Metrics for sqrt A (should all be same)

analyze0.0ms (0%)

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
100%	100%	0%	0%	0%	0%	0%	2

Compiler

Compiled 10 to 5 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

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

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

const: 0.0ms (0% of total)

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

backward-pass: 0.0ms (0% of total)

sample681.0ms (32%)

Results

519.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 246.0ms

ival-mult: 103.0ms (41.8% of total)

ival-sqrt: 71.0ms (28.8% of total)

ival-add: 62.0ms (25.2% of total)

const: 7.0ms (2.8% of total)

backward-pass: 3.0ms (1.2% of total)

Bogosity

preprocess23.0ms (1.1%)

Algorithm

2×	egg-herbie

Rules

170×	`fmsub-define`
166×	`fnmadd-define`
160×	`fnmsub-define`
108×	`fma-define`
80×	`sum3-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	32	10
2	77	10
3	199	10
4	394	10
5	617	10
6	684	10
7	687	10
0	4	3
1	11	3
2	14	3
3	17	3
0	17	3

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(sqrt (+ (* x x) (* x x)))

Outputs
(sqrt (+ (* x x) (* x x)))
(hypot.f64 x x)

Call 2

Inputs
(sqrt (+ (* x x) (* x x)))
(sqrt (+ (* (neg x) (neg x)) (* (neg x) (neg x))))
(neg (sqrt (+ (* (neg x) (neg x)) (* (neg x) (neg x)))))

Outputs
(sqrt (+ (* x x) (* x x)))
(hypot x x)
(sqrt (+ (* (neg x) (neg x)) (* (neg x) (neg x))))
(hypot x x)
(neg (sqrt (+ (* (neg x) (neg x)) (* (neg x) (neg x)))))
(neg (hypot x x))

Symmetry

(abs x)

explain72.0ms (3.4%)

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
134	-	3	(2.3378134110701497e-161)	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
0	-	0	-	`x`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`(+.f64 (.f64 x x) (.f64 x x))`

Results

50.0ms

512×

valid

Compiler

Compiled 51 to 14 computations (72.5% saved)

Precisions

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

ival-mult: 5.0ms (36.2% of total)

ival-add: 4.0ms (29% of total)

ival-sqrt: 4.0ms (29% of total)

const: 1.0ms (7.2% of total)

backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 4 to 2 computations (50% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)

Compiler

Compiled 4 to 2 computations (50% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(hypot.f64 x x)

Rules

14×	`-lowering-.f32`
14×	`-lowering-.f64`
4×	`*-commutative`
4×	`+-lowering-+.f64`
4×	`count-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	11	4
2	14	4
3	17	4
0	17	4

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(sqrt (+ (* x x) (* x x)))
x

Outputs
(sqrt (+ (* x x) (* x x)))
(hypot.f64 x x)
x

localize30.0ms (1.4%)

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(hypot.f64 x x)

Results

25.0ms

256×

valid

Compiler

Compiled 6 to 3 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 33.0ms

compiled-spec: 17.0ms (51.7% of total)

ival-mult: 12.0ms (36.5% of total)

ival-add: 2.0ms (6.1% of total)

ival-sqrt: 2.0ms (6.1% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series1.0ms (0.1%)

Counts

1 → 12

Calls

Call 1

Inputs
#<alt (sqrt (+ (* x x) (* x x)))>

Outputs
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(sqrt (+ (* x x) (* x x)))
0.0ms	x	@	inf	(sqrt (+ (* x x) (* x x)))
0.0ms	x	@	-inf	(sqrt (+ (* x x) (* x x)))

rewrite185.0ms (8.7%)

Algorithm

1×	batch-egg-rewrite

Rules

3032×	`-lowering-.f32`
3032×	`-lowering-.f64`
1606×	`sum3-define`
1196×	`+-lowering-+.f64`
1196×	`+-lowering-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	3
1	14	3
2	35	3
3	72	3
4	149	3
5	309	3
6	872	3
7	4528	3
0	8099	3

Stop Event

1×	iter limit
1×	node limit

Counts

1 → 32

Calls

Call 1

Inputs
(sqrt (+ (* x x) (* x x)))

Outputs
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 (*.f64 x x) #s(literal 2 binary64)))))
(hypot.f64 x x)
(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
(neg.f64 (hypot.f64 x x))
(pow.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (.f64 (.f64 x x) #s(literal 2 binary64))))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x #s(literal 2 binary64))))
(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(*.f64 #s(literal 1 binary64) (hypot.f64 x x))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/2 binary64)))))
(*.f64 #s(literal -1 binary64) (hypot.f64 x x))
(.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 7/4 binary64))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 7/4 binary64)))))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 3/8 binary64)) (sqrt.f64 (*.f64 x #s(literal 2 binary64)))))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/2 binary64))))))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 7/4 binary64))))))
(.f64 (pow.f64 x #s(literal 3/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (sqrt.f64 (*.f64 x #s(literal 2 binary64)))))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 7/4 binary64))) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/8 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 7/4 binary64)))) (pow.f64 x #s(literal 1/8 binary64)))
(.f64 (.f64 (sqrt.f64 (*.f64 x #s(literal 2 binary64))) (pow.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/8 binary64)))
(.f64 (.f64 (sqrt.f64 (*.f64 x #s(literal 2 binary64))) (pow.f64 x #s(literal 3/8 binary64))) (pow.f64 x #s(literal 1/8 binary64)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) x)
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) x)
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))
(.f64 (.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (pow.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 1/8 binary64)))
(.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 7/4 binary64))))) (pow.f64 x #s(literal 1/8 binary64)))

simplify8.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

88×	`sum3-define`
76×	`fma-define`
32×	`fma-lowering-fma.f32`
32×	`fma-lowering-fma.f64`
24×	`fmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	52
1	11	52
2	24	52
3	28	52
4	32	52
5	54	52
6	86	52
7	98	52
8	121	52
9	188	52
0	188	52

