Metrics for Falkner and Boettcher, Appendix B, 2

analyze4.0ms (0%)

Memory

7.2MiB live, 7.2MiB 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)

sample1.3s (16.3%)

Memory

-110.8MiB live, 1 663.1MiB allocated

Samples

972.0ms	8 256×	0	valid
1.0ms	12×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 804.0ms

ival-div: 367.0ms (45.7% of total)

ival-mult: 208.0ms (25.9% of total)

ival-sqrt: 127.0ms (15.8% of total)

ival-sub: 78.0ms (9.7% of total)

exact: 14.0ms (1.7% of total)

ival-true: 6.0ms (0.7% of total)

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

Bogosity

preprocess343.0ms (4.3%)

Memory

0.8MiB live, 445.3MiB allocated

Algorithm

1×	egg-herbie

Rules

7 438×	`lower-fma.f64`
7 438×	`lower-fma.f32`
3 206×	`lower-*.f32`
3 198×	`lower-*.f64`
1 088×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	39
1	53	38
2	168	38
3	591	38
4	1654	38
5	2972	38
6	4007	38
7	4338	38
8	4392	38
9	4452	38
10	4548	38
11	5258	38
12	6044	38
13	7156	38
14	7502	38
0	14	19
0	23	19
1	45	19
2	97	19
3	230	19
4	651	19
5	1485	19
6	2032	19
7	3628	19
8	4929	19
9	6447	19
10	7423	19
0	8047	17

Stop Event

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

Calls

Call 1

Inputs

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

Symmetry

(abs v)

explain218.0ms (2.7%)

Memory

-26.6MiB live, 347.9MiB 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

49.0ms

512×

valid

Compiler

Compiled 186 to 60 computations (67.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 32.0ms

ival-mult: 15.0ms (46.4% of total)

ival-sqrt: 8.0ms (24.8% of total)

ival-sub: 5.0ms (15.5% of total)

ival-div: 4.0ms (12.4% of total)

exact: 1.0ms (3.1% 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

2.4MiB live, 2.4MiB 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)

simplify286.0ms (3.6%)

Memory

10.5MiB live, 363.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

7 438×	`lower-fma.f64`
7 438×	`lower-fma.f32`
3 206×	`lower-*.f32`
3 198×	`lower-*.f64`
1 088×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	71
0	23	71
1	45	71
2	97	71
3	230	71
4	651	71
5	1485	71
6	2032	71
7	3628	71
8	4929	71
9	6447	71
10	7423	71
0	8047	66

Stop Event

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

Calls

Call 1

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

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

localize60.0ms (0.8%)

Memory

12.6MiB live, 89.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))
✓	accuracy	100.0%	(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	99.8%	(.f64 #s(literal 3 binary64) (.f64 v v))

Samples

44.0ms

256×

valid

Compiler

Compiled 73 to 16 computations (78.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-sqrt: 24.0ms (67.1% of total)

ival-mult: 7.0ms (19.6% of total)

ival-div: 2.0ms (5.6% of total)

ival-sub: 2.0ms (5.6% of total)

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

exact: 0.0ms (0% of total)

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

series10.0ms (0.1%)

Memory

-25.1MiB live, 15.2MiB allocated

Counts

7 → 60

Calls

Call 1

Inputs
#<alt (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64))>
#<alt (.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)))>
#<alt (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v)))>
#<alt (.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)))))>
#<alt (.f64 #s(literal 3 binary64) (.f64 v v))>
#<alt (sqrt.f64 #s(literal 2 binary64))>
#<alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 v v))))>

Outputs
#<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 (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 (+ (* -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 (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)))))))>

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)))
0.0ms	v	@	-inf	(* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v)))))
0.0ms	v	@	inf	(* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v)))))
0.0ms	v	@	0	(* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v)))))

rewrite268.0ms (3.4%)

Memory

23.4MiB live, 580.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 304×	`lower-fma.f64`
4 304×	`lower-fma.f32`
4 064×	`lower-*.f32`
4 056×	`lower-*.f64`
2 112×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	58
0	23	58
1	80	56
2	492	56
3	4847	56
0	8499	51

Stop Event

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

Counts

7 → 450

Calls

Call 1

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

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

simplify532.0ms (6.7%)

Memory

-7.7MiB live, 993.3MiB allocated

Algorithm

1×	egg-herbie

Rules

21 458×	`lower-fma.f64`
21 458×	`lower-fma.f32`
5 772×	`lower-*.f64`
5 772×	`lower-*.f32`
3 222×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	174	1058
1	538	1029
2	2038	972
3	5879	963
0	8242	908

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

Inputs
(* 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 (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))
(+ (* -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 (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)))))))

