Metrics for sqrt D (should all be same)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
100%	100%	0%	0%	0%	0%	0%	1

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample694.0ms (6%)

Memory

13.3MiB live, 718.0MiB allocated

Samples

475.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 319.0ms

ival-pow2: 190.0ms (59.6% of total)

ival-sqrt: 66.0ms (20.7% of total)

ival-mult: 49.0ms (15.4% of total)

ival-true: 6.0ms (1.9% of total)

exact: 5.0ms (1.6% of total)

ival-assert: 3.0ms (0.9% of total)

Bogosity

explain63.0ms (0.5%)

Memory

-11.7MiB live, 116.6MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
136	-	3	(-2.1684764398252252e-157)	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
0	-	0	-	`(pow.f64 x #s(literal 2 binary64))`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`	uflow-rescue	67	0
↳	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`	underflow	67
↳	`(pow.f64 x #s(literal 2 binary64))`	underflow	67
`sqrt.f64`	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`	oflow-rescue	66	0
↳	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`	overflow	66
↳	`(pow.f64 x #s(literal 2 binary64))`	overflow	66

Confusion

	Predicted +	Predicted -
+	133	3
-	0	120

Precision

1.0

Recall

0.9779411764705882

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	133	0	3
-	0	0	120

Precision?

1.0

Recall?

0.9779411764705882

Freqs

test

number	freq
0	123
1	133

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

29.0ms

512×

valid

Compiler

Compiled 58 to 24 computations (58.6% saved)

Precisions

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

ival-mult: 7.0ms (41.3% of total)

ival-pow2: 6.0ms (35.4% of total)

ival-sqrt: 3.0ms (17.7% of total)

ival-true: 1.0ms (5.9% of total)

exact: 0.0ms (0% of total)

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

preprocess14.0ms (0.1%)

Memory

21.0MiB live, 21.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	15	13
2	34	13
3	124	13
4	250	13
5	276	13
6	286	13
0	5	6
0	8	6
1	10	6
2	14	6
3	16	6
0	16	6

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))

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

Compiler

Compiled 6 to 5 computations (16.7% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.2MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	51.2%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify47.0ms (0.4%)

Memory

-31.3MiB live, 7.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
cost-diff	0	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
cost-diff	6144	(pow.f64 x #s(literal 2 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	16
0	8	16
1	10	16
2	14	16
3	16	16
0	16	16

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
#s(literal 2 binary64)
(pow.f64 x #s(literal 2 binary64))
x

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

localize17.0ms (0.1%)

Memory

25.8MiB live, 25.8MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(pow.f64 x #s(literal 2 binary64))
accuracy	0.00390625	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
accuracy	31.212960840710743	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))

Samples

12.0ms

256×

valid

Compiler

Compiled 34 to 12 computations (64.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-pow2: 3.0ms (43.1% of total)

ival-sqrt: 2.0ms (28.7% of total)

ival-mult: 1.0ms (14.4% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0%)

Memory

6.0MiB live, 6.0MiB allocated

Counts

3 → 4

Calls

Call 1

Inputs
(pow.f64 x #s(literal 2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))

Outputs
(pow x 2)
(* x (sqrt 2))
(* 2 (pow x 2))
(* -1 (* x (sqrt 2)))

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	((pow x 2) (sqrt (* 2 (pow x 2))) (* 2 (pow x 2)))
1.0ms	x	@	0	((pow x 2) (sqrt (* 2 (pow x 2))) (* 2 (pow x 2)))
1.0ms	x	@	-inf	((pow x 2) (sqrt (* 2 (pow x 2))) (* 2 (pow x 2)))

simplify7.0ms (0.1%)

Memory

-38.3MiB live, 4.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	15	17
2	32	17
3	38	17
4	42	17
5	54	17
6	66	17
7	77	17
8	97	17
9	102	17
0	102	17

Stop Event

1×	iter limit
1×	saturated

Counts

4 → 4

Calls

Call 1

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

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

rewrite145.0ms (1.2%)

Memory

23.1MiB live, 96.5MiB allocated

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	5	14
0	8	14
1	22	12
2	57	12
3	186	12
4	765	4
5	6179	4
0	9030	4