Stop Event

1×	iter limit
1×	saturated

Counts

12 → 12

Calls

Call 1

Inputs
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))

Outputs
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) x))

eval7.0ms (0.3%)

Compiler: Compiled 347 to 81 computations (76.7% saved)

prune4.0ms (0.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	43	1	44
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	43	2	45

Accuracy

100.0%

Counts

45 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	99.4%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3/4 binary64)))

Compiler

Compiled 15 to 11 computations (26.7% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(*.f64 #s(literal 2 binary64) (sqrt.f64 x))
✓	cost-diff	64	(pow.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64))
✓	cost-diff	64	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3/4 binary64)))

Rules

8×	`-lowering-.f32`
8×	`-lowering-.f64`
4×	`*-commutative`
4×	`sqrt-lowering-sqrt.f64`
4×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	12	27
0	12	27

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* (pow (* 2 (sqrt x)) 1/2) (pow x 3/4))
(pow (* 2 (sqrt x)) 1/2)
(* 2 (sqrt x))
2
(sqrt x)
x
1/2
(pow x 3/4)
3/4

Outputs
(* (pow (* 2 (sqrt x)) 1/2) (pow x 3/4))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x))) (pow.f64 x #s(literal 3/4 binary64)))
(pow (* 2 (sqrt x)) 1/2)
(sqrt.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)))
(* 2 (sqrt x))
(*.f64 #s(literal 2 binary64) (sqrt.f64 x))
2
#s(literal 2 binary64)
(sqrt x)
(sqrt.f64 x)
x
1/2
#s(literal 1/2 binary64)
(pow x 3/4)
(pow.f64 x #s(literal 3/4 binary64))
3/4
#s(literal 3/4 binary64)

localize57.0ms (2.7%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.8%	(pow.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64))
✓	accuracy	99.5%	(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3/4 binary64)))

Results

46.0ms

256×

valid

Compiler

Compiled 31 to 10 computations (67.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-pow: 10.0ms (58.9% of total)

ival-mult: 4.0ms (23.6% of total)

ival-sqrt: 2.0ms (11.8% of total)

const: 1.0ms (5.9% of total)

backward-pass: 0.0ms (0% of total)

series100.0ms (4.7%)

Counts

4 → 48

Calls

Call 1

Inputs
#<alt (* (pow (* 2 (sqrt x)) 1/2) (pow x 3/4))>
#<alt (pow (* 2 (sqrt x)) 1/2)>
#<alt (* 2 (sqrt x))>
#<alt (sqrt x)>

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

Calls

12 calls:

Time	Variable		Point	Expression
30.0ms	x	@	0	(* 2 (sqrt x))
30.0ms	x	@	-inf	(* (pow (* 2 (sqrt x)) 1/2) (pow x 3/4))
30.0ms	x	@	0	(pow (* 2 (sqrt x)) 1/2)
7.0ms	x	@	inf	(pow (* 2 (sqrt x)) 1/2)
1.0ms	x	@	-inf	(pow (* 2 (sqrt x)) 1/2)

rewrite241.0ms (11.3%)

Algorithm

1×	batch-egg-rewrite

Rules

2232×	`-lowering-.f32`
2232×	`-lowering-.f64`
1758×	`+-lowering-+.f64`
1758×	`+-lowering-+.f32`
1644×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	22	20
2	53	17
3	103	15
4	166	15
5	277	15
6	544	15
7	2251	15
8	7218	15
0	8167	15

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 105

Calls

Call 1

Inputs
(* (pow (* 2 (sqrt x)) 1/2) (pow x 3/4))
(pow (* 2 (sqrt x)) 1/2)
(* 2 (sqrt x))
(sqrt x)