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) (+ (* -3/2 (sqrt 2)) (* -1 (sqrt 2))))))
(fma.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 v v) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -5/8 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 #s(literal 1/4 binary64) (.f64 v 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 (* (pow v 3) (* (sqrt -3) (sqrt 2))))
(.f64 (.f64 v v) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v (*.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 (.f64 v v)) (fma.f64 #s(literal -1/4 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 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) (*.f64 v v)))))
(* (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 v (.f64 (.f64 v v) (fma.f64 #s(literal 1/4 binary64) (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 v 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 #s(literal 1/24 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal -3 binary64)))) (pow.f64 v #s(literal 6 binary64))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 v 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 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 v (.f64 v v)) (*.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 v) (.f64 v (fma.f64 #s(literal -1/4 binary64) (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 v 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 #s(literal 1/24 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal -3 binary64)))) (pow.f64 v #s(literal 6 binary64))) (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 v 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 (pow v 2)))
(fma.f64 v (*.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))
(+ 1 (* -3 (pow v 2)))
(fma.f64 v (*.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))
(+ 1 (* -3 (pow v 2)))
(fma.f64 v (*.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))
(* -3 (pow v 2))
(.f64 v (.f64 v #s(literal -3 binary64)))
(* (pow v 2) (- (/ 1 (pow v 2)) 3))
(fma.f64 v (*.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))
(* (pow v 2) (- (/ 1 (pow v 2)) 3))
(fma.f64 v (*.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))
(* (pow v 2) (- (/ 1 (pow v 2)) 3))
(fma.f64 v (*.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))
(* -3 (pow v 2))
(.f64 v (.f64 v #s(literal -3 binary64)))
(* (pow v 2) (- (/ 1 (pow v 2)) 3))
(fma.f64 v (*.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))
(* (pow v 2) (- (/ 1 (pow v 2)) 3))
(fma.f64 v (*.f64 v #s(literal -3 binary64)) #s(literal 1 binary64))
(* (pow v 2) (- (/ 1 (pow v 2)) 3))
(fma.f64 v (*.f64 v #s(literal -3 binary64)) #s(literal 1 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 v (.f64 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 v) (.f64 (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 v (.f64 v #s(literal -3/8 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 v v) (.f64 (.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 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -3 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) v))
(* 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 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -3 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) v)))
(* 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 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #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 (/.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 #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 v (*.f64 #s(literal -1/4 binary64) (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 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal -1/4 binary64) (.f64 v (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))))))
(* -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 #s(literal -1/4 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) (fma.f64 #s(literal -1/8 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 v v) (sqrt.f64 #s(literal -3 binary64)))) (.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)))))
(* -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 #s(literal -1/4 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(literal -3 binary64))) (fma.f64 #s(literal -1/8 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 v v) (sqrt.f64 #s(literal -3 binary64)))) (.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))))))
(* 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 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 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 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))))))
(.f64 v (+.f64 (sqrt.f64 #s(literal -3 binary64)) (+.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 (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 v v) (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))))))))
(* -1 (* v (sqrt -3)))
(*.f64 (sqrt.f64 #s(literal -3 binary64)) (neg.f64 v))
(* -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 (sqrt.f64 #s(literal -3 binary64)) (neg.f64 v)))
(* -1 (* v (- (+ (sqrt -3) (/ 1/2 (* (pow v 2) (sqrt -3)))) (/ 1/8 (* (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 (sqrt.f64 #s(literal -3 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 (*.f64 v v) (sqrt.f64 #s(literal -3 binary64)))))))
(* -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 (sqrt.f64 #s(literal -3 binary64)) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 v v) (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))))))))

eval63.0ms (0.8%)

Memory: 24.9MiB live, 180.2MiB allocated
Compiler: Compiled 15 253 to 1 771 computations (88.4% saved)

prune105.0ms (1.3%)

Memory

-20.5MiB live, 178.9MiB 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
▶	99.8%	(fma.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 v v) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -5/8 binary64))))
▶	100.0%	(.f64 (.f64 (sqrt.f64 (fma.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -3 binary64))) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
▶	99.8%	(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 v (.f64 v #s(literal -3/8 binary64)) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v)))
▶	99.4%	(.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
	99.9%	(.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))))
▶	99.4%	(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))

Compiler

Compiled 162 to 118 computations (27.2% saved)

simplify344.0ms (4.3%)

Memory

1.7MiB live, 643.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 v v)
✓	cost-diff	0	(.f64 (.f64 v v) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -5/8 binary64)))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	960	(fma.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 v v) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -5/8 binary64))))
✓	cost-diff	0	(fma.f64 v (*.f64 v #s(literal -3/8 binary64)) #s(literal 1/4 binary64))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 v (.f64 v #s(literal -3/8 binary64)) #s(literal 1/4 binary64)))
✓	cost-diff	128	(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 v (.f64 v #s(literal -3/8 binary64)) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v)))
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (*.f64 v v))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 #s(literal 1/4 binary64) (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	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(sqrt.f64 (fma.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -3 binary64))) #s(literal 2 binary64)))
✓	cost-diff	0	(.f64 (sqrt.f64 (fma.f64 #s(literal 2 binary64) (.f64 v (*.f64 v #s(literal -3 binary64))) #s(literal 2 binary64))) #s(literal 1/4 binary64))
✓	cost-diff	128	(.f64 (.f64 (sqrt.f64 (fma.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -3 binary64))) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
✓	cost-diff	320	(fma.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -3 binary64))) #s(literal 2 binary64))

Rules

14 150×	`lower-fma.f32`
14 144×	`lower-fma.f64`
3 552×	`lower-*.f32`
3 528×	`lower-*.f64`
2 206×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	183
0	45	183
1	87	179
2	205	177
3	512	177
4	1494	177
5	2984	177
6	5506	177
0	8020	169

Stop Event

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

Calls

Call 1

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

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

localize95.0ms (1.2%)

Memory

-20.2MiB live, 225.9MiB allocated

Localize:

Found 18 expressions of interest:

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

Samples

51.0ms

256×

valid

Compiler

Compiled 193 to 29 computations (85% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.0ms

ival-mult: 20.0ms (66.7% of total)

ival-add: 4.0ms (13.3% of total)

ival-sqrt: 3.0ms (10% of total)

ival-sub: 1.0ms (3.3% of total)

exact: 1.0ms (3.3% of total)

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

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

series13.0ms (0.2%)

Memory

27.0MiB live, 27.0MiB allocated

Counts

17 → 180

Calls

Call 1

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

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

Calls

45 calls:

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

rewrite408.0ms (5.1%)

Memory

-1.0MiB live, 784.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

9 774×	`lower-fma.f32`
9 768×	`lower-fma.f64`
7 134×	`lower-*.f32`
7 110×	`lower-*.f64`
2 706×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	130
0	45	130
1	144	126
2	922	124
0	8750	117

