Metrics for Falkner and Boettcher, Appendix B, 2

analyze3.0ms (0%)

Memory

9.2MiB live, 9.2MiB 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)

sample1.1s (10.4%)

Memory

39.9MiB live, 1 829.0MiB allocated

Samples

786.0ms	8 256×	0	valid
1.0ms	8×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 536.0ms

ival-mult: 228.0ms (42.5% of total)

ival-sqrt: 134.0ms (25% of total)

ival-sub: 91.0ms (17% of total)

ival-div: 61.0ms (11.4% of total)

exact: 13.0ms (2.4% of total)

ival-true: 5.0ms (0.9% of total)

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

Bogosity

preprocess446.0ms (4.3%)

Memory

25.0MiB live, 538.0MiB 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)))

(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (sqrt.f64 (fma.f64 v (fma.f64 v #s(literal -3 binary64) #s(literal 0 binary64)) #s(literal 1 binary64))) (fma.f64 v (fma.f64 v #s(literal -1/4 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)) #s(literal 0 binary64)) #s(literal 0 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)

explain172.0ms (1.7%)

Memory

-3.1MiB live, 409.5MiB 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

64.0ms

512×

valid

Compiler

Compiled 186 to 60 computations (67.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 46.0ms

ival-sqrt: 25.0ms (53.8% of total)

ival-mult: 12.0ms (25.8% of total)

ival-div: 4.0ms (8.6% of total)

ival-sub: 4.0ms (8.6% of total)

exact: 1.0ms (2.2% of total)

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

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

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

2.0MiB live, 2.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(.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)))

Status

Accuracy

Program

▶

100.0%

(*.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)))

Compiler

Compiled 20 to 14 computations (30% saved)

simplify245.0ms (2.4%)

Memory

-7.0MiB live, 539.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	128	(.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)))
✓	cost-diff	192	(-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v)))
✓	cost-diff	320	(/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64))

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	14	71
1	36	71
2	88	71
3	219	71
4	646	71
5	1458	71
6	2003	71
7	3601	71
8	4895	71
9	6414	71
10	7378	71
0	8003	66

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

Outputs
(* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v)))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (sqrt.f64 (fma.f64 v (fma.f64 v #s(literal -3 binary64) #s(literal 0 binary64)) #s(literal 1 binary64))) (fma.f64 v (fma.f64 v #s(literal -1/4 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))
(* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v)))))
(fma.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64) #s(literal 0 binary64)) (sqrt.f64 (fma.f64 v (fma.f64 v #s(literal -3 binary64) #s(literal 0 binary64)) #s(literal 1 binary64))) #s(literal 0 binary64))
(/ (sqrt 2) 4)
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64) #s(literal 0 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
4
#s(literal 4 binary64)
(sqrt (- 1 (* 3 (* v v))))
(sqrt.f64 (fma.f64 v (fma.f64 v #s(literal -3 binary64) #s(literal 0 binary64)) #s(literal 1 binary64)))
(- 1 (* 3 (* v v)))
(fma.f64 v (fma.f64 v #s(literal -3 binary64) #s(literal 0 binary64)) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(* 3 (* v v))
(fma.f64 #s(literal 3 binary64) (fma.f64 v v #s(literal 0 binary64)) #s(literal 0 binary64))
3
#s(literal 3 binary64)
(* v v)
(fma.f64 v v #s(literal 0 binary64))
v
(- 1 (* v v))
(-.f64 #s(literal 1 binary64) (fma.f64 v v #s(literal 0 binary64)))

localize77.0ms (0.7%)

Memory

-11.2MiB live, 121.0MiB allocated

Localize:

Found 4 expressions of interest:

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

Samples

58.0ms

256×

valid

Compiler

Compiled 73 to 16 computations (78.1% saved)

Precisions

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

ival-sqrt: 36.0ms (73.1% of total)

ival-div: 5.0ms (10.2% of total)

ival-mult: 5.0ms (10.2% of total)

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

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

exact: 0.0ms (0% of total)

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

series7.0ms (0.1%)

Memory

14.3MiB live, 14.3MiB allocated

Counts

7 → 60

Calls

Call 1

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

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

Calls

15 calls:

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

rewrite332.0ms (3.2%)

Memory

2.9MiB live, 634.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 304×	`accelerator-lowering-fma.f32`
4 304×	`accelerator-lowering-fma.f64`
4 064×	`-lowering-.f32`
4 064×	`-lowering-.f64`
2 112×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	58
1	71	56
2	483	56
3	4843	56
0	8493	51

Stop Event

1×	iter limit
1×	node limit

Counts

7 → 450

Calls

Call 1

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

Outputs
(exp.f64 (.f64 (-.f64 #s(literal 0 binary64) (log.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/4 binary64)))
(neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/4 binary64)))
(neg.f64 (.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/4 binary64))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 4 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 4 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -4 binary64))
(/.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -4 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -4 binary64))
(pow.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 4 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 4 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 4 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64))
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(.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (fma.f64 v (*.f64 #s(literal 3 binary64) v) #s(literal 1 binary64))))) #s(literal -1/4 binary64))
(.f64 (pow.f64 (fma.f64 v (.f64 #s(literal 3 binary64) v) #s(literal 1 binary64)) #s(literal 1/4 binary64)) (.f64 (pow.f64 (fma.f64 v (.f64 #s(literal 3 binary64) v) #s(literal 1 binary64)) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))))
(.f64 (pow.f64 (fma.f64 v (.f64 #s(literal 3 binary64) v) #s(literal 1 binary64)) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (fma.f64 v (*.f64 #s(literal 3 binary64) v) #s(literal 1 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal 4 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 #s(literal 3 binary64) v) #s(literal 1 binary64))) #s(literal 1/4 binary64))))
(.f64 (.f64 (sqrt.f64 (fma.f64 v (*.f64 #s(literal 3 binary64) v) #s(literal 1 binary64))) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (fma.f64 v (.f64 #s(literal 3 binary64) v) #s(literal 1 binary64))))) #s(literal 1/4 binary64))
(.f64 (/.f64 (pow.f64 (fma.f64 v (.f64 #s(literal 3 binary64) v) #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal 4 binary64)) (/.f64 (pow.f64 (fma.f64 v (*.f64 #s(literal 3 binary64) v) #s(literal 1 binary64)) #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 v (.f64 #s(literal 3 binary64) v) #s(literal 1 binary64)) #s(literal 1/4 binary64))) (pow.f64 (fma.f64 v (*.f64 #s(literal 3 binary64) v) #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(.f64 (/.f64 (sqrt.f64 (fma.f64 v (.f64 #s(literal 3 binary64) v) #s(literal 1 binary64))) #s(literal 1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(.f64 (/.f64 (sqrt.f64 (fma.f64 v (.f64 #s(literal 3 binary64) v) #s(literal 1 binary64))) #s(literal -4 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))))

simplify861.0ms (8.3%)

Memory

-265.1MiB live, 911.5MiB allocated

Algorithm

1×	egg-herbie

Rules

21 458×	`accelerator-lowering-fma.f32`
21 458×	`accelerator-lowering-fma.f64`
5 772×	`-lowering-.f32`
5 772×	`-lowering-.f64`
3 222×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	174	1058
1	538	1029
2	2040	972
3	5880	963
0	8237	908

