(literal 6 binary64))) (+.f64 (/.f64 #s(literal -1/64 binary64) (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal 1/96 binary64) (sqrt.f64 #s(literal -3 binary64))))))))
(* 1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 v v) (*.f64 v (sqrt.f64 #s(literal -3 binary64)))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* -1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (/ (* (sqrt -3) (sqrt 2)) (pow v 2)))))))
(.f64 (.f64 v (.f64 v v)) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -3 binary64)))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v v)) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -3 binary64))))))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* -1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (+ (* 1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 4) (sqrt -3)))) (* 1/4 (/ (* (sqrt -3) (sqrt 2)) (pow v 2)))))))))
(.f64 (+.f64 (+.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -3 binary64)))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v (.f64 v (.f64 v v)))) (+.f64 (/.f64 #s(literal -1/96 binary64) (sqrt.f64 #s(literal -3 binary64))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -3 binary64)))))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v v)) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -3 binary64)))))) (-.f64 #s(literal 0 binary64) (.f64 v (.f64 v v))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* -1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (+ (* -1/32 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 3)))) (+ (* -1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 4) (sqrt -3)))) (* 1/4 (/ (* (sqrt -3) (sqrt 2)) (pow v 2)))))))))))
(.f64 (+.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -3 binary64)))) (+.f64 (+.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v v)) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -3 binary64))))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v (.f64 v (.f64 v v)))) (+.f64 (/.f64 #s(literal -1/96 binary64) (sqrt.f64 #s(literal -3 binary64))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -3 binary64)))))) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 v #s(literal 6 binary64))) (+.f64 (/.f64 #s(literal -1/64 binary64) (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal 1/96 binary64) (sqrt.f64 #s(literal -3 binary64))))))) (-.f64 #s(literal 0 binary64) (.f64 v (*.f64 v v))))
1/4
#s(literal 1/4 binary64)
(+ 1/4 (* -5/8 (pow v 2)))
(+.f64 #s(literal 1/4 binary64) (.f64 v (.f64 v #s(literal -5/8 binary64))))
(+ 1/4 (* (pow v 2) (- (* 3/32 (pow v 2)) 5/8)))
(+.f64 #s(literal 1/4 binary64) (.f64 (.f64 v v) (+.f64 #s(literal -5/8 binary64) (.f64 (.f64 v v) #s(literal 3/32 binary64)))))
(+ 1/4 (* (pow v 2) (- (* (pow v 2) (+ 3/32 (* -9/64 (pow v 2)))) 5/8)))
(+.f64 #s(literal 1/4 binary64) (.f64 (.f64 v v) (+.f64 #s(literal -5/8 binary64) (.f64 (.f64 v v) (+.f64 #s(literal 3/32 binary64) (.f64 (.f64 v v) #s(literal -9/64 binary64)))))))
(* -1/4 (* (pow v 3) (sqrt -3)))
(.f64 (.f64 v v) (.f64 v (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -3 binary64)))))
(* (pow v 3) (- (+ (* -1/4 (sqrt -3)) (* 1/4 (/ (sqrt -3) (pow v 2)))) (/ 1/8 (* (pow v 2) (sqrt -3)))))
(.f64 (.f64 v (.f64 v v)) (+.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -3 binary64))) (+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 v v)) (/.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -3 binary64))))))
(* (pow v 3) (- (+ (* -1/4 (sqrt -3)) (+ (* 1/4 (/ (sqrt -3) (pow v 2))) (+ (* 1/8 (/ 1 (* (pow v 4) (sqrt -3)))) (* 1/32 (/ 1 (* (pow v 4) (pow (sqrt -3) 3))))))) (/ 1/8 (* (pow v 2) (sqrt -3)))))
(.f64 v (.f64 (.f64 v v) (+.f64 (+.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -3 binary64))) (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 v v))) (+.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 v (.f64 v (.f64 v v)))) (+.f64 (/.f64 (/.f64 #s(literal -1/96 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 v (.f64 v (.f64 v v)))) (/.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -3 binary64))))))))
(* (pow v 3) (- (+ (* -1 (/ (+ (* 1/64 (/ 1 (pow (sqrt -3) 5))) (* 1/32 (/ 1 (pow (sqrt -3) 3)))) (pow v 6))) (+ (* -1/4 (sqrt -3)) (+ (* 1/4 (/ (sqrt -3) (pow v 2))) (+ (* 1/8 (/ 1 (* (pow v 4) (sqrt -3)))) (* 1/32 (/ 1 (* (pow v 4) (pow (sqrt -3) 3)))))))) (/ 1/8 (* (pow v 2) (sqrt -3)))))
(.f64 (.f64 v (.f64 v v)) (+.f64 (+.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -3 binary64))) (+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 v v)) (/.f64 (/.f64 #s(literal -1/8 binary64) (.f64 v v)) (sqrt.f64 #s(literal -3 binary64))))) (+.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 v (.f64 v (.f64 v v)))) (/.f64 (/.f64 #s(literal -1/96 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 v (.f64 v (*.f64 v v))))) (/.f64 (+.f64 (/.f64 #s(literal -1/64 binary64) (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal 1/96 binary64) (sqrt.f64 #s(literal -3 binary64)))) (pow.f64 v #s(literal 6 binary64))))))
(* 1/4 (* (pow v 3) (sqrt -3)))
(.f64 (.f64 v v) (.f64 v (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -3 binary64)))))
(* -1 (* (pow v 3) (- (+ (* -1/4 (sqrt -3)) (* 1/4 (/ (sqrt -3) (pow v 2)))) (/ 1/8 (* (pow v 2) (sqrt -3))))))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 v (.f64 v v)) (+.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -3 binary64))) (+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 v v)) (/.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -3 binary64)))))))
(* -1 (* (pow v 3) (- (+ (* -1/4 (sqrt -3)) (+ (* 1/4 (/ (sqrt -3) (pow v 2))) (+ (* 1/8 (/ 1 (* (pow v 4) (sqrt -3)))) (* 1/32 (/ 1 (* (pow v 4) (pow (sqrt -3) 3))))))) (/ 1/8 (* (pow v 2) (sqrt -3))))))
(.f64 (.f64 v (.f64 v v)) (-.f64 #s(literal 0 binary64) (+.f64 (+.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -3 binary64))) (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 v v))) (+.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 v (.f64 v (.f64 v v)))) (+.f64 (/.f64 (/.f64 #s(literal -1/96 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 v (.f64 v (.f64 v v)))) (/.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -3 binary64))))))))
(* -1 (* (pow v 3) (- (+ (* -1 (/ (+ (* 1/64 (/ 1 (pow (sqrt -3) 5))) (* 1/32 (/ 1 (pow (sqrt -3) 3)))) (pow v 6))) (+ (* -1/4 (sqrt -3)) (+ (* 1/4 (/ (sqrt -3) (pow v 2))) (+ (* 1/8 (/ 1 (* (pow v 4) (sqrt -3)))) (* 1/32 (/ 1 (* (pow v 4) (pow (sqrt -3) 3)))))))) (/ 1/8 (* (pow v 2) (sqrt -3))))))
(.f64 (+.f64 (+.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -3 binary64))) (+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 v v)) (/.f64 (/.f64 #s(literal -1/8 binary64) (.f64 v v)) (sqrt.f64 #s(literal -3 binary64))))) (+.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 v (.f64 v (.f64 v v)))) (/.f64 (/.f64 #s(literal -1/96 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 v (.f64 v (.f64 v v))))) (/.f64 (+.f64 (/.f64 #s(literal -1/64 binary64) (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal 1/96 binary64) (sqrt.f64 #s(literal -3 binary64)))) (pow.f64 v #s(literal 6 binary64))))) (-.f64 #s(literal 0 binary64) (.f64 v (*.f64 v v))))
1
#s(literal 1 binary64)
(+ 1 (* -3/2 (pow v 2)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 v v) #s(literal -3/2 binary64)))
(+ 1 (* (pow v 2) (- (* -9/8 (pow v 2)) 3/2)))
(+.f64 #s(literal 1 binary64) (.f64 v (.f64 v (+.f64 #s(literal -3/2 binary64) (.f64 v (.f64 v #s(literal -9/8 binary64)))))))
(+ 1 (* (pow v 2) (- (* (pow v 2) (- (* -27/16 (pow v 2)) 9/8)) 3/2)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 v v) (+.f64 #s(literal -3/2 binary64) (.f64 (.f64 v v) (+.f64 #s(literal -9/8 binary64) (.f64 (.f64 v v) #s(literal -27/16 binary64)))))))
(* v (sqrt -3))
(*.f64 v (sqrt.f64 #s(literal -3 binary64)))
(* v (+ (sqrt -3) (* 1/2 (/ 1 (* (pow v 2) (sqrt -3))))))
(.f64 v (+.f64 (sqrt.f64 #s(literal -3 binary64)) (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 v v)) (sqrt.f64 #s(literal -3 binary64)))))
(* v (- (+ (sqrt -3) (/ 1/2 (* (pow v 2) (sqrt -3)))) (/ 1/8 (* (pow v 4) (pow (sqrt -3) 3)))))
(.f64 v (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 v v)) (sqrt.f64 #s(literal -3 binary64))) (-.f64 (sqrt.f64 #s(literal -3 binary64)) (/.f64 (/.f64 #s(literal -1/24 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 v (.f64 v (*.f64 v v)))))))
(* v (- (+ (sqrt -3) (+ (/ 1/2 (* (pow v 2) (sqrt -3))) (* 1/16 (/ 1 (* (pow v 6) (pow (sqrt -3) 5)))))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -3) 3))))))
(.f64 v (+.f64 (sqrt.f64 #s(literal -3 binary64)) (+.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 v v)) (sqrt.f64 #s(literal -3 binary64))) (/.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 v #s(literal 6 binary64))) (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64)))) (/.f64 #s(literal 1/24 binary64) (.f64 (sqrt.f64 #s(literal -3 binary64)) (.f64 v (.f64 v (.f64 v v))))))))
(* -1 (* v (sqrt -3)))
(-.f64 #s(literal 0 binary64) (*.f64 v (sqrt.f64 #s(literal -3 binary64))))
(* -1 (* v (+ (sqrt -3) (* 1/2 (/ 1 (* (pow v 2) (sqrt -3)))))))
(.f64 (+.f64 (sqrt.f64 #s(literal -3 binary64)) (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 v v)) (sqrt.f64 #s(literal -3 binary64)))) (-.f64 #s(literal 0 binary64) v))
(* -1 (* v (- (+ (sqrt -3) (/ 1/2 (* (pow v 2) (sqrt -3)))) (/ 1/8 (* (pow v 4) (pow (sqrt -3) 3))))))
(.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 v v)) (sqrt.f64 #s(literal -3 binary64))) (-.f64 (sqrt.f64 #s(literal -3 binary64)) (/.f64 (/.f64 #s(literal -1/24 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 v (.f64 v (*.f64 v v)))))) (-.f64 #s(literal 0 binary64) v))
(* -1 (* v (- (+ (sqrt -3) (+ (/ 1/2 (* (pow v 2) (sqrt -3))) (* 1/16 (/ 1 (* (pow v 6) (pow (sqrt -3) 5)))))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -3) 3)))))))
(.f64 (+.f64 (sqrt.f64 #s(literal -3 binary64)) (+.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 v v)) (sqrt.f64 #s(literal -3 binary64))) (/.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 v #s(literal 6 binary64))) (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64)))) (/.f64 #s(literal 1/24 binary64) (.f64 (sqrt.f64 #s(literal -3 binary64)) (.f64 v (.f64 v (.f64 v v))))))) (-.f64 #s(literal 0 binary64) v))
(* 3 (pow v 2))
(.f64 v (.f64 v #s(literal 3 binary64)))
(* 3 (pow v 2))
(.f64 v (.f64 v #s(literal 3 binary64)))
(* 3 (pow v 2))
(.f64 v (.f64 v #s(literal 3 binary64)))
(* 3 (pow v 2))
(.f64 v (.f64 v #s(literal 3 binary64)))
(* 3 (pow v 2))
(.f64 v (.f64 v #s(literal 3 binary64)))
(* 3 (pow v 2))
(.f64 v (.f64 v #s(literal 3 binary64)))
(* 3 (pow v 2))
(.f64 v (.f64 v #s(literal 3 binary64)))
(* 3 (pow v 2))
(.f64 v (.f64 v #s(literal 3 binary64)))
(* 3 (pow v 2))
(.f64 v (.f64 v #s(literal 3 binary64)))
(* 3 (pow v 2))
(.f64 v (.f64 v #s(literal 3 binary64)))
(* 3 (pow v 2))
(.f64 v (.f64 v #s(literal 3 binary64)))
(* 3 (pow v 2))
(.f64 v (.f64 v #s(literal 3 binary64)))

eval32.0ms (0.3%)

Memory: -19.0MiB live, 97.2MiB allocated
Compiler: Compiled 8 111 to 830 computations (89.8% saved)

prune30.0ms (0.3%)

Memory

26.3MiB live, 103.3MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	233	6	239
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	234	6	240

Accuracy

100.0%

Counts

240 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal -4 binary64)))))
	98.5%	(.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v)))) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal 4 binary64)))))
▶	100.0%	(.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal -4 binary64))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64)))))
▶	99.3%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 v v) (+.f64 #s(literal -5/8 binary64) (.f64 (*.f64 v v) #s(literal 3/32 binary64))))))
▶	98.9%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 v (*.f64 v #s(literal -5/8 binary64)))))
▶	98.4%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))

Compiler

Compiled 192 to 140 computations (27.1% saved)

simplify33.0ms (0.3%)

Memory

-26.4MiB live, 53.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 #s(literal 2 binary64) (.f64 (.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64)))
✓	cost-diff	0	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64))))
✓	cost-diff	128	(.f64 (.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64))
✓	cost-diff	128	(/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal -4 binary64)))))
✓	cost-diff	0	(.f64 (.f64 v v) (+.f64 #s(literal -5/8 binary64) (.f64 (.f64 v v) #s(literal 3/32 binary64))))
✓	cost-diff	0	(+.f64 #s(literal 1/4 binary64) (.f64 (.f64 v v) (+.f64 #s(literal -5/8 binary64) (.f64 (.f64 v v) #s(literal 3/32 binary64)))))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 v v) (+.f64 #s(literal -5/8 binary64) (.f64 (*.f64 v v) #s(literal 3/32 binary64))))))
✓	cost-diff	0	(.f64 v (.f64 v #s(literal -5/8 binary64)))
✓	cost-diff	0	(+.f64 #s(literal 1/4 binary64) (.f64 v (.f64 v #s(literal -5/8 binary64))))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 v (*.f64 v #s(literal -5/8 binary64)))))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
✓	cost-diff	0	(/.f64 (*.f64 v v) #s(literal -4 binary64))
✓	cost-diff	0	(+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal -4 binary64)))
✓	cost-diff	0	(.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal -4 binary64))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64)))))
✓	cost-diff	128	(.f64 (.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64))

Rules

428×	`accelerator-lowering-fma.f32`
428×	`accelerator-lowering-fma.f64`
416×	`-lowering-.f32`
416×	`-lowering-.f64`
168×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	233
1	78	233
2	175	233
3	343	233
4	454	233
5	472	233
6	504	233
7	538	233
8	538	233
9	542	233
10	548	233
11	548	233
0	548	214

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* (+ 1/4 (/ (* v v) -4)) (sqrt (+ 2 (* (* (* v v) -3) 2))))
(+ 1/4 (/ (* v v) -4))
1/4
(/ (* v v) -4)
(* v v)
v
-4
(sqrt (+ 2 (* (* (* v v) -3) 2)))
(+ 2 (* (* (* v v) -3) 2))
2
(* (* (* v v) -3) 2)
(* (* v v) -3)
-3
(* (sqrt 2) 1/4)
(sqrt 2)
2
1/4
(* (sqrt 2) (+ 1/4 (* v (* v -5/8))))
(sqrt 2)
2
(+ 1/4 (* v (* v -5/8)))
1/4
(* v (* v -5/8))
v
(* v -5/8)
-5/8
(* (sqrt 2) (+ 1/4 (* (* v v) (+ -5/8 (* (* v v) 3/32)))))
(sqrt 2)
2
(+ 1/4 (* (* v v) (+ -5/8 (* (* v v) 3/32))))
1/4
(* (* v v) (+ -5/8 (* (* v v) 3/32)))
(* v v)
v
(+ -5/8 (* (* v v) 3/32))
-5/8
(* (* v v) 3/32)
3/32
(/ (sqrt (+ 2 (* (* (* v v) -3) 2))) (/ 1 (+ 1/4 (/ (* v v) -4))))
(sqrt (+ 2 (* (* (* v v) -3) 2)))
(+ 2 (* (* (* v v) -3) 2))
2
(* (* (* v v) -3) 2)
(* (* v v) -3)
(* v v)
v
-3
(/ 1 (+ 1/4 (/ (* v v) -4)))
1
(+ 1/4 (/ (* v v) -4))
1/4
(/ (* v v) -4)
-4

Outputs
(* (+ 1/4 (/ (* v v) -4)) (sqrt (+ 2 (* (* (* v v) -3) 2))))
(.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal -4 binary64))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal -6 binary64)))))
(+ 1/4 (/ (* v v) -4))
(+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal -4 binary64)))
1/4
#s(literal 1/4 binary64)
(/ (* v v) -4)
(/.f64 (*.f64 v v) #s(literal -4 binary64))
(* v v)
(*.f64 v v)
v
-4
#s(literal -4 binary64)
(sqrt (+ 2 (* (* (* v v) -3) 2)))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal -6 binary64))))
(+ 2 (* (* (* v v) -3) 2))
(+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal -6 binary64)))
2
#s(literal 2 binary64)
(* (* (* v v) -3) 2)
(.f64 (.f64 v v) #s(literal -6 binary64))
(* (* v v) -3)
(.f64 v (.f64 v #s(literal -3 binary64)))
-3
#s(literal -3 binary64)
(* (sqrt 2) 1/4)
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
1/4
#s(literal 1/4 binary64)
(* (sqrt 2) (+ 1/4 (* v (* v -5/8))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 (*.f64 v v) #s(literal -5/8 binary64))))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(+ 1/4 (* v (* v -5/8)))
(+.f64 #s(literal 1/4 binary64) (.f64 (.f64 v v) #s(literal -5/8 binary64)))
1/4
#s(literal 1/4 binary64)
(* v (* v -5/8))
(.f64 (.f64 v v) #s(literal -5/8 binary64))
v
(* v -5/8)
(*.f64 v #s(literal -5/8 binary64))
-5/8
#s(literal -5/8 binary64)
(* (sqrt 2) (+ 1/4 (* (* v v) (+ -5/8 (* (* v v) 3/32)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 v (.f64 v (+.f64 #s(literal -5/8 binary64) (.f64 (*.f64 v v) #s(literal 3/32 binary64)))))))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(+ 1/4 (* (* v v) (+ -5/8 (* (* v v) 3/32))))
(+.f64 #s(literal 1/4 binary64) (.f64 v (.f64 v (+.f64 #s(literal -5/8 binary64) (.f64 (.f64 v v) #s(literal 3/32 binary64))))))
1/4
#s(literal 1/4 binary64)
(* (* v v) (+ -5/8 (* (* v v) 3/32)))
(.f64 v (.f64 v (+.f64 #s(literal -5/8 binary64) (.f64 (.f64 v v) #s(literal 3/32 binary64)))))
(* v v)
(*.f64 v v)
v
(+ -5/8 (* (* v v) 3/32))
(+.f64 #s(literal -5/8 binary64) (.f64 (.f64 v v) #s(literal 3/32 binary64)))
-5/8
#s(literal -5/8 binary64)
(* (* v v) 3/32)
(.f64 (.f64 v v) #s(literal 3/32 binary64))
3/32
#s(literal 3/32 binary64)
(/ (sqrt (+ 2 (* (* (* v v) -3) 2))) (/ 1 (+ 1/4 (/ (* v v) -4))))
(.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal -4 binary64))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal -6 binary64)))))
(sqrt (+ 2 (* (* (* v v) -3) 2)))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal -6 binary64))))
(+ 2 (* (* (* v v) -3) 2))
(+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal -6 binary64)))
2
#s(literal 2 binary64)
(* (* (* v v) -3) 2)
(.f64 (.f64 v v) #s(literal -6 binary64))
(* (* v v) -3)
(.f64 v (.f64 v #s(literal -3 binary64)))
(* v v)
(*.f64 v v)
v
-3
#s(literal -3 binary64)
(/ 1 (+ 1/4 (/ (* v v) -4)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal -4 binary64))))
1
#s(literal 1 binary64)
(+ 1/4 (/ (* v v) -4))
(+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal -4 binary64)))
1/4
#s(literal 1/4 binary64)
(/ (* v v) -4)
(/.f64 (*.f64 v v) #s(literal -4 binary64))
-4
#s(literal -4 binary64)

localize234.0ms (2.2%)

Memory

44.6MiB live, 271.6MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64))))
✓	accuracy	100.0%	(.f64 (.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64))
✓	accuracy	100.0%	(/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal -4 binary64)))))
✓	accuracy	99.7%	(.f64 (.f64 v v) #s(literal -3 binary64))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 v v) (+.f64 #s(literal -5/8 binary64) (.f64 (*.f64 v v) #s(literal 3/32 binary64))))))
✓	accuracy	99.8%	(.f64 (.f64 v v) (+.f64 #s(literal -5/8 binary64) (.f64 (.f64 v v) #s(literal 3/32 binary64))))
✓	accuracy	99.7%	(.f64 (.f64 v v) #s(literal 3/32 binary64))
✓	accuracy	100.0%	(*.f64 v #s(literal -5/8 binary64))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 v (*.f64 v #s(literal -5/8 binary64)))))
✓	accuracy	99.8%	(.f64 v (.f64 v #s(literal -5/8 binary64)))
✓	accuracy	100.0%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64))))
✓	accuracy	100.0%	(.f64 (.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64))
✓	accuracy	100.0%	(.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal -4 binary64))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64)))))
✓	accuracy	99.7%	(.f64 (.f64 v v) #s(literal -3 binary64))