Stop Event

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

Counts

17 → 806

Calls

Call 1

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

Outputs
(+.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -6 binary64))))
(+.f64 (.f64 v (.f64 v #s(literal -6 binary64))) #s(literal 2 binary64))
(+.f64 (/.f64 (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64)) (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal -2 binary64))) (neg.f64 (/.f64 #s(literal 4 binary64) (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal -2 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64)) (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal -2 binary64))) (/.f64 #s(literal 4 binary64) (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal -2 binary64))))
(-.f64 (/.f64 #s(literal 4 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal 6 binary64)))) (/.f64 (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64)) (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal 6 binary64)))))
(fma.f64 #s(literal 2 binary64) (.f64 #s(literal -3 binary64) (.f64 v v)) #s(literal 2 binary64))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(fma.f64 #s(literal -3 binary64) (.f64 #s(literal 2 binary64) (.f64 v v)) #s(literal 2 binary64))
(fma.f64 #s(literal -3 binary64) (.f64 (.f64 v v) #s(literal 2 binary64)) #s(literal 2 binary64))
(fma.f64 (.f64 v #s(literal -3 binary64)) (.f64 #s(literal 2 binary64) v) #s(literal 2 binary64))
(fma.f64 (.f64 #s(literal -3 binary64) (.f64 v v)) #s(literal 2 binary64) #s(literal 2 binary64))
(fma.f64 #s(literal 1 binary64) (.f64 v (.f64 v #s(literal -6 binary64))) #s(literal 2 binary64))
(fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))
(fma.f64 (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal -2 binary64))) (neg.f64 (/.f64 #s(literal 4 binary64) (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal -2 binary64)))))
(fma.f64 (.f64 #s(literal 2 binary64) v) (.f64 v #s(literal -3 binary64)) #s(literal 2 binary64))
(fma.f64 (*.f64 v #s(literal -6 binary64)) v #s(literal 2 binary64))
(fma.f64 (.f64 #s(literal 2 binary64) (.f64 v v)) #s(literal -3 binary64) #s(literal 2 binary64))
(fma.f64 #s(literal -6 binary64) (*.f64 v v) #s(literal 2 binary64))
(neg.f64 (/.f64 (fma.f64 (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v)))) #s(literal -216 binary64) #s(literal 8 binary64)) (neg.f64 (-.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal 4 binary64)) (.f64 (.f64 v v) #s(literal -12 binary64))))))
(neg.f64 (/.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal -4 binary64)) (fma.f64 (.f64 v v) #s(literal 6 binary64) #s(literal 2 binary64))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v)))) #s(literal -216 binary64) #s(literal 8 binary64))) (-.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal 4 binary64)) (.f64 (.f64 v v) #s(literal -12 binary64)))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal -4 binary64))) (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal -2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 4 binary64) (.f64 (.f64 v (.f64 v #s(literal -6 binary64))) (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal -2 binary64)))) (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 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 v v) #s(literal 6 binary64))) (-.f64 #s(literal 4 binary64) (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64)))))
(/.f64 (fma.f64 (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v)))) #s(literal -216 binary64) #s(literal 8 binary64)) (-.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal 4 binary64)) (.f64 (.f64 v v) #s(literal -12 binary64))))
(/.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 4 binary64) (.f64 (.f64 v (.f64 v #s(literal -6 binary64))) (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal -2 binary64)))))
(/.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal -4 binary64)) (fma.f64 v (.f64 v #s(literal -6 binary64)) #s(literal -2 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v)))) #s(literal -216 binary64) #s(literal 8 binary64))) (neg.f64 (-.f64 (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 36 binary64) #s(literal 4 binary64)) (.f64 (.f64 v v) #s(literal -12 binary64)))))
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(pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (*.f64 v v) #s(literal 1/4 binary64))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -5/8 binary64) (*.f64 v v))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 1/4 binary64) (.f64 (*.f64 v v) #s(literal -5/8 binary64))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal 1/4 binary64)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal -5/8 binary64) (.f64 v v)))) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal -5/8 binary64) (.f64 v v)))))))
(.f64 (.f64 (fma.f64 (.f64 v v) (-.f64 (.f64 (.f64 v v) #s(literal 25/32 binary64)) #s(literal -5/16 binary64)) #s(literal 1/8 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 v v) (-.f64 (.f64 (.f64 v v) #s(literal 25/32 binary64)) #s(literal -5/16 binary64)) #s(literal 1/8 binary64))))
(.f64 (.f64 (fma.f64 (.f64 v v) (-.f64 (.f64 (.f64 v v) #s(literal 25/32 binary64)) #s(literal -5/16 binary64)) #s(literal 1/8 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 25/32 binary64))) (+.f64 #s(literal 1/8 binary64) (.f64 #s(literal 5/16 binary64) (.f64 v v))))))
(.f64 (fma.f64 (.f64 v v) (-.f64 (.f64 (.f64 v v) #s(literal 25/32 binary64)) #s(literal -5/16 binary64)) #s(literal 1/8 binary64)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 v v) (-.f64 (.f64 (.f64 v v) #s(literal 25/32 binary64)) #s(literal -5/16 binary64)) #s(literal 1/8 binary64)))))
(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal -25/32 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal -5/8 binary64) (.f64 v v))))))
(.f64 (neg.f64 (.f64 (fma.f64 (.f64 v v) (-.f64 (.f64 (.f64 v v) #s(literal 25/32 binary64)) #s(literal -5/16 binary64)) #s(literal 1/8 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal -5/8 binary64) (.f64 v v) #s(literal 1/4 binary64))))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 v v) (-.f64 (.f64 (.f64 v v) #s(literal 25/32 binary64)) #s(literal -5/16 binary64)) #s(literal 1/8 binary64)))))
(.f64 (neg.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal -25/32 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal -5/8 binary64) (.f64 v v)))))))
(.f64 (fma.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 25/32 binary64))) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (.f64 #s(literal -5/8 binary64) (*.f64 v v)) #s(literal 1/4 binary64)))))
(.f64 v (.f64 v (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -5/8 binary64))))
(.f64 #s(literal 1 binary64) (.f64 #s(literal -5/8 binary64) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) v) v)))
(.f64 (.f64 v v) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -5/8 binary64)))
(.f64 (.f64 v v) (.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -5/8 binary64))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (*.f64 v v) #s(literal -5/8 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal -5/8 binary64) (*.f64 v v)))
(.f64 #s(literal -5/8 binary64) (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) v) v))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -5/8 binary64)) (*.f64 v v))
(.f64 (.f64 #s(literal -5/8 binary64) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) v) v)) #s(literal 1 binary64))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) v) v) #s(literal -5/8 binary64))
(.f64 (.f64 v (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -5/8 binary64))) v)
(.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 #s(literal -5/8 binary64) (.f64 v v))))
(.f64 (.f64 v (sqrt.f64 #s(literal 2 binary64))) (*.f64 #s(literal -5/8 binary64) v))
(.f64 (.f64 v #s(literal -5/8 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) v))
(.f64 (.f64 (*.f64 v v) #s(literal -5/8 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (.f64 #s(literal -5/8 binary64) (*.f64 v v)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (.f64 #s(literal -5/8 binary64) v) (*.f64 v (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -5/8 binary64)) #s(literal 1 binary64)) (.f64 v v))
(.f64 (.f64 (.f64 (.f64 v v) #s(literal -5/8 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(exp.f64 (log.f64 (*.f64 v v)))
(pow.f64 v #s(literal 2 binary64))
(pow.f64 (*.f64 v v) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 v)) #s(literal 2 binary64))
(*.f64 v v)
(.f64 v (.f64 v #s(literal 1 binary64)))
(.f64 #s(literal 1 binary64) (.f64 v v))
(.f64 (.f64 v v) #s(literal 1 binary64))
(*.f64 (exp.f64 (log.f64 v)) (exp.f64 (log.f64 v)))
(.f64 v (.f64 v #s(literal -3 binary64)))
(.f64 #s(literal -3 binary64) (.f64 v v))
(.f64 (.f64 v #s(literal -3 binary64)) v)
(.f64 (.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 (.f64 v v) #s(literal -3 binary64))
(*.f64 v #s(literal -3 binary64))
(*.f64 #s(literal -3 binary64) v)
(*.f64 v #s(literal -3/8 binary64))
(*.f64 #s(literal -3/8 binary64) v)