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

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

Outputs
1
#s(literal 1 binary64)
(+ 1 (* -3 (pow v 2)))
(fma.f64 #s(literal -3 binary64) (*.f64 v v) #s(literal 1 binary64))
(+ 1 (* -3 (pow v 2)))
(fma.f64 #s(literal -3 binary64) (*.f64 v v) #s(literal 1 binary64))
(+ 1 (* -3 (pow v 2)))
(fma.f64 #s(literal -3 binary64) (*.f64 v v) #s(literal 1 binary64))
(* -3 (pow v 2))
(.f64 #s(literal -3 binary64) (.f64 v v))
(* (pow v 2) (- (/ 1 (pow v 2)) 3))
(fma.f64 #s(literal -3 binary64) (*.f64 v v) #s(literal 1 binary64))
(* (pow v 2) (- (/ 1 (pow v 2)) 3))
(fma.f64 #s(literal -3 binary64) (*.f64 v v) #s(literal 1 binary64))
(* (pow v 2) (- (/ 1 (pow v 2)) 3))
(fma.f64 #s(literal -3 binary64) (*.f64 v v) #s(literal 1 binary64))
(* -3 (pow v 2))
(.f64 #s(literal -3 binary64) (.f64 v v))
(* (pow v 2) (- (/ 1 (pow v 2)) 3))
(fma.f64 #s(literal -3 binary64) (*.f64 v v) #s(literal 1 binary64))
(* (pow v 2) (- (/ 1 (pow v 2)) 3))
(fma.f64 #s(literal -3 binary64) (*.f64 v v) #s(literal 1 binary64))
(* (pow v 2) (- (/ 1 (pow v 2)) 3))
(fma.f64 #s(literal -3 binary64) (*.f64 v v) #s(literal 1 binary64))
(* 1/4 (sqrt 2))
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))
(fma.f64 v (.f64 v (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -5/8 binary64))) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))) (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))))))
(.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 v v) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) #s(literal 3/8 binary64) #s(literal -5/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -27/16 (sqrt 2)) (* 9/8 (sqrt 2))))) (* 1/4 (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2)))))))))
(fma.f64 (.f64 v v) (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) #s(literal -9/16 binary64) #s(literal 3/8 binary64))) (.f64 (.f64 v v) #s(literal 1/4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -5/8 binary64))) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* -1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(.f64 v (.f64 (.f64 v v) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -3 binary64))))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2)))))
(.f64 (.f64 v v) (fma.f64 #s(literal 1 binary64) (.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64)))) (/.f64 #s(literal 1/4 binary64) v)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal -1/4 binary64) (*.f64 v (sqrt.f64 #s(literal -3 binary64)))))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))
(.f64 (.f64 v (.f64 v v)) (fma.f64 #s(literal 1/4 binary64) (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v (.f64 v (sqrt.f64 #s(literal -3 binary64))))) (/.f64 #s(literal 11/24 binary64) (.f64 v v)) (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64)))) (.f64 v v))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -3 binary64))))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(.f64 (.f64 v (.f64 v v)) (fma.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/24 binary64)) (sqrt.f64 #s(literal -3 binary64)))) (pow.f64 v #s(literal 6 binary64))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v (.f64 v (sqrt.f64 #s(literal -3 binary64))))) (/.f64 #s(literal 11/24 binary64) (.f64 v v)) (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64)))) (.f64 v v)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -3 binary64))))))
(* 1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(.f64 v (.f64 (.f64 v v) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -3 binary64))))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))))))
(.f64 (.f64 v (.f64 v v)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64)))) (.f64 v v)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -3 binary64))))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(.f64 (.f64 v (.f64 v v)) (fma.f64 #s(literal -1/4 binary64) (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v (.f64 v (sqrt.f64 #s(literal -3 binary64))))) (/.f64 #s(literal 11/24 binary64) (.f64 v v)) (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64)))) (.f64 v v))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -3 binary64))))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))))
(.f64 (.f64 v (.f64 v v)) (fma.f64 #s(literal -1/4 binary64) (+.f64 (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/24 binary64)) (sqrt.f64 #s(literal -3 binary64)))) (pow.f64 v #s(literal 6 binary64))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v (.f64 v (sqrt.f64 #s(literal -3 binary64))))) (/.f64 #s(literal 11/24 binary64) (.f64 v v)) (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64)))) (.f64 v v)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #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)))
(* 3 (pow v 2))
(.f64 v (.f64 v #s(literal 3 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -3/2 (pow v 2)))
(fma.f64 v (*.f64 v #s(literal -3/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow v 2) (- (* -9/8 (pow v 2)) 3/2)))
(fma.f64 (.f64 v v) (fma.f64 (.f64 v v) #s(literal -9/8 binary64) #s(literal -3/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow v 2) (- (* (pow v 2) (- (* -27/16 (pow v 2)) 9/8)) 3/2)))
(fma.f64 (.f64 v v) (fma.f64 v (.f64 v (fma.f64 v (*.f64 v #s(literal -27/16 binary64)) #s(literal -9/8 binary64))) #s(literal -3/2 binary64)) #s(literal 1 binary64))
(* v (sqrt -3))
(*.f64 v (sqrt.f64 #s(literal -3 binary64)))
(* v (+ (sqrt -3) (* 1/2 (/ 1 (* (pow v 2) (sqrt -3))))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 v (sqrt.f64 #s(literal -3 binary64)))) (.f64 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)))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 v (sqrt.f64 #s(literal -3 binary64)))) (.f64 (+.f64 (sqrt.f64 #s(literal -3 binary64)) (/.f64 #s(literal 1/24 binary64) (.f64 (sqrt.f64 #s(literal -3 binary64)) (.f64 (.f64 v v) (.f64 v 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))))))
(fma.f64 #s(literal 1/24 binary64) (/.f64 v (.f64 (sqrt.f64 #s(literal -3 binary64)) (.f64 (.f64 v v) (.f64 v v)))) (fma.f64 v (+.f64 (sqrt.f64 #s(literal -3 binary64)) (/.f64 #s(literal 1/16 binary64) (.f64 (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64)) (pow.f64 v #s(literal 6 binary64))))) (.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 v (sqrt.f64 #s(literal -3 binary64)))))))
(* -1 (* v (sqrt -3)))
(*.f64 v (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -3 binary64))))
(* -1 (* v (+ (sqrt -3) (* 1/2 (/ 1 (* (pow v 2) (sqrt -3)))))))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 v (sqrt.f64 #s(literal -3 binary64)))) (.f64 v (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -3 binary64)))))
(* -1 (* v (- (+ (sqrt -3) (/ 1/2 (* (pow v 2) (sqrt -3)))) (/ 1/8 (* (pow v 4) (pow (sqrt -3) 3))))))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 v (sqrt.f64 #s(literal -3 binary64)))) (neg.f64 (.f64 (+.f64 (sqrt.f64 #s(literal -3 binary64)) (/.f64 #s(literal 1/24 binary64) (.f64 (sqrt.f64 #s(literal -3 binary64)) (.f64 (.f64 v v) (.f64 v v))))) 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 v (-.f64 (/.f64 #s(literal -1/24 binary64) (.f64 (sqrt.f64 #s(literal -3 binary64)) (.f64 (.f64 v v) (.f64 v v)))) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 v (.f64 v (sqrt.f64 #s(literal -3 binary64))))) (+.f64 (sqrt.f64 #s(literal -3 binary64)) (/.f64 #s(literal 1/16 binary64) (.f64 (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64)) (pow.f64 v #s(literal 6 binary64))))))))
(* 1/4 (sqrt 2))
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -3/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) #s(literal -3/8 binary64) #s(literal 1/4 binary64)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* -9/32 (* (pow v 2) (sqrt 2))))))
(fma.f64 (.f64 v v) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 v (.f64 v #s(literal -9/32 binary64)) #s(literal -3/8 binary64))) (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* (pow v 2) (+ (* -27/64 (* (pow v 2) (sqrt 2))) (* -9/32 (sqrt 2)))))))
(fma.f64 (.f64 v v) (.f64 (.f64 v (.f64 v (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (.f64 v v) #s(literal -27/64 binary64) #s(literal -9/32 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 v v) #s(literal -3/8 binary64) #s(literal 1/4 binary64))))
(* 1/4 (* v (* (sqrt -3) (sqrt 2))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (*.f64 v (sqrt.f64 #s(literal -3 binary64)))))
(* v (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))
(fma.f64 #s(literal 1 binary64) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64)) (.f64 v (sqrt.f64 #s(literal -3 binary64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (*.f64 v (sqrt.f64 #s(literal -3 binary64))))))
(* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))
(fma.f64 #s(literal 1 binary64) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64)) (.f64 v (sqrt.f64 #s(literal -3 binary64)))) (.f64 v (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal -3 binary64)) (.f64 (.f64 v v) (.f64 v v)))) #s(literal 1/96 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -3 binary64)))))))
(* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))))
(fma.f64 v (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal -3 binary64)) (.f64 (.f64 v v) (.f64 v v)))) #s(literal 1/96 binary64) (fma.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)) #s(literal 1/64 binary64)) (.f64 (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64)) (pow.f64 v #s(literal 6 binary64)))))) (.f64 #s(literal 1 binary64) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64)) (.f64 v (sqrt.f64 #s(literal -3 binary64))))))
(* -1/4 (* v (* (sqrt -3) (sqrt 2))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal -1/4 binary64) (*.f64 v (sqrt.f64 #s(literal -3 binary64)))))
(* -1 (* v (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))
(fma.f64 #s(literal -1 binary64) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64)) (.f64 v (sqrt.f64 #s(literal -3 binary64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal -1/4 binary64) (*.f64 v (sqrt.f64 #s(literal -3 binary64))))))
(* -1 (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))))
(.f64 v (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal -3 binary64)) (.f64 (.f64 v v) (.f64 v v)))) #s(literal -1/96 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v (.f64 v (sqrt.f64 #s(literal -3 binary64))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -3 binary64)))))))
(* -1 (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))))
(.f64 v (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal -3 binary64)) (.f64 (.f64 v v) (.f64 v v)))) #s(literal -1/96 binary64) (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64)) (pow.f64 v #s(literal 6 binary64)))) #s(literal -1/64 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v (.f64 v (sqrt.f64 #s(literal -3 binary64))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -3 binary64))))))))

eval68.0ms (0.7%)

Memory: 10.2MiB live, 161.7MiB allocated
Compiler: Compiled 15 440 to 1 766 computations (88.6% saved)

prune66.0ms (0.6%)

Memory

-2.1MiB live, 166.4MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	504	6	510
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	505	6	511

Accuracy

100.0%

Counts

511 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(fma.f64 v (.f64 v (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -5/8 binary64))) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))))
▶	100.0%	(.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (.f64 v v)))
▶	99.7%	(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) #s(literal -3/8 binary64) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v)))
▶	99.5%	(.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
	99.7%	(.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 v v) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) #s(literal 3/8 binary64) #s(literal -5/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
▶	99.5%	(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))

Compiler

Compiled 166 to 118 computations (28.9% saved)

simplify363.0ms (3.5%)

Memory

14.6MiB live, 610.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -5/8 binary64))
✓	cost-diff	0	(.f64 v (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -5/8 binary64)))
✓	cost-diff	896	(fma.f64 v (.f64 v (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -5/8 binary64))) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (*.f64 v v))
✓	cost-diff	0	(fma.f64 (*.f64 v v) #s(literal -3/8 binary64) #s(literal 1/4 binary64))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	128	(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) #s(literal -3/8 binary64) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v)))
✓	cost-diff	-64	(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (*.f64 v v))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	128	(.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
✓	cost-diff	-64	(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	128	(.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))) (-.f64 #s(literal 1 binary64) (.f64 v v)))
✓	cost-diff	192	(-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v)))

Rules

13 594×	`accelerator-lowering-fma.f32`
13 594×	`accelerator-lowering-fma.f64`
3 500×	`-lowering-.f32`
3 500×	`-lowering-.f64`
1 670×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	188
1	73	188
2	203	185
3	594	185
4	1874	185
5	3678	185
6	6538	185
0	8311	174

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

Outputs
(* (* (* (sqrt 2) 1/4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v)))
(fma.f64 (sqrt.f64 (fma.f64 (fma.f64 v v #s(literal 0 binary64)) #s(literal -3 binary64) #s(literal 1 binary64))) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 v (fma.f64 v #s(literal -1/4 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))
(* (* (sqrt 2) 1/4) (sqrt (- 1 (* 3 (* v v)))))
(fma.f64 #s(literal 1/4 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (fma.f64 (fma.f64 v v #s(literal 0 binary64)) #s(literal -3 binary64) #s(literal 1 binary64))) #s(literal 0 binary64)) #s(literal 0 binary64))
(* (sqrt 2) 1/4)
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64) #s(literal 0 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
1/4
#s(literal 1/4 binary64)
(sqrt (- 1 (* 3 (* v v))))
(sqrt.f64 (fma.f64 (fma.f64 v v #s(literal 0 binary64)) #s(literal -3 binary64) #s(literal 1 binary64)))
(- 1 (* 3 (* v v)))
(fma.f64 (fma.f64 v v #s(literal 0 binary64)) #s(literal -3 binary64) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(* 3 (* v v))
(fma.f64 #s(literal 3 binary64) (fma.f64 v v #s(literal 0 binary64)) #s(literal 0 binary64))
3
#s(literal 3 binary64)
(* v v)
(fma.f64 v v #s(literal 0 binary64))
v
(- 1 (* v v))
(-.f64 #s(literal 1 binary64) (fma.f64 v v #s(literal 0 binary64)))
(* 1/4 (sqrt 2))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64) #s(literal 0 binary64))
1/4
#s(literal 1/4 binary64)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(* (* 1/4 (sqrt 2)) (- 1 (* v v)))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 v (fma.f64 v #s(literal -1/4 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)) #s(literal 0 binary64))
(* 1/4 (sqrt 2))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64) #s(literal 0 binary64))
1/4
#s(literal 1/4 binary64)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(- 1 (* v v))
(-.f64 #s(literal 1 binary64) (fma.f64 v v #s(literal 0 binary64)))
1
#s(literal 1 binary64)
(* v v)
(fma.f64 v v #s(literal 0 binary64))
v
(* (* (sqrt 2) (+ (* (* v v) -3/8) 1/4)) (- 1 (* v v)))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (fma.f64 v v #s(literal 0 binary64)) (fma.f64 (fma.f64 v v #s(literal -1 binary64)) #s(literal 3/8 binary64) #s(literal -1/4 binary64)) #s(literal 1/4 binary64)) #s(literal 0 binary64))
(* (sqrt 2) (+ (* (* v v) -3/8) 1/4))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 v (fma.f64 v #s(literal -3/8 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)) #s(literal 0 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(+ (* (* v v) -3/8) 1/4)
(fma.f64 v (fma.f64 v #s(literal -3/8 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64))
(* v v)
(fma.f64 v v #s(literal 0 binary64))
v
-3/8
#s(literal -3/8 binary64)
1/4
#s(literal 1/4 binary64)
(- 1 (* v v))
(-.f64 #s(literal 1 binary64) (fma.f64 v v #s(literal 0 binary64)))
1
#s(literal 1 binary64)
(+ (* v (* v (* (sqrt 2) -5/8))) (* 1/4 (sqrt 2)))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (fma.f64 v v #s(literal 0 binary64)) #s(literal -5/8 binary64) #s(literal 1/4 binary64)) #s(literal 0 binary64))
v
(* v (* (sqrt 2) -5/8))
(.f64 v (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -5/8 binary64)))
(* (sqrt 2) -5/8)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -5/8 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
-5/8
#s(literal -5/8 binary64)
(* 1/4 (sqrt 2))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64) #s(literal 0 binary64))
1/4
#s(literal 1/4 binary64)

localize101.0ms (1%)