Stop Event

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

Counts

3 → 46

Calls

Call 1

Inputs
(pow.f64 x #s(literal 2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))

Outputs
x
#s(literal 1 binary64)
(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64)) x) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/32 binary64)) x))
(*.f64 (pow.f64 (pow.f64 (sqrt.f64 (E.f64)) (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))) x) (pow.f64 (pow.f64 (sqrt.f64 (E.f64)) (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))) x))
(*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/32 binary64)) x) (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64)) x))
(*.f64 (pow.f64 (pow.f64 #s(literal 8 binary64) #s(literal 1/8 binary64)) x) (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal 1/32 binary64)))
(*.f64 (pow.f64 (sqrt.f64 (E.f64)) (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (sqrt.f64 (E.f64)) (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))))
(*.f64 (pow.f64 #s(literal 8 binary64) #s(literal 1/8 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/32 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64)))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (pow.f64 (pow.f64 #s(literal 8 binary64) #s(literal 1/8 binary64)) x))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (pow.f64 #s(literal 8 binary64) #s(literal 1/8 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(*.f64 (pow.f64 #s(literal 16 binary64) #s(literal 1/16 binary64)) (pow.f64 #s(literal 16 binary64) #s(literal 1/16 binary64)))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (pow.f64 (sqrt.f64 (E.f64)) (*.f64 (log.f64 #s(literal 2 binary64)) (log.f64 #s(literal 1/2 binary64)))) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(pow.f64 (pow.f64 (sqrt.f64 (E.f64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64))) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal -2 binary64)))
(pow.f64 (pow.f64 (sqrt.f64 (E.f64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal -1 binary64)))
(pow.f64 (pow.f64 (sqrt.f64 (E.f64)) (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 1/4 binary64)) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))
(pow.f64 (exp.f64 #s(literal 1/4 binary64)) (log.f64 #s(literal 4 binary64)))
(pow.f64 #s(literal 16 binary64) #s(literal 1/8 binary64))
(pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/32 binary64)) #s(literal 8 binary64))
(pow.f64 (sqrt.f64 (E.f64)) (+.f64 (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))))
(pow.f64 (sqrt.f64 (E.f64)) (*.f64 (log.f64 #s(literal 2 binary64)) x))
(pow.f64 (sqrt.f64 (E.f64)) (log.f64 #s(literal 2 binary64)))
(pow.f64 (E.f64) (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))
(pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) #s(literal 4 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 2 binary64))))
(pow.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(pow.f64 (pow.f64 #s(literal 16 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(/.f64 (pow.f64 (sqrt.f64 (E.f64)) (/.f64 #s(literal 0 binary64) (log.f64 #s(literal 1/2 binary64)))) (pow.f64 (sqrt.f64 (E.f64)) (/.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (log.f64 #s(literal 1/2 binary64)))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (E.f64)) (/.f64 #s(literal 0 binary64) (log.f64 #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
(exp.f64 (+.f64 (fma.f64 (log.f64 #s(literal 4 binary64)) #s(literal 1/8 binary64) (.f64 #s(literal 1/8 binary64) (log.f64 #s(literal 2 binary64)))) (.f64 #s(literal 1/8 binary64) (log.f64 #s(literal 2 binary64)))))
(exp.f64 (+.f64 (fma.f64 #s(literal 1/16 binary64) (log.f64 #s(literal 4 binary64)) (.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 2 binary64)))) (.f64 #s(literal 1/8 binary64) (log.f64 #s(literal 2 binary64)))))
(exp.f64 (fma.f64 #s(literal 1/16 binary64) (log.f64 #s(literal 4 binary64)) (fma.f64 (log.f64 #s(literal 4 binary64)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/8 binary64) (log.f64 #s(literal 2 binary64))))))
(exp.f64 (fma.f64 #s(literal 1/16 binary64) (log.f64 #s(literal 4 binary64)) (fma.f64 #s(literal 1/16 binary64) (log.f64 #s(literal 4 binary64)) (*.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 2 binary64))))))
(exp.f64 (*.f64 (log.f64 #s(literal 16 binary64)) #s(literal 1/8 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/8 binary64) (log.f64 #s(literal 2 binary64))) #s(literal 4 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))) x))
(exp.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))
#s(literal 2 binary64)

eval6.0ms (0.1%)