Samples

108.0ms

256×

valid

Compiler

Compiled 253 to 31 computations (87.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 82.0ms

ival-mult: 66.0ms (80.6% of total)

ival-add: 7.0ms (8.6% of total)

ival-div: 5.0ms (6.1% of total)

ival-sqrt: 3.0ms (3.7% of total)

exact: 1.0ms (1.2% of total)

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

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

series136.0ms (1.3%)

Memory

-73.8MiB live, 46.0MiB allocated

Counts

18 → 192

Calls

Call 1

Inputs
#<alt (* (* (* v v) -3) 2)>
#<alt (* (+ 1/4 (/ (* v v) -4)) (sqrt (+ 2 (* (* (* v v) -3) 2))))>
#<alt (+ 1/4 (/ (* v v) -4))>
#<alt (/ (* v v) -4)>
#<alt (* (sqrt 2) 1/4)>
#<alt (sqrt 2)>
#<alt (* (sqrt 2) (+ 1/4 (* v (* v -5/8))))>
#<alt (+ 1/4 (* v (* v -5/8)))>
#<alt (* v (* v -5/8))>
#<alt (* (sqrt 2) (+ 1/4 (* (* v v) (+ -5/8 (* (* v v) 3/32)))))>
#<alt (+ 1/4 (* (* v v) (+ -5/8 (* (* v v) 3/32))))>
#<alt (* (* v v) (+ -5/8 (* (* v v) 3/32)))>
#<alt (/ (sqrt (+ 2 (* (* (* v v) -3) 2))) (/ 1 (+ 1/4 (/ (* v v) -4))))>
#<alt (sqrt (+ 2 (* (* (* v v) -3) 2)))>
#<alt (+ 2 (* (* (* v v) -3) 2))>
#<alt (* (* v v) -3)>
#<alt (* v -5/8)>
#<alt (* (* v v) 3/32)>

Outputs
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* 1/4 (sqrt 2))>
#<alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (* -1/4 (sqrt 2)) (* 3/4 (/ 1 (sqrt 2))))))>
#<alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (+ (* -1/4 (sqrt 2)) (* (pow v 2) (- (* 3/4 (/ 1 (sqrt 2))) (* 9/8 (/ 1 (pow (sqrt 2) 3)))))) (* 3/4 (/ 1 (sqrt 2))))))>
#<alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (+ (* -1/4 (sqrt 2)) (* (pow v 2) (- (+ (* 3/4 (/ 1 (sqrt 2))) (* (pow v 2) (- (* 9/8 (/ 1 (pow (sqrt 2) 3))) (* 27/8 (/ 1 (pow (sqrt 2) 5)))))) (* 9/8 (/ 1 (pow (sqrt 2) 3)))))) (* 3/4 (/ 1 (sqrt 2))))))>
#<alt (* -1/4 (* (pow v 3) (sqrt -6)))>
#<alt (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (* 1/4 (/ (sqrt -6) (pow v 2)))) (/ 1/4 (* (pow v 2) (sqrt -6)))))>
#<alt (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))) (/ 1/4 (* (pow v 2) (sqrt -6)))))>
#<alt (* (pow v 3) (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (pow (sqrt -6) 3))) (* 1/8 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))) (/ 1/4 (* (pow v 2) (sqrt -6)))))>
#<alt (* 1/4 (* (pow v 3) (sqrt -6)))>
#<alt (* -1 (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (* 1/4 (/ (sqrt -6) (pow v 2)))) (/ 1/4 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))) (/ 1/4 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* (pow v 3) (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (pow (sqrt -6) 3))) (* 1/8 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))) (/ 1/4 (* (pow v 2) (sqrt -6))))))>
#<alt 1/4>
#<alt (+ 1/4 (* -1/4 (pow v 2)))>
#<alt (+ 1/4 (* -1/4 (pow v 2)))>
#<alt (+ 1/4 (* -1/4 (pow v 2)))>
#<alt (* -1/4 (pow v 2))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))>
#<alt (* -1/4 (pow v 2))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))>
#<alt (* -1/4 (pow v 2))>
#<alt (* -1/4 (pow v 2))>
#<alt (* -1/4 (pow v 2))>
#<alt (* -1/4 (pow v 2))>
#<alt (* -1/4 (pow v 2))>
#<alt (* -1/4 (pow v 2))>
#<alt (* -1/4 (pow v 2))>
#<alt (* -1/4 (pow v 2))>
#<alt (* -1/4 (pow v 2))>
#<alt (* -1/4 (pow v 2))>
#<alt (* -1/4 (pow v 2))>
#<alt (* -1/4 (pow v 2))>
#<alt (* 1/4 (sqrt 2))>
#<alt (+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))>
#<alt (+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))>
#<alt (+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))>
#<alt (* -5/8 (* (pow v 2) (sqrt 2)))>
#<alt (* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt (* -5/8 (* (pow v 2) (sqrt 2)))>
#<alt (* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt 1/4>
#<alt (+ 1/4 (* -5/8 (pow v 2)))>
#<alt (+ 1/4 (* -5/8 (pow v 2)))>
#<alt (+ 1/4 (* -5/8 (pow v 2)))>
#<alt (* -5/8 (pow v 2))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))>
#<alt (* -5/8 (pow v 2))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* 1/4 (sqrt 2))>
#<alt (+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))>
#<alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 3/32 (* (pow v 2) (sqrt 2))))))>
#<alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 3/32 (* (pow v 2) (sqrt 2))))))>
#<alt (* 3/32 (* (pow v 4) (sqrt 2)))>
#<alt (* (pow v 4) (+ (* -5/8 (/ (sqrt 2) (pow v 2))) (* 3/32 (sqrt 2))))>
#<alt (* (pow v 4) (+ (* -5/8 (/ (sqrt 2) (pow v 2))) (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 4))))))>
#<alt (* (pow v 4) (+ (* -5/8 (/ (sqrt 2) (pow v 2))) (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 4))))))>
#<alt (* 3/32 (* (pow v 4) (sqrt 2)))>
#<alt (* (pow v 4) (+ (* -5/8 (/ (sqrt 2) (pow v 2))) (* 3/32 (sqrt 2))))>
#<alt (* (pow v 4) (+ (* -5/8 (/ (sqrt 2) (pow v 2))) (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 4))))))>
#<alt (* (pow v 4) (+ (* -5/8 (/ (sqrt 2) (pow v 2))) (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 4))))))>
#<alt 1/4>
#<alt (+ 1/4 (* -5/8 (pow v 2)))>
#<alt (+ 1/4 (* (pow v 2) (- (* 3/32 (pow v 2)) 5/8)))>
#<alt (+ 1/4 (* (pow v 2) (- (* 3/32 (pow v 2)) 5/8)))>
#<alt (* 3/32 (pow v 4))>
#<alt (* (pow v 4) (- 3/32 (* 5/8 (/ 1 (pow v 2)))))>
#<alt (* (pow v 4) (- (+ 3/32 (/ 1/4 (pow v 4))) (* 5/8 (/ 1 (pow v 2)))))>
#<alt (* (pow v 4) (- (+ 3/32 (/ 1/4 (pow v 4))) (* 5/8 (/ 1 (pow v 2)))))>
#<alt (* 3/32 (pow v 4))>
#<alt (* (pow v 4) (- 3/32 (* 5/8 (/ 1 (pow v 2)))))>
#<alt (* (pow v 4) (- (+ 3/32 (/ 1/4 (pow v 4))) (* 5/8 (/ 1 (pow v 2)))))>
#<alt (* (pow v 4) (- (+ 3/32 (/ 1/4 (pow v 4))) (* 5/8 (/ 1 (pow v 2)))))>
#<alt (* -5/8 (pow v 2))>
#<alt (* (pow v 2) (- (* 3/32 (pow v 2)) 5/8))>
#<alt (* (pow v 2) (- (* 3/32 (pow v 2)) 5/8))>
#<alt (* (pow v 2) (- (* 3/32 (pow v 2)) 5/8))>
#<alt (* 3/32 (pow v 4))>
#<alt (* (pow v 4) (- 3/32 (* 5/8 (/ 1 (pow v 2)))))>
#<alt (* (pow v 4) (- 3/32 (* 5/8 (/ 1 (pow v 2)))))>
#<alt (* (pow v 4) (- 3/32 (* 5/8 (/ 1 (pow v 2)))))>
#<alt (* 3/32 (pow v 4))>
#<alt (* (pow v 4) (- 3/32 (* 5/8 (/ 1 (pow v 2)))))>
#<alt (* (pow v 4) (- 3/32 (* 5/8 (/ 1 (pow v 2)))))>
#<alt (* (pow v 4) (- 3/32 (* 5/8 (/ 1 (pow v 2)))))>
#<alt (* 1/4 (sqrt 2))>
#<alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (* -1/4 (sqrt 2)) (* 3/4 (/ 1 (sqrt 2))))))>
#<alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (+ (* -1/4 (sqrt 2)) (* (pow v 2) (- (* 3/4 (/ 1 (sqrt 2))) (* 9/8 (/ 1 (pow (sqrt 2) 3)))))) (* 3/4 (/ 1 (sqrt 2))))))>
#<alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (+ (* -1/4 (sqrt 2)) (* (pow v 2) (- (+ (* 3/4 (/ 1 (sqrt 2))) (* (pow v 2) (- (* 9/8 (/ 1 (pow (sqrt 2) 3))) (* 27/8 (/ 1 (pow (sqrt 2) 5)))))) (* 9/8 (/ 1 (pow (sqrt 2) 3)))))) (* 3/4 (/ 1 (sqrt 2))))))>
#<alt (* -1/4 (* (pow v 3) (sqrt -6)))>
#<alt (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (* 1/4 (/ (sqrt -6) (pow v 2)))) (/ 1/4 (* (pow v 2) (sqrt -6)))))>
#<alt (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))) (/ 1/4 (* (pow v 2) (sqrt -6)))))>
#<alt (* (pow v 3) (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (pow (sqrt -6) 3))) (* 1/8 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))) (/ 1/4 (* (pow v 2) (sqrt -6)))))>
#<alt (* 1/4 (* (pow v 3) (sqrt -6)))>
#<alt (* -1 (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (* 1/4 (/ (sqrt -6) (pow v 2)))) (/ 1/4 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))) (/ 1/4 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* (pow v 3) (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (pow (sqrt -6) 3))) (* 1/8 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))) (/ 1/4 (* (pow v 2) (sqrt -6))))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (* v (sqrt -6))>
#<alt (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))>
#<alt (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))>
#<alt (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (sqrt -6)))>
#<alt (* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))>
#<alt 2>
#<alt (+ 2 (* -6 (pow v 2)))>
#<alt (+ 2 (* -6 (pow v 2)))>
#<alt (+ 2 (* -6 (pow v 2)))>
#<alt (* -6 (pow v 2))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* -6 (pow v 2))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* -3 (pow v 2))>
#<alt (* -3 (pow v 2))>
#<alt (* -3 (pow v 2))>
#<alt (* -3 (pow v 2))>
#<alt (* -3 (pow v 2))>
#<alt (* -3 (pow v 2))>
#<alt (* -3 (pow v 2))>
#<alt (* -3 (pow v 2))>
#<alt (* -3 (pow v 2))>
#<alt (* -3 (pow v 2))>
#<alt (* -3 (pow v 2))>
#<alt (* -3 (pow v 2))>
#<alt (* -5/8 v)>
#<alt (* -5/8 v)>
#<alt (* -5/8 v)>
#<alt (* -5/8 v)>
#<alt (* -5/8 v)>
#<alt (* -5/8 v)>
#<alt (* -5/8 v)>
#<alt (* -5/8 v)>
#<alt (* -5/8 v)>
#<alt (* -5/8 v)>
#<alt (* -5/8 v)>
#<alt (* -5/8 v)>
#<alt (* 3/32 (pow v 2))>
#<alt (* 3/32 (pow v 2))>
#<alt (* 3/32 (pow v 2))>
#<alt (* 3/32 (pow v 2))>
#<alt (* 3/32 (pow v 2))>
#<alt (* 3/32 (pow v 2))>
#<alt (* 3/32 (pow v 2))>
#<alt (* 3/32 (pow v 2))>
#<alt (* 3/32 (pow v 2))>
#<alt (* 3/32 (pow v 2))>
#<alt (* 3/32 (pow v 2))>
#<alt (* 3/32 (pow v 2))>

Calls

48 calls:

Time	Variable		Point	Expression
89.0ms	v	@	inf	(* (+ 1/4 (/ (* v v) -4)) (sqrt (+ 2 (* (* (* v v) -3) 2))))
1.0ms	v	@	inf	(* (sqrt 2) (+ 1/4 (* v (* v -5/8))))
1.0ms	v	@	0	(* (+ 1/4 (/ (* v v) -4)) (sqrt (+ 2 (* (* (* v v) -3) 2))))
1.0ms	v	@	inf	(sqrt (+ 2 (* (* (* v v) -3) 2)))
0.0ms	v	@	inf	(* (sqrt 2) (+ 1/4 (* (* v v) (+ -5/8 (* (* v v) 3/32)))))

rewrite671.0ms (6.3%)

Memory

25.7MiB live, 739.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 998×	`accelerator-lowering-fma.f32`
5 998×	`accelerator-lowering-fma.f64`
4 414×	`-lowering-.f32`
4 414×	`-lowering-.f64`
3 364×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	145
1	168	145
2	1247	145
0	8312	131

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 683

Calls

Call 1

Inputs
(* (* (* v v) -3) 2)
(* (+ 1/4 (/ (* v v) -4)) (sqrt (+ 2 (* (* (* v v) -3) 2))))
(+ 1/4 (/ (* v v) -4))
(/ (* v v) -4)
(* (sqrt 2) 1/4)
(sqrt 2)
(* (sqrt 2) (+ 1/4 (* v (* v -5/8))))
(+ 1/4 (* v (* v -5/8)))
(* v (* v -5/8))
(* (sqrt 2) (+ 1/4 (* (* v v) (+ -5/8 (* (* v v) 3/32)))))
(+ 1/4 (* (* v v) (+ -5/8 (* (* v v) 3/32))))
(* (* v v) (+ -5/8 (* (* v v) 3/32)))
(/ (sqrt (+ 2 (* (* (* v v) -3) 2))) (/ 1 (+ 1/4 (/ (* v v) -4))))
(sqrt (+ 2 (* (* (* v v) -3) 2)))
(+ 2 (* (* (* v v) -3) 2))
(* (* v v) -3)
(* v -5/8)
(* (* v v) 3/32)

Outputs
(.f64 v (.f64 v #s(literal -6 binary64)))
(.f64 v (.f64 (*.f64 v #s(literal -3 binary64)) #s(literal 2 binary64)))
(.f64 (.f64 v v) #s(literal -6 binary64))
(.f64 #s(literal -3 binary64) (.f64 (*.f64 v v) #s(literal 2 binary64)))
(.f64 (.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 (*.f64 v v) #s(literal -3 binary64)))
(.f64 #s(literal -6 binary64) (.f64 v v))
(.f64 (.f64 #s(literal 2 binary64) (*.f64 v v)) #s(literal -3 binary64))
(.f64 (.f64 #s(literal 2 binary64) v) (*.f64 v #s(literal -3 binary64)))
(+.f64 (.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal -6 binary64)))) #s(literal 1/4 binary64)) (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal -6 binary64)))) (/.f64 #s(literal -4 binary64) (.f64 v v))))
(+.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal -6 binary64)))) (/.f64 #s(literal -4 binary64) (.f64 v v))) (.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal -6 binary64)))) #s(literal 1/4 binary64)))
(+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64))) (/.f64 (/.f64 (.f64 v v) #s(literal -4 binary64)) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64))))
(+.f64 (/.f64 (/.f64 (.f64 v v) #s(literal -4 binary64)) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64))))
(+.f64 (.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal -6 binary64)))) #s(literal 1/4 binary64))) (.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal -6 binary64)))) (/.f64 #s(literal -4 binary64) (.f64 v v)))))
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(/.f64 (-.f64 (.f64 #s(literal 4 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal 6 binary64)))) (.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal 6 binary64))) (.f64 (.f64 (.f64 v v) (.f64 v v)) #s(literal 36 binary64)))) (.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal 6 binary64))) (+.f64 #s(literal 2 binary64) (.f64 (*.f64 v v) #s(literal 6 binary64)))))
(/.f64 (neg.f64 (+.f64 (neg.f64 (.f64 (.f64 (.f64 v v) (.f64 (.f64 v v) (.f64 v v))) #s(literal -216 binary64))) #s(literal -8 binary64))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 v v) #s(literal -6 binary64)) (+.f64 (.f64 (*.f64 v v) #s(literal -6 binary64)) #s(literal -2 binary64)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 v v) (.f64 v v)) #s(literal 36 binary64))))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal 6 binary64))))))
(/.f64 (neg.f64 (+.f64 (.f64 (.f64 (.f64 v v) (.f64 v v)) #s(literal 36 binary64)) #s(literal -4 binary64))) (neg.f64 (+.f64 (.f64 (.f64 v v) #s(literal -6 binary64)) #s(literal -2 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal 6 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 (.f64 (.f64 v v) (.f64 v v)) #s(literal 36 binary64)) (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal 6 binary64)))) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 #s(literal 4 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal 6 binary64)))) (/.f64 #s(literal 4 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal 6 binary64))))) (+.f64 (.f64 (/.f64 (.f64 (.f64 (.f64 v v) (.f64 v v)) #s(literal 36 binary64)) (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal 6 binary64)))) (/.f64 (.f64 (.f64 (.f64 v v) (.f64 v v)) #s(literal 36 binary64)) (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal 6 binary64))))) (.f64 (/.f64 #s(literal 4 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal 6 binary64)))) (/.f64 (.f64 (.f64 (.f64 v v) (.f64 v v)) #s(literal 36 binary64)) (+.f64 #s(literal 2 binary64) (.f64 (*.f64 v v) #s(literal 6 binary64))))))))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 4 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal 6 binary64)))) (/.f64 #s(literal 4 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal 6 binary64))))) (.f64 (/.f64 (.f64 (.f64 (.f64 v v) (.f64 v v)) #s(literal 36 binary64)) (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal 6 binary64)))) (/.f64 (.f64 (.f64 (.f64 v v) (.f64 v v)) #s(literal 36 binary64)) (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal 6 binary64)))))) (+.f64 (/.f64 #s(literal 4 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal 6 binary64)))) (/.f64 (.f64 (.f64 (.f64 v v) (.f64 v v)) #s(literal 36 binary64)) (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal 6 binary64))))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal -6 binary64)))) #s(literal -1 binary64))
(.f64 #s(literal 2 binary64) (+.f64 (.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 1 binary64)))
(.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (*.f64 v v) #s(literal -6 binary64))))
(.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 (.f64 v v) (.f64 (.f64 v v) (.f64 v v))) #s(literal -216 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 v v) #s(literal -6 binary64)) (+.f64 (.f64 (.f64 v v) #s(literal -6 binary64)) #s(literal -2 binary64))))))
(.f64 (+.f64 #s(literal 8 binary64) (.f64 (.f64 (.f64 v v) (.f64 (.f64 v v) (.f64 v v))) #s(literal -216 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 (.f64 v v) (.f64 v v)) #s(literal 36 binary64)) (+.f64 #s(literal 4 binary64) (.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal 6 binary64)))))))
(.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 v v) (.f64 v v)) #s(literal 36 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (*.f64 v v) #s(literal 6 binary64)))))
(.f64 (+.f64 (.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(.f64 (+.f64 (neg.f64 (.f64 (.f64 (.f64 v v) (.f64 (.f64 v v) (.f64 v v))) #s(literal -216 binary64))) #s(literal -8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 v v) #s(literal -6 binary64)) (+.f64 (.f64 (.f64 v v) #s(literal -6 binary64)) #s(literal -2 binary64)))))))
(.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 4 binary64) (.f64 (.f64 (.f64 v v) (.f64 v v)) #s(literal 36 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 2 binary64) (.f64 (*.f64 v v) #s(literal 6 binary64))))))
(.f64 (+.f64 (.f64 (.f64 (.f64 v v) (.f64 v v)) #s(literal 36 binary64)) #s(literal -4 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (*.f64 v v) #s(literal -6 binary64)) #s(literal -2 binary64))))
(.f64 v (.f64 v #s(literal -3 binary64)))
(.f64 (.f64 v v) #s(literal -3 binary64))
(.f64 #s(literal -3 binary64) (.f64 v v))
(.f64 (.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 1 binary64))
(.f64 (.f64 v #s(literal -3 binary64)) v)
(*.f64 v #s(literal -5/8 binary64))
(*.f64 #s(literal -5/8 binary64) v)
(.f64 v (.f64 v #s(literal 3/32 binary64)))
(.f64 (.f64 v v) #s(literal 3/32 binary64))
(.f64 #s(literal 3/32 binary64) (.f64 v v))
(.f64 (.f64 v #s(literal 3/32 binary64)) v)

simplify582.0ms (5.5%)