Memory

9.9MiB live, 199.3MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(fma.f64 v (.f64 v (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -5/8 binary64))) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	99.6%	(.f64 v (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -5/8 binary64)))
✓	accuracy	100.0%	(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) #s(literal -3/8 binary64) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v)))
✓	accuracy	100.0%	(*.f64 v v)
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) #s(literal -3/8 binary64) #s(literal 1/4 binary64)))
✓	accuracy	100.0%	(*.f64 v v)
✓	accuracy	100.0%	(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
✓	accuracy	100.0%	(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v)))))
✓	accuracy	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))
✓	accuracy	99.7%	(.f64 #s(literal 3 binary64) (.f64 v v))

Samples

56.0ms

256×

valid

Compiler

Compiled 186 to 28 computations (84.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 38.0ms

ival-mult: 19.0ms (50.1% of total)

ival-sub: 12.0ms (31.7% of total)

ival-sqrt: 4.0ms (10.6% of total)

ival-add: 2.0ms (5.3% of total)

exact: 1.0ms (2.6% of total)

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

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

series12.0ms (0.1%)

Memory

-18.2MiB live, 17.5MiB allocated

Counts

16 → 156

Calls

Call 1

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

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

Calls

39 calls:

Time	Variable		Point	Expression
4.0ms	v	@	0	(+ (* v (* v (* (sqrt 2) -5/8))) (* 1/4 (sqrt 2)))
1.0ms	v	@	inf	(+ (* v (* v (* (sqrt 2) -5/8))) (* 1/4 (sqrt 2)))
1.0ms	v	@	0	(* v (* (sqrt 2) -5/8))
0.0ms	v	@	inf	(* (* (sqrt 2) (+ (* (* v v) -3/8) 1/4)) (- 1 (* v v)))
0.0ms	v	@	0	(* (* 1/4 (sqrt 2)) (- 1 (* v v)))

rewrite480.0ms (4.6%)

Memory

12.5MiB live, 891.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

9 554×	`accelerator-lowering-fma.f32`
9 554×	`accelerator-lowering-fma.f64`
6 822×	`-lowering-.f32`
6 822×	`-lowering-.f64`
2 686×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	132
1	125	132
2	915	127
0	8634	119

Stop Event

1×	iter limit
1×	node limit

Counts

16 → 900

Calls

Call 1

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

Outputs
(+.f64 #s(literal 1 binary64) (.f64 (.f64 v v) #s(literal -3 binary64)))
(+.f64 (.f64 (.f64 v v) #s(literal -3 binary64)) #s(literal 1 binary64))
(+.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 v v) (fma.f64 (.f64 v v) #s(literal 9 binary64) #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (/.f64 (.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 27 binary64))) (fma.f64 (.f64 v v) (fma.f64 (.f64 v v) #s(literal 9 binary64) #s(literal 3 binary64)) #s(literal 1 binary64)))))
(+.f64 (/.f64 #s(literal -1 binary64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal -1 binary64))) (neg.f64 (/.f64 (.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 9 binary64)))) (fma.f64 #s(literal 3 binary64) (.f64 v v) #s(literal 1 binary64)))))
(-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v)))
(-.f64 #s(literal 0 binary64) (-.f64 (.f64 #s(literal 3 binary64) (.f64 v v)) #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 v v) (fma.f64 (.f64 v v) #s(literal 9 binary64) #s(literal 3 binary64)) #s(literal 1 binary64))) (/.f64 (.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 27 binary64))) (fma.f64 (.f64 v v) (fma.f64 (.f64 v v) #s(literal 9 binary64) #s(literal 3 binary64)) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal -1 binary64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal -1 binary64))) (/.f64 (.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 9 binary64)))) (fma.f64 #s(literal 3 binary64) (.f64 v v) #s(literal 1 binary64))))
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 v v) #s(literal -3 binary64)) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 v v) (fma.f64 (.f64 v v) #s(literal 9 binary64) #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (/.f64 (.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 27 binary64))) (fma.f64 (.f64 v v) (fma.f64 (.f64 v v) #s(literal 9 binary64) #s(literal 3 binary64)) #s(literal 1 binary64)))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal -1 binary64))) (neg.f64 (/.f64 (.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 9 binary64)))) (fma.f64 #s(literal 3 binary64) (.f64 v v) #s(literal 1 binary64)))))
(fma.f64 #s(literal 3 binary64) (-.f64 #s(literal 0 binary64) (*.f64 v v)) #s(literal 1 binary64))
(fma.f64 v (*.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))
(fma.f64 (*.f64 v v) #s(literal -3 binary64) #s(literal 1 binary64))
(fma.f64 (.f64 #s(literal 3 binary64) (.f64 v v)) #s(literal -1 binary64) #s(literal 1 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (*.f64 v v)) #s(literal 3 binary64) #s(literal 1 binary64))
(fma.f64 (.f64 (.f64 v v) #s(literal -3 binary64)) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) v) (*.f64 #s(literal 3 binary64) v) #s(literal 1 binary64))
(fma.f64 #s(literal -3 binary64) (*.f64 v v) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal 3 binary64) v) (-.f64 #s(literal 0 binary64) v) #s(literal 1 binary64))
(fma.f64 #s(literal -1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v)) #s(literal 1 binary64))
(fma.f64 (*.f64 v #s(literal -3 binary64)) v #s(literal 1 binary64))
(fma.f64 (.f64 #s(literal 1 binary64) (.f64 v #s(literal -3 binary64))) v #s(literal 1 binary64))
(fma.f64 (.f64 (.f64 #s(literal 3 binary64) v) #s(literal -1 binary64)) v #s(literal 1 binary64))
(neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 v (.f64 v v)) (.f64 v (.f64 v v))) #s(literal -27 binary64))) (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 v v) (fma.f64 (.f64 v v) #s(literal 9 binary64) #s(literal 3 binary64)) #s(literal 1 binary64)))))
(neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal -9 binary64))) (fma.f64 v (*.f64 v #s(literal -3 binary64)) #s(literal -1 binary64))))
(neg.f64 (/.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (.f64 (.f64 (.f64 v (.f64 v v)) (.f64 v (.f64 v v))) #s(literal -27 binary64)))) (fma.f64 (.f64 v v) (fma.f64 (.f64 v v) #s(literal 9 binary64) #s(literal 3 binary64)) #s(literal 1 binary64))))
(neg.f64 (/.f64 (+.f64 #s(literal -1 binary64) (.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 9 binary64))))) (fma.f64 #s(literal 3 binary64) (*.f64 v v) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 v (*.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 v (*.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 v (.f64 v v)) (.f64 v (.f64 v v))) #s(literal -27 binary64))) (fma.f64 (.f64 v v) (fma.f64 (.f64 v v) #s(literal 9 binary64) #s(literal 3 binary64)) #s(literal 1 binary64)))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal -9 binary64))) (fma.f64 #s(literal 3 binary64) (*.f64 v v) #s(literal 1 binary64)))
(/.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (.f64 (.f64 (.f64 v (.f64 v v)) (.f64 v (.f64 v v))) #s(literal -27 binary64)))) (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 v v) (fma.f64 (.f64 v v) #s(literal 9 binary64) #s(literal 3 binary64)) #s(literal 1 binary64))))
(/.f64 (+.f64 #s(literal -1 binary64) (.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 9 binary64))))) (fma.f64 v (*.f64 v #s(literal -3 binary64)) #s(literal -1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 v (*.f64 v #s(literal -3 binary64)) #s(literal 1 binary64)))))
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(.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -3 binary64)) #s(literal 1 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (pow.f64 (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 1 binary64)) #s(literal 1/4 binary64)) (.f64 (pow.f64 (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 1 binary64)) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))))
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(pow.f64 (*.f64 v v) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 v)) #s(literal 2 binary64))
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(*.f64 v v)
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(.f64 (.f64 v v) #s(literal 1 binary64))
(*.f64 (exp.f64 (log.f64 v)) (exp.f64 (log.f64 v)))
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(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 v (.f64 v #s(literal -3/8 binary64)) #s(literal -1/4 binary64))) (fma.f64 #s(literal 2 binary64) (.f64 v (.f64 (.f64 v (.f64 v v)) #s(literal 9/64 binary64))) #s(literal -1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (fma.f64 v (.f64 (.f64 v (.f64 v v)) #s(literal 9/64 binary64)) #s(literal 1/16 binary64)) (.f64 (.f64 v v) #s(literal 3/32 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (*.f64 v v)) #s(literal -27/512 binary64)) #s(literal 1/64 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 v (.f64 v #s(literal -3/8 binary64)) #s(literal -1/4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 v (.f64 (.f64 v (*.f64 v v)) #s(literal 9/64 binary64)) #s(literal -1/16 binary64)))))
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(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 v (.f64 v #s(literal -3/8 binary64)) #s(literal -1/4 binary64)) (.f64 (fma.f64 v (.f64 (.f64 v (*.f64 v v)) #s(literal 9/64 binary64)) #s(literal -1/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 v (*.f64 v #s(literal -3/8 binary64)) #s(literal 1/4 binary64))))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 v (.f64 v v)) (.f64 v (.f64 v v))) #s(literal -27/512 binary64)) (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/32 binary64))) (-.f64 (fma.f64 #s(literal 2 binary64) (.f64 v (.f64 (.f64 v (.f64 v v)) #s(literal 9/64 binary64))) #s(literal 1/8 binary64)) (.f64 (.f64 v (*.f64 v #s(literal -3/8 binary64))) #s(literal 1/2 binary64))))
(/.f64 (fma.f64 #s(literal 2 binary64) (.f64 v (.f64 (.f64 v (.f64 v v)) #s(literal 9/64 binary64))) #s(literal -1/8 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 v (.f64 v #s(literal -3/8 binary64)) #s(literal -1/4 binary64))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal -27/512 binary64)) #s(literal 1/64 binary64))) (+.f64 (fma.f64 v (.f64 (.f64 v (.f64 v v)) #s(literal 9/64 binary64)) #s(literal 1/16 binary64)) (.f64 (*.f64 v v) #s(literal 3/32 binary64))))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 v (.f64 (.f64 v (.f64 v v)) #s(literal 9/64 binary64)) #s(literal -1/16 binary64))) (fma.f64 v (*.f64 v #s(literal -3/8 binary64)) #s(literal -1/4 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal -27/512 binary64)) #s(literal 1/64 binary64)) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (fma.f64 v (.f64 (.f64 v (.f64 v v)) #s(literal 9/64 binary64)) #s(literal 1/16 binary64)) (.f64 (*.f64 v v) #s(literal 3/32 binary64))))
(/.f64 (.f64 (fma.f64 v (.f64 (.f64 v (.f64 v v)) #s(literal 9/64 binary64)) #s(literal -1/16 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 v (*.f64 v #s(literal -3/8 binary64)) #s(literal -1/4 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 (.f64 v (.f64 v v)) (.f64 v (.f64 v v))) #s(literal -27/512 binary64)) (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/32 binary64)))) (neg.f64 (-.f64 (fma.f64 #s(literal 2 binary64) (.f64 v (.f64 (.f64 v (.f64 v v)) #s(literal 9/64 binary64))) #s(literal 1/8 binary64)) (.f64 (.f64 v (*.f64 v #s(literal -3/8 binary64))) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 v (.f64 (.f64 v (.f64 v v)) #s(literal 9/64 binary64))) #s(literal -1/8 binary64))) (neg.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 v (.f64 v #s(literal -3/8 binary64)) #s(literal -1/4 binary64)))))
(/.f64 (neg.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal -27/512 binary64)) #s(literal 1/64 binary64)))) (-.f64 #s(literal 0 binary64) (+.f64 (fma.f64 v (.f64 (.f64 v (.f64 v v)) #s(literal 9/64 binary64)) #s(literal 1/16 binary64)) (.f64 (*.f64 v v) #s(literal 3/32 binary64)))))
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(/.f64 (neg.f64 (.f64 (fma.f64 v (.f64 (.f64 v (.f64 v v)) #s(literal 9/64 binary64)) #s(literal -1/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (*.f64 v v) #s(literal 3/8 binary64) #s(literal 1/4 binary64)))
(/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/32 binary64) (.f64 (.f64 (.f64 (.f64 v (.f64 v v)) (.f64 v (.f64 v v))) #s(literal -27/512 binary64)) (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))) (+.f64 #s(literal 1/8 binary64) (-.f64 (.f64 #s(literal 2 binary64) (.f64 v (.f64 (.f64 v (.f64 v v)) #s(literal 9/64 binary64)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 v (.f64 v (.f64 #s(literal -3/8 binary64) (sqrt.f64 #s(literal 2 binary64)))))))))
(/.f64 (-.f64 #s(literal 1/8 binary64) (.f64 #s(literal 2 binary64) (.f64 v (.f64 (.f64 v (.f64 v v)) #s(literal 9/64 binary64))))) (-.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 v (.f64 v (*.f64 #s(literal -3/8 binary64) (sqrt.f64 #s(literal 2 binary64)))))))
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(.f64 (fma.f64 v (.f64 (.f64 v (.f64 v v)) #s(literal 9/64 binary64)) #s(literal -1/16 binary64)) (.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 v v) #s(literal 3/8 binary64) #s(literal 1/4 binary64))) (sqrt.f64 #s(literal 2 binary64))))
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(.f64 (fma.f64 #s(literal 2 binary64) (.f64 v (.f64 (.f64 v (.f64 v v)) #s(literal 9/64 binary64))) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 v (*.f64 v #s(literal -3/8 binary64)) #s(literal -1/4 binary64)))))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (fma.f64 v (*.f64 v #s(literal -3/8 binary64)) #s(literal 1/4 binary64))))
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(.f64 (.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal -27/512 binary64)) #s(literal 1/64 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 v (.f64 (.f64 v (.f64 v v)) #s(literal 9/64 binary64)) #s(literal 1/16 binary64)) (.f64 (.f64 v v) #s(literal 3/32 binary64)))))
(.f64 (.f64 (fma.f64 v (.f64 (.f64 v (.f64 v v)) #s(literal 9/64 binary64)) #s(literal -1/16 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 v v) #s(literal 3/8 binary64) #s(literal 1/4 binary64))))
(.f64 (.f64 (fma.f64 v (*.f64 v #s(literal -3/8 binary64)) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))