Memory: 11.9MiB live, 11.9MiB allocated
Compiler: Compiled 405 to 127 computations (68.6% saved)

prune2.0ms (0%)

Memory

5.6MiB live, 5.6MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	46	4	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	4	51

Accuracy

99.6%

Counts

51 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.6%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
▶	51.2%	(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
▶	5.3%	(sqrt.f64 #s(literal 2 binary64))
▶	47.0%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 28 to 25 computations (10.7% saved)

simplify11.0ms (0.1%)

Memory

-29.6MiB live, 6.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (pow x 2) (*.f64 x x))
cost-diff	0	(.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))
cost-diff	0	(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(neg.f64 x)
cost-diff	0	(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	65
0	21	65
1	31	65
2	44	65
3	56	65
4	62	65
5	73	65
6	98	65
7	107	65
8	113	65
9	113	65
0	113	65

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(neg.f64 x)
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
(.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))
#s(literal 2 binary64)
#s(approx (pow x 2) (*.f64 x x))
(*.f64 x x)
x
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
x

Outputs
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x))
(neg.f64 x)
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
(sqrt.f64 (.f64 #s(approx (pow x 2) (.f64 x x)) #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))
(.f64 #s(approx (pow x 2) (.f64 x x)) #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (pow x 2) (*.f64 x x))
(*.f64 x x)
x
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
x

localize41.0ms (0.4%)

Memory

15.9MiB live, 67.4MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0.0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.41796875	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
accuracy	0.0	(*.f64 x x)
accuracy	0.0	#s(approx (pow x 2) (*.f64 x x))
accuracy	0.00390625	(.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))
accuracy	31.212960840710743	(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
accuracy	0.0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.0	(neg.f64 x)
accuracy	0.41796875	(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
accuracy	33.690072915294	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Samples

32.0ms

256×

valid

Compiler

Compiled 114 to 27 computations (76.3% saved)

Precisions

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

ival-mult: 6.0ms (44.1% of total)

ival-sqrt: 3.0ms (22% of total)

ival-pow2: 3.0ms (22% of total)

ival-neg: 1.0ms (7.3% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0%)

Memory

-27.0MiB live, 10.1MiB allocated

Counts

9 → 5

Calls

Call 1

Inputs
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(neg.f64 x)
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
(.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))
#s(approx (pow x 2) (*.f64 x x))
(*.f64 x x)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)

Outputs
(* x (sqrt 2))
(* -1 (* x (sqrt 2)))
(* -1 x)
(* 2 (pow x 2))
(pow x 2)

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	((sqrt (* 2 (pow x 2))) (* (neg x) (sqrt 2)) (neg x) (sqrt 2) (sqrt (* 2 (pow x 2))) (* 2 (pow x 2)) (pow x 2) (* x x) (* (sqrt 2) x))
1.0ms	x	@	-inf	((sqrt (* 2 (pow x 2))) (* (neg x) (sqrt 2)) (neg x) (sqrt 2) (sqrt (* 2 (pow x 2))) (* 2 (pow x 2)) (pow x 2) (* x x) (* (sqrt 2) x))
1.0ms	x	@	0	((sqrt (* 2 (pow x 2))) (* (neg x) (sqrt 2)) (neg x) (sqrt 2) (sqrt (* 2 (pow x 2))) (* 2 (pow x 2)) (pow x 2) (* x x) (* (sqrt 2) x))

Time

Variable

Point

Expression

1.0ms

inf

((sqrt (* 2 (pow x 2))) (* (neg x) (sqrt 2)) (neg x) (sqrt 2) (sqrt (* 2 (pow x 2))) (* 2 (pow x 2)) (pow x 2) (* x x) (* (sqrt 2) x))

1.0ms

-inf

((sqrt (* 2 (pow x 2))) (* (neg x) (sqrt 2)) (neg x) (sqrt 2) (sqrt (* 2 (pow x 2))) (* 2 (pow x 2)) (pow x 2) (* x x) (* (sqrt 2) x))

1.0ms

((sqrt (* 2 (pow x 2))) (* (neg x) (sqrt 2)) (neg x) (sqrt 2) (sqrt (* 2 (pow x 2))) (* 2 (pow x 2)) (pow x 2) (* x x) (* (sqrt 2) x))

simplify4.0ms (0%)