Memory

28.0MiB live, 924.2MiB allocated

Algorithm

1×	egg-herbie

Rules

14 300×	`accelerator-lowering-fma.f32`
14 300×	`accelerator-lowering-fma.f64`
5 186×	`-lowering-.f32`
5 186×	`-lowering-.f64`
3 074×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	182	2184
1	485	2104
2	1401	2078
3	4848	1940
0	8356	1841

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

Calls

Call 1

Inputs
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* 1/4 (sqrt 2))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (* -1/4 (sqrt 2)) (* 3/4 (/ 1 (sqrt 2))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (+ (* -1/4 (sqrt 2)) (* (pow v 2) (- (* 3/4 (/ 1 (sqrt 2))) (* 9/8 (/ 1 (pow (sqrt 2) 3)))))) (* 3/4 (/ 1 (sqrt 2))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (+ (* -1/4 (sqrt 2)) (* (pow v 2) (- (+ (* 3/4 (/ 1 (sqrt 2))) (* (pow v 2) (- (* 9/8 (/ 1 (pow (sqrt 2) 3))) (* 27/8 (/ 1 (pow (sqrt 2) 5)))))) (* 9/8 (/ 1 (pow (sqrt 2) 3)))))) (* 3/4 (/ 1 (sqrt 2))))))
(* -1/4 (* (pow v 3) (sqrt -6)))
(* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (* 1/4 (/ (sqrt -6) (pow v 2)))) (/ 1/4 (* (pow v 2) (sqrt -6)))))
(* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))) (/ 1/4 (* (pow v 2) (sqrt -6)))))
(* (pow v 3) (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (pow (sqrt -6) 3))) (* 1/8 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))) (/ 1/4 (* (pow v 2) (sqrt -6)))))
(* 1/4 (* (pow v 3) (sqrt -6)))
(* -1 (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (* 1/4 (/ (sqrt -6) (pow v 2)))) (/ 1/4 (* (pow v 2) (sqrt -6))))))
(* -1 (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))) (/ 1/4 (* (pow v 2) (sqrt -6))))))
(* -1 (* (pow v 3) (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (pow (sqrt -6) 3))) (* 1/8 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))) (/ 1/4 (* (pow v 2) (sqrt -6))))))
1/4
(+ 1/4 (* -1/4 (pow v 2)))
(+ 1/4 (* -1/4 (pow v 2)))
(+ 1/4 (* -1/4 (pow v 2)))
(* -1/4 (pow v 2))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))
(* -1/4 (pow v 2))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))
(* -1/4 (pow v 2))
(* -1/4 (pow v 2))
(* -1/4 (pow v 2))
(* -1/4 (pow v 2))
(* -1/4 (pow v 2))
(* -1/4 (pow v 2))
(* -1/4 (pow v 2))
(* -1/4 (pow v 2))
(* -1/4 (pow v 2))
(* -1/4 (pow v 2))
(* -1/4 (pow v 2))
(* -1/4 (pow v 2))
(* 1/4 (sqrt 2))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(* -5/8 (* (pow v 2) (sqrt 2)))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* -5/8 (* (pow v 2) (sqrt 2)))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
1/4
(+ 1/4 (* -5/8 (pow v 2)))
(+ 1/4 (* -5/8 (pow v 2)))
(+ 1/4 (* -5/8 (pow v 2)))
(* -5/8 (pow v 2))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(* -5/8 (pow v 2))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* 1/4 (sqrt 2))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 3/32 (* (pow v 2) (sqrt 2))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 3/32 (* (pow v 2) (sqrt 2))))))
(* 3/32 (* (pow v 4) (sqrt 2)))
(* (pow v 4) (+ (* -5/8 (/ (sqrt 2) (pow v 2))) (* 3/32 (sqrt 2))))
(* (pow v 4) (+ (* -5/8 (/ (sqrt 2) (pow v 2))) (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 4))))))
(* (pow v 4) (+ (* -5/8 (/ (sqrt 2) (pow v 2))) (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 4))))))
(* 3/32 (* (pow v 4) (sqrt 2)))
(* (pow v 4) (+ (* -5/8 (/ (sqrt 2) (pow v 2))) (* 3/32 (sqrt 2))))
(* (pow v 4) (+ (* -5/8 (/ (sqrt 2) (pow v 2))) (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 4))))))
(* (pow v 4) (+ (* -5/8 (/ (sqrt 2) (pow v 2))) (+ (* 3/32 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 4))))))
1/4
(+ 1/4 (* -5/8 (pow v 2)))
(+ 1/4 (* (pow v 2) (- (* 3/32 (pow v 2)) 5/8)))
(+ 1/4 (* (pow v 2) (- (* 3/32 (pow v 2)) 5/8)))
(* 3/32 (pow v 4))
(* (pow v 4) (- 3/32 (* 5/8 (/ 1 (pow v 2)))))
(* (pow v 4) (- (+ 3/32 (/ 1/4 (pow v 4))) (* 5/8 (/ 1 (pow v 2)))))
(* (pow v 4) (- (+ 3/32 (/ 1/4 (pow v 4))) (* 5/8 (/ 1 (pow v 2)))))
(* 3/32 (pow v 4))
(* (pow v 4) (- 3/32 (* 5/8 (/ 1 (pow v 2)))))
(* (pow v 4) (- (+ 3/32 (/ 1/4 (pow v 4))) (* 5/8 (/ 1 (pow v 2)))))
(* (pow v 4) (- (+ 3/32 (/ 1/4 (pow v 4))) (* 5/8 (/ 1 (pow v 2)))))
(* -5/8 (pow v 2))
(* (pow v 2) (- (* 3/32 (pow v 2)) 5/8))
(* (pow v 2) (- (* 3/32 (pow v 2)) 5/8))
(* (pow v 2) (- (* 3/32 (pow v 2)) 5/8))
(* 3/32 (pow v 4))
(* (pow v 4) (- 3/32 (* 5/8 (/ 1 (pow v 2)))))
(* (pow v 4) (- 3/32 (* 5/8 (/ 1 (pow v 2)))))
(* (pow v 4) (- 3/32 (* 5/8 (/ 1 (pow v 2)))))
(* 3/32 (pow v 4))
(* (pow v 4) (- 3/32 (* 5/8 (/ 1 (pow v 2)))))
(* (pow v 4) (- 3/32 (* 5/8 (/ 1 (pow v 2)))))
(* (pow v 4) (- 3/32 (* 5/8 (/ 1 (pow v 2)))))
(* 1/4 (sqrt 2))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (* -1/4 (sqrt 2)) (* 3/4 (/ 1 (sqrt 2))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (+ (* -1/4 (sqrt 2)) (* (pow v 2) (- (* 3/4 (/ 1 (sqrt 2))) (* 9/8 (/ 1 (pow (sqrt 2) 3)))))) (* 3/4 (/ 1 (sqrt 2))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (+ (* -1/4 (sqrt 2)) (* (pow v 2) (- (+ (* 3/4 (/ 1 (sqrt 2))) (* (pow v 2) (- (* 9/8 (/ 1 (pow (sqrt 2) 3))) (* 27/8 (/ 1 (pow (sqrt 2) 5)))))) (* 9/8 (/ 1 (pow (sqrt 2) 3)))))) (* 3/4 (/ 1 (sqrt 2))))))
(* -1/4 (* (pow v 3) (sqrt -6)))
(* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (* 1/4 (/ (sqrt -6) (pow v 2)))) (/ 1/4 (* (pow v 2) (sqrt -6)))))
(* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))) (/ 1/4 (* (pow v 2) (sqrt -6)))))
(* (pow v 3) (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (pow (sqrt -6) 3))) (* 1/8 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))) (/ 1/4 (* (pow v 2) (sqrt -6)))))
(* 1/4 (* (pow v 3) (sqrt -6)))
(* -1 (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (* 1/4 (/ (sqrt -6) (pow v 2)))) (/ 1/4 (* (pow v 2) (sqrt -6))))))
(* -1 (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))) (/ 1/4 (* (pow v 2) (sqrt -6))))))
(* -1 (* (pow v 3) (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (pow (sqrt -6) 3))) (* 1/8 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))) (/ 1/4 (* (pow v 2) (sqrt -6))))))
(sqrt 2)
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(* v (sqrt -6))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (sqrt -6)))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))
2
(+ 2 (* -6 (pow v 2)))
(+ 2 (* -6 (pow v 2)))
(+ 2 (* -6 (pow v 2)))
(* -6 (pow v 2))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* -6 (pow v 2))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* -3 (pow v 2))
(* -3 (pow v 2))
(* -3 (pow v 2))
(* -3 (pow v 2))
(* -3 (pow v 2))
(* -3 (pow v 2))
(* -3 (pow v 2))
(* -3 (pow v 2))
(* -3 (pow v 2))
(* -3 (pow v 2))
(* -3 (pow v 2))
(* -3 (pow v 2))
(* -5/8 v)
(* -5/8 v)
(* -5/8 v)
(* -5/8 v)
(* -5/8 v)
(* -5/8 v)
(* -5/8 v)
(* -5/8 v)
(* -5/8 v)
(* -5/8 v)
(* -5/8 v)
(* -5/8 v)
(* 3/32 (pow v 2))
(* 3/32 (pow v 2))
(* 3/32 (pow v 2))
(* 3/32 (pow v 2))
(* 3/32 (pow v 2))
(* 3/32 (pow v 2))
(* 3/32 (pow v 2))
(* 3/32 (pow v 2))
(* 3/32 (pow v 2))
(* 3/32 (pow v 2))
(* 3/32 (pow v 2))
(* 3/32 (pow v 2))

Outputs
(* -6 (pow v 2))
(.f64 #s(literal -6 binary64) (.f64 v v))
(* -6 (pow v 2))
(.f64 #s(literal -6 binary64) (.f64 v v))
(* -6 (pow v 2))
(.f64 #s(literal -6 binary64) (.f64 v v))
(* -6 (pow v 2))
(.f64 #s(literal -6 binary64) (.f64 v v))
(* -6 (pow v 2))
(.f64 #s(literal -6 binary64) (.f64 v v))
(* -6 (pow v 2))
(.f64 #s(literal -6 binary64) (.f64 v v))
(* -6 (pow v 2))
(.f64 #s(literal -6 binary64) (.f64 v v))
(* -6 (pow v 2))
(.f64 #s(literal -6 binary64) (.f64 v v))
(* -6 (pow v 2))
(.f64 #s(literal -6 binary64) (.f64 v v))
(* -6 (pow v 2))
(.f64 #s(literal -6 binary64) (.f64 v v))
(* -6 (pow v 2))
(.f64 #s(literal -6 binary64) (.f64 v v))
(* -6 (pow v 2))
(.f64 #s(literal -6 binary64) (.f64 v v))
(* 1/4 (sqrt 2))
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (* -1/4 (sqrt 2)) (* 3/4 (/ 1 (sqrt 2))))))
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(+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (+ (* -1/4 (sqrt 2)) (* (pow v 2) (- (* 3/4 (/ 1 (sqrt 2))) (* 9/8 (/ 1 (pow (sqrt 2) 3)))))) (* 3/4 (/ 1 (sqrt 2))))))
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(.f64 (.f64 (.f64 v v) (.f64 v v)) (+.f64 #s(literal 3/32 binary64) (/.f64 #s(literal -5/8 binary64) (*.f64 v v))))
(* (pow v 4) (- 3/32 (* 5/8 (/ 1 (pow v 2)))))
(.f64 (.f64 (.f64 v v) (.f64 v v)) (+.f64 #s(literal 3/32 binary64) (/.f64 #s(literal -5/8 binary64) (*.f64 v v))))
(* 3/32 (pow v 4))
(.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 3/32 binary64))))
(* (pow v 4) (- 3/32 (* 5/8 (/ 1 (pow v 2)))))
(.f64 (.f64 (.f64 v v) (.f64 v v)) (+.f64 #s(literal 3/32 binary64) (/.f64 #s(literal -5/8 binary64) (*.f64 v v))))
(* (pow v 4) (- 3/32 (* 5/8 (/ 1 (pow v 2)))))
(.f64 (.f64 (.f64 v v) (.f64 v v)) (+.f64 #s(literal 3/32 binary64) (/.f64 #s(literal -5/8 binary64) (*.f64 v v))))
(* (pow v 4) (- 3/32 (* 5/8 (/ 1 (pow v 2)))))
(.f64 (.f64 (.f64 v v) (.f64 v v)) (+.f64 #s(literal 3/32 binary64) (/.f64 #s(literal -5/8 binary64) (*.f64 v v))))
(* 1/4 (sqrt 2))
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (* -1/4 (sqrt 2)) (* 3/4 (/ 1 (sqrt 2))))))
(+.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 v (.f64 v #s(literal -1/4 binary64))))) (/.f64 (.f64 (*.f64 v v) #s(literal -3/4 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (+ (* -1/4 (sqrt 2)) (* (pow v 2) (- (* 3/4 (/ 1 (sqrt 2))) (* 9/8 (/ 1 (pow (sqrt 2) 3)))))) (* 3/4 (/ 1 (sqrt 2))))))
(+.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 v (.f64 v #s(literal -1/4 binary64))))) (.f64 (.f64 v v) (+.f64 (.f64 (*.f64 v v) (+.f64 (/.f64 #s(literal 3/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -9/16 binary64) (sqrt.f64 #s(literal 2 binary64))))) (/.f64 #s(literal -3/4 binary64) (sqrt.f64 #s(literal 2 binary64))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (+ (* -1/4 (sqrt 2)) (* (pow v 2) (- (+ (* 3/4 (/ 1 (sqrt 2))) (* (pow v 2) (- (* 9/8 (/ 1 (pow (sqrt 2) 3))) (* 27/8 (/ 1 (pow (sqrt 2) 5)))))) (* 9/8 (/ 1 (pow (sqrt 2) 3)))))) (* 3/4 (/ 1 (sqrt 2))))))
(+.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 v (.f64 v #s(literal -1/4 binary64))))) (.f64 v (.f64 v (+.f64 (.f64 (.f64 v v) (+.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -9/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (*.f64 v v) (+.f64 (/.f64 #s(literal 9/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -27/8 binary64) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))))))) (/.f64 #s(literal -3/4 binary64) (sqrt.f64 #s(literal 2 binary64)))))))
(* -1/4 (* (pow v 3) (sqrt -6)))
(.f64 (.f64 v (.f64 v v)) (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -6 binary64))))
(* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (* 1/4 (/ (sqrt -6) (pow v 2)))) (/ 1/4 (* (pow v 2) (sqrt -6)))))
(+.f64 (.f64 (.f64 v (.f64 v v)) (.f64 (sqrt.f64 #s(literal -6 binary64)) (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 v v))))) (.f64 #s(literal 1/4 binary64) (/.f64 v (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -6 binary64))))))
(* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))) (/ 1/4 (* (pow v 2) (sqrt -6)))))
(+.f64 (.f64 (.f64 v (.f64 v v)) (+.f64 (.f64 (sqrt.f64 #s(literal -6 binary64)) (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 v v)))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal -6 binary64)) (.f64 (.f64 v v) (.f64 v v)))) #s(literal 11/48 binary64)))) (*.f64 #s(literal 1/4 binary64) (/.f64 v (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -6 binary64))))))
(* (pow v 3) (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (pow (sqrt -6) 3))) (* 1/8 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))) (/ 1/4 (* (pow v 2) (sqrt -6)))))
(+.f64 (.f64 (.f64 v (.f64 v v)) (+.f64 (.f64 (sqrt.f64 #s(literal -6 binary64)) (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 v v)))) (+.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal -6 binary64)) (.f64 (.f64 v v) (.f64 v v)))) #s(literal 11/48 binary64)) (/.f64 (+.f64 (/.f64 #s(literal 1/48 binary64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))) (pow.f64 v #s(literal 6 binary64)))))) (*.f64 #s(literal 1/4 binary64) (/.f64 v (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -6 binary64))))))
(* 1/4 (* (pow v 3) (sqrt -6)))
(.f64 (.f64 v v) (.f64 v (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -6 binary64)))))
(* -1 (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (* 1/4 (/ (sqrt -6) (pow v 2)))) (/ 1/4 (* (pow v 2) (sqrt -6))))))
(-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 v (.f64 v v)) (.f64 (sqrt.f64 #s(literal -6 binary64)) (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 v v))))) (.f64 #s(literal 1/4 binary64) (/.f64 v (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -6 binary64)))))))
(* -1 (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))) (/ 1/4 (* (pow v 2) (sqrt -6))))))
(-.f64 (.f64 (+.f64 (.f64 (sqrt.f64 #s(literal -6 binary64)) (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 v v)))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal -6 binary64)) (.f64 (.f64 v v) (.f64 v v)))) #s(literal 11/48 binary64))) (.f64 v (-.f64 #s(literal 0 binary64) (.f64 v v)))) (*.f64 #s(literal 1/4 binary64) (/.f64 v (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -6 binary64))))))
(* -1 (* (pow v 3) (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (pow (sqrt -6) 3))) (* 1/8 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))) (/ 1/4 (* (pow v 2) (sqrt -6))))))
(-.f64 (.f64 (.f64 v (.f64 v v)) (-.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/48 binary64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 #s(literal 1/8 binary64) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))) (pow.f64 v #s(literal 6 binary64))) (+.f64 (.f64 (sqrt.f64 #s(literal -6 binary64)) (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 v v)))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal -6 binary64)) (.f64 (.f64 v v) (.f64 v v)))) #s(literal 11/48 binary64))))) (*.f64 #s(literal 1/4 binary64) (/.f64 v (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -6 binary64))))))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 (.f64 v v) #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 (.f64 v v) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal -3 binary64) (.f64 (.f64 v v) #s(literal -9/4 binary64)))))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 v v) (+.f64 (.f64 (.f64 v v) (+.f64 (/.f64 (.f64 (.f64 v v) #s(literal -27/2 binary64)) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -9/4 binary64) (sqrt.f64 #s(literal 2 binary64))))) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))))))
(* v (sqrt -6))
(*.f64 v (sqrt.f64 #s(literal -6 binary64)))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(+.f64 (.f64 v (sqrt.f64 #s(literal -6 binary64))) (/.f64 #s(literal 1 binary64) (.f64 v (sqrt.f64 #s(literal -6 binary64)))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 v (sqrt.f64 #s(literal -6 binary64)))) (.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal -6 binary64))) (.f64 (.f64 v v) (*.f64 v v)))) v))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(.f64 v (+.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 v v)) (sqrt.f64 #s(literal -6 binary64))) (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal -6 binary64))) (.f64 (.f64 v v) (*.f64 v v))))) (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 v #s(literal 6 binary64))) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))))
(* -1 (* v (sqrt -6)))
(-.f64 #s(literal 0 binary64) (*.f64 v (sqrt.f64 #s(literal -6 binary64))))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(-.f64 (/.f64 #s(literal -1 binary64) (.f64 v (sqrt.f64 #s(literal -6 binary64)))) (.f64 v (sqrt.f64 #s(literal -6 binary64))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(+.f64 (/.f64 #s(literal -1 binary64) (.f64 v (sqrt.f64 #s(literal -6 binary64)))) (.f64 v (-.f64 (/.f64 (/.f64 #s(literal -1/12 binary64) (sqrt.f64 #s(literal -6 binary64))) (.f64 (.f64 v v) (*.f64 v v))) (sqrt.f64 #s(literal -6 binary64)))))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))
(-.f64 (.f64 v (/.f64 (/.f64 #s(literal -1/12 binary64) (sqrt.f64 #s(literal -6 binary64))) (.f64 (.f64 v v) (.f64 v v)))) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 v (sqrt.f64 #s(literal -6 binary64)))) (.f64 v (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 v #s(literal 6 binary64))) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))))))
2
#s(literal 2 binary64)
(+ 2 (* -6 (pow v 2)))
(+.f64 #s(literal 2 binary64) (.f64 #s(literal -6 binary64) (.f64 v v)))
(+ 2 (* -6 (pow v 2)))
(+.f64 #s(literal 2 binary64) (.f64 #s(literal -6 binary64) (.f64 v v)))
(+ 2 (* -6 (pow v 2)))
(+.f64 #s(literal 2 binary64) (.f64 #s(literal -6 binary64) (.f64 v v)))
(* -6 (pow v 2))
(.f64 #s(literal -6 binary64) (.f64 v v))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(+.f64 #s(literal 2 binary64) (.f64 #s(literal -6 binary64) (.f64 v v)))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(+.f64 #s(literal 2 binary64) (.f64 #s(literal -6 binary64) (.f64 v v)))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(+.f64 #s(literal 2 binary64) (.f64 #s(literal -6 binary64) (.f64 v v)))
(* -6 (pow v 2))
(.f64 #s(literal -6 binary64) (.f64 v v))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(+.f64 #s(literal 2 binary64) (.f64 #s(literal -6 binary64) (.f64 v v)))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(+.f64 #s(literal 2 binary64) (.f64 #s(literal -6 binary64) (.f64 v v)))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(+.f64 #s(literal 2 binary64) (.f64 #s(literal -6 binary64) (.f64 v v)))
(* -3 (pow v 2))
(.f64 (.f64 v v) #s(literal -3 binary64))
(* -3 (pow v 2))
(.f64 (.f64 v v) #s(literal -3 binary64))
(* -3 (pow v 2))
(.f64 (.f64 v v) #s(literal -3 binary64))
(* -3 (pow v 2))
(.f64 (.f64 v v) #s(literal -3 binary64))
(* -3 (pow v 2))
(.f64 (.f64 v v) #s(literal -3 binary64))
(* -3 (pow v 2))
(.f64 (.f64 v v) #s(literal -3 binary64))
(* -3 (pow v 2))
(.f64 (.f64 v v) #s(literal -3 binary64))
(* -3 (pow v 2))
(.f64 (.f64 v v) #s(literal -3 binary64))
(* -3 (pow v 2))
(.f64 (.f64 v v) #s(literal -3 binary64))
(* -3 (pow v 2))
(.f64 (.f64 v v) #s(literal -3 binary64))
(* -3 (pow v 2))
(.f64 (.f64 v v) #s(literal -3 binary64))
(* -3 (pow v 2))
(.f64 (.f64 v v) #s(literal -3 binary64))
(* -5/8 v)
(*.f64 v #s(literal -5/8 binary64))
(* -5/8 v)
(*.f64 v #s(literal -5/8 binary64))
(* -5/8 v)
(*.f64 v #s(literal -5/8 binary64))
(* -5/8 v)
(*.f64 v #s(literal -5/8 binary64))
(* -5/8 v)
(*.f64 v #s(literal -5/8 binary64))
(* -5/8 v)
(*.f64 v #s(literal -5/8 binary64))
(* -5/8 v)
(*.f64 v #s(literal -5/8 binary64))
(* -5/8 v)
(*.f64 v #s(literal -5/8 binary64))
(* -5/8 v)
(*.f64 v #s(literal -5/8 binary64))
(* -5/8 v)
(*.f64 v #s(literal -5/8 binary64))
(* -5/8 v)
(*.f64 v #s(literal -5/8 binary64))
(* -5/8 v)
(*.f64 v #s(literal -5/8 binary64))
(* 3/32 (pow v 2))
(.f64 (.f64 v v) #s(literal 3/32 binary64))
(* 3/32 (pow v 2))
(.f64 (.f64 v v) #s(literal 3/32 binary64))
(* 3/32 (pow v 2))
(.f64 (.f64 v v) #s(literal 3/32 binary64))
(* 3/32 (pow v 2))
(.f64 (.f64 v v) #s(literal 3/32 binary64))
(* 3/32 (pow v 2))
(.f64 (.f64 v v) #s(literal 3/32 binary64))
(* 3/32 (pow v 2))
(.f64 (.f64 v v) #s(literal 3/32 binary64))
(* 3/32 (pow v 2))
(.f64 (.f64 v v) #s(literal 3/32 binary64))
(* 3/32 (pow v 2))
(.f64 (.f64 v v) #s(literal 3/32 binary64))
(* 3/32 (pow v 2))
(.f64 (.f64 v v) #s(literal 3/32 binary64))
(* 3/32 (pow v 2))
(.f64 (.f64 v v) #s(literal 3/32 binary64))
(* 3/32 (pow v 2))
(.f64 (.f64 v v) #s(literal 3/32 binary64))
(* 3/32 (pow v 2))
(.f64 (.f64 v v) #s(literal 3/32 binary64))

eval145.0ms (1.4%)