Outputs
(exp.f64 (+.f64 (log.f64 x) (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)))))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x))) (pow.f64 x #s(literal 3/4 binary64)))
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (pow.f64 x #s(literal 3/16 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 13/16 binary64))))
(.f64 (pow.f64 x #s(literal 1/16 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 15/16 binary64))))
(.f64 (pow.f64 x #s(literal 9/16 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 7/16 binary64))))
(.f64 (pow.f64 x #s(literal 9/64 binary64)) (.f64 (pow.f64 x #s(literal 3/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 13/16 binary64)))))
(.f64 (pow.f64 x #s(literal 9/64 binary64)) (.f64 (pow.f64 x #s(literal 27/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 7/16 binary64)))))
(.f64 (pow.f64 x #s(literal 3/64 binary64)) (.f64 (pow.f64 x #s(literal 9/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 13/16 binary64)))))
(.f64 (pow.f64 x #s(literal 3/64 binary64)) (.f64 (pow.f64 x #s(literal 1/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 15/16 binary64)))))
(.f64 (pow.f64 x #s(literal 1/64 binary64)) (.f64 (pow.f64 x #s(literal 3/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 15/16 binary64)))))
(.f64 (pow.f64 x #s(literal 27/64 binary64)) (.f64 (pow.f64 x #s(literal 9/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 7/16 binary64)))))
(.f64 (pow.f64 x #s(literal 15/16 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/16 binary64))))
(.f64 (pow.f64 x #s(literal 13/16 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64)))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 13/16 binary64))) (pow.f64 x #s(literal 3/16 binary64)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 7/16 binary64))) (pow.f64 x #s(literal 9/16 binary64)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 15/16 binary64))) (pow.f64 x #s(literal 1/16 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64)))) (pow.f64 x #s(literal 13/16 binary64)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 9/16 binary64))) (pow.f64 x #s(literal 7/16 binary64)))
(.f64 (pow.f64 x #s(literal 7/16 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 9/16 binary64))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/16 binary64))) (pow.f64 x #s(literal 15/16 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 9/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 13/16 binary64)))) (pow.f64 x #s(literal 3/64 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 3/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 13/16 binary64)))) (pow.f64 x #s(literal 9/64 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 27/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 7/16 binary64)))) (pow.f64 x #s(literal 9/64 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 1/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 15/16 binary64)))) (pow.f64 x #s(literal 3/64 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 3/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 15/16 binary64)))) (pow.f64 x #s(literal 1/64 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 9/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 7/16 binary64)))) (pow.f64 x #s(literal 27/64 binary64)))
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)))
(pow.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) (log.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (pow.f64 x #s(literal 3/16 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/16 binary64))))
(.f64 (pow.f64 x #s(literal 1/16 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64)))))
(.f64 (pow.f64 x #s(literal 9/64 binary64)) (.f64 (pow.f64 x #s(literal 3/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/16 binary64)))))
(.f64 (pow.f64 x #s(literal 9/64 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 3/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64))))))
(.f64 (pow.f64 x #s(literal 3/64 binary64)) (.f64 (pow.f64 x #s(literal 1/64 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))))))
(.f64 (pow.f64 x #s(literal 3/64 binary64)) (.f64 (pow.f64 x #s(literal 9/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/16 binary64)))))
(.f64 (pow.f64 x #s(literal 3/64 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))))))
(.f64 (pow.f64 x #s(literal 3/64 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 9/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64))))))
(.f64 (pow.f64 x #s(literal 1/64 binary64)) (.f64 (pow.f64 x #s(literal 3/64 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))))))
(.f64 (pow.f64 x #s(literal 1/64 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 3/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))))))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64)))) (pow.f64 x #s(literal 1/16 binary64)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/16 binary64))) (pow.f64 x #s(literal 3/16 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 3/64 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))))) (pow.f64 x #s(literal 1/64 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 1/64 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))))) (pow.f64 x #s(literal 3/64 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 3/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/16 binary64)))) (pow.f64 x #s(literal 9/64 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 9/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/16 binary64)))) (pow.f64 x #s(literal 3/64 binary64)))
(.f64 (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))))) (pow.f64 x #s(literal 3/64 binary64)))
(.f64 (sqrt.f64 (.f64 (pow.f64 x #s(literal 3/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))))) (pow.f64 x #s(literal 1/64 binary64)))
(.f64 (sqrt.f64 (.f64 (pow.f64 x #s(literal 3/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64))))) (pow.f64 x #s(literal 9/64 binary64)))
(.f64 (sqrt.f64 (.f64 (pow.f64 x #s(literal 9/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64))))) (pow.f64 x #s(literal 3/64 binary64)))
(exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x))))
(*.f64 #s(literal 2 binary64) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (exp.f64 (log.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))))))
(.f64 (pow.f64 x #s(literal 3/8 binary64)) (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64))))
(.f64 (pow.f64 x #s(literal 3/8 binary64)) (exp.f64 (log.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64))))))
(.f64 (pow.f64 x #s(literal 3/32 binary64)) (.f64 (pow.f64 x #s(literal 9/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64)))))
(.f64 (pow.f64 x #s(literal 3/32 binary64)) (.f64 (pow.f64 x #s(literal 1/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64)))))
(.f64 (pow.f64 x #s(literal 1/32 binary64)) (.f64 (pow.f64 x #s(literal 3/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64)))))
(.f64 (pow.f64 x #s(literal 9/32 binary64)) (.f64 (pow.f64 x #s(literal 3/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64)))))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))) (pow.f64 x #s(literal 1/8 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/8 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 9/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64)))) (pow.f64 x #s(literal 3/32 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 1/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64)))) (pow.f64 x #s(literal 3/32 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 3/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64)))) (pow.f64 x #s(literal 1/32 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 3/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64)))) (pow.f64 x #s(literal 9/32 binary64)))
(.f64 (exp.f64 (log.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))))) (pow.f64 x #s(literal 1/8 binary64)))
(.f64 (exp.f64 (log.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64))))) (pow.f64 x #s(literal 3/8 binary64)))
(exp.f64 (/.f64 (log.f64 x) #s(literal 2 binary64)))
(sqrt.f64 x)
(/.f64 #s(literal 1 binary64) (pow.f64 (E.f64) (/.f64 (log.f64 x) #s(literal -2 binary64))))
(/.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (log.f64 x) #s(literal -2 binary64))))
(pow.f64 x #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 x))
(pow.f64 (E.f64) (/.f64 (log.f64 x) #s(literal 2 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (E.f64) #s(literal 1/2 binary64)) (log.f64 x))
(pow.f64 (*.f64 (exp.f64 #s(literal 1/8 binary64)) (exp.f64 #s(literal 3/8 binary64))) (log.f64 x))
(pow.f64 (*.f64 (exp.f64 #s(literal 3/8 binary64)) (exp.f64 #s(literal 1/8 binary64))) (log.f64 x))
(*.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 x #s(literal 3/8 binary64)))
(*.f64 (pow.f64 x #s(literal 3/8 binary64)) (pow.f64 x #s(literal 1/8 binary64)))
(*.f64 (pow.f64 x #s(literal 3/32 binary64)) (pow.f64 x #s(literal 13/32 binary64)))
(*.f64 (pow.f64 x #s(literal 1/32 binary64)) (pow.f64 x #s(literal 15/32 binary64)))
(*.f64 (pow.f64 x #s(literal 9/32 binary64)) (pow.f64 x #s(literal 7/32 binary64)))
(*.f64 (pow.f64 x #s(literal 9/128 binary64)) (sqrt.f64 (pow.f64 x #s(literal 55/64 binary64))))
(*.f64 (pow.f64 x #s(literal 27/128 binary64)) (sqrt.f64 (pow.f64 x #s(literal 37/64 binary64))))
(*.f64 (pow.f64 x #s(literal 3/128 binary64)) (sqrt.f64 (pow.f64 x #s(literal 61/64 binary64))))
(*.f64 (pow.f64 x #s(literal 1/128 binary64)) (sqrt.f64 (pow.f64 x #s(literal 63/64 binary64))))
(*.f64 (pow.f64 x #s(literal 13/32 binary64)) (pow.f64 x #s(literal 3/32 binary64)))
(*.f64 (pow.f64 x #s(literal 15/32 binary64)) (pow.f64 x #s(literal 1/32 binary64)))
(*.f64 (pow.f64 x #s(literal 7/32 binary64)) (pow.f64 x #s(literal 9/32 binary64)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 55/64 binary64))) (pow.f64 x #s(literal 9/128 binary64)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 61/64 binary64))) (pow.f64 x #s(literal 3/128 binary64)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 63/64 binary64))) (pow.f64 x #s(literal 1/128 binary64)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 37/64 binary64))) (pow.f64 x #s(literal 27/128 binary64)))