Memory

10.9MiB live, 10.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	17	19
2	33	19
3	38	19
4	46	19
5	57	19
6	68	19
7	90	19
8	101	19
9	101	19
0	101	19

Stop Event

1×	iter limit
1×	saturated

Counts

5 → 5

Calls

Call 1

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

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

rewrite130.0ms (1.1%)

Memory

11.6MiB live, 131.2MiB allocated

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	14	54
0	21	55
1	46	53
2	112	53
3	469	53
4	3782	49
0	8402	49

Stop Event

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

Counts

9 → 835

Calls

Call 1

Inputs
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(neg.f64 x)
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
(.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))
#s(approx (pow x 2) (*.f64 x x))
(*.f64 x x)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)

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

eval59.0ms (0.5%)

Memory: 5.6MiB live, 115.4MiB allocated
Compiler: Compiled 10 072 to 1 621 computations (83.9% saved)

prune21.0ms (0.2%)

Memory

6.6MiB live, 52.2MiB allocated

Pruning

15 alts after pruning (11 fresh and 4 done)

	Pruned	Kept	Total
New	567	11	578
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	567	15	582

Accuracy

100.0%

Counts

582 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
	54.4%	(*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x)
✓	54.6%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
	25.6%	(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 x x)))))
▶	34.9%	(sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (pow x 2) (/.f64 (pow.f64 x #s(literal 3 binary64)) x))))
	50.6%	(sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (pow x 2) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64))))))
✓	51.2%	(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
✓	5.3%	(sqrt.f64 #s(literal 2 binary64))
	26.6%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))
▶	54.5%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal -1 binary64))))
▶	34.0%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))))
▶	47.0%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
	47.1%	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x) (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)))))
▶	53.6%	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)))
	46.9%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64))))
✓	47.0%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 332 to 271 computations (18.4% saved)

simplify201.0ms (1.7%)

Memory

9.9MiB live, 165.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
cost-diff	0	(pow.f64 x #s(literal 3/2 binary64))
cost-diff	0	(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x)))
cost-diff	0	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))))
cost-diff	0	#s(approx (pow x 2) (/.f64 (pow.f64 x #s(literal 3 binary64)) x))
cost-diff	0	(*.f64 #s(literal 2 binary64) #s(approx (pow x 2) (/.f64 (pow.f64 x #s(literal 3 binary64)) x)))
cost-diff	0	(sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (pow x 2) (/.f64 (pow.f64 x #s(literal 3 binary64)) x))))
cost-diff	6848	(/.f64 (pow.f64 x #s(literal 3 binary64)) x)
cost-diff	0	(pow.f64 x #s(literal -1 binary64))
cost-diff	0	(*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
cost-diff	7040	(/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1 binary64)))
cost-diff	0	(*.f64 x #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
cost-diff	0	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
cost-diff	0	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)))
cost-diff	0	(pow.f64 x #s(literal -1 binary64))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal -1 binary64))))
cost-diff	6848	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal -1 binary64)))

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	29	178
0	45	178
1	60	172
2	81	165
3	102	157
4	134	157
5	251	157
6	674	157
7	2677	157
8	4143	157
9	6697	157
0	8076	157

Stop Event

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

Calls

Call 1

Inputs
#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal -1 binary64))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal -1 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(pow.f64 x #s(literal -1 binary64))
x
#s(literal -1 binary64)
#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)))
(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
(*.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
(sqrt.f64 x)
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1 binary64)))
#s(literal -1 binary64)
(pow.f64 x #s(literal -1 binary64))
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (pow x 2) (/.f64 (pow.f64 x #s(literal 3 binary64)) x))))
(*.f64 #s(literal 2 binary64) #s(approx (pow x 2) (/.f64 (pow.f64 x #s(literal 3 binary64)) x)))
#s(literal 2 binary64)
#s(approx (pow x 2) (/.f64 (pow.f64 x #s(literal 3 binary64)) x))
(/.f64 (pow.f64 x #s(literal 3 binary64)) x)
(pow.f64 x #s(literal 3 binary64))
x
#s(literal 3 binary64)
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x)))
(pow.f64 x #s(literal 3/2 binary64))
x
#s(literal 3/2 binary64)
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 x)