Memory: -9.5MiB live, 347.2MiB allocated
Compiler: Compiled 33 319 to 2 219 computations (93.3% saved)

prune100.0ms (0.9%)

Memory

1.4MiB live, 276.8MiB allocated

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	1 148	4	1 152
Fresh	1	0	1
Picked	3	2	5
Done	0	0	0
Total	1 152	6	1 158

Accuracy

100.0%

Counts

1 158 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.5%	(/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal 4 binary64))) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64)))
▶	100.0%	(/.f64 (sqrt.f64 (+.f64 (.f64 (.f64 v v) #s(literal -6 binary64)) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal -4 binary64)))))
▶	98.9%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 v v) #s(literal -5/8 binary64)))))
▶	100.0%	(.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal 4 binary64))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal -6 binary64)))))
✓	98.9%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 v (*.f64 v #s(literal -5/8 binary64)))))
✓	98.4%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))

Compiler

Compiled 83 to 64 computations (22.9% saved)

simplify320.0ms (3%)

Memory

-15.7MiB live, 401.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 v v)
✓	cost-diff	0	(/.f64 (*.f64 v v) #s(literal 4 binary64))
✓	cost-diff	0	(-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal 4 binary64)))
✓	cost-diff	0	(/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal 4 binary64))) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64)))
✓	cost-diff	0	(+.f64 (.f64 (.f64 v v) #s(literal -6 binary64)) #s(literal 2 binary64))
✓	cost-diff	0	(sqrt.f64 (+.f64 (.f64 (.f64 v v) #s(literal -6 binary64)) #s(literal 2 binary64)))
✓	cost-diff	0	(/.f64 (sqrt.f64 (+.f64 (.f64 (.f64 v v) #s(literal -6 binary64)) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal -4 binary64)))))
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal -4 binary64))))
✓	cost-diff	0	(+.f64 #s(literal 1/4 binary64) (.f64 (.f64 v v) #s(literal -5/8 binary64)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 v v) #s(literal -5/8 binary64))))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	128	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 v v) #s(literal -5/8 binary64)))))
✓	cost-diff	0	(*.f64 v v)
✓	cost-diff	0	(/.f64 (*.f64 v v) #s(literal 4 binary64))
✓	cost-diff	0	(-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal 4 binary64)))
✓	cost-diff	0	(.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal 4 binary64))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal -6 binary64)))))

Rules

4 316×	`accelerator-lowering-fma.f32`
4 316×	`accelerator-lowering-fma.f64`
2 318×	`-lowering-.f32`
2 318×	`-lowering-.f64`
1 708×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	224
1	55	222
2	105	222
3	210	222
4	427	222
5	630	222
6	847	222
7	1070	222
8	1649	222
9	2608	222
10	3229	220
11	3729	220
12	4217	220
13	4989	220
14	6102	220
15	6639	220
16	7866	220
0	8020	201

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (- 1/4 (/ (* v v) 4)) (sqrt (+ 2 (* (* v v) -6))))
(- 1/4 (/ (* v v) 4))
1/4
(/ (* v v) 4)
(* v v)
v
4
(sqrt (+ 2 (* (* v v) -6)))
(+ 2 (* (* v v) -6))
2
(* (* v v) -6)
-6
(/ (sqrt 2) (/ 1 (+ 1/4 (* (* v v) -5/8))))
(sqrt 2)
2
(/ 1 (+ 1/4 (* (* v v) -5/8)))
1
(+ 1/4 (* (* v v) -5/8))
1/4
(* (* v v) -5/8)
(* v v)
v
-5/8
(/ (sqrt (+ (* (* v v) -6) 2)) (/ 1 (+ 1/4 (/ (* v v) -4))))
(sqrt (+ (* (* v v) -6) 2))
(+ (* (* v v) -6) 2)
(* (* v v) -6)
(* v v)
v
-6
2
(/ 1 (+ 1/4 (/ (* v v) -4)))
1
(+ 1/4 (/ (* v v) -4))
1/4
(/ (* v v) -4)
-4
(/ (- 1/4 (/ (* v v) 4)) (pow (+ 2 (* (* v v) -6)) -1/2))
(- 1/4 (/ (* v v) 4))
1/4
(/ (* v v) 4)
(* v v)
v
4
(pow (+ 2 (* (* v v) -6)) -1/2)
(+ 2 (* (* v v) -6))
2
(* (* v v) -6)
-6
-1/2

Outputs
(* (- 1/4 (/ (* v v) 4)) (sqrt (+ 2 (* (* v v) -6))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal 6 binary64)))) (/.f64 #s(literal 4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(- 1/4 (/ (* v v) 4))
(+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal -4 binary64)))
1/4
#s(literal 1/4 binary64)
(/ (* v v) 4)
(/.f64 (*.f64 v v) #s(literal 4 binary64))
(* v v)
(*.f64 v v)
v
4
#s(literal 4 binary64)
(sqrt (+ 2 (* (* v v) -6)))
(sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal 6 binary64))))
(+ 2 (* (* v v) -6))
(-.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal 6 binary64)))
2
#s(literal 2 binary64)
(* (* v v) -6)
(.f64 (.f64 v v) #s(literal -6 binary64))
-6
#s(literal -6 binary64)
(/ (sqrt 2) (/ 1 (+ 1/4 (* (* v v) -5/8))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 v (*.f64 v #s(literal -5/8 binary64)))))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(/ 1 (+ 1/4 (* (* v v) -5/8)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 v (.f64 v #s(literal -5/8 binary64)))))
1
#s(literal 1 binary64)
(+ 1/4 (* (* v v) -5/8))
(+.f64 #s(literal 1/4 binary64) (.f64 v (.f64 v #s(literal -5/8 binary64))))
1/4
#s(literal 1/4 binary64)
(* (* v v) -5/8)
(.f64 v (.f64 v #s(literal -5/8 binary64)))
(* v v)
(*.f64 v v)
v
-5/8
#s(literal -5/8 binary64)
(/ (sqrt (+ (* (* v v) -6) 2)) (/ 1 (+ 1/4 (/ (* v v) -4))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal 6 binary64)))) (/.f64 #s(literal 4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(sqrt (+ (* (* v v) -6) 2))
(sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal 6 binary64))))
(+ (* (* v v) -6) 2)
(-.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal 6 binary64)))
(* (* v v) -6)
(.f64 (.f64 v v) #s(literal -6 binary64))
(* v v)
(*.f64 v v)
v
-6
#s(literal -6 binary64)
2
#s(literal 2 binary64)
(/ 1 (+ 1/4 (/ (* v v) -4)))
(/.f64 #s(literal 4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
1
#s(literal 1 binary64)
(+ 1/4 (/ (* v v) -4))
(+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal -4 binary64)))
1/4
#s(literal 1/4 binary64)
(/ (* v v) -4)
(/.f64 (*.f64 v v) #s(literal -4 binary64))
-4
#s(literal -4 binary64)
(/ (- 1/4 (/ (* v v) 4)) (pow (+ 2 (* (* v v) -6)) -1/2))
(/.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal -4 binary64))) (pow.f64 (-.f64 #s(literal 2 binary64) (.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64)))
(- 1/4 (/ (* v v) 4))
(+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal -4 binary64)))
1/4
#s(literal 1/4 binary64)
(/ (* v v) 4)
(/.f64 (*.f64 v v) #s(literal 4 binary64))
(* v v)
(*.f64 v v)
v
4
#s(literal 4 binary64)
(pow (+ 2 (* (* v v) -6)) -1/2)
(pow.f64 (-.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64))
(+ 2 (* (* v v) -6))
(-.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal 6 binary64)))
2
#s(literal 2 binary64)
(* (* v v) -6)
(.f64 (.f64 v v) #s(literal -6 binary64))
-6
#s(literal -6 binary64)
-1/2
#s(literal -1/2 binary64)

localize195.0ms (1.8%)

Memory

-4.9MiB live, 232.1MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 v v)
✓	accuracy	100.0%	(pow.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64))
✓	accuracy	99.7%	(.f64 (.f64 v v) #s(literal -6 binary64))
✓	accuracy	98.5%	(/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal 4 binary64))) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal -4 binary64))))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 (.f64 (.f64 v v) #s(literal -6 binary64)) #s(literal 2 binary64)))
✓	accuracy	100.0%	(/.f64 (sqrt.f64 (+.f64 (.f64 (.f64 v v) #s(literal -6 binary64)) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal -4 binary64)))))
✓	accuracy	99.7%	(.f64 (.f64 v v) #s(literal -6 binary64))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 v v) #s(literal -5/8 binary64))))
✓	accuracy	100.0%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 v v) #s(literal -5/8 binary64)))))
✓	accuracy	99.8%	(.f64 (.f64 v v) #s(literal -5/8 binary64))
✓	accuracy	100.0%	(*.f64 v v)
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal -6 binary64))))
✓	accuracy	100.0%	(.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal 4 binary64))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal -6 binary64)))))
✓	accuracy	99.7%	(.f64 (.f64 v v) #s(literal -6 binary64))

Samples

99.0ms

256×

valid

Compiler

Compiled 228 to 31 computations (86.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 57.0ms

ival-div: 34.0ms (60.1% of total)

ival-mult: 7.0ms (12.4% of total)

ival-sqrt: 5.0ms (8.8% of total)

ival-add: 4.0ms (7.1% of total)

ival-pow: 4.0ms (7.1% of total)

ival-sub: 1.0ms (1.8% of total)

exact: 1.0ms (1.8% of total)

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

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

series8.0ms (0.1%)

Memory

16.5MiB live, 16.5MiB allocated

Counts

17 → 192

Calls

Call 1

Inputs
#<alt (* (- 1/4 (/ (* v v) 4)) (sqrt (+ 2 (* (* v v) -6))))>
#<alt (- 1/4 (/ (* v v) 4))>
#<alt (/ (* v v) 4)>
#<alt (* v v)>
#<alt (/ (sqrt 2) (/ 1 (+ 1/4 (* (* v v) -5/8))))>
#<alt (sqrt 2)>
#<alt (/ 1 (+ 1/4 (* (* v v) -5/8)))>
#<alt (+ 1/4 (* (* v v) -5/8))>
#<alt (/ 1 (+ 1/4 (/ (* v v) -4)))>
#<alt (/ (sqrt (+ (* (* v v) -6) 2)) (/ 1 (+ 1/4 (/ (* v v) -4))))>
#<alt (sqrt (+ (* (* v v) -6) 2))>
#<alt (+ (* (* v v) -6) 2)>
#<alt (/ (- 1/4 (/ (* v v) 4)) (pow (+ 2 (* (* v v) -6)) -1/2))>
#<alt (* (* v v) -6)>
#<alt (sqrt (+ 2 (* (* v v) -6)))>
#<alt (* (* v v) -5/8)>
#<alt (pow (+ 2 (* (* v v) -6)) -1/2)>

Outputs
#<alt (* 1/4 (sqrt 2))>
#<alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (* -1/4 (sqrt 2)) (* 3/4 (/ 1 (sqrt 2))))))>
#<alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (+ (* -1/4 (sqrt 2)) (* (pow v 2) (- (* 3/4 (/ 1 (sqrt 2))) (* 9/8 (/ 1 (pow (sqrt 2) 3)))))) (* 3/4 (/ 1 (sqrt 2))))))>
#<alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (+ (* -1/4 (sqrt 2)) (* (pow v 2) (- (+ (* 3/4 (/ 1 (sqrt 2))) (* (pow v 2) (- (* 9/8 (/ 1 (pow (sqrt 2) 3))) (* 27/8 (/ 1 (pow (sqrt 2) 5)))))) (* 9/8 (/ 1 (pow (sqrt 2) 3)))))) (* 3/4 (/ 1 (sqrt 2))))))>
#<alt (* -1/4 (* (pow v 3) (sqrt -6)))>
#<alt (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (* 1/4 (/ (sqrt -6) (pow v 2)))) (/ 1/4 (* (pow v 2) (sqrt -6)))))>
#<alt (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))) (/ 1/4 (* (pow v 2) (sqrt -6)))))>
#<alt (* (pow v 3) (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (pow (sqrt -6) 3))) (* 1/8 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))) (/ 1/4 (* (pow v 2) (sqrt -6)))))>
#<alt (* 1/4 (* (pow v 3) (sqrt -6)))>
#<alt (* -1 (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (* 1/4 (/ (sqrt -6) (pow v 2)))) (/ 1/4 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))) (/ 1/4 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* (pow v 3) (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (pow (sqrt -6) 3))) (* 1/8 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))) (/ 1/4 (* (pow v 2) (sqrt -6))))))>
#<alt 1/4>
#<alt (+ 1/4 (* -1/4 (pow v 2)))>
#<alt (+ 1/4 (* -1/4 (pow v 2)))>
#<alt (+ 1/4 (* -1/4 (pow v 2)))>
#<alt (* -1/4 (pow v 2))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))>
#<alt (* -1/4 (pow v 2))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))>
#<alt (* 1/4 (pow v 2))>
#<alt (* 1/4 (pow v 2))>
#<alt (* 1/4 (pow v 2))>
#<alt (* 1/4 (pow v 2))>
#<alt (* 1/4 (pow v 2))>
#<alt (* 1/4 (pow v 2))>
#<alt (* 1/4 (pow v 2))>
#<alt (* 1/4 (pow v 2))>
#<alt (* 1/4 (pow v 2))>
#<alt (* 1/4 (pow v 2))>
#<alt (* 1/4 (pow v 2))>
#<alt (* 1/4 (pow v 2))>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (* 1/4 (sqrt 2))>
#<alt (+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))>
#<alt (+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))>
#<alt (+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))>
#<alt (* -5/8 (* (pow v 2) (sqrt 2)))>
#<alt (* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt (* -5/8 (* (pow v 2) (sqrt 2)))>
#<alt (* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))>
#<alt 4>
#<alt (+ 4 (* 10 (pow v 2)))>
#<alt (+ 4 (* (pow v 2) (+ 10 (* 25 (pow v 2)))))>
#<alt (+ 4 (* (pow v 2) (+ 10 (* (pow v 2) (+ 25 (* 125/2 (pow v 2)))))))>
#<alt (/ -8/5 (pow v 2))>
#<alt (* -1 (/ (+ 8/5 (* 16/25 (/ 1 (pow v 2)))) (pow v 2)))>
#<alt (/ (- (* -1 (/ (+ 16/25 (* 32/125 (/ 1 (pow v 2)))) (pow v 2))) 8/5) (pow v 2))>
#<alt (/ (- (* -1 (/ (+ 32/125 (* 64/625 (/ 1 (pow v 2)))) (pow v 4))) (+ 8/5 (* 16/25 (/ 1 (pow v 2))))) (pow v 2))>
#<alt (/ -8/5 (pow v 2))>
#<alt (* -1 (/ (+ 8/5 (* 16/25 (/ 1 (pow v 2)))) (pow v 2)))>
#<alt (/ (- (* -1 (/ (+ 16/25 (* 32/125 (/ 1 (pow v 2)))) (pow v 2))) 8/5) (pow v 2))>
#<alt (/ (- (* -1 (/ (+ 32/125 (* 64/625 (/ 1 (pow v 2)))) (pow v 4))) (+ 8/5 (* 16/25 (/ 1 (pow v 2))))) (pow v 2))>
#<alt 1/4>
#<alt (+ 1/4 (* -5/8 (pow v 2)))>
#<alt (+ 1/4 (* -5/8 (pow v 2)))>
#<alt (+ 1/4 (* -5/8 (pow v 2)))>
#<alt (* -5/8 (pow v 2))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))>
#<alt (* -5/8 (pow v 2))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))>
#<alt 4>
#<alt (+ 4 (* 4 (pow v 2)))>
#<alt (+ 4 (* (pow v 2) (+ 4 (* 4 (pow v 2)))))>
#<alt (+ 4 (* (pow v 2) (+ 4 (* (pow v 2) (+ 4 (* 4 (pow v 2)))))))>
#<alt (/ -4 (pow v 2))>
#<alt (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 2)))>
#<alt (/ (- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 2))) 4) (pow v 2))>
#<alt (/ (- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 4))) (+ 4 (* 4 (/ 1 (pow v 2))))) (pow v 2))>
#<alt (/ -4 (pow v 2))>
#<alt (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 2)))>
#<alt (/ (- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 2))) 4) (pow v 2))>
#<alt (/ (- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 4))) (+ 4 (* 4 (/ 1 (pow v 2))))) (pow v 2))>
#<alt (* 1/4 (sqrt 2))>
#<alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (* -1/4 (sqrt 2)) (* 3/4 (/ 1 (sqrt 2))))))>
#<alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (+ (* -1/4 (sqrt 2)) (* (pow v 2) (- (* 3/4 (/ 1 (sqrt 2))) (* 9/8 (/ 1 (pow (sqrt 2) 3)))))) (* 3/4 (/ 1 (sqrt 2))))))>
#<alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (+ (* -1/4 (sqrt 2)) (* (pow v 2) (- (+ (* 3/4 (/ 1 (sqrt 2))) (* (pow v 2) (- (* 9/8 (/ 1 (pow (sqrt 2) 3))) (* 27/8 (/ 1 (pow (sqrt 2) 5)))))) (* 9/8 (/ 1 (pow (sqrt 2) 3)))))) (* 3/4 (/ 1 (sqrt 2))))))>
#<alt (* -1/4 (* (pow v 3) (sqrt -6)))>
#<alt (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (* 1/4 (/ (sqrt -6) (pow v 2)))) (/ 1/4 (* (pow v 2) (sqrt -6)))))>
#<alt (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))) (/ 1/4 (* (pow v 2) (sqrt -6)))))>
#<alt (* (pow v 3) (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (pow (sqrt -6) 3))) (* 1/8 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))) (/ 1/4 (* (pow v 2) (sqrt -6)))))>
#<alt (* 1/4 (* (pow v 3) (sqrt -6)))>
#<alt (* -1 (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (* 1/4 (/ (sqrt -6) (pow v 2)))) (/ 1/4 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))) (/ 1/4 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* (pow v 3) (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (pow (sqrt -6) 3))) (* 1/8 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))) (/ 1/4 (* (pow v 2) (sqrt -6))))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (* v (sqrt -6))>
#<alt (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))>
#<alt (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))>
#<alt (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (sqrt -6)))>
#<alt (* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))>
#<alt 2>
#<alt (+ 2 (* -6 (pow v 2)))>
#<alt (+ 2 (* -6 (pow v 2)))>
#<alt (+ 2 (* -6 (pow v 2)))>
#<alt (* -6 (pow v 2))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* -6 (pow v 2))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* 1/4 (sqrt 2))>
#<alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (* -1/4 (sqrt 2)) (* 3/4 (/ 1 (sqrt 2))))))>
#<alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (+ (* -1/4 (sqrt 2)) (* (pow v 2) (- (* 3/4 (/ 1 (sqrt 2))) (* 9/8 (/ 1 (pow (sqrt 2) 3)))))) (* 3/4 (/ 1 (sqrt 2))))))>
#<alt (+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (+ (* -1/4 (sqrt 2)) (* (pow v 2) (- (+ (* 3/4 (/ 1 (sqrt 2))) (* (pow v 2) (- (* 9/8 (/ 1 (pow (sqrt 2) 3))) (* 27/8 (/ 1 (pow (sqrt 2) 5)))))) (* 9/8 (/ 1 (pow (sqrt 2) 3)))))) (* 3/4 (/ 1 (sqrt 2))))))>
#<alt (* -1/4 (* (pow v 3) (sqrt -6)))>
#<alt (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (* 1/4 (/ (sqrt -6) (pow v 2)))) (/ 1/4 (* (pow v 2) (sqrt -6)))))>
#<alt (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))) (/ 1/4 (* (pow v 2) (sqrt -6)))))>
#<alt (* (pow v 3) (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (pow (sqrt -6) 3))) (* 1/8 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))) (/ 1/4 (* (pow v 2) (sqrt -6)))))>
#<alt (* 1/4 (* (pow v 3) (sqrt -6)))>
#<alt (* -1 (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (* 1/4 (/ (sqrt -6) (pow v 2)))) (/ 1/4 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))) (/ 1/4 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* (pow v 3) (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (pow (sqrt -6) 3))) (* 1/8 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))) (/ 1/4 (* (pow v 2) (sqrt -6))))))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (* v (sqrt -6))>
#<alt (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))>
#<alt (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))>
#<alt (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (sqrt -6)))>
#<alt (* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (* -5/8 (pow v 2))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 3/4 (/ (pow v 2) (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* (pow v 2) (+ (* 1/2 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 3/4 (/ 1 (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (* (pow v 2) (+ (* (pow v 2) (+ (* 1/2 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2))))) (* 3/4 (/ 1 (sqrt 1/2))))))>
#<alt (/ (sqrt -1/6) v)>
#<alt (/ (- (sqrt -1/6) (* 1/36 (/ 1 (* (pow v 2) (sqrt -1/6))))) v)>
#<alt (/ (- (+ (sqrt -1/6) (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6))))) (/ 1/36 (* (pow v 2) (sqrt -1/6)))) v)>
#<alt (/ (- (+ (sqrt -1/6) (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (sqrt -1/6)))) (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6)))))) (/ 1/36 (* (pow v 2) (sqrt -1/6)))) v)>
#<alt (* -1 (/ (sqrt -1/6) v))>
#<alt (* -1 (/ (- (sqrt -1/6) (* 1/36 (/ 1 (* (pow v 2) (sqrt -1/6))))) v))>
#<alt (* -1 (/ (- (+ (sqrt -1/6) (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6))))) (/ 1/36 (* (pow v 2) (sqrt -1/6)))) v))>
#<alt (* -1 (/ (- (+ (sqrt -1/6) (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (sqrt -1/6)))) (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6)))))) (/ 1/36 (* (pow v 2) (sqrt -1/6)))) v))>