simplify1.1s (10.7%)

Memory

10.2MiB live, 972.2MiB allocated

Algorithm

1×	egg-herbie

Rules

21 584×	`accelerator-lowering-fma.f32`
21 584×	`accelerator-lowering-fma.f64`
5 860×	`-lowering-.f32`
5 860×	`-lowering-.f64`
4 308×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	216	2025
1	665	1948
2	2386	1816
3	6237	1807
0	8215	1731

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 156

Calls

Call 1

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

Outputs
1
#s(literal 1 binary64)
(+ 1 (* -3 (pow v 2)))
(fma.f64 #s(literal -3 binary64) (*.f64 v v) #s(literal 1 binary64))
(+ 1 (* -3 (pow v 2)))
(fma.f64 #s(literal -3 binary64) (*.f64 v v) #s(literal 1 binary64))
(+ 1 (* -3 (pow v 2)))
(fma.f64 #s(literal -3 binary64) (*.f64 v v) #s(literal 1 binary64))
(* -3 (pow v 2))
(.f64 #s(literal -3 binary64) (.f64 v v))
(* (pow v 2) (- (/ 1 (pow v 2)) 3))
(fma.f64 #s(literal -3 binary64) (*.f64 v v) #s(literal 1 binary64))
(* (pow v 2) (- (/ 1 (pow v 2)) 3))
(fma.f64 #s(literal -3 binary64) (*.f64 v v) #s(literal 1 binary64))
(* (pow v 2) (- (/ 1 (pow v 2)) 3))
(fma.f64 #s(literal -3 binary64) (*.f64 v v) #s(literal 1 binary64))
(* -3 (pow v 2))
(.f64 #s(literal -3 binary64) (.f64 v v))
(* (pow v 2) (- (/ 1 (pow v 2)) 3))
(fma.f64 #s(literal -3 binary64) (*.f64 v v) #s(literal 1 binary64))
(* (pow v 2) (- (/ 1 (pow v 2)) 3))
(fma.f64 #s(literal -3 binary64) (*.f64 v v) #s(literal 1 binary64))
(* (pow v 2) (- (/ 1 (pow v 2)) 3))
(fma.f64 #s(literal -3 binary64) (*.f64 v v) #s(literal 1 binary64))
(* 1/4 (sqrt 2))
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) #s(literal -5/8 binary64) #s(literal 1/4 binary64)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))) (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))))))
(.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) #s(literal 3/8 binary64) #s(literal -5/2 binary64))) (.f64 v v) (sqrt.f64 #s(literal 2 binary64))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -27/16 (sqrt 2)) (* 9/8 (sqrt 2))))) (* 1/4 (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2)))))))))
(fma.f64 (.f64 v v) (.f64 (.f64 v v) (.f64 #s(literal 1/4 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -9/16 binary64) (.f64 v v) #s(literal 3/8 binary64))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) #s(literal -5/8 binary64) #s(literal 1/4 binary64))))
(* -1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(.f64 (.f64 v (.f64 v v)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -3 binary64)))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2)))))
(.f64 (.f64 v v) (fma.f64 #s(literal 1 binary64) (.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64)))) (/.f64 #s(literal 1/4 binary64) v)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) (*.f64 v #s(literal -1/4 binary64)))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))
(.f64 (.f64 v (.f64 v v)) (fma.f64 #s(literal 1/4 binary64) (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v (.f64 v (sqrt.f64 #s(literal -3 binary64))))) (/.f64 #s(literal 11/24 binary64) (.f64 v v)) (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64)))) (.f64 v v))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -3 binary64))))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(.f64 v (.f64 (.f64 v v) (fma.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/24 binary64)) (sqrt.f64 #s(literal -3 binary64)))) (pow.f64 v #s(literal 6 binary64))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v (.f64 v (sqrt.f64 #s(literal -3 binary64))))) (/.f64 #s(literal 11/24 binary64) (.f64 v v)) (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64)))) (.f64 v v)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -3 binary64)))))))
(* 1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(.f64 (.f64 v (.f64 v v)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -3 binary64)))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))))))
(.f64 (.f64 v (.f64 v v)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64)))) (.f64 v v)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -3 binary64))))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(.f64 (.f64 v (.f64 v v)) (fma.f64 #s(literal -1/4 binary64) (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v (.f64 v (sqrt.f64 #s(literal -3 binary64))))) (/.f64 #s(literal 11/24 binary64) (.f64 v v)) (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64)))) (.f64 v v))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -3 binary64))))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))))
(.f64 (.f64 v (.f64 v v)) (fma.f64 #s(literal -1/4 binary64) (+.f64 (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/24 binary64)) (sqrt.f64 #s(literal -3 binary64)))) (pow.f64 v #s(literal 6 binary64))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v (.f64 v (sqrt.f64 #s(literal -3 binary64))))) (/.f64 #s(literal 11/24 binary64) (.f64 v v)) (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64)))) (.f64 v v)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -3 binary64))))))
1
#s(literal 1 binary64)
(+ 1 (* -3/2 (pow v 2)))
(fma.f64 (*.f64 v v) #s(literal -3/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow v 2) (- (* -9/8 (pow v 2)) 3/2)))
(fma.f64 (.f64 v v) (fma.f64 v (.f64 v #s(literal -9/8 binary64)) #s(literal -3/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow v 2) (- (* (pow v 2) (- (* -27/16 (pow v 2)) 9/8)) 3/2)))
(fma.f64 (.f64 v v) (fma.f64 (.f64 v v) (fma.f64 (*.f64 v v) #s(literal -27/16 binary64) #s(literal -9/8 binary64)) #s(literal -3/2 binary64)) #s(literal 1 binary64))
(* v (sqrt -3))
(*.f64 v (sqrt.f64 #s(literal -3 binary64)))
(* v (+ (sqrt -3) (* 1/2 (/ 1 (* (pow v 2) (sqrt -3))))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 v (sqrt.f64 #s(literal -3 binary64)))) (.f64 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)))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 v (sqrt.f64 #s(literal -3 binary64)))) (.f64 v (+.f64 (sqrt.f64 #s(literal -3 binary64)) (/.f64 #s(literal 1/24 binary64) (.f64 (sqrt.f64 #s(literal -3 binary64)) (.f64 (.f64 v 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))))))
(fma.f64 v (sqrt.f64 #s(literal -3 binary64)) (fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 v (sqrt.f64 #s(literal -3 binary64)))) (.f64 v (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64)) (pow.f64 v #s(literal 6 binary64)))) (/.f64 #s(literal 1/24 binary64) (.f64 (sqrt.f64 #s(literal -3 binary64)) (.f64 (.f64 v v) (*.f64 v v))))))))
(* -1 (* v (sqrt -3)))
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1/4
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(.f64 v (fma.f64 #s(literal -1/96 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal -3 binary64)) (.f64 (.f64 v v) (.f64 v v)))) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 #s(literal -1/8 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v (*.f64 v (sqrt.f64 #s(literal -3 binary64)))))))))
(* -1 (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))))
(.f64 v (fma.f64 #s(literal -1/64 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64)) (pow.f64 v #s(literal 6 binary64)))) (fma.f64 #s(literal -1/96 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal -3 binary64)) (.f64 (.f64 v v) (.f64 v v)))) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -3 binary64))) (.f64 #s(literal -1/8 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v (.f64 v (sqrt.f64 #s(literal -3 binary64))))))))))
(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)))
(+ (* -3/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) #s(literal -3/8 binary64) #s(literal 1/4 binary64)))
(+ (* -3/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) #s(literal -3/8 binary64) #s(literal 1/4 binary64)))
(+ (* -3/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) #s(literal -3/8 binary64) #s(literal 1/4 binary64)))
(* -3/8 (* (pow v 2) (sqrt 2)))
(.f64 (.f64 v v) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -3/8 binary64)))
(* (pow v 2) (+ (* -3/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(fma.f64 (.f64 v v) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -3/8 binary64)) (.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64)))
(* (pow v 2) (+ (* -3/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(fma.f64 (.f64 v v) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -3/8 binary64)) (.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64)))
(* (pow v 2) (+ (* -3/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(fma.f64 (.f64 v v) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -3/8 binary64)) (.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64)))
(* -3/8 (* (pow v 2) (sqrt 2)))
(.f64 (.f64 v v) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -3/8 binary64)))
(* (pow v 2) (+ (* -3/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(fma.f64 (.f64 v v) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -3/8 binary64)) (.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64)))
(* (pow v 2) (+ (* -3/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(fma.f64 (.f64 v v) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -3/8 binary64)) (.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64)))
(* (pow v 2) (+ (* -3/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(fma.f64 (.f64 v v) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -3/8 binary64)) (.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64)))

eval392.0ms (3.8%)