simplify137.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

2772×	`fma-define`
1646×	`fnmadd-define`
1038×	`sum3-define`
936×	`fma-lowering-fma.f32`
936×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	27	248
1	59	248
2	161	244
3	434	244
4	839	244
5	1232	244
6	2368	244
7	3312	244
8	4113	244
9	4930	244
10	5181	244
11	5183	244
12	5183	244
13	5308	244
0	5308	244

Stop Event

1×	iter limit
1×	saturated

Counts

48 → 48

Calls

Call 1

Inputs
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(* (pow (* 1 x) 1/4) (sqrt 2))
(* (pow (* 1 x) 1/4) (sqrt 2))
(* (pow (* 1 x) 1/4) (sqrt 2))
(* (pow (* 1 x) 1/4) (sqrt 2))
(* (pow (* 1 x) 1/4) (sqrt 2))
(* (pow (* 1 x) 1/4) (sqrt 2))
(* (pow (* 1 x) 1/4) (sqrt 2))
(* (pow (* 1 x) 1/4) (sqrt 2))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(* 2 (sqrt x))
(* 2 (sqrt x))
(* 2 (sqrt x))
(* 2 (sqrt x))
(* 2 (sqrt x))
(* 2 (sqrt x))
(* 2 (sqrt x))
(* 2 (sqrt x))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))

Outputs
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(.f64 (.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64)))) (pow.f64 #s(literal -1 binary64) #s(literal 5/4 binary64)))
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(.f64 (.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64)))) (pow.f64 #s(literal -1 binary64) #s(literal 5/4 binary64)))
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(.f64 (.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64)))) (pow.f64 #s(literal -1 binary64) #s(literal 5/4 binary64)))
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(.f64 (.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64)))) (pow.f64 #s(literal -1 binary64) #s(literal 5/4 binary64)))
(* (pow (* 1 x) 1/4) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(* (pow (* 1 x) 1/4) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(* (pow (* 1 x) 1/4) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(* (pow (* 1 x) 1/4) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(* (pow (* 1 x) 1/4) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(* (pow (* 1 x) 1/4) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(* (pow (* 1 x) 1/4) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(* (pow (* 1 x) 1/4) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/4 binary64))))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/4 binary64))))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/4 binary64))))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/4 binary64))))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)

eval25.0ms (1.2%)

Compiler: Compiled 1951 to 378 computations (80.6% saved)

prune13.0ms (0.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	153	2	155

Accuracy

100.0%

Counts

155 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	99.4%	(.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x))))

Compiler

Compiled 14 to 10 computations (28.6% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

8×	`-lowering-.f32`
8×	`-lowering-.f64`
4×	`*-commutative`
4×	`sqrt-lowering-sqrt.f64`
4×	`sqrt-lowering-sqrt.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	26
1	10	26
0	10	26

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* (pow x 3/4) (sqrt (* 2 (sqrt x))))
(pow x 3/4)
x
3/4
(sqrt (* 2 (sqrt x)))
(* 2 (sqrt x))
2
(sqrt x)