Calls

48 calls:

Time	Variable		Point	Expression
1.0ms	v	@	inf	(pow (+ 2 (* (* v v) -6)) -1/2)
1.0ms	v	@	0	(pow (+ 2 (* (* v v) -6)) -1/2)
0.0ms	v	@	inf	(/ (* v v) 4)
0.0ms	v	@	0	(* (- 1/4 (/ (* v v) 4)) (sqrt (+ 2 (* (* v v) -6))))
0.0ms	v	@	inf	(/ 1 (+ 1/4 (* (* v v) -5/8)))

rewrite464.0ms (4.4%)

Memory

-0.1MiB live, 924.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 964×	`accelerator-lowering-fma.f32`
4 964×	`accelerator-lowering-fma.f64`
4 068×	`/-lowering-/.f32`
4 068×	`/-lowering-/.f64`
3 778×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	144
1	171	142
2	1273	142
0	8528	127

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 1 014

Calls

Call 1

Inputs
(* (- 1/4 (/ (* v v) 4)) (sqrt (+ 2 (* (* v v) -6))))
(- 1/4 (/ (* v v) 4))
(/ (* v v) 4)
(* v v)
(/ (sqrt 2) (/ 1 (+ 1/4 (* (* v v) -5/8))))
(sqrt 2)
(/ 1 (+ 1/4 (* (* v v) -5/8)))
(+ 1/4 (* (* v v) -5/8))
(/ 1 (+ 1/4 (/ (* v v) -4)))
(/ (sqrt (+ (* (* v v) -6) 2)) (/ 1 (+ 1/4 (/ (* v v) -4))))
(sqrt (+ (* (* v v) -6) 2))
(+ (* (* v v) -6) 2)
(/ (- 1/4 (/ (* v v) 4)) (pow (+ 2 (* (* v v) -6)) -1/2))
(* (* v v) -6)
(sqrt (+ 2 (* (* v v) -6)))
(* (* v v) -5/8)
(pow (+ 2 (* (* v v) -6)) -1/2)

Outputs
(+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 v (/.f64 #s(literal 4 binary64) v)) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)))))
(+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))) (/.f64 (/.f64 (.f64 v v) #s(literal -4 binary64)) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))))
(+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))) (.f64 (-.f64 #s(literal 0 binary64) v) (/.f64 (/.f64 v #s(literal 4 binary64)) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)))))
(+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))) (.f64 (-.f64 #s(literal 0 binary64) (.f64 v v)) (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)))))
(+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))) (.f64 (neg.f64 (/.f64 v (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/4 binary64)))) (/.f64 (/.f64 v #s(literal 4 binary64)) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/4 binary64)))))
(+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))) (.f64 (neg.f64 (/.f64 (.f64 v v) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/4 binary64)))) (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/4 binary64)))))
(+.f64 (.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64))))) #s(literal 1/4 binary64)) (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64))))) (/.f64 #s(literal -4 binary64) (.f64 v v))))
(+.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64))))) (/.f64 #s(literal -4 binary64) (.f64 v v))) (.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64))))) #s(literal 1/4 binary64)))
(+.f64 (/.f64 (/.f64 (.f64 v v) #s(literal -4 binary64)) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal -4 binary64))))) #s(literal -1 binary64)))
(exp.f64 (-.f64 (.f64 (log.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64))))) #s(literal 1/2 binary64)) (.f64 (log.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal -4 binary64)))) #s(literal -1 binary64))))
(exp.f64 (-.f64 (-.f64 #s(literal 0 binary64) (.f64 #s(literal -1/2 binary64) (log.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64))))))) (.f64 (log.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal -4 binary64)))) #s(literal -1 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 (+.f64 (/.f64 v (/.f64 #s(literal 4 binary64) v)) #s(literal -1/4 binary64)) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))))
(-.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))) (/.f64 (/.f64 v (/.f64 #s(literal 4 binary64) v)) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)))) (/.f64 (+.f64 (/.f64 v (/.f64 #s(literal 4 binary64) v)) #s(literal -1/4 binary64)) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))))
(-.f64 (/.f64 (/.f64 #s(literal 1/64 binary64) (+.f64 #s(literal 1/16 binary64) (/.f64 (+.f64 (/.f64 (.f64 v v) #s(literal -4 binary64)) #s(literal -1/4 binary64)) (/.f64 #s(literal -4 binary64) (.f64 v v))))) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))) (/.f64 (/.f64 (/.f64 (.f64 (.f64 v v) (.f64 (.f64 v v) (.f64 v v))) #s(literal 64 binary64)) (+.f64 #s(literal 1/16 binary64) (/.f64 (+.f64 (/.f64 (.f64 v v) #s(literal -4 binary64)) #s(literal -1/4 binary64)) (/.f64 #s(literal -4 binary64) (.f64 v v))))) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))))
(-.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (+.f64 #s(literal 1/4 binary64) (/.f64 v (/.f64 #s(literal 4 binary64) v)))) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))) (/.f64 (.f64 (/.f64 (.f64 (.f64 v v) (.f64 v v)) (+.f64 (.f64 v v) #s(literal 1 binary64))) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))))
(-.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))) #s(literal 1 binary64)) (/.f64 (/.f64 (/.f64 v (/.f64 #s(literal 4 binary64) v)) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 v (/.f64 #s(literal 4 binary64) v)) #s(literal -1/4 binary64)))) (/.f64 (+.f64 (/.f64 v (/.f64 #s(literal 4 binary64) v)) #s(literal -1/4 binary64)) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))))
(-.f64 (/.f64 #s(literal 1/64 binary64) (.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (+.f64 #s(literal 1/16 binary64) (/.f64 (+.f64 (/.f64 (.f64 v v) #s(literal -4 binary64)) #s(literal -1/4 binary64)) (/.f64 #s(literal -4 binary64) (.f64 v v)))))) (/.f64 (/.f64 (.f64 (.f64 v v) (.f64 (.f64 v v) (.f64 v v))) #s(literal 64 binary64)) (.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (+.f64 #s(literal 1/16 binary64) (/.f64 (+.f64 (/.f64 (.f64 v v) #s(literal -4 binary64)) #s(literal -1/4 binary64)) (/.f64 #s(literal -4 binary64) (*.f64 v v)))))))
(-.f64 (/.f64 #s(literal 1/16 binary64) (.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (+.f64 #s(literal 1/4 binary64) (/.f64 v (/.f64 #s(literal 4 binary64) v))))) (/.f64 (.f64 (.f64 v v) (.f64 (.f64 v v) #s(literal 1/16 binary64))) (.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (+.f64 #s(literal 1/4 binary64) (/.f64 v (/.f64 #s(literal 4 binary64) v))))))
(-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1 binary64))) (/.f64 (.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (/.f64 v (/.f64 #s(literal 4 binary64) v))) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1 binary64))))
(-.f64 (/.f64 (/.f64 #s(literal 1/64 binary64) (pow.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (/.f64 v (/.f64 #s(literal 4 binary64) v)) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))) #s(literal 2 binary64)) (/.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))) (/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (/.f64 v (/.f64 #s(literal 4 binary64) v))))))) (/.f64 (pow.f64 (/.f64 (/.f64 v (/.f64 #s(literal 4 binary64) v)) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))) #s(literal 3 binary64)) (+.f64 (pow.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (/.f64 v (/.f64 #s(literal 4 binary64) v)) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))) #s(literal 2 binary64)) (/.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))) (/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (/.f64 v (/.f64 #s(literal 4 binary64) v))))))))
(-.f64 (/.f64 (pow.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))) #s(literal 2 binary64)) (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))) (/.f64 (/.f64 v (/.f64 #s(literal 4 binary64) v)) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))))) (/.f64 (pow.f64 (/.f64 (/.f64 v (/.f64 #s(literal 4 binary64) v)) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))) #s(literal 2 binary64)) (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))) (/.f64 (/.f64 v (/.f64 #s(literal 4 binary64) v)) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))))))
(fma.f64 #s(literal 1/4 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64))))) (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 v (/.f64 #s(literal 4 binary64) v)) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)))))
(fma.f64 #s(literal 1/4 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64))))) (/.f64 (/.f64 (.f64 v v) #s(literal -4 binary64)) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))))
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(.f64 (sqrt.f64 (+.f64 (.f64 (.f64 v v) (.f64 (.f64 v v) #s(literal 36 binary64))) #s(literal -4 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 v (*.f64 v #s(literal -6 binary64))) #s(literal -2 binary64))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (+.f64 (.f64 (.f64 v v) (.f64 (.f64 v v) #s(literal 36 binary64))) #s(literal -4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 v (*.f64 v #s(literal -6 binary64))) #s(literal -2 binary64)))))
(.f64 (sqrt.f64 (+.f64 (.f64 (.f64 v v) (.f64 (.f64 v v) #s(literal 36 binary64))) #s(literal -4 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (.f64 v (*.f64 v #s(literal -6 binary64))) #s(literal -2 binary64)))))
(.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 v v) (.f64 (.f64 v v) #s(literal 36 binary64))))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (.f64 v (*.f64 v #s(literal -6 binary64))))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 v v) (.f64 (.f64 v v) #s(literal 36 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (.f64 v (*.f64 v #s(literal -6 binary64)))))))
(.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 v v) (.f64 (.f64 v v) #s(literal 36 binary64))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 v (*.f64 v #s(literal -6 binary64)))))))
(.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)))
(.f64 v (.f64 v #s(literal -5/8 binary64)))
(.f64 (.f64 v v) #s(literal -5/8 binary64))
(.f64 #s(literal -5/8 binary64) (.f64 v v))
(.f64 (.f64 v #s(literal -5/8 binary64)) v)
(exp.f64 (.f64 #s(literal -1/2 binary64) (log.f64 (+.f64 #s(literal 2 binary64) (.f64 v (*.f64 v #s(literal -6 binary64)))))))
(exp.f64 (.f64 (log.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))))) #s(literal -1/4 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64))))) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (.f64 (log.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64))))) #s(literal -1/4 binary64)) (.f64 (log.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64))))) #s(literal -1/4 binary64))))
(exp.f64 (neg.f64 (.f64 (log.f64 (+.f64 #s(literal 2 binary64) (.f64 v (*.f64 v #s(literal -6 binary64))))) #s(literal 1/2 binary64))))
(exp.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 #s(literal -1/2 binary64) (log.f64 (+.f64 #s(literal 2 binary64) (.f64 v (*.f64 v #s(literal -6 binary64)))))))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))))
(neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64))))))
(/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))) #s(literal -1 binary64))
(pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64))))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) (+.f64 #s(literal 2 binary64) (.f64 v (*.f64 v #s(literal -6 binary64))))) #s(literal -1/4 binary64))
(pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64))))))
(.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))))
(.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/4 binary64)) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/4 binary64)))
(.f64 (pow.f64 (+.f64 (.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal -216 binary64))) #s(literal 8 binary64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 v v) (.f64 (.f64 v v) #s(literal 36 binary64))) (-.f64 #s(literal 4 binary64) (.f64 (*.f64 v v) #s(literal -12 binary64))))) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (+.f64 (.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal -216 binary64))) #s(literal 8 binary64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (.f64 (.f64 v (.f64 v #s(literal -6 binary64))) (+.f64 (.f64 v (.f64 v #s(literal -6 binary64))) #s(literal -2 binary64))))) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (+.f64 (.f64 (.f64 v v) (.f64 (.f64 v v) #s(literal 36 binary64))) #s(literal -4 binary64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 v (*.f64 v #s(literal -6 binary64))) #s(literal -2 binary64))) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 v v) (.f64 (.f64 v v) #s(literal 36 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (.f64 v (*.f64 v #s(literal -6 binary64))))) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64)))) #s(literal -1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/4 binary64)) #s(literal 1 binary64)))

simplify436.0ms (4.1%)

Memory

-7.0MiB live, 944.5MiB allocated

Algorithm

1×	egg-herbie

Rules

9 600×	`accelerator-lowering-fma.f32`
9 600×	`accelerator-lowering-fma.f64`
5 024×	`-lowering-.f32`
5 024×	`-lowering-.f64`
3 252×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	277	2946
1	769	2767
2	2380	2711
3	7179	2708
0	8077	2599

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

Calls

Call 1

Inputs
(* 1/4 (sqrt 2))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (* -1/4 (sqrt 2)) (* 3/4 (/ 1 (sqrt 2))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (+ (* -1/4 (sqrt 2)) (* (pow v 2) (- (* 3/4 (/ 1 (sqrt 2))) (* 9/8 (/ 1 (pow (sqrt 2) 3)))))) (* 3/4 (/ 1 (sqrt 2))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (+ (* -1/4 (sqrt 2)) (* (pow v 2) (- (+ (* 3/4 (/ 1 (sqrt 2))) (* (pow v 2) (- (* 9/8 (/ 1 (pow (sqrt 2) 3))) (* 27/8 (/ 1 (pow (sqrt 2) 5)))))) (* 9/8 (/ 1 (pow (sqrt 2) 3)))))) (* 3/4 (/ 1 (sqrt 2))))))
(* -1/4 (* (pow v 3) (sqrt -6)))
(* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (* 1/4 (/ (sqrt -6) (pow v 2)))) (/ 1/4 (* (pow v 2) (sqrt -6)))))
(* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))) (/ 1/4 (* (pow v 2) (sqrt -6)))))
(* (pow v 3) (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (pow (sqrt -6) 3))) (* 1/8 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))) (/ 1/4 (* (pow v 2) (sqrt -6)))))
(* 1/4 (* (pow v 3) (sqrt -6)))
(* -1 (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (* 1/4 (/ (sqrt -6) (pow v 2)))) (/ 1/4 (* (pow v 2) (sqrt -6))))))
(* -1 (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))) (/ 1/4 (* (pow v 2) (sqrt -6))))))
(* -1 (* (pow v 3) (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (pow (sqrt -6) 3))) (* 1/8 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))) (/ 1/4 (* (pow v 2) (sqrt -6))))))
1/4
(+ 1/4 (* -1/4 (pow v 2)))
(+ 1/4 (* -1/4 (pow v 2)))
(+ 1/4 (* -1/4 (pow v 2)))
(* -1/4 (pow v 2))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))
(* -1/4 (pow v 2))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))
(* 1/4 (pow v 2))
(* 1/4 (pow v 2))
(* 1/4 (pow v 2))
(* 1/4 (pow v 2))
(* 1/4 (pow v 2))
(* 1/4 (pow v 2))
(* 1/4 (pow v 2))
(* 1/4 (pow v 2))
(* 1/4 (pow v 2))
(* 1/4 (pow v 2))
(* 1/4 (pow v 2))
(* 1/4 (pow v 2))
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(* 1/4 (sqrt 2))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(* -5/8 (* (pow v 2) (sqrt 2)))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* -5/8 (* (pow v 2) (sqrt 2)))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
4
(+ 4 (* 10 (pow v 2)))
(+ 4 (* (pow v 2) (+ 10 (* 25 (pow v 2)))))
(+ 4 (* (pow v 2) (+ 10 (* (pow v 2) (+ 25 (* 125/2 (pow v 2)))))))
(/ -8/5 (pow v 2))
(* -1 (/ (+ 8/5 (* 16/25 (/ 1 (pow v 2)))) (pow v 2)))
(/ (- (* -1 (/ (+ 16/25 (* 32/125 (/ 1 (pow v 2)))) (pow v 2))) 8/5) (pow v 2))
(/ (- (* -1 (/ (+ 32/125 (* 64/625 (/ 1 (pow v 2)))) (pow v 4))) (+ 8/5 (* 16/25 (/ 1 (pow v 2))))) (pow v 2))
(/ -8/5 (pow v 2))
(* -1 (/ (+ 8/5 (* 16/25 (/ 1 (pow v 2)))) (pow v 2)))
(/ (- (* -1 (/ (+ 16/25 (* 32/125 (/ 1 (pow v 2)))) (pow v 2))) 8/5) (pow v 2))
(/ (- (* -1 (/ (+ 32/125 (* 64/625 (/ 1 (pow v 2)))) (pow v 4))) (+ 8/5 (* 16/25 (/ 1 (pow v 2))))) (pow v 2))
1/4
(+ 1/4 (* -5/8 (pow v 2)))
(+ 1/4 (* -5/8 (pow v 2)))
(+ 1/4 (* -5/8 (pow v 2)))
(* -5/8 (pow v 2))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(* -5/8 (pow v 2))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
4
(+ 4 (* 4 (pow v 2)))
(+ 4 (* (pow v 2) (+ 4 (* 4 (pow v 2)))))
(+ 4 (* (pow v 2) (+ 4 (* (pow v 2) (+ 4 (* 4 (pow v 2)))))))
(/ -4 (pow v 2))
(* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 2)))
(/ (- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 2))) 4) (pow v 2))
(/ (- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 4))) (+ 4 (* 4 (/ 1 (pow v 2))))) (pow v 2))
(/ -4 (pow v 2))
(* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 2)))
(/ (- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 2))) 4) (pow v 2))
(/ (- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 4))) (+ 4 (* 4 (/ 1 (pow v 2))))) (pow v 2))
(* 1/4 (sqrt 2))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (* -1/4 (sqrt 2)) (* 3/4 (/ 1 (sqrt 2))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (+ (* -1/4 (sqrt 2)) (* (pow v 2) (- (* 3/4 (/ 1 (sqrt 2))) (* 9/8 (/ 1 (pow (sqrt 2) 3)))))) (* 3/4 (/ 1 (sqrt 2))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (+ (* -1/4 (sqrt 2)) (* (pow v 2) (- (+ (* 3/4 (/ 1 (sqrt 2))) (* (pow v 2) (- (* 9/8 (/ 1 (pow (sqrt 2) 3))) (* 27/8 (/ 1 (pow (sqrt 2) 5)))))) (* 9/8 (/ 1 (pow (sqrt 2) 3)))))) (* 3/4 (/ 1 (sqrt 2))))))
(* -1/4 (* (pow v 3) (sqrt -6)))
(* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (* 1/4 (/ (sqrt -6) (pow v 2)))) (/ 1/4 (* (pow v 2) (sqrt -6)))))
(* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))) (/ 1/4 (* (pow v 2) (sqrt -6)))))
(* (pow v 3) (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (pow (sqrt -6) 3))) (* 1/8 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))) (/ 1/4 (* (pow v 2) (sqrt -6)))))
(* 1/4 (* (pow v 3) (sqrt -6)))
(* -1 (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (* 1/4 (/ (sqrt -6) (pow v 2)))) (/ 1/4 (* (pow v 2) (sqrt -6))))))
(* -1 (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))) (/ 1/4 (* (pow v 2) (sqrt -6))))))
(* -1 (* (pow v 3) (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (pow (sqrt -6) 3))) (* 1/8 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))) (/ 1/4 (* (pow v 2) (sqrt -6))))))
(sqrt 2)
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(* v (sqrt -6))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (sqrt -6)))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))
2
(+ 2 (* -6 (pow v 2)))
(+ 2 (* -6 (pow v 2)))
(+ 2 (* -6 (pow v 2)))
(* -6 (pow v 2))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* -6 (pow v 2))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* 1/4 (sqrt 2))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (* -1/4 (sqrt 2)) (* 3/4 (/ 1 (sqrt 2))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (+ (* -1/4 (sqrt 2)) (* (pow v 2) (- (* 3/4 (/ 1 (sqrt 2))) (* 9/8 (/ 1 (pow (sqrt 2) 3)))))) (* 3/4 (/ 1 (sqrt 2))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (+ (* -1/4 (sqrt 2)) (* (pow v 2) (- (+ (* 3/4 (/ 1 (sqrt 2))) (* (pow v 2) (- (* 9/8 (/ 1 (pow (sqrt 2) 3))) (* 27/8 (/ 1 (pow (sqrt 2) 5)))))) (* 9/8 (/ 1 (pow (sqrt 2) 3)))))) (* 3/4 (/ 1 (sqrt 2))))))
(* -1/4 (* (pow v 3) (sqrt -6)))
(* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (* 1/4 (/ (sqrt -6) (pow v 2)))) (/ 1/4 (* (pow v 2) (sqrt -6)))))
(* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))) (/ 1/4 (* (pow v 2) (sqrt -6)))))
(* (pow v 3) (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (pow (sqrt -6) 3))) (* 1/8 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))) (/ 1/4 (* (pow v 2) (sqrt -6)))))
(* 1/4 (* (pow v 3) (sqrt -6)))
(* -1 (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (* 1/4 (/ (sqrt -6) (pow v 2)))) (/ 1/4 (* (pow v 2) (sqrt -6))))))
(* -1 (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))) (/ 1/4 (* (pow v 2) (sqrt -6))))))
(* -1 (* (pow v 3) (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (pow (sqrt -6) 3))) (* 1/8 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))) (/ 1/4 (* (pow v 2) (sqrt -6))))))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(sqrt 2)
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(* v (sqrt -6))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (sqrt -6)))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(* -5/8 (pow v 2))
(sqrt 1/2)
(+ (sqrt 1/2) (* 3/4 (/ (pow v 2) (sqrt 1/2))))
(+ (sqrt 1/2) (* (pow v 2) (+ (* 1/2 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 3/4 (/ 1 (sqrt 1/2))))))
(+ (sqrt 1/2) (* (pow v 2) (+ (* (pow v 2) (+ (* 1/2 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2))))) (* 3/4 (/ 1 (sqrt 1/2))))))
(/ (sqrt -1/6) v)
(/ (- (sqrt -1/6) (* 1/36 (/ 1 (* (pow v 2) (sqrt -1/6))))) v)
(/ (- (+ (sqrt -1/6) (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6))))) (/ 1/36 (* (pow v 2) (sqrt -1/6)))) v)
(/ (- (+ (sqrt -1/6) (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (sqrt -1/6)))) (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6)))))) (/ 1/36 (* (pow v 2) (sqrt -1/6)))) v)
(* -1 (/ (sqrt -1/6) v))
(* -1 (/ (- (sqrt -1/6) (* 1/36 (/ 1 (* (pow v 2) (sqrt -1/6))))) v))
(* -1 (/ (- (+ (sqrt -1/6) (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6))))) (/ 1/36 (* (pow v 2) (sqrt -1/6)))) v))
(* -1 (/ (- (+ (sqrt -1/6) (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (sqrt -1/6)))) (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6)))))) (/ 1/36 (* (pow v 2) (sqrt -1/6)))) v))