Memory: 18.8MiB live, 403.2MiB allocated
Compiler: Compiled 38 118 to 2 804 computations (92.6% saved)

prune280.0ms (2.7%)

Memory

-15.7MiB live, 282.5MiB allocated

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	1 327	2	1 329
Fresh	1	0	1
Picked	4	1	5
Done	0	0	0
Total	1 332	3	1 335

Accuracy

100.0%

Counts

1 335 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

▶

100.0%

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

▶

99.7%

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

✓

99.5%

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

Compiler

Compiled 33 to 26 computations (21.2% saved)

simplify519.0ms (5%)

Memory

-11.6MiB live, 432.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 (.f64 (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (*.f64 v v))
✓	cost-diff	128	(.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (.f64 #s(literal 1/4 binary64) (sqrt.f64 (.f64 (fma.f64 v (*.f64 v #s(literal -3 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))))
✓	cost-diff	320	(.f64 (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
✓	cost-diff	-64	(*.f64 v v)
✓	cost-diff	-64	(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) #s(literal -5/8 binary64) #s(literal 1/4 binary64)))
✓	cost-diff	0	(fma.f64 (*.f64 v v) #s(literal -5/8 binary64) #s(literal 1/4 binary64))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))

Rules

12 164×	`accelerator-lowering-fma.f32`
12 164×	`accelerator-lowering-fma.f64`
2 356×	`+-lowering-+.f64`
2 356×	`+-lowering-+.f32`
2 280×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	98
1	46	98
2	92	90
3	183	90
4	369	90
5	657	90
6	903	90
7	1783	90
8	2566	90
9	3734	90
10	4577	90
11	5662	90
12	6102	90
13	7006	90
0	8003	82

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

Outputs
(* (sqrt 2) (+ (* (* v v) -5/8) 1/4))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 v (fma.f64 v #s(literal -5/8 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)) #s(literal 0 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(+ (* (* v v) -5/8) 1/4)
(fma.f64 v (fma.f64 v #s(literal -5/8 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64))
(* v v)
(fma.f64 v v #s(literal 0 binary64))
v
-5/8
#s(literal -5/8 binary64)
1/4
#s(literal 1/4 binary64)
(* (- 1 (* v v)) (* 1/4 (sqrt (* (+ (* v (* v -3)) 1) 2))))
(fma.f64 (sqrt.f64 (fma.f64 v (fma.f64 v #s(literal -6 binary64) #s(literal 0 binary64)) #s(literal 2 binary64))) (fma.f64 v (fma.f64 v #s(literal -1/4 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)) #s(literal 0 binary64))
(- 1 (* v v))
(fma.f64 v (-.f64 #s(literal 0 binary64) v) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(* v v)
(fma.f64 v v #s(literal 0 binary64))
v
(* 1/4 (sqrt (* (+ (* v (* v -3)) 1) 2)))
(fma.f64 #s(literal 1/4 binary64) (sqrt.f64 (fma.f64 v (fma.f64 v #s(literal -6 binary64) #s(literal 0 binary64)) #s(literal 2 binary64))) #s(literal 0 binary64))
1/4
#s(literal 1/4 binary64)
(sqrt (* (+ (* v (* v -3)) 1) 2))
(sqrt.f64 (fma.f64 v (fma.f64 v #s(literal -6 binary64) #s(literal 0 binary64)) #s(literal 2 binary64)))
(* (+ (* v (* v -3)) 1) 2)
(fma.f64 v (fma.f64 v #s(literal -6 binary64) #s(literal 0 binary64)) #s(literal 2 binary64))
(+ (* v (* v -3)) 1)
(fma.f64 (fma.f64 v v #s(literal 0 binary64)) #s(literal -3 binary64) #s(literal 1 binary64))
(* v -3)
(fma.f64 v #s(literal -3 binary64) #s(literal 0 binary64))
-3
#s(literal -3 binary64)
2
#s(literal 2 binary64)

localize86.0ms (0.8%)

Memory

2.1MiB live, 41.6MiB allocated

Localize:

Found 8 expressions of interest:

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

Samples

66.0ms

256×

valid

Compiler

Compiled 93 to 21 computations (77.4% saved)

Precisions

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

ival-sqrt: 41.0ms (73.8% of total)

ival-mult: 11.0ms (19.8% of total)

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

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

exact: 1.0ms (1.8% of total)

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

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

series5.0ms (0%)

Memory

5.6MiB live, 5.6MiB allocated

Counts

10 → 108

Calls

Call 1

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

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

Calls

27 calls:

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

rewrite645.0ms (6.2%)

Memory

-37.6MiB live, 570.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

7 406×	`accelerator-lowering-fma.f32`
7 406×	`accelerator-lowering-fma.f64`
5 336×	`-lowering-.f32`
5 336×	`-lowering-.f64`
1 924×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	79
1	89	79
2	605	71
3	5087	71
0	8780	63