Outputs
(* (pow x 3/4) (sqrt (* 2 (sqrt x))))
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x))))
(pow x 3/4)
(pow.f64 x #s(literal 3/4 binary64))
x
3/4
#s(literal 3/4 binary64)
(sqrt (* 2 (sqrt x)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)))
(* 2 (sqrt x))
(*.f64 #s(literal 2 binary64) (sqrt.f64 x))
2
#s(literal 2 binary64)
(sqrt x)
(sqrt.f64 x)

localize73.0ms (3.4%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.8%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)))
✓	accuracy	99.5%	(.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x))))

Results

34.0ms

256×

valid

Compiler

Compiled 28 to 9 computations (67.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-pow: 8.0ms (50.1% of total)

ival-sqrt: 4.0ms (25% of total)

ival-mult: 3.0ms (18.8% of total)

const: 1.0ms (6.3% of total)

backward-pass: 0.0ms (0% of total)

series26.0ms (1.2%)

Counts

5 → 60

Calls

Call 1

Inputs
#<alt (* (pow x 3/4) (sqrt (* 2 (sqrt x))))>
#<alt (pow x 3/4)>
#<alt (sqrt (* 2 (sqrt x)))>
#<alt (* 2 (sqrt x))>
#<alt (sqrt x)>

Outputs
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))>
#<alt (* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))>
#<alt (* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))>
#<alt (* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))>
#<alt (pow (* 1 (pow x 3)) 1/4)>
#<alt (pow (* 1 (pow x 3)) 1/4)>
#<alt (pow (* 1 (pow x 3)) 1/4)>
#<alt (pow (* 1 (pow x 3)) 1/4)>
#<alt (pow (* 1 (pow x 3)) 1/4)>
#<alt (pow (* 1 (pow x 3)) 1/4)>
#<alt (pow (* 1 (pow x 3)) 1/4)>
#<alt (pow (* 1 (pow x 3)) 1/4)>
#<alt (exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))>
#<alt (exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))>
#<alt (exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))>
#<alt (exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))>
#<alt (* (pow (* 1 x) 1/4) (sqrt 2))>
#<alt (* (pow (* 1 x) 1/4) (sqrt 2))>
#<alt (* (pow (* 1 x) 1/4) (sqrt 2))>
#<alt (* (pow (* 1 x) 1/4) (sqrt 2))>
#<alt (* (pow (* 1 x) 1/4) (sqrt 2))>
#<alt (* (pow (* 1 x) 1/4) (sqrt 2))>
#<alt (* (pow (* 1 x) 1/4) (sqrt 2))>
#<alt (* (pow (* 1 x) 1/4) (sqrt 2))>
#<alt (* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))>
#<alt (* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))>
#<alt (* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))>
#<alt (* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))>
#<alt (* 2 (sqrt x))>
#<alt (* 2 (sqrt x))>
#<alt (* 2 (sqrt x))>
#<alt (* 2 (sqrt x))>
#<alt (* 2 (sqrt x))>
#<alt (* 2 (sqrt x))>
#<alt (* 2 (sqrt x))>
#<alt (* 2 (sqrt x))>
#<alt (* -2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>

Calls

15 calls:

Time	Variable		Point	Expression
9.0ms	x	@	inf	(pow x 3/4)
8.0ms	x	@	0	(pow x 3/4)
7.0ms	x	@	-inf	(pow x 3/4)
0.0ms	x	@	-inf	(sqrt (* 2 (sqrt x)))
0.0ms	x	@	inf	(sqrt (* 2 (sqrt x)))

rewrite192.0ms (9%)

Algorithm

1×	batch-egg-rewrite

Rules

2232×	`-lowering-.f32`
2232×	`-lowering-.f64`
1758×	`+-lowering-+.f64`
1758×	`+-lowering-+.f32`
1644×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	19	23
2	38	20
3	74	18
4	133	18
5	265	18
6	560	18
7	2335	18
8	7295	18
0	8244	18

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 121

Calls

Call 1

Inputs
(* (pow x 3/4) (sqrt (* 2 (sqrt x))))
(pow x 3/4)
(sqrt (* 2 (sqrt x)))
(* 2 (sqrt x))
(sqrt x)