Outputs
(* 1/4 (sqrt 2))
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (* -1/4 (sqrt 2)) (* 3/4 (/ 1 (sqrt 2))))))
(+.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 v (.f64 v (+.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/4 binary64)) (/.f64 #s(literal -3/4 binary64) (sqrt.f64 #s(literal 2 binary64)))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (+ (* -1/4 (sqrt 2)) (* (pow v 2) (- (* 3/4 (/ 1 (sqrt 2))) (* 9/8 (/ 1 (pow (sqrt 2) 3)))))) (* 3/4 (/ 1 (sqrt 2))))))
(+.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 v v) (+.f64 (+.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/4 binary64)) (/.f64 #s(literal -3/4 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (.f64 v v) (-.f64 (/.f64 #s(literal 3/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 9/16 binary64) (sqrt.f64 #s(literal 2 binary64))))))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (- (+ (* -1/4 (sqrt 2)) (* (pow v 2) (- (+ (* 3/4 (/ 1 (sqrt 2))) (* (pow v 2) (- (* 9/8 (/ 1 (pow (sqrt 2) 3))) (* 27/8 (/ 1 (pow (sqrt 2) 5)))))) (* 9/8 (/ 1 (pow (sqrt 2) 3)))))) (* 3/4 (/ 1 (sqrt 2))))))
(+.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 v v) (+.f64 (+.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/4 binary64)) (/.f64 #s(literal -3/4 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (.f64 v v) (+.f64 (/.f64 #s(literal 3/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (.f64 (.f64 v v) (+.f64 (/.f64 #s(literal 9/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -27/8 binary64) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))))) (/.f64 #s(literal -9/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))))))
(* -1/4 (* (pow v 3) (sqrt -6)))
(.f64 v (.f64 (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64)))) #s(literal -1/4 binary64)))
(* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (* 1/4 (/ (sqrt -6) (pow v 2)))) (/ 1/4 (* (pow v 2) (sqrt -6)))))
(.f64 (.f64 v (.f64 v v)) (+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (.f64 v v)) (-.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 #s(literal 1/4 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64))))))))
(* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))) (/ 1/4 (* (pow v 2) (sqrt -6)))))
(.f64 v (.f64 (.f64 v v) (+.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (+.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (.f64 v (.f64 v (.f64 v v)))) (+.f64 (/.f64 (/.f64 #s(literal -1/48 binary64) (sqrt.f64 #s(literal -6 binary64))) (.f64 v (.f64 v (.f64 v v)))) (+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (.f64 v v)) (/.f64 #s(literal -1/4 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64)))))))))))
(* (pow v 3) (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (pow (sqrt -6) 3))) (* 1/8 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))) (/ 1/4 (* (pow v 2) (sqrt -6)))))
(.f64 (.f64 v (.f64 v v)) (+.f64 (+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (.f64 v v)) (-.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 #s(literal 1/4 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64))))))) (+.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (.f64 v (.f64 v (.f64 v v)))) (/.f64 (/.f64 #s(literal -1/48 binary64) (sqrt.f64 #s(literal -6 binary64))) (.f64 v (.f64 v (.f64 v v))))) (/.f64 (+.f64 (/.f64 #s(literal 1/48 binary64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))) (pow.f64 v #s(literal 6 binary64))))))
(* 1/4 (* (pow v 3) (sqrt -6)))
(.f64 #s(literal 1/4 binary64) (.f64 v (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64))))))
(* -1 (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (* 1/4 (/ (sqrt -6) (pow v 2)))) (/ 1/4 (* (pow v 2) (sqrt -6))))))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 v (.f64 v v)) (+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (.f64 v v)) (-.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 #s(literal 1/4 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64)))))))))
(* -1 (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))) (/ 1/4 (* (pow v 2) (sqrt -6))))))
(.f64 (.f64 v (.f64 v v)) (-.f64 (-.f64 #s(literal 0 binary64) (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -6 binary64)))) (+.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (.f64 v (.f64 v (.f64 v v)))) (+.f64 (/.f64 (/.f64 #s(literal -1/48 binary64) (sqrt.f64 #s(literal -6 binary64))) (.f64 v (.f64 v (.f64 v v)))) (+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (.f64 v v)) (/.f64 #s(literal -1/4 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64))))))))))
(* -1 (* (pow v 3) (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (pow (sqrt -6) 3))) (* 1/8 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))) (/ 1/4 (* (pow v 2) (sqrt -6))))))
(.f64 (+.f64 (+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (.f64 v v)) (-.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 #s(literal 1/4 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64))))))) (+.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (.f64 v (.f64 v (.f64 v v)))) (/.f64 (/.f64 #s(literal -1/48 binary64) (sqrt.f64 #s(literal -6 binary64))) (.f64 v (.f64 v (.f64 v v))))) (/.f64 (+.f64 (/.f64 #s(literal 1/48 binary64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))) (pow.f64 v #s(literal 6 binary64))))) (-.f64 #s(literal 0 binary64) (.f64 v (.f64 v v))))
1/4
#s(literal 1/4 binary64)
(+ 1/4 (* -1/4 (pow v 2)))
(+.f64 #s(literal 1/4 binary64) (.f64 (.f64 v v) #s(literal -1/4 binary64)))
(+ 1/4 (* -1/4 (pow v 2)))
(+.f64 #s(literal 1/4 binary64) (.f64 (.f64 v v) #s(literal -1/4 binary64)))
(+ 1/4 (* -1/4 (pow v 2)))
(+.f64 #s(literal 1/4 binary64) (.f64 (.f64 v v) #s(literal -1/4 binary64)))
(* -1/4 (pow v 2))
(.f64 (.f64 v v) #s(literal -1/4 binary64))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))
(.f64 v (.f64 v (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 v v)))))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))
(.f64 v (.f64 v (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 v v)))))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))
(.f64 v (.f64 v (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 v v)))))
(* -1/4 (pow v 2))
(.f64 (.f64 v v) #s(literal -1/4 binary64))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))
(.f64 v (.f64 v (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 v v)))))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))
(.f64 v (.f64 v (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 v v)))))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))
(.f64 v (.f64 v (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 v v)))))
(* 1/4 (pow v 2))
(.f64 #s(literal 1/4 binary64) (.f64 v v))
(* 1/4 (pow v 2))
(.f64 #s(literal 1/4 binary64) (.f64 v v))
(* 1/4 (pow v 2))
(.f64 #s(literal 1/4 binary64) (.f64 v v))
(* 1/4 (pow v 2))
(.f64 #s(literal 1/4 binary64) (.f64 v v))
(* 1/4 (pow v 2))
(.f64 #s(literal 1/4 binary64) (.f64 v v))
(* 1/4 (pow v 2))
(.f64 #s(literal 1/4 binary64) (.f64 v v))
(* 1/4 (pow v 2))
(.f64 #s(literal 1/4 binary64) (.f64 v v))
(* 1/4 (pow v 2))
(.f64 #s(literal 1/4 binary64) (.f64 v v))
(* 1/4 (pow v 2))
(.f64 #s(literal 1/4 binary64) (.f64 v v))
(* 1/4 (pow v 2))
(.f64 #s(literal 1/4 binary64) (.f64 v v))
(* 1/4 (pow v 2))
(.f64 #s(literal 1/4 binary64) (.f64 v v))
(* 1/4 (pow v 2))
(.f64 #s(literal 1/4 binary64) (.f64 v v))
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(* 1/4 (sqrt 2))
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 v (*.f64 v #s(literal -5/8 binary64)))))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 v (*.f64 v #s(literal -5/8 binary64)))))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 v (*.f64 v #s(literal -5/8 binary64)))))
(* -5/8 (* (pow v 2) (sqrt 2)))
(.f64 v (.f64 v (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -5/8 binary64))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(.f64 (.f64 v v) (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 v v)) #s(literal -5/8 binary64))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(.f64 (.f64 v v) (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 v v)) #s(literal -5/8 binary64))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(.f64 (.f64 v v) (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 v v)) #s(literal -5/8 binary64))))
(* -5/8 (* (pow v 2) (sqrt 2)))
(.f64 v (.f64 v (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -5/8 binary64))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(.f64 (.f64 v v) (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 v v)) #s(literal -5/8 binary64))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(.f64 (.f64 v v) (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 v v)) #s(literal -5/8 binary64))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(.f64 (.f64 v v) (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 v v)) #s(literal -5/8 binary64))))
4
#s(literal 4 binary64)
(+ 4 (* 10 (pow v 2)))
(+.f64 #s(literal 4 binary64) (.f64 (.f64 v v) #s(literal 10 binary64)))
(+ 4 (* (pow v 2) (+ 10 (* 25 (pow v 2)))))
(+.f64 #s(literal 4 binary64) (.f64 (.f64 v v) (+.f64 #s(literal 10 binary64) (.f64 (.f64 v v) #s(literal 25 binary64)))))
(+ 4 (* (pow v 2) (+ 10 (* (pow v 2) (+ 25 (* 125/2 (pow v 2)))))))
(+.f64 #s(literal 4 binary64) (.f64 (.f64 v v) (+.f64 #s(literal 10 binary64) (.f64 (.f64 v v) (+.f64 #s(literal 25 binary64) (.f64 (.f64 v v) #s(literal 125/2 binary64)))))))
(/ -8/5 (pow v 2))
(/.f64 #s(literal -8/5 binary64) (*.f64 v v))
(* -1 (/ (+ 8/5 (* 16/25 (/ 1 (pow v 2)))) (pow v 2)))
(/.f64 (+.f64 #s(literal -8/5 binary64) (/.f64 #s(literal -16/25 binary64) (.f64 v v))) (.f64 v v))
(/ (- (* -1 (/ (+ 16/25 (* 32/125 (/ 1 (pow v 2)))) (pow v 2))) 8/5) (pow v 2))
(/.f64 (+.f64 #s(literal -8/5 binary64) (/.f64 (+.f64 #s(literal -16/25 binary64) (/.f64 #s(literal -32/125 binary64) (.f64 v v))) (.f64 v v))) (*.f64 v v))
(/ (- (* -1 (/ (+ 32/125 (* 64/625 (/ 1 (pow v 2)))) (pow v 4))) (+ 8/5 (* 16/25 (/ 1 (pow v 2))))) (pow v 2))
(/.f64 (-.f64 (+.f64 #s(literal -8/5 binary64) (/.f64 #s(literal -16/25 binary64) (.f64 v v))) (/.f64 (+.f64 #s(literal 32/125 binary64) (/.f64 #s(literal 64/625 binary64) (.f64 v v))) (.f64 v (.f64 v (.f64 v v))))) (.f64 v v))
(/ -8/5 (pow v 2))
(/.f64 #s(literal -8/5 binary64) (*.f64 v v))
(* -1 (/ (+ 8/5 (* 16/25 (/ 1 (pow v 2)))) (pow v 2)))
(/.f64 (+.f64 #s(literal -8/5 binary64) (/.f64 #s(literal -16/25 binary64) (.f64 v v))) (.f64 v v))
(/ (- (* -1 (/ (+ 16/25 (* 32/125 (/ 1 (pow v 2)))) (pow v 2))) 8/5) (pow v 2))
(/.f64 (+.f64 #s(literal -8/5 binary64) (/.f64 (+.f64 #s(literal -16/25 binary64) (/.f64 #s(literal -32/125 binary64) (.f64 v v))) (.f64 v v))) (*.f64 v v))
(/ (- (* -1 (/ (+ 32/125 (* 64/625 (/ 1 (pow v 2)))) (pow v 4))) (+ 8/5 (* 16/25 (/ 1 (pow v 2))))) (pow v 2))
(/.f64 (-.f64 (+.f64 #s(literal -8/5 binary64) (/.f64 #s(literal -16/25 binary64) (.f64 v v))) (/.f64 (+.f64 #s(literal 32/125 binary64) (/.f64 #s(literal 64/625 binary64) (.f64 v v))) (.f64 v (.f64 v (.f64 v v))))) (.f64 v v))
1/4
#s(literal 1/4 binary64)
(+ 1/4 (* -5/8 (pow v 2)))
(+.f64 #s(literal 1/4 binary64) (.f64 v (.f64 v #s(literal -5/8 binary64))))
(+ 1/4 (* -5/8 (pow v 2)))
(+.f64 #s(literal 1/4 binary64) (.f64 v (.f64 v #s(literal -5/8 binary64))))
(+ 1/4 (* -5/8 (pow v 2)))
(+.f64 #s(literal 1/4 binary64) (.f64 v (.f64 v #s(literal -5/8 binary64))))
(* -5/8 (pow v 2))
(.f64 v (.f64 v #s(literal -5/8 binary64)))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(.f64 v (.f64 v (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 v v)) #s(literal -5/8 binary64))))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(.f64 v (.f64 v (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 v v)) #s(literal -5/8 binary64))))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(.f64 v (.f64 v (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 v v)) #s(literal -5/8 binary64))))
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(sqrt 2)
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2
#s(literal 2 binary64)
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(.f64 #s(literal 1/4 binary64) (.f64 v (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64))))))
(* -1 (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (* 1/4 (/ (sqrt -6) (pow v 2)))) (/ 1/4 (* (pow v 2) (sqrt -6))))))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 v (.f64 v v)) (+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (.f64 v v)) (-.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 #s(literal 1/4 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64)))))))))
(* -1 (* (pow v 3) (- (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))) (/ 1/4 (* (pow v 2) (sqrt -6))))))
(.f64 (.f64 v (.f64 v v)) (-.f64 (-.f64 #s(literal 0 binary64) (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -6 binary64)))) (+.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (.f64 v (.f64 v (.f64 v v)))) (+.f64 (/.f64 (/.f64 #s(literal -1/48 binary64) (sqrt.f64 #s(literal -6 binary64))) (.f64 v (.f64 v (.f64 v v)))) (+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (.f64 v v)) (/.f64 #s(literal -1/4 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64))))))))))
(* -1 (* (pow v 3) (- (+ (* -1 (/ (+ (* 1/8 (/ 1 (pow (sqrt -6) 3))) (* 1/8 (/ 1 (pow (sqrt -6) 5)))) (pow v 6))) (+ (* -1/4 (sqrt -6)) (+ (* 1/4 (/ (sqrt -6) (pow v 2))) (+ (* 1/4 (/ 1 (* (pow v 4) (sqrt -6)))) (* 1/8 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))) (/ 1/4 (* (pow v 2) (sqrt -6))))))
(.f64 (+.f64 (+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (.f64 v v)) (-.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 #s(literal 1/4 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64))))))) (+.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -6 binary64))) (.f64 v (.f64 v (.f64 v v)))) (/.f64 (/.f64 #s(literal -1/48 binary64) (sqrt.f64 #s(literal -6 binary64))) (.f64 v (.f64 v (.f64 v v))))) (/.f64 (+.f64 (/.f64 #s(literal 1/48 binary64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 #s(literal -1/8 binary64) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))) (pow.f64 v #s(literal 6 binary64))))) (-.f64 #s(literal 0 binary64) (.f64 v (.f64 v v))))
(* -6 (pow v 2))
(.f64 v (.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(.f64 v (.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(.f64 v (.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(.f64 v (.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(.f64 v (.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(.f64 v (.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(.f64 v (.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(.f64 v (.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(.f64 v (.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(.f64 v (.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(.f64 v (.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(.f64 v (.f64 v #s(literal -6 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 (.f64 v v) #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 v v) (+.f64 (/.f64 (.f64 (.f64 v v) #s(literal -9/4 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))))))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 v v) (+.f64 (.f64 (.f64 v v) (+.f64 (/.f64 (.f64 (.f64 v v) #s(literal -27/2 binary64)) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -9/4 binary64) (sqrt.f64 #s(literal 2 binary64))))) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))))))
(* v (sqrt -6))
(*.f64 v (sqrt.f64 #s(literal -6 binary64)))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(.f64 v (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1 binary64) (.f64 v (*.f64 v (sqrt.f64 #s(literal -6 binary64)))))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(.f64 v (+.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64)))))) (/.f64 #s(literal 1/12 binary64) (.f64 (sqrt.f64 #s(literal -6 binary64)) (.f64 v (.f64 v (*.f64 v v)))))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(.f64 v (+.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64)))))) (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 v #s(literal 6 binary64))) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal 1/12 binary64) (.f64 (sqrt.f64 #s(literal -6 binary64)) (.f64 v (.f64 v (*.f64 v v))))))))
(* -1 (* v (sqrt -6)))
(-.f64 #s(literal 0 binary64) (*.f64 v (sqrt.f64 #s(literal -6 binary64))))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1 binary64) (.f64 v (*.f64 v (sqrt.f64 #s(literal -6 binary64)))))) (-.f64 #s(literal 0 binary64) v))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(-.f64 #s(literal 0 binary64) (.f64 v (+.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64)))))) (/.f64 #s(literal 1/12 binary64) (.f64 (sqrt.f64 #s(literal -6 binary64)) (.f64 v (.f64 v (*.f64 v v))))))))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))
(.f64 v (-.f64 (-.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 #s(literal 1 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -6 binary64)))))) (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 v #s(literal 6 binary64))) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal 1/12 binary64) (.f64 (sqrt.f64 #s(literal -6 binary64)) (.f64 v (.f64 v (*.f64 v v))))))))
(* -5/8 (pow v 2))
(.f64 v (.f64 v #s(literal -5/8 binary64)))
(* -5/8 (pow v 2))
(.f64 v (.f64 v #s(literal -5/8 binary64)))
(* -5/8 (pow v 2))
(.f64 v (.f64 v #s(literal -5/8 binary64)))
(* -5/8 (pow v 2))
(.f64 v (.f64 v #s(literal -5/8 binary64)))
(* -5/8 (pow v 2))
(.f64 v (.f64 v #s(literal -5/8 binary64)))
(* -5/8 (pow v 2))
(.f64 v (.f64 v #s(literal -5/8 binary64)))
(* -5/8 (pow v 2))
(.f64 v (.f64 v #s(literal -5/8 binary64)))
(* -5/8 (pow v 2))
(.f64 v (.f64 v #s(literal -5/8 binary64)))
(* -5/8 (pow v 2))
(.f64 v (.f64 v #s(literal -5/8 binary64)))
(* -5/8 (pow v 2))
(.f64 v (.f64 v #s(literal -5/8 binary64)))
(* -5/8 (pow v 2))
(.f64 v (.f64 v #s(literal -5/8 binary64)))
(* -5/8 (pow v 2))
(.f64 v (.f64 v #s(literal -5/8 binary64)))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 3/4 (/ (pow v 2) (sqrt 1/2))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (.f64 (.f64 v v) #s(literal 3/4 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (sqrt 1/2) (* (pow v 2) (+ (* 1/2 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 3/4 (/ 1 (sqrt 1/2))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (.f64 v v) (+.f64 (/.f64 #s(literal 3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (.f64 (.f64 v v) #s(literal 27/16 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))))
(+ (sqrt 1/2) (* (pow v 2) (+ (* (pow v 2) (+ (* 1/2 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2))))) (* 3/4 (/ 1 (sqrt 1/2))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 v (.f64 v (+.f64 (/.f64 #s(literal 3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (.f64 v v) (+.f64 (/.f64 (.f64 (.f64 v v) #s(literal 135/32 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 27/16 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))))))
(/ (sqrt -1/6) v)
(/.f64 (sqrt.f64 #s(literal -1/6 binary64)) v)
(/ (- (sqrt -1/6) (* 1/36 (/ 1 (* (pow v 2) (sqrt -1/6))))) v)
(/.f64 (+.f64 (sqrt.f64 #s(literal -1/6 binary64)) (/.f64 #s(literal -1/36 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -1/6 binary64)))))) v)
(/ (- (+ (sqrt -1/6) (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6))))) (/ 1/36 (* (pow v 2) (sqrt -1/6)))) v)
(/.f64 (+.f64 (+.f64 (sqrt.f64 #s(literal -1/6 binary64)) (/.f64 #s(literal -1/36 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -1/6 binary64)))))) (/.f64 (/.f64 #s(literal -1/144 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (.f64 v (.f64 v (*.f64 v v))))) v)
(/ (- (+ (sqrt -1/6) (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (sqrt -1/6)))) (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6)))))) (/ 1/36 (* (pow v 2) (sqrt -1/6)))) v)
(/.f64 (+.f64 (+.f64 (sqrt.f64 #s(literal -1/6 binary64)) (/.f64 #s(literal -1/36 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -1/6 binary64)))))) (.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (+.f64 (/.f64 #s(literal 1/72 binary64) (.f64 v (.f64 v (.f64 v v)))) (/.f64 #s(literal 5/1296 binary64) (pow.f64 v #s(literal 6 binary64)))))) v)
(* -1 (/ (sqrt -1/6) v))
(-.f64 #s(literal 0 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) v))
(* -1 (/ (- (sqrt -1/6) (* 1/36 (/ 1 (* (pow v 2) (sqrt -1/6))))) v))
(/.f64 (-.f64 (/.f64 #s(literal 1/36 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -1/6 binary64))))) (sqrt.f64 #s(literal -1/6 binary64))) v)
(* -1 (/ (- (+ (sqrt -1/6) (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6))))) (/ 1/36 (* (pow v 2) (sqrt -1/6)))) v))
(/.f64 (-.f64 (/.f64 #s(literal 1/36 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -1/6 binary64))))) (+.f64 (sqrt.f64 #s(literal -1/6 binary64)) (/.f64 (/.f64 #s(literal -1/144 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (.f64 v (.f64 v (*.f64 v v)))))) v)
(* -1 (/ (- (+ (sqrt -1/6) (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (sqrt -1/6)))) (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6)))))) (/ 1/36 (* (pow v 2) (sqrt -1/6)))) v))
(/.f64 (-.f64 (/.f64 #s(literal 1/36 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -1/6 binary64))))) (+.f64 (sqrt.f64 #s(literal -1/6 binary64)) (.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (+.f64 (/.f64 #s(literal 1/72 binary64) (.f64 v (.f64 v (.f64 v v)))) (/.f64 #s(literal 5/1296 binary64) (pow.f64 v #s(literal 6 binary64))))))) v)