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

localize71.0ms (0.6%)

Memory

2.4MiB live, 117.0MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.0	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))))
accuracy	0.278007519536884	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
accuracy	12.681608396527276	(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x)))
accuracy	0.0	#s(approx (pow x 2) (/.f64 (pow.f64 x #s(literal 3 binary64)) x))
accuracy	0.00390625	(*.f64 #s(literal 2 binary64) #s(approx (pow x 2) (/.f64 (pow.f64 x #s(literal 3 binary64)) x)))
accuracy	5.942291306751584	(/.f64 (pow.f64 x #s(literal 3 binary64)) x)
accuracy	18.11288050739403	(sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (pow x 2) (/.f64 (pow.f64 x #s(literal 3 binary64)) x))))
accuracy	0.0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.09765625	(/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1 binary64)))
accuracy	0.203125	(*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64)))
accuracy	33.690072915294	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.0	(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
accuracy	0.0	(sqrt.f64 x)
accuracy	0.0	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)))
accuracy	0.1953125	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
accuracy	0.0	(pow.f64 x #s(literal -1 binary64))
accuracy	0.0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.0	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal -1 binary64))))
accuracy	0.234375	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal -1 binary64)))

Samples

26.0ms	138×	0	valid
25.0ms	118×	0	invalid

Compiler

Compiled 306 to 54 computations (82.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

ival-pow: 11.0ms (30% of total)

ival-mult: 8.0ms (21.8% of total)

ival-div: 7.0ms (19.1% of total)

ival-sqrt: 6.0ms (16.3% of total)

ival-pow2: 3.0ms (8.2% of total)

exact: 1.0ms (2.7% of total)

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

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

series18.0ms (0.2%)

Memory

-34.2MiB live, 17.6MiB allocated

Counts

20 → 15

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal -1 binary64)))
#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal -1 binary64))))
(sqrt.f64 #s(literal 2 binary64))
(pow.f64 x #s(literal -1 binary64))
#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)))
(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
(*.f64 x #s(literal 2 binary64))
(/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1 binary64)))
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (pow.f64 x #s(literal 3 binary64)) x)
(sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (pow x 2) (/.f64 (pow.f64 x #s(literal 3 binary64)) x))))
(*.f64 #s(literal 2 binary64) #s(approx (pow x 2) (/.f64 (pow.f64 x #s(literal 3 binary64)) x)))
#s(approx (pow x 2) (/.f64 (pow.f64 x #s(literal 3 binary64)) x))
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x)))
(pow.f64 x #s(literal 3/2 binary64))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(sqrt.f64 x)

Outputs
(* x (sqrt 2))
(/ 1 x)
(* (sqrt x) (sqrt 2))
(* 2 x)
(* -1 x)
(* -1 (* x (sqrt 2)))
(pow x 2)
(* 2 (pow x 2))
(sqrt (pow x 3))
(* (sqrt (/ 1 x)) (sqrt 2))
(sqrt x)
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(* (sqrt (pow x 3)) (pow (sqrt -1) 2))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))

Calls

3 calls:

Time

Variable

Point

Expression

10.0ms

inf

((/ (sqrt 2) (pow x -1)) (sqrt (* 2 (pow x 2))) (sqrt 2) (pow x -1) (sqrt (* 2 (pow x 2))) (* (sqrt (* x 2)) (sqrt x)) (sqrt (* x 2)) (* x 2) (/ -1 (pow x -1)) (sqrt (* 2 (pow x 2))) (* (/ -1 (pow x -1)) (sqrt 2)) (/ (pow x 3) x) (sqrt (* 2 (pow x 2))) (* 2 (pow x 2)) (pow x 2) (sqrt (* 2 (pow x 2))) (* (pow x 3/2) (/ (sqrt 2) (sqrt x))) (pow x 3/2) (/ (sqrt 2) (sqrt x)) (sqrt x))