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 419

Calls

Call 1

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

Outputs
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 #s(literal 4 binary64)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))))
(sqrt.f64 #s(literal 2 binary64))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(+.f64 (.f64 (.f64 v v) #s(literal -5/8 binary64)) #s(literal 1/4 binary64))
(+.f64 #s(literal 1/4 binary64) (.f64 (.f64 v v) #s(literal -5/8 binary64)))
(+.f64 (/.f64 (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 25/64 binary64)) (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64))) (neg.f64 (/.f64 #s(literal 1/16 binary64) (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64)))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal 1/4 binary64)))) #s(literal -1 binary64)))
(-.f64 (/.f64 (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 25/64 binary64)) (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64))) (/.f64 #s(literal 1/16 binary64) (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64))))
(-.f64 (/.f64 #s(literal 1/16 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 v v) #s(literal -5/8 binary64)))) (/.f64 (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 25/64 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 v v) #s(literal -5/8 binary64)))))
(fma.f64 v (*.f64 v #s(literal -5/8 binary64)) #s(literal 1/4 binary64))
(fma.f64 v (/.f64 (.f64 v (.f64 (.f64 v v) #s(literal 25/64 binary64))) (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64))) (neg.f64 (/.f64 #s(literal 1/16 binary64) (fma.f64 v (*.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64)))))
(fma.f64 v (exp.f64 (log.f64 (*.f64 v #s(literal -5/8 binary64)))) #s(literal 1/4 binary64))
(fma.f64 (*.f64 v v) #s(literal -5/8 binary64) #s(literal 1/4 binary64))
(fma.f64 (.f64 v v) (/.f64 (.f64 (.f64 v v) #s(literal 25/64 binary64)) (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64))) (neg.f64 (/.f64 #s(literal 1/16 binary64) (fma.f64 v (*.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64)))))
(fma.f64 (*.f64 v v) (exp.f64 (log.f64 #s(literal -5/8 binary64))) #s(literal 1/4 binary64))
(fma.f64 #s(literal -5/8 binary64) (*.f64 v v) #s(literal 1/4 binary64))
(fma.f64 #s(literal -5/8 binary64) (/.f64 (.f64 v (.f64 v (.f64 (.f64 v v) #s(literal -5/8 binary64)))) (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64))) (neg.f64 (/.f64 #s(literal 1/16 binary64) (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64)))))
(fma.f64 (.f64 (.f64 v v) #s(literal -5/8 binary64)) #s(literal 1 binary64) #s(literal 1/4 binary64))
(fma.f64 (.f64 (.f64 v v) #s(literal -5/8 binary64)) (/.f64 (.f64 (.f64 v v) #s(literal -5/8 binary64)) (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64))) (neg.f64 (/.f64 #s(literal 1/16 binary64) (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64)))))
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 v v) #s(literal -5/8 binary64)) #s(literal 1/4 binary64))
(fma.f64 (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 25/64 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64))) (neg.f64 (/.f64 #s(literal 1/16 binary64) (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64)))))
(fma.f64 (.f64 v (.f64 v (.f64 v v))) (/.f64 #s(literal 25/64 binary64) (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64))) (neg.f64 (/.f64 #s(literal 1/16 binary64) (fma.f64 v (*.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64)))))
(fma.f64 (*.f64 v #s(literal -5/8 binary64)) v #s(literal 1/4 binary64))
(fma.f64 (.f64 (.f64 v v) #s(literal 25/64 binary64)) (/.f64 (.f64 v v) (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64))) (neg.f64 (/.f64 #s(literal 1/16 binary64) (fma.f64 v (*.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64)))))
(fma.f64 #s(literal 25/64 binary64) (/.f64 (.f64 v (.f64 v (.f64 v v))) (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64))) (neg.f64 (/.f64 #s(literal 1/16 binary64) (fma.f64 v (*.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64)))))
(fma.f64 (.f64 v (.f64 (.f64 v v) #s(literal -5/8 binary64))) (/.f64 (.f64 v #s(literal -5/8 binary64)) (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64))) (neg.f64 (/.f64 #s(literal 1/16 binary64) (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64)))))
(fma.f64 (.f64 v (.f64 v (.f64 (.f64 v v) #s(literal -5/8 binary64)))) (/.f64 #s(literal -5/8 binary64) (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64))) (neg.f64 (/.f64 #s(literal 1/16 binary64) (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64)))))
(fma.f64 (/.f64 (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 25/64 binary64)) (fma.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 25/64 binary64))) #s(literal -1/16 binary64))) (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal 1/4 binary64)) (neg.f64 (/.f64 #s(literal 1/16 binary64) (fma.f64 v (*.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64)))))
(fma.f64 (/.f64 (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 25/64 binary64)) (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal -125/512 binary64)) #s(literal -1/64 binary64))) (fma.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 25/64 binary64))) (fma.f64 (.f64 v v) #s(literal -5/32 binary64) #s(literal 1/16 binary64))) (neg.f64 (/.f64 #s(literal 1/16 binary64) (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64)))))
(fma.f64 (exp.f64 (log.f64 (*.f64 v #s(literal -5/8 binary64)))) v #s(literal 1/4 binary64))
(fma.f64 (exp.f64 (log.f64 #s(literal -5/8 binary64))) (*.f64 v v) #s(literal 1/4 binary64))
(neg.f64 (/.f64 (fma.f64 (.f64 v v) (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal -125/512 binary64)) #s(literal 1/64 binary64)) (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 v v) (-.f64 (.f64 (.f64 v v) #s(literal 25/64 binary64)) #s(literal -5/32 binary64)) #s(literal 1/16 binary64)))))
(neg.f64 (/.f64 (fma.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 25/64 binary64))) #s(literal -1/16 binary64)) (fma.f64 (.f64 v v) #s(literal 5/8 binary64) #s(literal 1/4 binary64))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 v v) (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal -125/512 binary64)) #s(literal 1/64 binary64))) (fma.f64 (.f64 v v) (-.f64 (.f64 (.f64 v v) #s(literal 25/64 binary64)) #s(literal -5/32 binary64)) #s(literal 1/16 binary64))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (fma.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 25/64 binary64))) #s(literal -1/16 binary64))) (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 v (*.f64 v #s(literal -5/8 binary64)) #s(literal 1/4 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 v (*.f64 v #s(literal -5/8 binary64)) #s(literal 1/4 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 v v) #s(literal -5/8 binary64))) (+.f64 #s(literal 1/16 binary64) (.f64 #s(literal -25/64 binary64) (.f64 v (.f64 v (.f64 v v)))))))
(/.f64 (fma.f64 (.f64 v v) (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal -125/512 binary64)) #s(literal 1/64 binary64)) (fma.f64 (.f64 v v) (-.f64 (.f64 (.f64 v v) #s(literal 25/64 binary64)) #s(literal -5/32 binary64)) #s(literal 1/16 binary64)))
(/.f64 (fma.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 25/64 binary64))) #s(literal -1/16 binary64)) (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 v v) (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal -125/512 binary64)) #s(literal 1/64 binary64))) (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 v v) (-.f64 (.f64 (.f64 v v) #s(literal 25/64 binary64)) #s(literal -5/32 binary64)) #s(literal 1/16 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (fma.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 25/64 binary64))) #s(literal -1/16 binary64))) (fma.f64 (.f64 v v) #s(literal 5/8 binary64) #s(literal 1/4 binary64)))
(/.f64 (fma.f64 (.f64 (.f64 v (.f64 v (.f64 v (.f64 v (.f64 v v))))) (.f64 (.f64 v (.f64 v (.f64 v (.f64 v (.f64 v v))))) (.f64 v (.f64 v (.f64 v (.f64 v (.f64 v v))))))) #s(literal -1953125/134217728 binary64) #s(literal 1/262144 binary64)) (.f64 (fma.f64 (.f64 v v) (-.f64 (.f64 (.f64 v v) #s(literal 25/64 binary64)) #s(literal -5/32 binary64)) #s(literal 1/16 binary64)) (-.f64 (fma.f64 (.f64 v (.f64 v (.f64 v (.f64 v (.f64 v v))))) (.f64 (.f64 v (.f64 v (.f64 v (.f64 v (.f64 v v))))) #s(literal 15625/262144 binary64)) #s(literal 1/4096 binary64)) (.f64 (.f64 v (.f64 v (.f64 v (.f64 v (.f64 v v))))) #s(literal -125/32768 binary64)))))
(/.f64 (fma.f64 (.f64 v (.f64 v (.f64 v (.f64 v (.f64 v v))))) (.f64 (.f64 v (.f64 v (.f64 v (.f64 v (.f64 v v))))) #s(literal 15625/262144 binary64)) #s(literal -1/4096 binary64)) (.f64 (fma.f64 (.f64 v v) (-.f64 (.f64 (.f64 v v) #s(literal 25/64 binary64)) #s(literal -5/32 binary64)) #s(literal 1/16 binary64)) (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal -125/512 binary64)) #s(literal -1/64 binary64))))
(/.f64 (fma.f64 (.f64 v (.f64 v (.f64 v (.f64 v (.f64 v v))))) (.f64 (.f64 v (.f64 v (.f64 v (.f64 v (.f64 v v))))) #s(literal 15625/262144 binary64)) #s(literal -1/4096 binary64)) (.f64 (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64)) (fma.f64 (.f64 (.f64 v (.f64 v (.f64 v v))) (.f64 v (.f64 v (.f64 v v)))) #s(literal 625/4096 binary64) (fma.f64 (.f64 v (.f64 v (*.f64 v v))) #s(literal 25/1024 binary64) #s(literal 1/256 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 v (*.f64 v #s(literal -5/8 binary64)) #s(literal 1/4 binary64)))))
(/.f64 (+.f64 #s(literal 1/16 binary64) (.f64 #s(literal -25/64 binary64) (.f64 v (.f64 v (.f64 v v))))) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 v v) #s(literal -5/8 binary64))))
(/.f64 (fma.f64 (.f64 (.f64 v (.f64 v (.f64 v v))) (.f64 v (.f64 v (.f64 v v)))) #s(literal 625/4096 binary64) #s(literal -1/256 binary64)) (.f64 (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64)) (fma.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 25/64 binary64))) #s(literal 1/16 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 25/64 binary64)) (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64))) (.f64 (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64)) #s(literal 1/16 binary64))) (.f64 (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64)) (fma.f64 v (*.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 v (.f64 v (.f64 v (.f64 v (.f64 v v))))) (.f64 (.f64 v (.f64 v (.f64 v (.f64 v (.f64 v v))))) (.f64 v (.f64 v (.f64 v (.f64 v (.f64 v v))))))) #s(literal -1953125/134217728 binary64) #s(literal 1/262144 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 (fma.f64 (.f64 v (.f64 v (.f64 v (.f64 v (.f64 v v))))) (.f64 (.f64 v (.f64 v (.f64 v (.f64 v (.f64 v v))))) #s(literal 15625/262144 binary64)) #s(literal 1/4096 binary64)) (.f64 (.f64 v (.f64 v (.f64 v (.f64 v (.f64 v v))))) #s(literal -125/32768 binary64))) (fma.f64 (.f64 v v) (-.f64 (.f64 (*.f64 v v) #s(literal 25/64 binary64)) #s(literal -5/32 binary64)) #s(literal 1/16 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 v (.f64 v (.f64 v (.f64 v (.f64 v v))))) (.f64 (.f64 v (.f64 v (.f64 v (.f64 v (.f64 v v))))) #s(literal 15625/262144 binary64)) #s(literal -1/4096 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal -125/512 binary64)) #s(literal -1/64 binary64)) (fma.f64 (.f64 v v) (-.f64 (.f64 (*.f64 v v) #s(literal 25/64 binary64)) #s(literal -5/32 binary64)) #s(literal 1/16 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 v (.f64 v (.f64 v (.f64 v (.f64 v v))))) (.f64 (.f64 v (.f64 v (.f64 v (.f64 v (.f64 v v))))) #s(literal 15625/262144 binary64)) #s(literal -1/4096 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 v (.f64 v (.f64 v v))) (.f64 v (.f64 v (.f64 v v)))) #s(literal 625/4096 binary64) (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 25/1024 binary64) #s(literal 1/256 binary64))) (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 v (.f64 v (.f64 v v))) (.f64 v (.f64 v (.f64 v v)))) #s(literal 625/4096 binary64) #s(literal -1/256 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 25/64 binary64))) #s(literal 1/16 binary64)) (fma.f64 v (*.f64 v #s(literal -5/8 binary64)) #s(literal -1/4 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 v v) (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal -125/512 binary64)) #s(literal 1/64 binary64)))) (neg.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 v v) (-.f64 (.f64 (.f64 v v) #s(literal 25/64 binary64)) #s(literal -5/32 binary64)) #s(literal 1/16 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (fma.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 25/64 binary64))) #s(literal -1/16 binary64)))) (neg.f64 (fma.f64 (.f64 v v) #s(literal 5/8 binary64) #s(literal 1/4 binary64))))
(/.f64 (neg.f64 (+.f64 #s(literal 1/16 binary64) (.f64 #s(literal -25/64 binary64) (.f64 v (.f64 v (.f64 v v)))))) (neg.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 v v) #s(literal -5/8 binary64)))))
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(.f64 (/.f64 (fma.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v))) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 v (.f64 v (.f64 v v))) (.f64 (fma.f64 v v #s(literal 1 binary64)) (fma.f64 v v #s(literal 1 binary64)))))) (-.f64 #s(literal 1 binary64) (.f64 v (.f64 v (fma.f64 v v #s(literal 1 binary64))))))
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
(exp.f64 (.f64 (log.f64 (pow.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)) (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)) (.f64 (log.f64 (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))) #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)))))
(exp.f64 (fma.f64 (log.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) #s(literal 1/4 binary64) (.f64 (log.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) #s(literal 1/4 binary64))))
(sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))
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(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))))
(.f64 (sqrt.f64 (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (pow.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -3 binary64)) #s(literal 1 binary64)))))
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(/.f64 (.f64 (sqrt.f64 (fma.f64 (.f64 v v) (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal -27 binary64)) #s(literal 1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (sqrt.f64 (fma.f64 (.f64 v v) (-.f64 (.f64 (.f64 v v) #s(literal 9 binary64)) #s(literal -3 binary64)) #s(literal 1 binary64))))
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(.f64 (.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 1/4 binary64) (pow.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (pow.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(.f64 (.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (fma.f64 v (.f64 v #s(literal -3 binary64)) #s(literal 1 binary64)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(*.f64 v #s(literal -3 binary64))
(*.f64 #s(literal -3 binary64) v)
(.f64 (.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 v #s(literal -3 binary64)))

simplify579.0ms (5.6%)

Memory

23.1MiB live, 1 244.1MiB allocated

Algorithm

1×	egg-herbie

Rules

23 390×	`accelerator-lowering-fma.f32`
23 390×	`accelerator-lowering-fma.f64`
6 226×	`-lowering-.f32`
6 226×	`-lowering-.f64`
3 898×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	186	1474
1	584	1391
2	2260	1338
3	5928	1329
0	8067	1261