simplify550.0ms (6.9%)

Memory

0.5MiB live, 1 077.9MiB allocated

Algorithm

1×	egg-herbie

Rules

19 818×	`lower-fma.f64`
19 818×	`lower-fma.f32`
6 992×	`lower-*.f64`
6 992×	`lower-*.f32`
2 464×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	215	1938
1	628	1801
2	1984	1767
3	6728	1762
0	8244	1672

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

Calls

Call 1

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

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

eval179.0ms (2.2%)

Memory: 20.5MiB live, 449.7MiB allocated
Compiler: Compiled 32 833 to 2 578 computations (92.1% saved)

prune119.0ms (1.5%)

Memory

1.5MiB live, 365.7MiB allocated

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	1 219	2	1 221
Fresh	0	1	1
Picked	4	1	5
Done	0	0	0
Total	1 223	4	1 227

Accuracy

100.0%

Counts

1 227 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 v v) #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))
▶	99.8%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal 1/4 binary64)))
▶	99.9%	(.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))))
✓	99.4%	(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))

Compiler

Compiled 48 to 35 computations (27.1% saved)

simplify99.0ms (1.2%)

Memory

-12.4MiB live, 101.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
✓	cost-diff	0	(*.f64 v v)
✓	cost-diff	0	(fma.f64 #s(literal -1/4 binary64) (*.f64 v v) #s(literal 1/4 binary64))
✓	cost-diff	0	(.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 v v) #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))
✓	cost-diff	0	(*.f64 v #s(literal -5/8 binary64))
✓	cost-diff	0	(fma.f64 v (*.f64 v #s(literal -5/8 binary64)) #s(literal 1/4 binary64))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal 1/4 binary64)))
✓	cost-diff	0	(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) #s(literal 3/8 binary64) #s(literal -5/2 binary64)))
✓	cost-diff	0	(*.f64 v v)
✓	cost-diff	320	(.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))))
✓	cost-diff	640	(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)))

Rules

1 484×	`lower-fma.f32`
1 474×	`lower-fma.f64`
1 452×	`lower-*.f32`
1 438×	`lower-*.f64`
1 256×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	125
0	41	125
1	83	125
2	193	125
3	534	125
4	1191	125
5	1866	125
6	2365	125
7	2690	125
8	2947	125
9	3011	123
10	3667	123
11	3667	123
12	3668	123
13	3777	123
14	3777	123
15	3785	123
16	3785	123
0	3785	121

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize75.0ms (0.9%)

Memory

11.1MiB live, 165.8MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 v v) #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))
✓	accuracy	100.0%	(*.f64 v v)
✓	accuracy	100.0%	(*.f64 v #s(literal -6 binary64))
✓	accuracy	100.0%	(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
✓	accuracy	100.0%	(fma.f64 v (*.f64 v #s(literal -5/8 binary64)) #s(literal 1/4 binary64))
✓	accuracy	100.0%	(*.f64 v #s(literal -5/8 binary64))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal 1/4 binary64)))
✓	accuracy	100.0%	(.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))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(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)))
✓	accuracy	100.0%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) #s(literal 3/8 binary64) #s(literal -5/2 binary64)))

Samples

41.0ms

256×

valid

Compiler

Compiled 140 to 29 computations (79.3% saved)

Precisions

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

ival-mult: 18.0ms (63.3% of total)

ival-add: 5.0ms (17.6% of total)

ival-sqrt: 3.0ms (10.6% of total)

exact: 1.0ms (3.5% of total)

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

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

series10.0ms (0.1%)

Memory

20.7MiB live, 20.7MiB allocated

Counts

12 → 132

Calls

Call 1

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

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

Calls

33 calls:

Time	Variable		Point	Expression
2.0ms	v	@	0	(* v -5/8)
1.0ms	v	@	inf	(* (+ (* -1/4 (* v v)) 1/4) (sqrt (+ (* v (* v -6)) 2)))
0.0ms	v	@	inf	(+ (* (* v v) (* (sqrt 2) (+ (* (* v v) 3/8) -5/2))) (sqrt 2))
0.0ms	v	@	0	(* (+ (* -1/4 (* v v)) 1/4) (sqrt (+ (* v (* v -6)) 2)))
0.0ms	v	@	0	(+ (* (* v v) (* (sqrt 2) (+ (* (* v v) 3/8) -5/2))) (sqrt 2))

rewrite494.0ms (6.2%)

Memory

-8.8MiB live, 785.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

12 342×	`lower-fma.f32`
12 332×	`lower-fma.f64`
7 490×	`lower-*.f32`
7 476×	`lower-*.f64`
2 908×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	94
0	41	94
1	152	94
2	1067	94
0	9212	92

Stop Event

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

Counts

12 → 508

Calls

Call 1

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

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

simplify393.0ms (4.9%)

Memory

-17.0MiB live, 722.9MiB allocated

Algorithm

1×	egg-herbie

Rules

14 198×	`lower-fma.f64`
14 198×	`lower-fma.f32`
5 584×	`lower-*.f64`
5 584×	`lower-*.f32`
3 060×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	183	1593
1	508	1517
2	1483	1455
3	5063	1371
0	8196	1297

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

Calls

Call 1

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

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

eval122.0ms (1.5%)

Memory: 0.5MiB live, 188.2MiB allocated
Compiler: Compiled 20 545 to 1 803 computations (91.2% saved)

prune68.0ms (0.8%)