5.0ms

-inf

((/ (sqrt 2) (pow x -1)) (sqrt (* 2 (pow x 2))) (sqrt 2) (pow x -1) (sqrt (* 2 (pow x 2))) (* (sqrt (* x 2)) (sqrt x)) (sqrt (* x 2)) (* x 2) (/ -1 (pow x -1)) (sqrt (* 2 (pow x 2))) (* (/ -1 (pow x -1)) (sqrt 2)) (/ (pow x 3) x) (sqrt (* 2 (pow x 2))) (* 2 (pow x 2)) (pow x 2) (sqrt (* 2 (pow x 2))) (* (pow x 3/2) (/ (sqrt 2) (sqrt x))) (pow x 3/2) (/ (sqrt 2) (sqrt x)) (sqrt x))

3.0ms

((/ (sqrt 2) (pow x -1)) (sqrt (* 2 (pow x 2))) (sqrt 2) (pow x -1) (sqrt (* 2 (pow x 2))) (* (sqrt (* x 2)) (sqrt x)) (sqrt (* x 2)) (* x 2) (/ -1 (pow x -1)) (sqrt (* 2 (pow x 2))) (* (/ -1 (pow x -1)) (sqrt 2)) (/ (pow x 3) x) (sqrt (* 2 (pow x 2))) (* 2 (pow x 2)) (pow x 2) (sqrt (* 2 (pow x 2))) (* (pow x 3/2) (/ (sqrt 2) (sqrt x))) (pow x 3/2) (/ (sqrt 2) (sqrt x)) (sqrt x))

simplify207.0ms (1.8%)

Memory

17.5MiB live, 55.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	31	71
1	66	68
2	156	67
3	284	67
4	523	67
5	893	67
6	1266	67
7	1463	67
8	1562	67
9	1646	67
10	1891	67
11	2252	67
12	2309	67
13	2337	67
14	2344	67
15	2344	67
16	2344	67
17	2397	67
18	2711	67
19	4117	67
20	4390	67
21	4594	67
22	4702	67
23	4708	67
24	4708	67
25	4708	67
26	4804	67
27	4844	67
28	4844	67
29	5068	67
30	6051	67
31	6075	67
0	6075	67

Stop Event

1×	iter limit
1×	saturated

Counts

15 → 15

Calls

Call 1

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

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

rewrite129.0ms (1.1%)

Memory

3.4MiB live, 118.1MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	29	152
0	45	143
1	121	106
2	430	106
0	3285	106

Stop Event

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

Counts

20 → 706

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal -1 binary64)))
#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal -1 binary64))))
(sqrt.f64 #s(literal 2 binary64))
(pow.f64 x #s(literal -1 binary64))
#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)))
(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
(*.f64 x #s(literal 2 binary64))
(/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1 binary64)))
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (pow.f64 x #s(literal 3 binary64)) x)
(sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (pow x 2) (/.f64 (pow.f64 x #s(literal 3 binary64)) x))))
(*.f64 #s(literal 2 binary64) #s(approx (pow x 2) (/.f64 (pow.f64 x #s(literal 3 binary64)) x)))
#s(approx (pow x 2) (/.f64 (pow.f64 x #s(literal 3 binary64)) x))
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x)))
(pow.f64 x #s(literal 3/2 binary64))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(sqrt.f64 x)