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 108

Calls

Call 1

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

Outputs
1/4
#s(literal 1/4 binary64)
(+ 1/4 (* -5/8 (pow v 2)))
(fma.f64 #s(literal -5/8 binary64) (*.f64 v v) #s(literal 1/4 binary64))
(+ 1/4 (* -5/8 (pow v 2)))
(fma.f64 #s(literal -5/8 binary64) (*.f64 v v) #s(literal 1/4 binary64))
(+ 1/4 (* -5/8 (pow v 2)))
(fma.f64 #s(literal -5/8 binary64) (*.f64 v v) #s(literal 1/4 binary64))
(* -5/8 (pow v 2))
(.f64 #s(literal -5/8 binary64) (.f64 v v))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(.f64 (.f64 v v) (+.f64 #s(literal -5/8 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 v v))))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(.f64 (.f64 v v) (+.f64 #s(literal -5/8 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 v v))))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(.f64 (.f64 v v) (+.f64 #s(literal -5/8 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 v v))))
(* -5/8 (pow v 2))
(.f64 #s(literal -5/8 binary64) (.f64 v v))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(.f64 (.f64 v v) (+.f64 #s(literal -5/8 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 v v))))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(.f64 (.f64 v v) (+.f64 #s(literal -5/8 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 v v))))
(* (pow v 2) (- (* 1/4 (/ 1 (pow v 2))) 5/8))
(.f64 (.f64 v v) (+.f64 #s(literal -5/8 binary64) (/.f64 #s(literal 1/4 binary64) (*.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)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))
(+ (* -5/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))
(* -5/8 (* (pow v 2) (sqrt 2)))
(.f64 (.f64 v v) (*.f64 #s(literal -5/8 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))
(* -5/8 (* (pow v 2) (sqrt 2)))
(.f64 (.f64 v v) (*.f64 #s(literal -5/8 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))
(* (pow v 2) (+ (* -5/8 (sqrt 2)) (* 1/4 (/ (sqrt 2) (pow v 2)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))
(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)
2
#s(literal 2 binary64)
(+ 2 (* -6 (pow v 2)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(+ 2 (* -6 (pow v 2)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(+ 2 (* -6 (pow v 2)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(* -6 (pow v 2))
(.f64 (.f64 v v) #s(literal -6 binary64))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(.f64 (.f64 v v) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v))))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(.f64 (.f64 v v) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v))))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(.f64 (.f64 v v) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v))))
(* -6 (pow v 2))
(.f64 (.f64 v v) #s(literal -6 binary64))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(.f64 (.f64 v v) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v))))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(.f64 (.f64 v v) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v))))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(.f64 (.f64 v v) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v))))
(* 1/4 (sqrt 2))
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* 1/4 (sqrt 2)) (* 1/4 (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2))))) (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))))))
(.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 3/8 binary64) (.f64 v v) #s(literal -5/2 binary64))) (.f64 v v) (sqrt.f64 #s(literal 2 binary64))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* 1/4 (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2)))) (* (pow v 2) (+ (* 1/4 (* (pow v 2) (+ (* -27/16 (sqrt 2)) (* 9/8 (sqrt 2))))) (* 1/4 (+ (* -9/8 (sqrt 2)) (* 3/2 (sqrt 2)))))))))
(fma.f64 (.f64 v v) (.f64 (.f64 #s(literal 1/4 binary64) (.f64 v v)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -9/16 binary64) (.f64 v v) #s(literal 3/8 binary64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64))))
(* -1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(.f64 (.f64 v v) (.f64 (.f64 v (sqrt.f64 #s(literal -3 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/4 binary64))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2)))))
(.f64 (.f64 v v) (fma.f64 (.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64)) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -3 binary64)))) (/.f64 #s(literal 1/4 binary64) v)) #s(literal 1 binary64) (.f64 (.f64 v (sqrt.f64 #s(literal -3 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/4 binary64)))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))
(.f64 (.f64 v v) (.f64 v (fma.f64 #s(literal 1/4 binary64) (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v (.f64 v (sqrt.f64 #s(literal -3 binary64))))) (/.f64 #s(literal 11/24 binary64) (.f64 v v)) (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64)) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -3 binary64)))) (.f64 v v))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -3 binary64)))))))
(* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(.f64 (.f64 v (.f64 v v)) (fma.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64)) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -3 binary64)))) (.f64 v v)) (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v (.f64 v (sqrt.f64 #s(literal -3 binary64))))) (/.f64 #s(literal 11/24 binary64) (.f64 v v)) (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1/24 binary64) (sqrt.f64 #s(literal -3 binary64))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/16 binary64)) (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64)))) (pow.f64 v #s(literal 6 binary64))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -3 binary64))))))
(* 1/4 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(.f64 (.f64 v v) (.f64 (.f64 v (sqrt.f64 #s(literal -3 binary64))) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))))))
(.f64 (.f64 v (.f64 v v)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64)) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -3 binary64)))) (.f64 v v)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -3 binary64))))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4)))))))
(.f64 (.f64 v v) (.f64 v (fma.f64 #s(literal 1/4 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) (.f64 #s(literal -1/4 binary64) (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v (.f64 v (sqrt.f64 #s(literal -3 binary64))))) (/.f64 #s(literal 11/24 binary64) (.f64 v v)) (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64)) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -3 binary64)))) (.f64 v v)))))))
(* -1 (* (pow v 3) (+ (* -1/4 (* (sqrt -3) (sqrt 2))) (+ (* 1/4 (/ (+ (* -1/2 (/ (sqrt 2) (sqrt -3))) (* (sqrt -3) (sqrt 2))) (pow v 2))) (+ (* 1/4 (/ (+ (* -1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* -1/16 (/ (sqrt 2) (pow (sqrt -3) 5)))) (pow v 6))) (* 1/4 (/ (+ (* 1/8 (/ (sqrt 2) (pow (sqrt -3) 3))) (* 1/2 (/ (sqrt 2) (sqrt -3)))) (pow v 4))))))))
(.f64 (.f64 v (.f64 v v)) (fma.f64 #s(literal -1/4 binary64) (+.f64 (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64)) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -3 binary64)))) (.f64 v v)) (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v (.f64 v (sqrt.f64 #s(literal -3 binary64))))) (/.f64 #s(literal 11/24 binary64) (.f64 v v)) (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1/24 binary64) (sqrt.f64 #s(literal -3 binary64))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/16 binary64)) (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64)))) (pow.f64 v #s(literal 6 binary64))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -3 binary64))))))
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow v 2)))
(-.f64 #s(literal 0 binary64) (fma.f64 v v #s(literal -1 binary64)))
(+ 1 (* -1 (pow v 2)))
(-.f64 #s(literal 0 binary64) (fma.f64 v v #s(literal -1 binary64)))
(+ 1 (* -1 (pow v 2)))
(-.f64 #s(literal 0 binary64) (fma.f64 v v #s(literal -1 binary64)))
(* -1 (pow v 2))
(-.f64 #s(literal 0 binary64) (*.f64 v v))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(-.f64 #s(literal 0 binary64) (fma.f64 v v #s(literal -1 binary64)))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(-.f64 #s(literal 0 binary64) (fma.f64 v v #s(literal -1 binary64)))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(-.f64 #s(literal 0 binary64) (fma.f64 v v #s(literal -1 binary64)))
(* -1 (pow v 2))
(-.f64 #s(literal 0 binary64) (*.f64 v v))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(-.f64 #s(literal 0 binary64) (fma.f64 v v #s(literal -1 binary64)))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(-.f64 #s(literal 0 binary64) (fma.f64 v v #s(literal -1 binary64)))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(-.f64 #s(literal 0 binary64) (fma.f64 v v #s(literal -1 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* -3/2 (* (pow v 2) (sqrt 2))))
(.f64 (fma.f64 (.f64 v v) #s(literal -3/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* -9/8 (* (pow v 2) (sqrt 2))))))
(fma.f64 (.f64 v (.f64 v (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (*.f64 v v) #s(literal -9/8 binary64) #s(literal -3/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* (pow v 2) (+ (* -3/2 (sqrt 2)) (* (pow v 2) (+ (* -27/16 (* (pow v 2) (sqrt 2))) (* -9/8 (sqrt 2)))))))
(fma.f64 (.f64 v v) (.f64 (.f64 v (.f64 v (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (.f64 v v) #s(literal -27/16 binary64) #s(literal -9/8 binary64))) (.f64 (fma.f64 (*.f64 v v) #s(literal -3/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(* v (* (sqrt -3) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v (sqrt.f64 #s(literal -3 binary64))))
(* v (+ (* 1/2 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* (sqrt -3) (sqrt 2))))
(fma.f64 v (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v (sqrt.f64 #s(literal -3 binary64)))) #s(literal 1 binary64))))
(* v (+ (* -1/8 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/2 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* (sqrt -3) (sqrt 2)))))
(fma.f64 v (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64)) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/24 binary64)) (.f64 (.f64 (.f64 v v) (.f64 v v)) (sqrt.f64 #s(literal -3 binary64))))) (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v (sqrt.f64 #s(literal -3 binary64)))) #s(literal 1 binary64))))
(* v (+ (* -1/8 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/16 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/2 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* (sqrt -3) (sqrt 2))))))
(fma.f64 v (fma.f64 #s(literal 1/24 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal -3 binary64)) (.f64 (.f64 v v) (.f64 v v)))) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64)) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/16 binary64)) (.f64 (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64)) (pow.f64 v #s(literal 6 binary64)))))) (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 v (sqrt.f64 #s(literal -3 binary64)))) #s(literal 1 binary64))))
(* -1 (* v (* (sqrt -3) (sqrt 2))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (.f64 v (sqrt.f64 #s(literal -3 binary64)))))
(* -1 (* v (+ (* 1/2 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* (sqrt -3) (sqrt 2)))))
(-.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 v (sqrt.f64 #s(literal -3 binary64)))) #s(literal 0 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v (sqrt.f64 #s(literal -3 binary64)))))
(* -1 (* v (+ (* -1/8 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/2 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* (sqrt -3) (sqrt 2))))))
(-.f64 #s(literal 0 binary64) (fma.f64 v (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64)) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/24 binary64)) (.f64 (.f64 (.f64 v v) (.f64 v v)) (sqrt.f64 #s(literal -3 binary64))))) (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v (sqrt.f64 #s(literal -3 binary64)))) #s(literal 1 binary64)))))
(* -1 (* v (+ (* -1/8 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/16 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/2 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* (sqrt -3) (sqrt 2)))))))
(fma.f64 (-.f64 #s(literal 0 binary64) v) (fma.f64 #s(literal 1/24 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal -3 binary64)) (.f64 (.f64 v v) (.f64 v v)))) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64)) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/16 binary64)) (.f64 (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64)) (pow.f64 v #s(literal 6 binary64)))))) (fma.f64 #s(literal -1 binary64) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 v (sqrt.f64 #s(literal -3 binary64)))) #s(literal 0 binary64)))
(* 1/4 (sqrt 2))
(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -3/8 (* (pow v 2) (sqrt 2))) (* 1/4 (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) #s(literal -3/8 binary64) #s(literal 1/4 binary64)))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* -9/32 (* (pow v 2) (sqrt 2))))))
(fma.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 v (.f64 v (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (.f64 v v) #s(literal -9/32 binary64) #s(literal -3/8 binary64))))
(+ (* 1/4 (sqrt 2)) (* (pow v 2) (+ (* -3/8 (sqrt 2)) (* (pow v 2) (+ (* -27/64 (* (pow v 2) (sqrt 2))) (* -9/32 (sqrt 2)))))))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) #s(literal -3/8 binary64) #s(literal 1/4 binary64)) (.f64 (.f64 (.f64 v v) (.f64 v v)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 v v) #s(literal -27/64 binary64) #s(literal -9/32 binary64)))))
(* 1/4 (* v (* (sqrt -3) (sqrt 2))))
(.f64 (.f64 v (sqrt.f64 #s(literal -3 binary64))) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* v (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))
(fma.f64 #s(literal 1 binary64) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64)) (.f64 v (sqrt.f64 #s(literal -3 binary64)))) (.f64 (.f64 v (sqrt.f64 #s(literal -3 binary64))) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))
(fma.f64 v (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal -3 binary64)) (.f64 (.f64 v v) (.f64 v v)))) #s(literal 1/96 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -3 binary64))))) (.f64 #s(literal 1 binary64) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64)) (*.f64 v (sqrt.f64 #s(literal -3 binary64))))))
(* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))))
(fma.f64 v (fma.f64 #s(literal 1/4 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal -3 binary64)) (.f64 (.f64 v v) (.f64 v v)))) #s(literal 1/96 binary64) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/64 binary64)) (.f64 (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64)) (pow.f64 v #s(literal 6 binary64)))))) (.f64 #s(literal 1 binary64) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64)) (.f64 v (sqrt.f64 #s(literal -3 binary64))))))
(* -1/4 (* v (* (sqrt -3) (sqrt 2))))
(.f64 (.f64 v (sqrt.f64 #s(literal -3 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/4 binary64)))
(* -1 (* v (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))
(fma.f64 #s(literal -1 binary64) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64)) (.f64 v (sqrt.f64 #s(literal -3 binary64)))) (.f64 (.f64 v (sqrt.f64 #s(literal -3 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/4 binary64))))
(* -1 (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2)))))))
(.f64 v (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal -3 binary64)) (.f64 (.f64 v v) (.f64 v v)))) #s(literal -1/96 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v (.f64 v (sqrt.f64 #s(literal -3 binary64))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -3 binary64)))))))
(* -1 (* v (+ (* -1/32 (/ (sqrt 2) (* (pow v 4) (pow (sqrt -3) 3)))) (+ (* 1/64 (/ (sqrt 2) (* (pow v 6) (pow (sqrt -3) 5)))) (+ (* 1/8 (/ (sqrt 2) (* (pow v 2) (sqrt -3)))) (* 1/4 (* (sqrt -3) (sqrt 2))))))))
(.f64 v (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (pow.f64 (sqrt.f64 #s(literal -3 binary64)) #s(literal 5 binary64)) (pow.f64 v #s(literal 6 binary64)))) #s(literal -1/64 binary64) (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal -3 binary64)) (.f64 (.f64 v v) (.f64 v v)))) #s(literal -1/96 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v (.f64 v (sqrt.f64 #s(literal -3 binary64))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal -1/4 binary64) (sqrt.f64 #s(literal -3 binary64))))))))
(* -3 v)
(*.f64 v #s(literal -3 binary64))
(* -3 v)
(*.f64 v #s(literal -3 binary64))
(* -3 v)
(*.f64 v #s(literal -3 binary64))
(* -3 v)
(*.f64 v #s(literal -3 binary64))
(* -3 v)
(*.f64 v #s(literal -3 binary64))
(* -3 v)
(*.f64 v #s(literal -3 binary64))
(* -3 v)
(*.f64 v #s(literal -3 binary64))
(* -3 v)
(*.f64 v #s(literal -3 binary64))
(* -3 v)
(*.f64 v #s(literal -3 binary64))
(* -3 v)
(*.f64 v #s(literal -3 binary64))
(* -3 v)
(*.f64 v #s(literal -3 binary64))
(* -3 v)
(*.f64 v #s(literal -3 binary64))