Memory

6.3MiB live, 164.0MiB allocated

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	689	1	690
Fresh	0	0	0
Picked	1	2	3
Done	0	1	1
Total	690	4	694

Accuracy

100.0%

Counts

694 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 v v) #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))
▶	99.9%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 (*.f64 v v) #s(literal 3/32 binary64) #s(literal -5/8 binary64)) #s(literal 1/4 binary64)))
✓	99.8%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal 1/4 binary64)))
✓	99.4%	(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))

Compiler

Compiled 45 to 34 computations (24.4% saved)

simplify18.0ms (0.2%)

Memory

-8.8MiB live, 30.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

376×	`lower-fma.f32`
372×	`lower-fma.f64`
304×	`lower-*.f32`
300×	`lower-*.f64`
162×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	41
0	17	41
1	38	41
2	105	41
3	251	41
4	378	41
5	384	41
6	386	41
0	386	41

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize36.0ms (0.5%)

Memory

24.5MiB live, 96.0MiB allocated

Localize:

Found 4 expressions of interest:

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

Samples

25.0ms

256×

valid

Compiler

Compiled 48 to 14 computations (70.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-mult: 6.0ms (47.3% of total)

ival-add: 3.0ms (23.6% of total)

ival-sqrt: 3.0ms (23.6% of total)

exact: 1.0ms (7.9% of total)

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

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

series2.0ms (0%)

Memory

5.2MiB live, 5.2MiB allocated

Counts

5 → 48

Calls

Call 1

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

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

Calls

12 calls:

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

rewrite425.0ms (5.3%)

Memory

-3.6MiB live, 635.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

7 504×	`lower-fma.f32`
7 500×	`lower-fma.f64`
5 842×	`lower-*.f32`
5 838×	`lower-*.f64`
1 920×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	36
0	17	36
1	70	36
2	510	36
3	5196	36
0	8723	36