eval207.0ms (2%)

Memory: 7.2MiB live, 522.4MiB allocated
Compiler: Compiled 46 828 to 2 532 computations (94.6% saved)

prune111.0ms (1%)

Memory

16.7MiB live, 336.0MiB allocated

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	1 494	1	1 495
Fresh	0	0	0
Picked	0	4	4
Done	0	2	2
Total	1 494	7	1 501

Accuracy

100.0%

Counts

1 501 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.5%	(/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal 4 binary64))) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64)))
▶	96.9%	(/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal 4 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
✓	100.0%	(/.f64 (sqrt.f64 (+.f64 (.f64 (.f64 v v) #s(literal -6 binary64)) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal -4 binary64)))))
✓	98.9%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 v v) #s(literal -5/8 binary64)))))
✓	100.0%	(.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal 4 binary64))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal -6 binary64)))))
✓	98.9%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 v (*.f64 v #s(literal -5/8 binary64)))))
✓	98.4%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))

Compiler

Compiled 94 to 73 computations (22.3% saved)

simplify247.0ms (2.3%)

Memory

-22.0MiB live, 386.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 v v)
✓	cost-diff	(/.f64 (*.f64 v v) #s(literal 4 binary64))
✓	cost-diff	(-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal 4 binary64)))
✓	cost-diff	(/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal 4 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))

Rules

7 132×	`accelerator-lowering-fma.f32`
7 132×	`accelerator-lowering-fma.f64`
2 118×	`-lowering-.f32`
2 118×	`-lowering-.f64`
1 422×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	31
1	16	31
2	38	31
3	78	31
4	160	31
5	269	31
6	373	31
7	501	31
8	811	31
9	1663	31
10	2445	31
11	2576	31
12	2984	31
13	3933	31
14	5071	31
15	6395	31
16	7444	31
0	8102	29

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (- 1/4 (/ (* v v) 4)) (sqrt 1/2))
(- 1/4 (/ (* v v) 4))
1/4
(/ (* v v) 4)
(* v v)
v
4
(sqrt 1/2)
1/2

Outputs
(/ (- 1/4 (/ (* v v) 4)) (sqrt 1/2))
(/.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal -4 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(- 1/4 (/ (* v v) 4))
(+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal -4 binary64)))
1/4
#s(literal 1/4 binary64)
(/ (* v v) 4)
(/.f64 (*.f64 v v) #s(literal 4 binary64))
(* v v)
(*.f64 v v)
v
4
#s(literal 4 binary64)
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)

localize31.0ms (0.3%)

Memory

5.9MiB live, 77.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal 4 binary64)))
✓	accuracy	100.0%	(*.f64 v v)
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/2 binary64))
✓	accuracy	98.5%	(/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal 4 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))

Samples

18.0ms

256×

valid

Compiler

Compiled 33 to 11 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-div: 6.0ms (52.3% of total)

ival-mult: 2.0ms (17.4% of total)

ival-sqrt: 2.0ms (17.4% of total)

ival-sub: 1.0ms (8.7% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0%)

Memory

10.2MiB live, 10.2MiB allocated

Counts

5 → 48

Calls

Call 1

Inputs
#<alt (/ (- 1/4 (/ (* v v) 4)) (sqrt 1/2))>
#<alt (- 1/4 (/ (* v v) 4))>
#<alt (/ (* v v) 4)>
#<alt (* v v)>
#<alt (sqrt 1/2)>

Outputs
#<alt (/ 1/4 (sqrt 1/2))>
#<alt (+ (* -1/4 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))>
#<alt (+ (* -1/4 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))>
#<alt (+ (* -1/4 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))>
#<alt (* -1/4 (/ (pow v 2) (sqrt 1/2)))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 1/4 (/ 1 (sqrt 1/2)))))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 1/4 (/ 1 (sqrt 1/2)))))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 1/4 (/ 1 (sqrt 1/2)))))>
#<alt (* -1/4 (/ (pow v 2) (sqrt 1/2)))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 1/4 (/ 1 (sqrt 1/2)))))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 1/4 (/ 1 (sqrt 1/2)))))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 1/4 (/ 1 (sqrt 1/2)))))>
#<alt 1/4>
#<alt (+ 1/4 (* -1/4 (pow v 2)))>
#<alt (+ 1/4 (* -1/4 (pow v 2)))>
#<alt (+ 1/4 (* -1/4 (pow v 2)))>
#<alt (* -1/4 (pow v 2))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))>
#<alt (* -1/4 (pow v 2))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))>
#<alt (* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))>
#<alt (* 1/4 (pow v 2))>
#<alt (* 1/4 (pow v 2))>
#<alt (* 1/4 (pow v 2))>
#<alt (* 1/4 (pow v 2))>
#<alt (* 1/4 (pow v 2))>
#<alt (* 1/4 (pow v 2))>
#<alt (* 1/4 (pow v 2))>
#<alt (* 1/4 (pow v 2))>
#<alt (* 1/4 (pow v 2))>
#<alt (* 1/4 (pow v 2))>
#<alt (* 1/4 (pow v 2))>
#<alt (* 1/4 (pow v 2))>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	v	@	0	(/ (- 1/4 (/ (* v v) 4)) (sqrt 1/2))
0.0ms	v	@	inf	(/ (- 1/4 (/ (* v v) 4)) (sqrt 1/2))
0.0ms	v	@	-inf	(/ (* v v) 4)
0.0ms	v	@	-inf	(/ (- 1/4 (/ (* v v) 4)) (sqrt 1/2))
0.0ms	v	@	inf	(* v v)

rewrite260.0ms (2.5%)

Memory

4.8MiB live, 572.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

3 384×	`-lowering-.f32`
3 384×	`-lowering-.f64`
2 722×	`accelerator-lowering-fma.f32`
2 722×	`accelerator-lowering-fma.f64`
2 574×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	50	27
2	384	27
3	5690	27
0	8115	25

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 339

Calls

Call 1

Inputs
(/ (- 1/4 (/ (* v v) 4)) (sqrt 1/2))
(- 1/4 (/ (* v v) 4))
(/ (* v v) 4)
(* v v)
(sqrt 1/2)

Outputs
(+.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (.f64 v v) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -4 binary64))))
(+.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 #s(literal 1 binary64) (/.f64 (.f64 v v) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -4 binary64)))))
(+.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (/.f64 (.f64 v v) #s(literal -4 binary64))))
(+.f64 (/.f64 (.f64 v v) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -4 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(+.f64 (.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (/.f64 (.f64 v v) #s(literal -4 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(+.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64)) (.f64 (/.f64 (.f64 v v) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -4 binary64))) #s(literal 1 binary64)))
(exp.f64 (.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal -4 binary64))))) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (*.f64 v v) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 v v) #s(literal -4 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (-.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 v v) #s(literal -4 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))
(-.f64 (/.f64 (/.f64 #s(literal 1/64 binary64) (+.f64 #s(literal 1/16 binary64) (.f64 (+.f64 (.f64 v v) #s(literal 1 binary64)) (/.f64 (.f64 v v) #s(literal 16 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (/.f64 (.f64 (.f64 v (.f64 v v)) (/.f64 (.f64 v (.f64 v v)) #s(literal 64 binary64))) (+.f64 #s(literal 1/16 binary64) (.f64 (+.f64 (.f64 v v) #s(literal 1 binary64)) (/.f64 (*.f64 v v) #s(literal 16 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))))
(-.f64 (/.f64 (/.f64 #s(literal -1/16 binary64) (+.f64 (/.f64 (.f64 v v) #s(literal -4 binary64)) #s(literal -1/4 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (.f64 (/.f64 (.f64 v (.f64 v (.f64 v v))) (+.f64 (.f64 v v) #s(literal 1 binary64))) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
(-.f64 (/.f64 #s(literal 1/64 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal 1/16 binary64) (.f64 (+.f64 (.f64 v v) #s(literal 1 binary64)) (/.f64 (.f64 v v) #s(literal 16 binary64)))))) (/.f64 (.f64 (.f64 v (.f64 v v)) (/.f64 (.f64 v (.f64 v v)) #s(literal 64 binary64))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal 1/16 binary64) (.f64 (+.f64 (.f64 v v) #s(literal 1 binary64)) (/.f64 (*.f64 v v) #s(literal 16 binary64)))))))
(-.f64 (/.f64 #s(literal 1/16 binary64) (.f64 (+.f64 (.f64 v v) #s(literal 1 binary64)) (pow.f64 #s(literal 1/4 binary64) #s(literal 5/4 binary64)))) (/.f64 (/.f64 (.f64 v v) (/.f64 #s(literal 16 binary64) (.f64 v v))) (.f64 (+.f64 (.f64 v v) #s(literal 1 binary64)) (pow.f64 #s(literal 1/4 binary64) #s(literal 5/4 binary64)))))
(-.f64 (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 5/4 binary64)) #s(literal 1/2 binary64)) (/.f64 (.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 5/4 binary64)) (.f64 v v)) #s(literal 1/2 binary64)))
(-.f64 (/.f64 (pow.f64 #s(literal 1/8 binary64) #s(literal 3/2 binary64)) (+.f64 #s(literal 1/8 binary64) (+.f64 (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 1/8 binary64)) (/.f64 (/.f64 (.f64 v v) #s(literal 16 binary64)) #s(literal 1/2 binary64))))) (/.f64 (pow.f64 (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 1/8 binary64)) #s(literal 3/2 binary64)) (+.f64 #s(literal 1/8 binary64) (+.f64 (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 1/8 binary64)) (/.f64 (/.f64 (.f64 v v) #s(literal 16 binary64)) #s(literal 1/2 binary64))))))
(-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal -4 binary64))))) (/.f64 (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal -4 binary64))))))
(fma.f64 #s(literal 1/4 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (/.f64 (.f64 v v) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -4 binary64))))
(fma.f64 #s(literal 1/4 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (.f64 #s(literal 1 binary64) (/.f64 (.f64 v v) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -4 binary64)))))
(fma.f64 #s(literal 1/4 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (/.f64 (.f64 v v) #s(literal -4 binary64))))
(fma.f64 v (neg.f64 (/.f64 v (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(fma.f64 (*.f64 v v) (neg.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(fma.f64 (/.f64 v (/.f64 #s(literal 4 binary64) v)) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(fma.f64 (-.f64 #s(literal 0 binary64) (*.f64 v v)) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(fma.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64) (.f64 (/.f64 (.f64 v v) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -4 binary64))) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (.f64 v v) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -4 binary64))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 #s(literal 1 binary64) (/.f64 (.f64 v v) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -4 binary64)))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (/.f64 (.f64 v v) #s(literal -4 binary64))))
(fma.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) #s(literal 1/4 binary64) (/.f64 (.f64 v v) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -4 binary64))))
(fma.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) #s(literal 1/4 binary64) (.f64 #s(literal 1 binary64) (/.f64 (.f64 v v) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -4 binary64)))))
(fma.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) #s(literal 1/4 binary64) (.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (/.f64 (.f64 v v) #s(literal -4 binary64))))
(fma.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (/.f64 (*.f64 v v) #s(literal -4 binary64)) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(fma.f64 (/.f64 (*.f64 v v) #s(literal -4 binary64)) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 v v) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(fma.f64 #s(literal -1/4 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (.f64 v v) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -4 binary64))))
(fma.f64 #s(literal -1/4 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 #s(literal 1 binary64) (/.f64 (.f64 v v) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -4 binary64)))))
(fma.f64 #s(literal -1/4 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (/.f64 (.f64 v v) #s(literal -4 binary64))))
(fma.f64 (-.f64 #s(literal 0 binary64) v) (/.f64 v (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(neg.f64 (/.f64 (-.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 v v) #s(literal -4 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))
(neg.f64 (.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1/4 binary64) (/.f64 (.f64 v v) #s(literal -4 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal -4 binary64))))))
(/.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal -4 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 v v) #s(literal -4 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 v (.f64 v v)) (/.f64 (.f64 v (.f64 v v)) #s(literal 64 binary64)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal 1/16 binary64) (.f64 (+.f64 (.f64 v v) #s(literal 1 binary64)) (/.f64 (*.f64 v v) #s(literal 16 binary64))))))
(/.f64 (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 v (.f64 v v)) (/.f64 (.f64 v (.f64 v v)) #s(literal 64 binary64)))) (.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/16 binary64) (.f64 (+.f64 (.f64 v v) #s(literal 1 binary64)) (/.f64 (*.f64 v v) #s(literal 16 binary64))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 v (.f64 v v)) (/.f64 (.f64 v (.f64 v v)) #s(literal 64 binary64)))) (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/16 binary64) (.f64 (+.f64 (.f64 v v) #s(literal 1 binary64)) (/.f64 (*.f64 v v) #s(literal 16 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal -4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (-.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 5/4 binary64)) (.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 5/4 binary64)) (.f64 v v)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (+.f64 (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 1/8 binary64)) (/.f64 (/.f64 (.f64 v v) #s(literal 16 binary64)) #s(literal 1/2 binary64)))) (.f64 (+.f64 #s(literal 1/8 binary64) (+.f64 (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 1/8 binary64)) (/.f64 (/.f64 (.f64 v v) #s(literal 16 binary64)) #s(literal 1/2 binary64)))) (/.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal -4 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal -4 binary64)))) (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 1/8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/16 binary64) (.f64 (+.f64 (.f64 v v) #s(literal 1 binary64)) (/.f64 (.f64 v v) #s(literal 16 binary64)))) (/.f64 (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 v (.f64 v v)) (/.f64 (.f64 v (.f64 v v)) #s(literal 64 binary64)))) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal -4 binary64))) (/.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (.f64 v v) (/.f64 #s(literal -16 binary64) (*.f64 v v)))) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal -4 binary64)))))
(/.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (.f64 v v) (/.f64 #s(literal -16 binary64) (.f64 v v)))) (.f64 (+.f64 (.f64 v v) #s(literal 1 binary64)) (pow.f64 #s(literal 1/4 binary64) #s(literal 5/4 binary64))))
(/.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (.f64 v v) (/.f64 #s(literal -16 binary64) (.f64 v v)))) (.f64 (+.f64 (/.f64 (.f64 v v) #s(literal -4 binary64)) #s(literal -1/4 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (.f64 v v) (/.f64 #s(literal -16 binary64) (.f64 v v)))) (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 (/.f64 (.f64 v v) #s(literal -4 binary64)) #s(literal -1/4 binary64))))
(/.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 v v) #s(literal -4 binary64)))))
(/.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal -4 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 (-.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 5/4 binary64)) (.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 5/4 binary64)) (.f64 v v))) #s(literal 1/2 binary64))
(/.f64 (+.f64 #s(literal -1/64 binary64) (.f64 (.f64 v (.f64 v v)) (/.f64 (.f64 v (.f64 v v)) #s(literal 64 binary64)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/16 binary64) (.f64 (+.f64 (.f64 v v) #s(literal 1 binary64)) (/.f64 (*.f64 v v) #s(literal 16 binary64)))))))
(/.f64 (+.f64 #s(literal -1/64 binary64) (.f64 (.f64 v (.f64 v v)) (/.f64 (.f64 v (.f64 v v)) #s(literal 64 binary64)))) (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 #s(literal 1/16 binary64) (.f64 (+.f64 (.f64 v v) #s(literal 1 binary64)) (/.f64 (*.f64 v v) #s(literal 16 binary64))))))
(/.f64 (+.f64 #s(literal -1/64 binary64) (.f64 (.f64 v (.f64 v v)) (/.f64 (.f64 v (.f64 v v)) #s(literal 64 binary64)))) (neg.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal 1/16 binary64) (.f64 (+.f64 (.f64 v v) #s(literal 1 binary64)) (/.f64 (*.f64 v v) #s(literal 16 binary64)))))))
(/.f64 (+.f64 #s(literal -1/16 binary64) (/.f64 (.f64 v v) (/.f64 #s(literal 16 binary64) (.f64 v v)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 (.f64 v v) #s(literal -4 binary64)) #s(literal -1/4 binary64))))
(/.f64 (+.f64 #s(literal -1/16 binary64) (/.f64 (.f64 v v) (/.f64 #s(literal 16 binary64) (.f64 v v)))) (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal -4 binary64)))))
(/.f64 (+.f64 #s(literal -1/16 binary64) (/.f64 (.f64 v v) (/.f64 #s(literal 16 binary64) (.f64 v v)))) (neg.f64 (.f64 (+.f64 (.f64 v v) #s(literal 1 binary64)) (pow.f64 #s(literal 1/4 binary64) #s(literal 5/4 binary64)))))
(/.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (+.f64 (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 1/8 binary64)) (/.f64 (/.f64 (.f64 v v) #s(literal 16 binary64)) #s(literal 1/2 binary64)))) (/.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal -4 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/8 binary64) (+.f64 (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 1/8 binary64)) (/.f64 (/.f64 (.f64 v v) #s(literal 16 binary64)) #s(literal 1/2 binary64)))))
(/.f64 (-.f64 #s(literal 1/262144 binary64) (/.f64 (.f64 (.f64 (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v)))) (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v))))) (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v))))) #s(literal 262144 binary64))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 #s(literal 1/16 binary64) (.f64 (+.f64 (.f64 v v) #s(literal 1 binary64)) (/.f64 (.f64 v v) #s(literal 16 binary64))))) (+.f64 #s(literal 1/4096 binary64) (.f64 (.f64 (.f64 v (.f64 v v)) (/.f64 (.f64 v (.f64 v v)) #s(literal 64 binary64))) (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 v (.f64 v v)) (/.f64 (.f64 v (*.f64 v v)) #s(literal 64 binary64))))))))
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(.f64 (+.f64 #s(literal -1/16 binary64) (/.f64 (.f64 v v) (/.f64 #s(literal 16 binary64) (.f64 v v)))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 v v) #s(literal -4 binary64)) #s(literal -1/4 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/16 binary64) (.f64 (+.f64 (.f64 v v) #s(literal 1 binary64)) (/.f64 (.f64 v v) #s(literal 16 binary64))))) (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 v (.f64 v v)) (/.f64 (.f64 v (*.f64 v v)) #s(literal 64 binary64)))))
(.f64 (/.f64 #s(literal -1 binary64) (+.f64 (/.f64 (.f64 v v) #s(literal -4 binary64)) #s(literal -1/4 binary64))) (+.f64 #s(literal 1/16 binary64) (/.f64 (.f64 v v) (/.f64 #s(literal -16 binary64) (.f64 v v)))))
(.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 v v)) #s(literal 1 binary64)) #s(literal 1/4 binary64))
(.f64 (/.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (.f64 v v) (/.f64 #s(literal -16 binary64) (.f64 v v)))) (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 v (.f64 v v)) (/.f64 (.f64 v (.f64 v v)) #s(literal 64 binary64))))) (+.f64 #s(literal 1/16 binary64) (/.f64 (-.f64 #s(literal -1/4 binary64) (/.f64 (.f64 v v) #s(literal -4 binary64))) (/.f64 #s(literal 4 binary64) (.f64 v v)))))
(.f64 (/.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 (.f64 v v) (/.f64 #s(literal -16 binary64) (.f64 v v)))) (+.f64 #s(literal 1/16 binary64) (/.f64 (.f64 v v) (/.f64 #s(literal -16 binary64) (.f64 v v))))) (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal -4 binary64))))
(.f64 (/.f64 (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 v (.f64 v v)) (/.f64 (.f64 v (.f64 v v)) #s(literal 64 binary64)))) (+.f64 #s(literal 1/4096 binary64) (.f64 (.f64 (+.f64 (.f64 v v) #s(literal 1 binary64)) (/.f64 (.f64 v v) #s(literal 16 binary64))) (.f64 (.f64 (+.f64 (.f64 v v) #s(literal 1 binary64)) (/.f64 (.f64 v v) #s(literal 16 binary64))) (.f64 (+.f64 (.f64 v v) #s(literal 1 binary64)) (/.f64 (.f64 v v) #s(literal 16 binary64))))))) (+.f64 #s(literal 1/256 binary64) (.f64 (.f64 (+.f64 (.f64 v v) #s(literal 1 binary64)) (/.f64 (.f64 v v) #s(literal 16 binary64))) (-.f64 (.f64 (+.f64 (.f64 v v) #s(literal 1 binary64)) (/.f64 (.f64 v v) #s(literal 16 binary64))) #s(literal 1/16 binary64)))))
(.f64 (/.f64 (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 v (.f64 v v)) (/.f64 (.f64 v (.f64 v v)) #s(literal 64 binary64)))) (-.f64 #s(literal 1/256 binary64) (.f64 (.f64 (+.f64 (.f64 v v) #s(literal 1 binary64)) (/.f64 (.f64 v v) #s(literal 16 binary64))) (.f64 (+.f64 (.f64 v v) #s(literal 1 binary64)) (/.f64 (.f64 v v) #s(literal 16 binary64)))))) (-.f64 #s(literal 1/16 binary64) (.f64 (+.f64 (.f64 v v) #s(literal 1 binary64)) (/.f64 (.f64 v v) #s(literal 16 binary64)))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 4 binary64) (.f64 v v))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 v (/.f64 #s(literal 4 binary64) v))) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 v v))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (*.f64 v v) #s(literal -4 binary64)))
(neg.f64 (/.f64 (*.f64 v v) #s(literal -4 binary64)))
(neg.f64 (.f64 (/.f64 (.f64 v v) #s(literal -4 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1 binary64) (*.f64 v v)))
(/.f64 v (/.f64 #s(literal 4 binary64) v))
(/.f64 (*.f64 v v) #s(literal 4 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 v v)) #s(literal -4 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 4 binary64) (*.f64 v v)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -4 binary64) (*.f64 v v)))
(/.f64 (*.f64 v #s(literal 1 binary64)) (/.f64 #s(literal 4 binary64) v))
(/.f64 (*.f64 #s(literal 1 binary64) v) (/.f64 #s(literal 4 binary64) v))
(pow.f64 (/.f64 v (/.f64 #s(literal 4 binary64) v)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 16 binary64) (.f64 v (.f64 v (*.f64 v v)))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 (/.f64 #s(literal 4 binary64) (*.f64 v v)))) #s(literal -1 binary64))
(.f64 #s(literal 1/4 binary64) (.f64 v v))
(*.f64 v (/.f64 v #s(literal 4 binary64)))
(.f64 v (.f64 (/.f64 v #s(literal 4 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 v v) #s(literal 1/4 binary64))
(*.f64 (/.f64 v (/.f64 #s(literal 4 binary64) v)) #s(literal 1 binary64))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 v v)) #s(literal -1/4 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 v (/.f64 #s(literal 4 binary64) v)))
(*.f64 (/.f64 v #s(literal 4 binary64)) v)
(.f64 (/.f64 v #s(literal 4 binary64)) (.f64 v #s(literal 1 binary64)))
(.f64 #s(literal -1 binary64) (/.f64 (.f64 v v) #s(literal -4 binary64)))
(.f64 #s(literal -1/4 binary64) (-.f64 #s(literal 0 binary64) (.f64 v v)))
(*.f64 (-.f64 #s(literal 0 binary64) v) (/.f64 v #s(literal -4 binary64)))
(.f64 (.f64 #s(literal 1 binary64) v) (/.f64 v #s(literal 4 binary64)))
(*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) v)) (/.f64 v #s(literal 4 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (.f64 v v)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 v)))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (.f64 v v))) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 v)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 v))) #s(literal 2 binary64)))
(exp.f64 (.f64 (neg.f64 (.f64 #s(literal 2 binary64) (log.f64 v))) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 v) #s(literal 1 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (.f64 (log.f64 v) #s(literal 1 binary64)) (.f64 (log.f64 v) #s(literal 1 binary64))))
(exp.f64 (neg.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (log.f64 v)))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (*.f64 v v)))
(neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 v v)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 v v)))
(pow.f64 v #s(literal 2 binary64))
(pow.f64 (*.f64 v v) #s(literal 1 binary64))
(pow.f64 (-.f64 #s(literal 0 binary64) v) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 v v)) #s(literal -1 binary64))
(pow.f64 (exp.f64 (log.f64 v)) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 v))
(*.f64 v v)
(.f64 v (.f64 v #s(literal 1 binary64)))
(*.f64 v (neg.f64 (-.f64 #s(literal 0 binary64) v)))
(.f64 (.f64 v v) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 v v))
(.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (.f64 v v)))
(*.f64 (-.f64 #s(literal 0 binary64) v) (-.f64 #s(literal 0 binary64) v))
(*.f64 (exp.f64 (log.f64 v)) (exp.f64 (log.f64 v)))
(.f64 (.f64 #s(literal 1 binary64) v) v)
(*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) v)) v)
(exp.f64 (*.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 1/4 binary64))))
(exp.f64 (*.f64 (log.f64 #s(literal 1/4 binary64)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 #s(literal 1/2 binary64)))) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))
(exp.f64 (neg.f64 (*.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal -1/2 binary64))))
(exp.f64 (neg.f64 (.f64 (.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 1/4 binary64))) #s(literal -1 binary64))))
(exp.f64 (neg.f64 (neg.f64 (*.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 1/4 binary64))))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt.f64 #s(literal 1/2 binary64))
(sqrt.f64 (exp.f64 (log.f64 #s(literal 1/2 binary64))))
(neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)))
(pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))
(pow.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal -1/4 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 #s(literal 1/2 binary64))) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64)) (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64)))
(*.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64)) (/.f64 (pow.f64 #s(literal 1/4 binary64) #s(literal 1/8 binary64)) #s(literal 1 binary64)))