Outputs
(exp.f64 (+.f64 (log.f64 x) (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)))))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 3/4 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (pow.f64 x #s(literal 9/16 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 7/16 binary64))))
(.f64 (pow.f64 x #s(literal 3/16 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 13/16 binary64))))
(.f64 (pow.f64 x #s(literal 1/16 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 15/16 binary64))))
(.f64 (pow.f64 x #s(literal 3/64 binary64)) (.f64 (pow.f64 x #s(literal 1/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 15/16 binary64)))))
(.f64 (pow.f64 x #s(literal 3/64 binary64)) (.f64 (pow.f64 x #s(literal 9/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 13/16 binary64)))))
(.f64 (pow.f64 x #s(literal 1/64 binary64)) (.f64 (pow.f64 x #s(literal 3/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 15/16 binary64)))))
(.f64 (pow.f64 x #s(literal 9/64 binary64)) (.f64 (pow.f64 x #s(literal 3/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 13/16 binary64)))))
(.f64 (pow.f64 x #s(literal 9/64 binary64)) (.f64 (pow.f64 x #s(literal 27/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 7/16 binary64)))))
(.f64 (pow.f64 x #s(literal 27/64 binary64)) (.f64 (pow.f64 x #s(literal 9/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 7/16 binary64)))))
(.f64 (pow.f64 x #s(literal 7/16 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 9/16 binary64))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 7/16 binary64))) (pow.f64 x #s(literal 9/16 binary64)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 15/16 binary64))) (pow.f64 x #s(literal 1/16 binary64)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 13/16 binary64))) (pow.f64 x #s(literal 3/16 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64)))) (pow.f64 x #s(literal 13/16 binary64)))
(.f64 (pow.f64 x #s(literal 13/16 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64)))))
(.f64 (pow.f64 x #s(literal 15/16 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/16 binary64))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 9/16 binary64))) (pow.f64 x #s(literal 7/16 binary64)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/16 binary64))) (pow.f64 x #s(literal 15/16 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 9/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 7/16 binary64)))) (pow.f64 x #s(literal 27/64 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 1/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 15/16 binary64)))) (pow.f64 x #s(literal 3/64 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 3/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 13/16 binary64)))) (pow.f64 x #s(literal 9/64 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 9/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 13/16 binary64)))) (pow.f64 x #s(literal 3/64 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 27/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 7/16 binary64)))) (pow.f64 x #s(literal 9/64 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 3/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 15/16 binary64)))) (pow.f64 x #s(literal 1/64 binary64)))
(exp.f64 (*.f64 #s(literal 3/4 binary64) (log.f64 x)))
(pow.f64 x #s(literal 3/4 binary64))
(pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 3/4 binary64)) (log.f64 x))
(pow.f64 (E.f64) (*.f64 #s(literal 3/4 binary64) (log.f64 x)))
(pow.f64 (pow.f64 (E.f64) #s(literal 3/4 binary64)) (log.f64 x))
(pow.f64 (*.f64 (exp.f64 #s(literal 9/16 binary64)) (exp.f64 #s(literal 3/16 binary64))) (log.f64 x))
(pow.f64 (*.f64 (exp.f64 #s(literal 3/16 binary64)) (exp.f64 #s(literal 9/16 binary64))) (log.f64 x))
(*.f64 (pow.f64 x #s(literal 9/16 binary64)) (pow.f64 x #s(literal 3/16 binary64)))
(*.f64 (pow.f64 x #s(literal 3/16 binary64)) (pow.f64 x #s(literal 9/16 binary64)))
(*.f64 (pow.f64 x #s(literal 3/64 binary64)) (pow.f64 x #s(literal 45/64 binary64)))
(*.f64 (pow.f64 x #s(literal 9/64 binary64)) (pow.f64 x #s(literal 39/64 binary64)))
(*.f64 (pow.f64 x #s(literal 27/64 binary64)) (pow.f64 x #s(literal 21/64 binary64)))
(*.f64 (pow.f64 x #s(literal 39/64 binary64)) (pow.f64 x #s(literal 9/64 binary64)))
(*.f64 (pow.f64 x #s(literal 45/64 binary64)) (pow.f64 x #s(literal 3/64 binary64)))
(*.f64 (pow.f64 x #s(literal 21/64 binary64)) (pow.f64 x #s(literal 27/64 binary64)))
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)))
(pow.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) (log.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x)))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (pow.f64 x #s(literal 3/16 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/16 binary64))))
(.f64 (pow.f64 x #s(literal 1/16 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64)))))
(.f64 (pow.f64 x #s(literal 3/64 binary64)) (.f64 (pow.f64 x #s(literal 1/64 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))))))
(.f64 (pow.f64 x #s(literal 3/64 binary64)) (.f64 (pow.f64 x #s(literal 9/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/16 binary64)))))
(.f64 (pow.f64 x #s(literal 3/64 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 9/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64))))))
(.f64 (pow.f64 x #s(literal 3/64 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))))))
(.f64 (pow.f64 x #s(literal 1/64 binary64)) (.f64 (pow.f64 x #s(literal 3/64 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))))))
(.f64 (pow.f64 x #s(literal 1/64 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 3/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))))))
(.f64 (pow.f64 x #s(literal 9/64 binary64)) (.f64 (pow.f64 x #s(literal 3/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/16 binary64)))))
(.f64 (pow.f64 x #s(literal 9/64 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 3/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64))))))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64)))) (pow.f64 x #s(literal 1/16 binary64)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/16 binary64))) (pow.f64 x #s(literal 3/16 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 1/64 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))))) (pow.f64 x #s(literal 3/64 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 9/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/16 binary64)))) (pow.f64 x #s(literal 3/64 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 3/64 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/16 binary64)))) (pow.f64 x #s(literal 9/64 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 3/64 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))))) (pow.f64 x #s(literal 1/64 binary64)))
(.f64 (sqrt.f64 (.f64 (pow.f64 x #s(literal 9/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64))))) (pow.f64 x #s(literal 3/64 binary64)))
(.f64 (sqrt.f64 (.f64 (pow.f64 x #s(literal 3/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))))) (pow.f64 x #s(literal 1/64 binary64)))
(.f64 (sqrt.f64 (.f64 (pow.f64 x #s(literal 3/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64))))) (pow.f64 x #s(literal 9/64 binary64)))
(.f64 (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))))) (pow.f64 x #s(literal 3/64 binary64)))
(exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x))))
(*.f64 #s(literal 2 binary64) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))))
(.f64 (pow.f64 x #s(literal 1/8 binary64)) (exp.f64 (log.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))))))
(.f64 (pow.f64 x #s(literal 3/8 binary64)) (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64))))
(.f64 (pow.f64 x #s(literal 3/8 binary64)) (exp.f64 (log.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64))))))
(.f64 (pow.f64 x #s(literal 3/32 binary64)) (.f64 (pow.f64 x #s(literal 1/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64)))))
(.f64 (pow.f64 x #s(literal 3/32 binary64)) (.f64 (pow.f64 x #s(literal 9/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64)))))
(.f64 (pow.f64 x #s(literal 1/32 binary64)) (.f64 (pow.f64 x #s(literal 3/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64)))))
(.f64 (pow.f64 x #s(literal 9/32 binary64)) (.f64 (pow.f64 x #s(literal 3/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64)))))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))) (pow.f64 x #s(literal 1/8 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/8 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 1/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64)))) (pow.f64 x #s(literal 3/32 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 3/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64)))) (pow.f64 x #s(literal 1/32 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 9/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64)))) (pow.f64 x #s(literal 3/32 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal 3/32 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64)))) (pow.f64 x #s(literal 9/32 binary64)))
(.f64 (exp.f64 (log.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/8 binary64))))) (pow.f64 x #s(literal 1/8 binary64)))
(.f64 (exp.f64 (log.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1/8 binary64))))) (pow.f64 x #s(literal 3/8 binary64)))
(exp.f64 (/.f64 (log.f64 x) #s(literal 2 binary64)))
(sqrt.f64 x)
(/.f64 #s(literal 1 binary64) (pow.f64 (E.f64) (/.f64 (log.f64 x) #s(literal -2 binary64))))
(/.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (log.f64 x) #s(literal -2 binary64))))
(pow.f64 x #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 x))
(pow.f64 (E.f64) (/.f64 (log.f64 x) #s(literal 2 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (E.f64) #s(literal 1/2 binary64)) (log.f64 x))
(pow.f64 (*.f64 (exp.f64 #s(literal 1/8 binary64)) (exp.f64 #s(literal 3/8 binary64))) (log.f64 x))
(pow.f64 (*.f64 (exp.f64 #s(literal 3/8 binary64)) (exp.f64 #s(literal 1/8 binary64))) (log.f64 x))
(*.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 x #s(literal 3/8 binary64)))
(*.f64 (pow.f64 x #s(literal 3/8 binary64)) (pow.f64 x #s(literal 1/8 binary64)))
(*.f64 (pow.f64 x #s(literal 3/32 binary64)) (pow.f64 x #s(literal 13/32 binary64)))
(*.f64 (pow.f64 x #s(literal 1/32 binary64)) (pow.f64 x #s(literal 15/32 binary64)))
(*.f64 (pow.f64 x #s(literal 9/32 binary64)) (pow.f64 x #s(literal 7/32 binary64)))
(*.f64 (pow.f64 x #s(literal 3/128 binary64)) (sqrt.f64 (pow.f64 x #s(literal 61/64 binary64))))
(*.f64 (pow.f64 x #s(literal 1/128 binary64)) (sqrt.f64 (pow.f64 x #s(literal 63/64 binary64))))
(*.f64 (pow.f64 x #s(literal 13/32 binary64)) (pow.f64 x #s(literal 3/32 binary64)))
(*.f64 (pow.f64 x #s(literal 9/128 binary64)) (sqrt.f64 (pow.f64 x #s(literal 55/64 binary64))))
(*.f64 (pow.f64 x #s(literal 27/128 binary64)) (sqrt.f64 (pow.f64 x #s(literal 37/64 binary64))))
(*.f64 (pow.f64 x #s(literal 7/32 binary64)) (pow.f64 x #s(literal 9/32 binary64)))
(*.f64 (pow.f64 x #s(literal 15/32 binary64)) (pow.f64 x #s(literal 1/32 binary64)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 61/64 binary64))) (pow.f64 x #s(literal 3/128 binary64)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 63/64 binary64))) (pow.f64 x #s(literal 1/128 binary64)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 55/64 binary64))) (pow.f64 x #s(literal 9/128 binary64)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 37/64 binary64))) (pow.f64 x #s(literal 27/128 binary64)))