Stop Event

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

Counts

5 → 327

Calls

Call 1

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

Outputs
(+.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 v v) (fma.f64 v (.f64 v #s(literal 3/32 binary64)) #s(literal -5/8 binary64)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(+.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 v v) (fma.f64 v (*.f64 v #s(literal 3/32 binary64)) #s(literal -5/8 binary64)))))
(+.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 3/32 binary64))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 v (*.f64 v #s(literal -5/8 binary64)) #s(literal 1/4 binary64))))
(+.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 3/32 binary64))))) (.f64 (fma.f64 v (*.f64 v #s(literal -5/8 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 3/32 binary64))))) (fma.f64 #s(literal -5/8 binary64) (.f64 v (.f64 (sqrt.f64 #s(literal 2 binary64)) v)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))))
(+.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 3/32 binary64))) #s(literal 1/4 binary64))) (.f64 #s(literal -5/8 binary64) (.f64 v (*.f64 (sqrt.f64 #s(literal 2 binary64)) v))))
(+.f64 (.f64 (fma.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 3/32 binary64))) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 #s(literal -5/8 binary64) (.f64 v (*.f64 (sqrt.f64 #s(literal 2 binary64)) v))))
(+.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 3/32 binary64)))))) (.f64 #s(literal -5/8 binary64) (.f64 v (.f64 (sqrt.f64 #s(literal 2 binary64)) v))))
(-.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 v (.f64 v (.f64 (fma.f64 v (.f64 v #s(literal 3/32 binary64)) #s(literal -5/8 binary64)) (.f64 (.f64 v v) (fma.f64 v (.f64 v #s(literal 3/32 binary64)) #s(literal -5/8 binary64))))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 v (.f64 v #s(literal 3/32 binary64)) #s(literal -5/8 binary64)) #s(literal -1/4 binary64)))) (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 v (.f64 v #s(literal 3/32 binary64)) #s(literal -5/8 binary64)) #s(literal -1/4 binary64)))))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 v v) (fma.f64 v (.f64 v #s(literal 3/32 binary64)) #s(literal -5/8 binary64)))))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 v v) (fma.f64 v (.f64 v #s(literal 3/32 binary64)) #s(literal -5/8 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 3/32 binary64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal 1/4 binary64))))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 3/32 binary64)))) (.f64 (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 3/32 binary64)))) (fma.f64 #s(literal -5/8 binary64) (.f64 v (.f64 (sqrt.f64 #s(literal 2 binary64)) v)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 3/32 binary64))) #s(literal 1/4 binary64)) (.f64 #s(literal -5/8 binary64) (.f64 v (.f64 (sqrt.f64 #s(literal 2 binary64)) v))))
(fma.f64 v (.f64 (fma.f64 v (.f64 v #s(literal 3/32 binary64)) #s(literal -5/8 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) v)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(fma.f64 v (.f64 (.f64 v (.f64 (.f64 v v) #s(literal 3/32 binary64))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 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 3/32 binary64))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 v (.f64 (.f64 v (.f64 (.f64 v v) #s(literal 3/32 binary64))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal -5/8 binary64) (.f64 v (.f64 (sqrt.f64 #s(literal 2 binary64)) v)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))))
(fma.f64 (.f64 v v) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 v (.f64 v #s(literal 3/32 binary64)) #s(literal -5/8 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(fma.f64 (.f64 v v) (.f64 (.f64 (.f64 v v) #s(literal 3/32 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal 1/4 binary64))))
(fma.f64 (.f64 v v) (.f64 (.f64 (.f64 v v) #s(literal 3/32 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 v v) (.f64 (.f64 (.f64 v v) #s(literal 3/32 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal -5/8 binary64) (.f64 v (.f64 (sqrt.f64 #s(literal 2 binary64)) v)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))))
(fma.f64 #s(literal 3/32 binary64) (.f64 (.f64 v (.f64 v (.f64 v v))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal 1/4 binary64))))
(fma.f64 #s(literal 3/32 binary64) (.f64 (.f64 v (.f64 v (.f64 v v))) (sqrt.f64 #s(literal 2 binary64))) (.f64 (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 #s(literal 3/32 binary64) (.f64 (.f64 v (.f64 v (.f64 v v))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal -5/8 binary64) (.f64 v (.f64 (sqrt.f64 #s(literal 2 binary64)) v)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))))
(fma.f64 (fma.f64 v (.f64 v #s(literal 3/32 binary64)) #s(literal -5/8 binary64)) (.f64 v (.f64 (sqrt.f64 #s(literal 2 binary64)) v)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
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(/.f64 (-.f64 (.f64 (.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 9/1024 binary64)))) (fma.f64 (.f64 v v) #s(literal 3/32 binary64) #s(literal 5/8 binary64))) (.f64 (fma.f64 (.f64 v v) #s(literal 3/32 binary64) #s(literal 5/8 binary64)) #s(literal 25/64 binary64))) (.f64 (fma.f64 (.f64 v v) #s(literal 3/32 binary64) #s(literal 5/8 binary64)) (fma.f64 (*.f64 v v) #s(literal 3/32 binary64) #s(literal 5/8 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 27/32768 binary64)) #s(literal -125/512 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 v v) (-.f64 (.f64 (*.f64 v v) #s(literal 9/1024 binary64)) #s(literal -15/256 binary64)) #s(literal 25/64 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 v v) (.f64 (.f64 v v) #s(literal 9/1024 binary64)) #s(literal -25/64 binary64)) #s(literal 1 binary64)) (fma.f64 (*.f64 v v) #s(literal 3/32 binary64) #s(literal 5/8 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v))))) (.f64 (.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v))))) #s(literal 19683/35184372088832 binary64)) #s(literal -1953125/134217728 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 (fma.f64 (.f64 (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v)))) (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v))))) #s(literal 729/1073741824 binary64) #s(literal 15625/262144 binary64)) (.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal -3375/16777216 binary64)))) (fma.f64 (.f64 v v) (-.f64 (.f64 (*.f64 v v) #s(literal 9/1024 binary64)) #s(literal -15/256 binary64)) #s(literal 25/64 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v)))) (.f64 (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v)))) #s(literal 729/1073741824 binary64)) #s(literal -15625/262144 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 27/32768 binary64)) #s(literal 125/512 binary64)) (fma.f64 (.f64 v v) (-.f64 (.f64 (*.f64 v v) #s(literal 9/1024 binary64)) #s(literal -15/256 binary64)) #s(literal 25/64 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v)))) (.f64 (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v)))) #s(literal 729/1073741824 binary64)) #s(literal -15625/262144 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 81/1048576 binary64) (fma.f64 (.f64 v (.f64 v (.f64 v v))) #s(literal 225/65536 binary64) #s(literal 625/4096 binary64))) (fma.f64 (.f64 v v) #s(literal 3/32 binary64) #s(literal 5/8 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 v (.f64 v (.f64 v v))) (.f64 v (.f64 v (.f64 v v)))) #s(literal 81/1048576 binary64) #s(literal -625/4096 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 v v) (.f64 (.f64 v v) #s(literal 9/1024 binary64)) #s(literal 25/64 binary64)) (fma.f64 (*.f64 v v) #s(literal 3/32 binary64) #s(literal 5/8 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 27/32768 binary64)) #s(literal -125/512 binary64)))) (neg.f64 (neg.f64 (fma.f64 (.f64 v v) (-.f64 (.f64 (.f64 v v) #s(literal 9/1024 binary64)) #s(literal -15/256 binary64)) #s(literal 25/64 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 v v) (.f64 (.f64 v v) #s(literal 9/1024 binary64)) #s(literal -25/64 binary64)))) (neg.f64 (fma.f64 (.f64 v v) #s(literal -3/32 binary64) #s(literal -5/8 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 25/64 binary64) (.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 9/1024 binary64)))))) (neg.f64 (-.f64 #s(literal -5/8 binary64) (.f64 (.f64 v v) #s(literal 3/32 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 (/.f64 (.