Outputs
(*.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (neg.f64 (sqrt.f64 x))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 x)))
(.f64 (/.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) #s(literal 1 binary64)) (sqrt.f64 x))
(.f64 (.f64 (*.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) x))) (pow.f64 x #s(literal 3/8 binary64))) (pow.f64 x #s(literal 3/8 binary64)))
(.f64 (.f64 (*.f64 (pow.f64 x #s(literal 3/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal -1/4 binary64))) (pow.f64 x #s(literal -1/4 binary64)))
(.f64 (.f64 (*.f64 (pow.f64 x #s(literal 3/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64)) (pow.f64 x #s(literal -1/2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (sqrt.f64 x))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (sqrt.f64 x)))
(.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 x #s(literal 2 binary64)))) (sqrt.f64 x))
(.f64 (.f64 (sqrt.f64 x) (pow.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/4 binary64))) (pow.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(.f64 (.f64 (sqrt.f64 (*.f64 x #s(literal 2 binary64))) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 x))
(*.f64 (pow.f64 (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) x) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) x) #s(literal -1/2 binary64)))
(*.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal -1 binary64)) (neg.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x))))
(.f64 (/.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 x #s(literal 1/4 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 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 x)) (/.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 x #s(literal -1/2 binary64))) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 x #s(literal -1/2 binary64))))
(*.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) x)))
(.f64 (neg.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64)))) (neg.f64 (sqrt.f64 x)))
(.f64 (.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) x))) (pow.f64 x #s(literal 3/4 binary64)))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (*.f64 x #s(literal 2 binary64)))))
(.f64 (pow.f64 x #s(literal 3/8 binary64)) (.f64 (pow.f64 x #s(literal 3/8 binary64)) (*.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) x)))))
(.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (sqrt.f64 x)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (sqrt.f64 x)))
(.f64 (pow.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (pow.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 x)))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) x))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 x #s(literal -1 binary64))))
(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
(.f64 (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(.f64 (.f64 (pow.f64 x #s(literal 3/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal -1/2 binary64)))
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) x))))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(.f64 (pow.f64 x #s(literal -1/2 binary64)) (.f64 (pow.f64 x #s(literal 3/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (neg.f64 x) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64)))))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (neg.f64 (sqrt.f64 x))))
(.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (pow.f64 x #s(literal 3/2 binary64))))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 x))
(.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x)) (pow.f64 x #s(literal 3/2 binary64)))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) x)))
(.f64 (.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64))
(*.f64 (sqrt.f64 x) (pow.f64 (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x #s(literal 2 binary64))))
(.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(pow.f64 (exp.f64 (log.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))) #s(literal 1/2 binary64))
(pow.f64 (.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) (.f64 (*.f64 x x) #s(literal 2 binary64))) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (sqrt.f64 x)) #s(literal 2 binary64))
(pow.f64 (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) x) #s(literal -1 binary64))
(pow.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1/2 binary64))
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(*.f64 (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 5/2 binary64)) #s(literal 3/4 binary64)) (pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 3/4 binary64)))
(*.f64 (pow.f64 (neg.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 3/4 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 3/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 3/4 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 3/4 binary64)) (pow.f64 (sqrt.f64 x) #s(literal 3/4 binary64)))
(*.f64 (pow.f64 x #s(literal 9/4 binary64)) (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 3/4 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 3/4 binary64)) (pow.f64 x #s(literal 9/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (sqrt.f64 x) #s(literal 3/2 binary64)) (pow.f64 (sqrt.f64 x) #s(literal 3/2 binary64)))
(.f64 (pow.f64 x #s(literal 3/8 binary64)) (.f64 (pow.f64 x #s(literal 3/8 binary64)) (pow.f64 x #s(literal 3/4 binary64))))
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
(*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3/2 binary64)))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal 3/4 binary64)))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 3/2 binary64)) (log.f64 x))
(pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -3/4 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/4 binary64))
(pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -3/2 binary64))
(pow.f64 x #s(literal 3/2 binary64))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 3/4 binary64) (*.f64 (log.f64 x) #s(literal 3/4 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 3/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 3/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 x #s(literal 3/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 x x)) #s(literal 3/4 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 3/2 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal -1/4 binary64))) (pow.f64 x #s(literal -1/4 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 x #s(literal -1/4 binary64))) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 x #s(literal -1/4 binary64))))
(.f64 (pow.f64 (sqrt.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(.f64 (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 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 x #s(literal -1/2 binary64))))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (sqrt.f64 x)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (pow.f64 x #s(literal -1 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal -1/2 binary64)))
(pow.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (sqrt.f64 x)))
(/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(/.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 (neg.f64 x)))
(/.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 x #s(literal 1/2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 x #s(literal 1/2 binary64)))))
(neg.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x)))))
(neg.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) x))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x))))
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x))))
(exp.f64 (-.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (log.f64 x) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 x) #s(literal -1/2 binary64) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64) (*.f64 (log.f64 x) #s(literal -1/2 binary64))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64)))
(*.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 x #s(literal 3/4 binary64)) x))
(*.f64 (/.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 x)) (/.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 x)))
(*.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))
(.f64 (.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 x #s(literal -1/2 binary64))) (*.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 x #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (pow.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 x))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (/.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 x #s(literal -1 binary64))))
(*.f64 (pow.f64 x #s(literal 3/4 binary64)) (/.f64 (pow.f64 x #s(literal 3/4 binary64)) x))
(*.f64 #s(literal 1 binary64) (sqrt.f64 x))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal -1 binary64)))
(*.f64 (sqrt.f64 x) #s(literal 1 binary64))
(*.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 x)))
(*.f64 x (pow.f64 x #s(literal -1/2 binary64)))
(pow.f64 (*.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 x #s(literal -1/2 binary64))) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1/2 binary64))
(pow.f64 x #s(literal 1/2 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/4 binary64))) (pow.f64 x #s(literal -1/4 binary64)))
(/.f64 (*.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal -1 binary64)) (neg.f64 x))
(/.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1 binary64)) x)
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) x)))
(/.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (pow.f64 x #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (pow.f64 x #s(literal 3/2 binary64))) (neg.f64 x))
(/.f64 (neg.f64 (sqrt.f64 x)) #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 x #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64)))
(/.f64 (pow.f64 x #s(literal 3/2 binary64)) x)
(/.f64 (sqrt.f64 x) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(/.f64 x (sqrt.f64 x))
(neg.f64 (neg.f64 (sqrt.f64 x)))
(sqrt.f64 x)
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 x)))
(fabs.f64 (sqrt.f64 x))
(exp.f64 (-.f64 (*.f64 (log.f64 x) #s(literal 3/2 binary64)) (log.f64 x)))
(exp.f64 (neg.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 3/2 binary64) (neg.f64 (log.f64 x))))
(exp.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)))