simplify127.0ms (6%)

Algorithm

1×	egg-herbie

Rules

2834×	`fma-define`
1646×	`fnmadd-define`
1070×	`sum3-define`
982×	`fma-lowering-fma.f32`
982×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	39	336
1	87	332
2	221	320
3	521	320
4	931	316
5	1327	316
6	2469	316
7	3419	316
8	4249	316
9	5087	316
10	5342	316
11	5347	316
12	5350	316
13	5350	316
14	5499	316
15	5503	316
0	5503	316

Stop Event

1×	iter limit
1×	saturated

Counts

60 → 60

Calls

Call 1

Inputs
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(pow (* 1 (pow x 3)) 1/4)
(pow (* 1 (pow x 3)) 1/4)
(pow (* 1 (pow x 3)) 1/4)
(pow (* 1 (pow x 3)) 1/4)
(pow (* 1 (pow x 3)) 1/4)
(pow (* 1 (pow x 3)) 1/4)
(pow (* 1 (pow x 3)) 1/4)
(pow (* 1 (pow x 3)) 1/4)
(exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))
(exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))
(exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))
(exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))
(* (pow (* 1 x) 1/4) (sqrt 2))
(* (pow (* 1 x) 1/4) (sqrt 2))
(* (pow (* 1 x) 1/4) (sqrt 2))
(* (pow (* 1 x) 1/4) (sqrt 2))
(* (pow (* 1 x) 1/4) (sqrt 2))
(* (pow (* 1 x) 1/4) (sqrt 2))
(* (pow (* 1 x) 1/4) (sqrt 2))
(* (pow (* 1 x) 1/4) (sqrt 2))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(* 2 (sqrt x))
(* 2 (sqrt x))
(* 2 (sqrt x))
(* 2 (sqrt x))
(* 2 (sqrt x))
(* 2 (sqrt x))
(* 2 (sqrt x))
(* 2 (sqrt x))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))