eval81.0ms (0.8%)

Memory: -2.7MiB live, 191.7MiB allocated
Compiler: Compiled 15 152 to 1 557 computations (89.7% saved)

prune55.0ms (0.5%)

Memory

15.1MiB live, 176.0MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	546	1	547
Fresh	0	0	0
Picked	1	1	2
Done	0	1	1
Total	547	3	550

Accuracy

100.0%

Counts

550 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

▶

100.0%

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

✓

99.7%

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

✓

99.5%

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

Compiler

Compiled 31 to 24 computations (22.6% saved)

simplify417.0ms (4%)

Memory

-1.3MiB live, 684.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

12 528×	`accelerator-lowering-fma.f32`
12 528×	`accelerator-lowering-fma.f64`
2 940×	`-lowering-.f32`
2 940×	`-lowering-.f64`
2 324×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	54
1	27	54
2	50	54
3	101	54
4	272	54
5	560	54
6	766	54
7	1743	54
8	2499	54
9	3674	54
10	4436	54
11	5121	54
12	5403	54
13	6107	54
14	7127	54
15	7613	54
16	7613	54
0	8026	49

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

Outputs
(* (- 1 (* v v)) (* (sqrt (+ (* (* v v) -6) 2)) 1/4))
(fma.f64 (sqrt.f64 (fma.f64 (fma.f64 v v #s(literal 0 binary64)) #s(literal -6 binary64) #s(literal 2 binary64))) (fma.f64 v (fma.f64 v #s(literal -1/4 binary64) #s(literal 0 binary64)) #s(literal 1/4 binary64)) #s(literal 0 binary64))
(- 1 (* v v))
(-.f64 #s(literal 0 binary64) (fma.f64 v v #s(literal -1 binary64)))
1
#s(literal 1 binary64)
(* v v)
(fma.f64 v v #s(literal 0 binary64))
v
(* (sqrt (+ (* (* v v) -6) 2)) 1/4)
(fma.f64 (sqrt.f64 (fma.f64 (fma.f64 v v #s(literal 0 binary64)) #s(literal -6 binary64) #s(literal 2 binary64))) #s(literal 1/4 binary64) #s(literal 0 binary64))
(sqrt (+ (* (* v v) -6) 2))
(sqrt.f64 (fma.f64 (fma.f64 v v #s(literal 0 binary64)) #s(literal -6 binary64) #s(literal 2 binary64)))
(+ (* (* v v) -6) 2)
(fma.f64 (fma.f64 v v #s(literal 0 binary64)) #s(literal -6 binary64) #s(literal 2 binary64))
-6
#s(literal -6 binary64)
2
#s(literal 2 binary64)
1/4
#s(literal 1/4 binary64)

localize31.0ms (0.3%)

Memory

-13.1MiB live, 64.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 (-.f64 #s(literal 1 binary64) (.f64 v v)) (.f64 (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
✓	accuracy	100.0%	(.f64 (sqrt.f64 (fma.f64 (.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) #s(literal 1/4 binary64))
✓	accuracy	100.0%	(*.f64 v v)
✓	accuracy	100.0%	(sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))

Samples

18.0ms

256×

valid

Compiler

Compiled 52 to 14 computations (73.1% saved)

Precisions

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

ival-mult: 6.0ms (54.2% of total)

ival-sqrt: 2.0ms (18.1% of total)

ival-sub: 1.0ms (9% of total)

ival-add: 1.0ms (9% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0%)

Memory

12.1MiB live, 12.1MiB allocated

Counts

6 → 72

Calls

Call 1

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

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

Calls

18 calls:

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

rewrite383.0ms (3.7%)

Memory

9.7MiB live, 691.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 242×	`accelerator-lowering-fma.f32`
5 242×	`accelerator-lowering-fma.f64`
4 478×	`-lowering-.f32`
4 478×	`-lowering-.f64`
3 326×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	49
1	57	49
2	366	49
3	3176	49
0	9361	43

Stop Event

1×	iter limit
1×	node limit

Counts

6 → 453

Calls

Call 1

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

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

simplify582.0ms (5.6%)

Memory

-10.5MiB live, 1 020.3MiB allocated

Algorithm

1×	egg-herbie

Rules

21 260×	`accelerator-lowering-fma.f32`
21 260×	`accelerator-lowering-fma.f64`
6 272×	`-lowering-.f32`
6 272×	`-lowering-.f64`
2 902×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	171	1010
1	503	963
2	1673	947
3	6065	929
0	8312	875

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

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

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

eval72.0ms (0.7%)

Memory: 21.2MiB live, 175.6MiB allocated
Compiler: Compiled 21 239 to 2 084 computations (90.2% saved)

prune58.0ms (0.6%)

Memory

7.0MiB live, 167.9MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	547	0	547
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	547	3	550

Accuracy

100.0%

Counts

550 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

✓

100.0%

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

✓

99.7%

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

✓

99.5%

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

Compiler

Compiled 169 to 72 computations (57.4% saved)

regimes10.0ms (0.1%)

Memory

-19.2MiB live, 20.1MiB allocated

Counts

10 → 1

Calls

Call 1

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

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

Calls

3 calls:

3.0ms

(*.f64 v v)

3.0ms

(*.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)

regimes5.0ms (0.1%)

Memory

12.8MiB live, 12.8MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

2.0ms

(*.f64 v v)

2.0ms

(*.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
99.7%	1	`v`
99.7%	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)))`
99.7%	1	`(*.f64 v v)`

Compiler

Compiled 26 to 17 computations (34.6% saved)

regimes3.0ms (0%)

Memory

9.5MiB live, 9.5MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

1.0ms

(*.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)))

1.0ms

(*.f64 v v)

Results

Accuracy	Segments	Branch
99.5%	1	`v`
99.5%	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)))`
99.5%	1	`(*.f64 v v)`

Compiler

Compiled 26 to 17 computations (34.6% saved)

simplify11.0ms (0.1%)

Memory

-23.6MiB live, 20.1MiB allocated

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
6×	`+-commutative_binary64`
6×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	28
1	28	28
2	35	28
3	39	28
4	41	28

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

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

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

Outputs

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

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

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

soundness716.0ms (6.9%)

Memory

-17.3MiB live, 704.4MiB allocated

Rules

21 584×	`accelerator-lowering-fma.f32`
21 584×	`accelerator-lowering-fma.f64`
21 458×	`accelerator-lowering-fma.f32`
21 458×	`accelerator-lowering-fma.f64`
9 554×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	174	1058
1	538	1029
2	2040	972
3	5880	963
0	8237	908
0	216	2025
1	665	1948
2	2386	1816
3	6237	1807
0	8215	1731
0	14	58
1	71	56
2	483	56
3	4843	56
0	8493	51
0	19	79
1	89	79
2	605	71
3	5087	71
0	8780	63
0	26	132
1	125	132
2	915	127
0	8634	119

Stop Event

1×	done
1×	iter limit
1×	node limit
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 118 to 81 computations (31.4% saved)

preprocess28.0ms (0.3%)

Memory: 39.6MiB live, 78.5MiB allocated
Remove: (abs v)
Compiler: Compiled 130 to 82 computations (36.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze3.0ms (0%)

sample1.1s (10.4%)

preprocess446.0ms (4.3%)

explain172.0ms (1.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify245.0ms (2.4%)

localize77.0ms (0.7%)

series7.0ms (0.1%)

rewrite332.0ms (3.2%)

simplify861.0ms (8.3%)

eval68.0ms (0.7%)

prune66.0ms (0.6%)

simplify363.0ms (3.5%)

localize101.0ms (1%)

series12.0ms (0.1%)

rewrite480.0ms (4.6%)

simplify1.1s (10.7%)

eval392.0ms (3.8%)

prune280.0ms (2.7%)

simplify519.0ms (5%)

localize86.0ms (0.8%)

series5.0ms (0%)

rewrite645.0ms (6.2%)

simplify579.0ms (5.6%)

eval81.0ms (0.8%)

prune55.0ms (0.5%)

simplify417.0ms (4%)

localize31.0ms (0.3%)

series5.0ms (0%)

rewrite383.0ms (3.7%)

simplify582.0ms (5.6%)

eval72.0ms (0.7%)

prune58.0ms (0.6%)

regimes10.0ms (0.1%)

regimes5.0ms (0.1%)

regimes3.0ms (0%)

simplify11.0ms (0.1%)

soundness716.0ms (6.9%)

preprocess28.0ms (0.3%)

end0.0ms (0%)

Profiling