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 9/1024 binary64)))) (fma.f64 (.f64 v v) #s(literal 3/32 binary64) #s(literal 5/8 binary64))) (/.f64 (.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 9/1024 binary64)))) (fma.f64 (.f64 v v) #s(literal 3/32 binary64) #s(literal 5/8 binary64)))) (/.f64 (.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 9/1024 binary64)))) (fma.f64 (.f64 v v) #s(literal 3/32 binary64) #s(literal 5/8 binary64)))) (.f64 (.f64 (/.f64 #s(literal 25/64 binary64) (fma.f64 (.f64 v v) #s(literal 3/32 binary64) #s(literal 5/8 binary64))) (/.f64 #s(literal 25/64 binary64) (fma.f64 (.f64 v v) #s(literal 3/32 binary64) #s(literal 5/8 binary64)))) (/.f64 #s(literal 25/64 binary64) (fma.f64 (.f64 v v) #s(literal 3/32 binary64) #s(literal 5/8 binary64))))) (fma.f64 (/.f64 (.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 9/1024 binary64)))) (fma.f64 (.f64 v v) #s(literal 3/32 binary64) #s(literal 5/8 binary64))) (/.f64 (.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 9/1024 binary64)))) (fma.f64 (.f64 v v) #s(literal 3/32 binary64) #s(literal 5/8 binary64))) (fma.f64 (/.f64 #s(literal 25/64 binary64) (fma.f64 (.f64 v v) #s(literal 3/32 binary64) #s(literal 5/8 binary64))) (/.f64 #s(literal 25/64 binary64) (fma.f64 (.f64 v v) #s(literal 3/32 binary64) #s(literal 5/8 binary64))) (.f64 (/.f64 (.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 9/1024 binary64)))) (fma.f64 (.f64 v v) #s(literal 3/32 binary64) #s(literal 5/8 binary64))) (/.f64 #s(literal 25/64 binary64) (fma.f64 (*.f64 v v) #s(literal 3/32 binary64) #s(literal 5/8 binary64)))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 9/1024 binary64)))) (fma.f64 (.f64 v v) #s(literal 3/32 binary64) #s(literal 5/8 binary64))) (/.f64 (.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 9/1024 binary64)))) (fma.f64 (.f64 v v) #s(literal 3/32 binary64) #s(literal 5/8 binary64)))) (.f64 (/.f64 #s(literal 25/64 binary64) (fma.f64 (.f64 v v) #s(literal 3/32 binary64) #s(literal 5/8 binary64))) (/.f64 #s(literal 25/64 binary64) (fma.f64 (.f64 v v) #s(literal 3/32 binary64) #s(literal 5/8 binary64))))) (fma.f64 v (/.f64 (.f64 v (.f64 (.f64 v v) #s(literal 9/1024 binary64))) (fma.f64 (.f64 v v) #s(literal 3/32 binary64) #s(literal 5/8 binary64))) (/.f64 #s(literal 25/64 binary64) (fma.f64 (*.f64 v v) #s(literal 3/32 binary64) #s(literal 5/8 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v))))) (.f64 (.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v))))) #s(literal 19683/35184372088832 binary64)) #s(literal -1953125/134217728 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 v v) (-.f64 (.f64 (.f64 v v) #s(literal 9/1024 binary64)) #s(literal -15/256 binary64)) #s(literal 25/64 binary64)))) (-.f64 (fma.f64 (.f64 (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v)))) (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v))))) #s(literal 729/1073741824 binary64) #s(literal 15625/262144 binary64)) (.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal -3375/16777216 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v)))) (.f64 (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v)))) #s(literal 729/1073741824 binary64)) #s(literal -15625/262144 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 v v) (-.f64 (.f64 (.f64 v v) #s(literal 9/1024 binary64)) #s(literal -15/256 binary64)) #s(literal 25/64 binary64)))) (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 27/32768 binary64)) #s(literal 125/512 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v)))) (.f64 (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v)))) #s(literal 729/1073741824 binary64)) #s(literal -15625/262144 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 v v) #s(literal 3/32 binary64) #s(literal 5/8 binary64)))) (fma.f64 (.f64 (.f64 v (.f64 v (.f64 v v))) (.f64 v (.f64 v (.f64 v v)))) #s(literal 81/1048576 binary64) (fma.f64 (.f64 v (.f64 v (*.f64 v v))) #s(literal 225/65536 binary64) #s(literal 625/4096 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 v (.f64 v (.f64 v v))) (.f64 v (.f64 v (.f64 v v)))) #s(literal 81/1048576 binary64) #s(literal -625/4096 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 v v) #s(literal 3/32 binary64) #s(literal 5/8 binary64)))) (fma.f64 (.f64 v v) (.f64 (.f64 v v) #s(literal 9/1024 binary64)) #s(literal 25/64 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 v (*.f64 v #s(literal 3/32 binary64)) #s(literal -5/8 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 v (*.f64 v #s(literal 3/32 binary64)) #s(literal -5/8 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 #s(literal -5/8 binary64) (.f64 (.f64 v v) #s(literal 3/32 binary64))) (-.f64 #s(literal 25/64 binary64) (.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 9/1024 binary64)))))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 27/32768 binary64)) #s(literal -125/512 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 v v) (-.f64 (.f64 (*.f64 v v) #s(literal 9/1024 binary64)) #s(literal -15/256 binary64)) #s(literal 25/64 binary64))))
(.f64 (fma.f64 (.f64 v v) (.f64 (.f64 v v) #s(literal 9/1024 binary64)) #s(literal -25/64 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 v v) #s(literal 3/32 binary64) #s(literal 5/8 binary64))))
(.f64 (neg.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 27/32768 binary64)) #s(literal -125/512 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 v v) (-.f64 (.f64 (*.f64 v v) #s(literal 9/1024 binary64)) #s(literal -15/256 binary64)) #s(literal 25/64 binary64)))))
(.f64 (neg.f64 (fma.f64 (.f64 v v) (.f64 (.f64 v v) #s(literal 9/1024 binary64)) #s(literal -25/64 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 v v) #s(literal -3/32 binary64) #s(literal -5/8 binary64))))
(.f64 #s(literal 1 binary64) (fma.f64 v (.f64 v #s(literal 3/32 binary64)) #s(literal -5/8 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 v v) (-.f64 (.f64 (.f64 v v) #s(literal 9/1024 binary64)) #s(literal -15/256 binary64)) #s(literal 25/64 binary64))) (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (*.f64 v v)) #s(literal 27/32768 binary64)) #s(literal -125/512 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 v v) #s(literal 3/32 binary64) #s(literal 5/8 binary64))) (fma.f64 (.f64 v v) (.f64 (*.f64 v v) #s(literal 9/1024 binary64)) #s(literal -25/64 binary64)))
(.f64 (-.f64 #s(literal 25/64 binary64) (.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 9/1024 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -5/8 binary64) (.f64 (*.f64 v v) #s(literal 3/32 binary64)))))
(.f64 (/.f64 (fma.f64 (.f64 v v) (.f64 (.f64 v v) #s(literal 9/1024 binary64)) #s(literal -25/64 binary64)) (fma.f64 (.f64 v v) (.f64 (.f64 v v) #s(literal 9/1024 binary64)) #s(literal -25/64 binary64))) (fma.f64 v (.f64 v #s(literal 3/32 binary64)) #s(literal -5/8 binary64)))
(.f64 (/.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 27/32768 binary64)) #s(literal -125/512 binary64)) (fma.f64 (fma.f64 (.f64 v v) #s(literal 15/256 binary64) #s(literal 25/64 binary64)) (.f64 (fma.f64 (.f64 v v) #s(literal 15/256 binary64) #s(literal 25/64 binary64)) (fma.f64 (.f64 v v) #s(literal 15/256 binary64) #s(literal 25/64 binary64))) (.f64 (.f64 (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v)))) (.f64 (.f64 v v) (.f64 v (.f64 v (.f64 v v))))) #s(literal 729/1073741824 binary64)))) (fma.f64 (fma.f64 (.f64 v v) #s(literal 15/256 binary64) #s(literal 25/64 binary64)) (-.f64 (fma.f64 (.f64 v v) #s(literal 15/256 binary64) #s(literal 25/64 binary64)) (.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 9/1024 binary64))))) (.f64 (.f64 (.f64 v (.f64 v (.f64 v v))) (.f64 v (.f64 v (.f64 v v)))) #s(literal 81/1048576 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 27/32768 binary64)) #s(literal -125/512 binary64)) (.f64 (fma.f64 (.f64 v v) (-.f64 (.f64 (.f64 v v) #s(literal 9/1024 binary64)) #s(literal -15/256 binary64)) #s(literal 25/64 binary64)) (+.f64 (fma.f64 (.f64 v v) (.f64 (.f64 v v) #s(literal 9/1024 binary64)) #s(literal -25/64 binary64)) (.f64 (.f64 v v) #s(literal -15/256 binary64))))) (+.f64 (fma.f64 (.f64 v v) (.f64 (.f64 v v) #s(literal 9/1024 binary64)) #s(literal -25/64 binary64)) (.f64 (.f64 v v) #s(literal -15/256 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 v v) (.f64 (.f64 v v) #s(literal 9/1024 binary64)) #s(literal -25/64 binary64)) (fma.f64 (.f64 v (.f64 v v)) (.f64 (.f64 v (.f64 v v)) #s(literal 27/32768 binary64)) #s(literal 125/512 binary64))) (fma.f64 v (.f64 v (.f64 (.f64 v v) #s(literal 9/1024 binary64))) (fma.f64 v (*.f64 v #s(literal -15/256 binary64)) #s(literal 25/64 binary64))))