Outputs
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(.f64 (.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64)))) (pow.f64 #s(literal -1 binary64) #s(literal 5/4 binary64)))
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(.f64 (.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64)))) (pow.f64 #s(literal -1 binary64) #s(literal 5/4 binary64)))
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(.f64 (.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64)))) (pow.f64 #s(literal -1 binary64) #s(literal 5/4 binary64)))
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(.f64 (.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64)))) (pow.f64 #s(literal -1 binary64) #s(literal 5/4 binary64)))
(pow (* 1 (pow x 3)) 1/4)
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1/4 binary64))
(pow (* 1 (pow x 3)) 1/4)
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1/4 binary64))
(pow (* 1 (pow x 3)) 1/4)
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1/4 binary64))
(pow (* 1 (pow x 3)) 1/4)
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1/4 binary64))
(pow (* 1 (pow x 3)) 1/4)
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1/4 binary64))
(pow (* 1 (pow x 3)) 1/4)
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1/4 binary64))
(pow (* 1 (pow x 3)) 1/4)
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1/4 binary64))
(pow (* 1 (pow x 3)) 1/4)
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1/4 binary64))
(exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -3/4 binary64)))
(exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -3/4 binary64)))
(exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -3/4 binary64)))
(exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -3/4 binary64)))
(* (pow (* 1 x) 1/4) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(* (pow (* 1 x) 1/4) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(* (pow (* 1 x) 1/4) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(* (pow (* 1 x) 1/4) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(* (pow (* 1 x) 1/4) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(* (pow (* 1 x) 1/4) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(* (pow (* 1 x) 1/4) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(* (pow (* 1 x) 1/4) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(.f64 (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64)))))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(.f64 (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64)))))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(.f64 (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64)))))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(.f64 (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/4 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64)))))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)

eval31.0ms (1.5%)

Compiler: Compiled 2244 to 431 computations (80.8% saved)

prune15.0ms (0.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	181	2	183

Accuracy

100.0%

Counts

183 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	99.4%	(.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x))))

Compiler

Compiled 45 to 25 computations (44.4% saved)

regimes7.0ms (0.3%)

Accuracy

Total -31.2b remaining (-798404.1%)

Threshold costs -31.2b (-798404.1%)

Counts

4 → 1

Calls

Call 1

Inputs
(hypot.f64 x x)
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3/4 binary64)))

Outputs
(hypot.f64 x x)

Calls

4 calls:

2.0ms	x
2.0ms	(*.f64 x x)
2.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
2.0ms	(+.f64 (.f64 x x) (.f64 x x))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
100.0%	1	`(+.f64 (.f64 x x) (.f64 x x))`
100.0%	1	`(*.f64 x x)`

Compiler

Compiled 23 to 10 computations (56.5% saved)

simplify35.0ms (1.7%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2	3

Stop Event

1×

saturated

Calls

Call 1

Inputs
(hypot.f64 x x)

Outputs
(hypot.f64 x x)

soundness4.0ms (0.2%)

Rules

14×	`-lowering-.f32`
14×	`-lowering-.f64`
4×	`*-commutative`
4×	`+-lowering-+.f64`
4×	`count-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	3
1	11	3
2	14	3
3	17	3
0	17	3

Stop Event

1×	done
1×	iter limit
1×	saturated

Compiler

Compiled 8 to 4 computations (50% saved)

preprocess20.0ms (0.9%)

Remove: (abs x)
Compiler: Compiled 42 to 20 computations (52.4% saved)

sqrt A (should all be same)

analyze0.0ms (0%)

sample681.0ms (32%)

preprocess23.0ms (1.1%)

explain72.0ms (3.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.2%)

localize30.0ms (1.4%)

series1.0ms (0.1%)

rewrite185.0ms (8.7%)

simplify8.0ms (0.4%)

eval7.0ms (0.3%)

prune4.0ms (0.2%)

simplify4.0ms (0.2%)

localize57.0ms (2.7%)

series100.0ms (4.7%)

rewrite241.0ms (11.3%)

simplify137.0ms (6.4%)

eval25.0ms (1.2%)

prune13.0ms (0.6%)

simplify4.0ms (0.2%)

localize73.0ms (3.4%)

series26.0ms (1.2%)

rewrite192.0ms (9%)

simplify127.0ms (6%)

eval31.0ms (1.5%)

prune15.0ms (0.7%)

regimes7.0ms (0.3%)

simplify35.0ms (1.7%)

soundness4.0ms (0.2%)

preprocess20.0ms (0.9%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	9	10
1	32	10
2	77	10
3	199	10
4	394	10
5	617	10
6	684	10
7	687	10
0	4	3
1	11	3
2	14	3
3	17	3
0	17	3

Iter	Nodes	Cost
0	9	10
1	32	10
2	77	10
3	199	10
4	394	10
5	617	10
6	684	10
7	687	10
0	4	3
1	11	3
2	14	3
3	17	3
0	17	3

Iter	Nodes	Cost
0	9	10
1	32	10
2	77	10
3	199	10
4	394	10
5	617	10
6	684	10
7	687	10
0	4	3
1	11	3
2	14	3
3	17	3
0	17	3