simplify451.0ms (4.3%)

Memory

4.6MiB live, 791.1MiB allocated

Algorithm

1×	egg-herbie

Rules

22 326×	`accelerator-lowering-fma.f32`
22 326×	`accelerator-lowering-fma.f64`
3 162×	`-lowering-.f32`
3 162×	`-lowering-.f64`
2 012×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	307
1	53	307
2	113	307
3	246	298
4	657	280
5	4049	280
6	7660	280
0	8149	262

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

Inputs
(/ 1/4 (sqrt 1/2))
(+ (* -1/4 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))
(+ (* -1/4 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))
(+ (* -1/4 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))
(* -1/4 (/ (pow v 2) (sqrt 1/2)))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 1/4 (/ 1 (sqrt 1/2)))))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 1/4 (/ 1 (sqrt 1/2)))))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 1/4 (/ 1 (sqrt 1/2)))))
(* -1/4 (/ (pow v 2) (sqrt 1/2)))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 1/4 (/ 1 (sqrt 1/2)))))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 1/4 (/ 1 (sqrt 1/2)))))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 1/4 (/ 1 (sqrt 1/2)))))
1/4
(+ 1/4 (* -1/4 (pow v 2)))
(+ 1/4 (* -1/4 (pow v 2)))
(+ 1/4 (* -1/4 (pow v 2)))
(* -1/4 (pow v 2))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))
(* -1/4 (pow v 2))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))
(* 1/4 (pow v 2))
(* 1/4 (pow v 2))
(* 1/4 (pow v 2))
(* 1/4 (pow v 2))
(* 1/4 (pow v 2))
(* 1/4 (pow v 2))
(* 1/4 (pow v 2))
(* 1/4 (pow v 2))
(* 1/4 (pow v 2))
(* 1/4 (pow v 2))
(* 1/4 (pow v 2))
(* 1/4 (pow v 2))
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)

Outputs
(/ 1/4 (sqrt 1/2))
(/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (* -1/4 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))
(/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/4 binary64) (.f64 v v))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (* -1/4 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))
(/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/4 binary64) (.f64 v v))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (* -1/4 (/ (pow v 2) (sqrt 1/2))) (* 1/4 (/ 1 (sqrt 1/2))))
(/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/4 binary64) (.f64 v v))) (sqrt.f64 #s(literal 1/2 binary64)))
(* -1/4 (/ (pow v 2) (sqrt 1/2)))
(.f64 v (.f64 v (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 1/4 (/ 1 (sqrt 1/2)))))
(/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/4 binary64) (.f64 v v))) (sqrt.f64 #s(literal 1/2 binary64)))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 1/4 (/ 1 (sqrt 1/2)))))
(/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/4 binary64) (.f64 v v))) (sqrt.f64 #s(literal 1/2 binary64)))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 1/4 (/ 1 (sqrt 1/2)))))
(/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/4 binary64) (.f64 v v))) (sqrt.f64 #s(literal 1/2 binary64)))
(* -1/4 (/ (pow v 2) (sqrt 1/2)))
(.f64 v (.f64 v (/.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 1/4 (/ 1 (sqrt 1/2)))))
(/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/4 binary64) (.f64 v v))) (sqrt.f64 #s(literal 1/2 binary64)))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 1/4 (/ 1 (sqrt 1/2)))))
(/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/4 binary64) (.f64 v v))) (sqrt.f64 #s(literal 1/2 binary64)))
(* (pow v 2) (- (* 1/4 (/ 1 (* (pow v 2) (sqrt 1/2)))) (* 1/4 (/ 1 (sqrt 1/2)))))
(/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/4 binary64) (.f64 v v))) (sqrt.f64 #s(literal 1/2 binary64)))
1/4
#s(literal 1/4 binary64)
(+ 1/4 (* -1/4 (pow v 2)))
(+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/4 binary64) (.f64 v v)))
(+ 1/4 (* -1/4 (pow v 2)))
(+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/4 binary64) (.f64 v v)))
(+ 1/4 (* -1/4 (pow v 2)))
(+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/4 binary64) (.f64 v v)))
(* -1/4 (pow v 2))
(.f64 #s(literal -1/4 binary64) (.f64 v v))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))
(+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/4 binary64) (.f64 v v)))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))
(+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/4 binary64) (.f64 v v)))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))
(+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/4 binary64) (.f64 v v)))
(* -1/4 (pow v 2))
(.f64 #s(literal -1/4 binary64) (.f64 v v))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))
(+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/4 binary64) (.f64 v v)))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))
(+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/4 binary64) (.f64 v v)))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 1/4))
(+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/4 binary64) (.f64 v v)))
(* 1/4 (pow v 2))
(.f64 #s(literal 1/4 binary64) (.f64 v v))
(* 1/4 (pow v 2))
(.f64 #s(literal 1/4 binary64) (.f64 v v))
(* 1/4 (pow v 2))
(.f64 #s(literal 1/4 binary64) (.f64 v v))
(* 1/4 (pow v 2))
(.f64 #s(literal 1/4 binary64) (.f64 v v))
(* 1/4 (pow v 2))
(.f64 #s(literal 1/4 binary64) (.f64 v v))
(* 1/4 (pow v 2))
(.f64 #s(literal 1/4 binary64) (.f64 v v))
(* 1/4 (pow v 2))
(.f64 #s(literal 1/4 binary64) (.f64 v v))
(* 1/4 (pow v 2))
(.f64 #s(literal 1/4 binary64) (.f64 v v))
(* 1/4 (pow v 2))
(.f64 #s(literal 1/4 binary64) (.f64 v v))
(* 1/4 (pow v 2))
(.f64 #s(literal 1/4 binary64) (.f64 v v))
(* 1/4 (pow v 2))
(.f64 #s(literal 1/4 binary64) (.f64 v v))
(* 1/4 (pow v 2))
(.f64 #s(literal 1/4 binary64) (.f64 v v))
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)

eval44.0ms (0.4%)

Memory: -8.1MiB live, 107.5MiB allocated
Compiler: Compiled 9 076 to 1 013 computations (88.8% saved)

prune118.0ms (1.1%)

Memory

-8.6MiB live, 128.7MiB allocated

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	386	1	387
Fresh	0	0	0
Picked	1	0	1
Done	0	6	6
Total	387	7	394

Accuracy

100.0%

Counts

394 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.5%	(/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal 4 binary64))) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64)))
✓	100.0%	(/.f64 (sqrt.f64 (+.f64 (.f64 (.f64 v v) #s(literal -6 binary64)) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal -4 binary64)))))
✓	98.9%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 v v) #s(literal -5/8 binary64)))))
	96.9%	(/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
✓	100.0%	(.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal 4 binary64))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal -6 binary64)))))
✓	98.9%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 v (*.f64 v #s(literal -5/8 binary64)))))
✓	98.4%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))

Compiler

Compiled 294 to 133 computations (54.8% saved)

regimes13.0ms (0.1%)

Memory

19.0MiB live, 19.0MiB allocated

Counts

14 → 1

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
(/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 v (*.f64 v #s(literal -5/8 binary64)))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal 4 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 v v) #s(literal -5/8 binary64)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 v v) (+.f64 #s(literal -5/8 binary64) (.f64 (*.f64 v v) #s(literal 3/32 binary64))))))
(.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal 4 binary64))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal -6 binary64)))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal 4 binary64))) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64)))
(.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal -4 binary64))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 (+.f64 (.f64 (.f64 v v) #s(literal -6 binary64)) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal -4 binary64)))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 (.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal -4 binary64)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v)))) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal 4 binary64)))))
(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v)))) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal 4 binary64)))))

Outputs
(.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal 4 binary64))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal -6 binary64)))))

Calls

3 calls:

4.0ms

(*.f64 v v)

4.0ms

(*.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 v v))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))

Results

Accuracy	Segments	Branch
100.0%	1	`v`
100.0%	1	`(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))`
100.0%	1	`(*.f64 v v)`

Compiler

Compiled 26 to 17 computations (34.6% saved)

regimes27.0ms (0.3%)

Memory

-30.8MiB live, 8.4MiB allocated

Counts

6 → 1

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
(/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 v (*.f64 v #s(literal -5/8 binary64)))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal 4 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 v v) #s(literal -5/8 binary64)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 v v) (+.f64 #s(literal -5/8 binary64) (.f64 (*.f64 v v) #s(literal 3/32 binary64))))))

Outputs
(.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 v v) (+.f64 #s(literal -5/8 binary64) (.f64 (*.f64 v v) #s(literal 3/32 binary64))))))

Calls

2 calls:

24.0ms	v
2.0ms	(*.f64 v v)

Results

Accuracy	Segments	Branch
99.3%	1	`v`
99.3%	1	`(*.f64 v v)`

Compiler

Compiled 6 to 3 computations (50% saved)

regimes4.0ms (0%)

Memory

9.1MiB live, 9.1MiB allocated

Counts

5 → 1

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
(/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 v (*.f64 v #s(literal -5/8 binary64)))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 v v) #s(literal 4 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 v v) #s(literal -5/8 binary64)))))

Outputs
(.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 v (*.f64 v #s(literal -5/8 binary64)))))

Calls

2 calls:

2.0ms	v
2.0ms	(*.f64 v v)

Results

Accuracy	Segments	Branch
98.9%	1	`v`
98.9%	1	`(*.f64 v v)`

Compiler

Compiled 6 to 3 computations (50% saved)

regimes2.0ms (0%)

Memory

4.2MiB live, 4.2MiB allocated

Accuracy

Total -1.0b remaining (-94.3%)

Threshold costs -1b (-94.3%)

Counts

2 → 1

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
(/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))

Outputs
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
98.4%	1	`v`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify9.0ms (0.1%)

Memory

20.4MiB live, 20.4MiB allocated

Algorithm

1×	egg-herbie

Rules

26×	`*-commutative_binary64`
18×	`+-commutative_binary64`
10×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	46
1	40	46
2	49	46
3	58	46
4	65	46
5	69	46
6	70	46

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal 4 binary64))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal -6 binary64)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 v v) (+.f64 #s(literal -5/8 binary64) (.f64 (*.f64 v v) #s(literal 3/32 binary64))))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 v (*.f64 v #s(literal -5/8 binary64)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))

Outputs
(.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (.f64 v v) #s(literal 4 binary64))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal -6 binary64)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 v v) (+.f64 #s(literal -5/8 binary64) (.f64 (*.f64 v v) #s(literal 3/32 binary64))))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 v (*.f64 v #s(literal -5/8 binary64)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))

soundness2.1s (20.3%)

Memory

-147.0MiB live, 2 821.4MiB allocated

Rules

22 876×	`accelerator-lowering-fma.f32`
22 876×	`accelerator-lowering-fma.f64`
7 438×	`accelerator-lowering-fma.f32`
7 438×	`accelerator-lowering-fma.f64`
6 326×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	19
1	36	19
2	88	19
3	219	19
4	646	19
5	1458	19
6	2003	19
7	3601	19
8	4895	19
9	6414	19
10	7378	19
0	8003	17
0	29	145
1	168	145
2	1247	145
0	8312	131
0	182	1054
1	500	1032
2	1780	924
3	7807	924
0	8459	876
0	15	50
1	72	49
2	509	49
3	6455	49
0	8146	44

Stop Event

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

Compiler

Compiled 178 to 124 computations (30.3% saved)

preprocess31.0ms (0.3%)

Memory: 1.7MiB live, 81.0MiB allocated
Remove: (abs v)
Compiler: Compiled 202 to 126 computations (37.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	29	233
1	78	233
2	175	233
3	343	233
4	454	233
5	472	233
6	504	233
7	538	233
8	538	233
9	542	233
10	548	233
11	548	233
0	548	214

Iter	Nodes	Cost
0	29	233
1	78	233
2	175	233
3	343	233
4	454	233
5	472	233
6	504	233
7	538	233
8	538	233
9	542	233
10	548	233
11	548	233
0	548	214

analyze4.0ms (0%)

sample1.3s (12.6%)

preprocess357.0ms (3.4%)

explain217.0ms (2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify367.0ms (3.5%)

localize54.0ms (0.5%)

series6.0ms (0.1%)

rewrite384.0ms (3.6%)

simplify783.0ms (7.4%)

eval32.0ms (0.3%)

prune30.0ms (0.3%)

simplify33.0ms (0.3%)

localize234.0ms (2.2%)

series136.0ms (1.3%)

rewrite671.0ms (6.3%)

simplify582.0ms (5.5%)

eval145.0ms (1.4%)

prune100.0ms (0.9%)

simplify320.0ms (3%)

localize195.0ms (1.8%)

series8.0ms (0.1%)

rewrite464.0ms (4.4%)

simplify436.0ms (4.1%)

eval207.0ms (2%)

prune111.0ms (1%)

simplify247.0ms (2.3%)

localize31.0ms (0.3%)

series4.0ms (0%)

rewrite260.0ms (2.5%)

simplify451.0ms (4.3%)

eval44.0ms (0.4%)

prune118.0ms (1.1%)

regimes13.0ms (0.1%)

regimes27.0ms (0.3%)

regimes4.0ms (0%)

regimes2.0ms (0%)

simplify9.0ms (0.1%)

soundness2.1s (20.3%)

preprocess31.0ms (0.3%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	29	233
1	78	233
2	175	233
3	343	233
4	454	233
5	472	233
6	504	233
7	538	233
8	538	233
9	542	233
10	548	233
11	548	233
0	548	214