simplify363.0ms (4.6%)

Memory

5.2MiB live, 519.3MiB allocated

Algorithm

1×	egg-herbie

Rules

11 748×	`lower-fma.f64`
11 748×	`lower-fma.f32`
5 540×	`lower-*.f64`
5 540×	`lower-*.f32`
1 622×	`lower-neg.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	427
1	115	406
2	266	400
3	615	382
4	1337	382
5	3256	382
6	5699	382
0	8498	343

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

eval56.0ms (0.7%)

Memory: 20.5MiB live, 136.2MiB allocated
Compiler: Compiled 13 759 to 1 067 computations (92.2% saved)

prune50.0ms (0.6%)

Memory

-41.5MiB live, 131.3MiB allocated

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	393	0	393
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	393	4	397

Accuracy

100.0%

Counts

397 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 v v) #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))
✓	99.9%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 (*.f64 v v) #s(literal 3/32 binary64) #s(literal -5/8 binary64)) #s(literal 1/4 binary64)))
✓	99.8%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 v (.f64 v #s(literal -5/8 binary64)) #s(literal 1/4 binary64)))
✓	99.4%	(*.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)))

Compiler

Compiled 177 to 87 computations (50.8% saved)

regimes9.0ms (0.1%)

Memory

24.0MiB live, 24.1MiB 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 v (.f64 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 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 (*.f64 v v) #s(literal 3/32 binary64) #s(literal -5/8 binary64)) #s(literal 1/4 binary64)))
(.f64 (fma.f64 #s(literal -1/4 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 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 v (.f64 v #s(literal -3/8 binary64)) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 v v)))
(fma.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 v v) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -5/8 binary64))))
(.f64 (.f64 (sqrt.f64 (fma.f64 #s(literal 2 binary64) (.f64 v (.f64 v #s(literal -3 binary64))) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(.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 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 (fma.f64 #s(literal -1/4 binary64) (.f64 v v) #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 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)

regimes6.0ms (0.1%)

Memory

-24.6MiB live, 14.9MiB 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 v (.f64 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 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 v v) (fma.f64 (*.f64 v v) #s(literal 3/32 binary64) #s(literal -5/8 binary64)) #s(literal 1/4 binary64)))

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

Calls

3 calls:

3.0ms

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
99.9%	1	`v`
99.9%	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)))`
99.9%	1	`(*.f64 v v)`

Compiler

Compiled 26 to 17 computations (34.6% saved)

regimes5.0ms (0.1%)

Memory

13.5MiB live, 13.5MiB allocated

Counts

3 → 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 v (*.f64 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)))

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

Calls

3 calls:

2.0ms

1.0ms

(*.f64 v v)

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)))

Results

Accuracy	Segments	Branch
99.8%	1	`v`
99.8%	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)))`
99.8%	1	`(*.f64 v v)`

Compiler

Compiled 26 to 17 computations (34.6% saved)

regimes3.0ms (0%)

Memory

10.5MiB live, 10.5MiB 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
99.4%	1	`v`
99.4%	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)))`
99.4%	1	`(*.f64 v v)`

Compiler

Compiled 26 to 17 computations (34.6% saved)

simplify7.0ms (0.1%)

Memory

-24.8MiB live, 15.4MiB allocated

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	41
1	27	41

Stop Event

1×

saturated

Calls

Call 1

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

soundness775.0ms (9.7%)

Memory

4.1MiB live, 567.1MiB allocated

Rules

21 458×	`lower-fma.f64`
21 458×	`lower-fma.f32`
14 198×	`lower-fma.f64`
14 198×	`lower-fma.f32`
9 774×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	183	1593
1	508	1517
2	1483	1455
3	5063	1371
0	8196	1297
0	174	1058
1	538	1029
2	2038	972
3	5879	963
0	8242	908
0	25	130
0	45	130
1	144	126
2	922	124
0	8750	117
0	14	58
0	23	58
1	80	56
2	492	56
3	4847	56
0	8499	51

Stop Event

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

Compiler

Compiled 74 to 47 computations (36.5% saved)

preprocess45.0ms (0.6%)

Memory: 13.4MiB live, 91.7MiB allocated
Remove: (abs v)
Compiler: Compiled 154 to 92 computations (40.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze4.0ms (0%)

sample1.3s (16.3%)

preprocess343.0ms (4.3%)

explain218.0ms (2.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify286.0ms (3.6%)

localize60.0ms (0.8%)

series10.0ms (0.1%)

rewrite268.0ms (3.4%)

simplify532.0ms (6.7%)

eval63.0ms (0.8%)

prune105.0ms (1.3%)

simplify344.0ms (4.3%)

localize95.0ms (1.2%)

series13.0ms (0.2%)

rewrite408.0ms (5.1%)

simplify550.0ms (6.9%)

eval179.0ms (2.2%)

prune119.0ms (1.5%)

simplify99.0ms (1.2%)

localize75.0ms (0.9%)

series10.0ms (0.1%)

rewrite494.0ms (6.2%)

simplify393.0ms (4.9%)

eval122.0ms (1.5%)

prune68.0ms (0.8%)

simplify18.0ms (0.2%)

localize36.0ms (0.5%)

series2.0ms (0%)

rewrite425.0ms (5.3%)

simplify363.0ms (4.6%)

eval56.0ms (0.7%)

prune50.0ms (0.6%)

regimes9.0ms (0.1%)

regimes6.0ms (0.1%)

regimes5.0ms (0.1%)

regimes3.0ms (0%)

simplify7.0ms (0.1%)

soundness775.0ms (9.7%)

preprocess45.0ms (0.6%)

end0.0ms (0%)

Profiling