eval89.0ms (0.8%)

Memory: -3.5MiB live, 109.3MiB allocated
Compiler: Compiled 11 996 to 2 280 computations (81% saved)

prune22.0ms (0.2%)

Memory

7.1MiB live, 53.4MiB allocated

Pruning

18 alts after pruning (13 fresh and 5 done)

	Pruned	Kept	Total
New	666	12	678
Fresh	5	1	6
Picked	4	1	5
Done	0	4	4
Total	675	18	693

Accuracy

100.0%

Counts

693 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	54.6%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
	51.2%	(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 (.f64 (neg.f64 x) x) (.f64 x (/.f64 #s(literal -1 binary64) x))))))
✓	51.2%	(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
✓	5.3%	(sqrt.f64 #s(literal 2 binary64))
	26.6%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))
▶	54.5%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) x)))
▶	47.0%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) x)))
	53.5%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (neg.f64 (sqrt.f64 (*.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))
	54.5%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 x (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
	47.0%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))
	47.1%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 #s(literal -1 binary64) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) x)))
	47.0%	#s(approx (sqrt (* 2 (pow x 2))) (*.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 -1 binary64) x))))
	47.1%	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (neg.f64 x))))
▶	18.2%	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (/.f64 #s(literal -1 binary64) (.f64 (pow.f64 x #s(literal -3 binary64)) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64))))
▶	53.5%	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (/.f64 x (sqrt.f64 x))))
▶	53.4%	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))))
✓	53.6%	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)))
✓	47.0%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 456 to 358 computations (21.5% saved)

simplify80.0ms (0.7%)

Memory

1.1MiB live, 72.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (/.f64 #s(literal -1 binary64) (.f64 (pow.f64 x #s(literal -3 binary64)) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (/.f64 #s(literal -1 binary64) (.f64 (pow.f64 x #s(literal -3 binary64)) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64))))
cost-diff	640	(.f64 (pow.f64 x #s(literal -3 binary64)) (.f64 x x))
cost-diff	7040	(/.f64 #s(literal -1 binary64) (.f64 (pow.f64 x #s(literal -3 binary64)) (.f64 x x)))
cost-diff	0	(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
cost-diff	0	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x))))
cost-diff	0	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))))
cost-diff	2240	(*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))
cost-diff	0	(*.f64 x #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
cost-diff	0	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (/.f64 x (sqrt.f64 x)))
cost-diff	0	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (/.f64 x (sqrt.f64 x))))
cost-diff	0	(/.f64 #s(literal -1 binary64) x)
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) x)))
cost-diff	960	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) x))
cost-diff	-5760	(/.f64 #s(literal 1 binary64) x)
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) x)))
cost-diff	6848	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) x))

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	31	205
0	49	174
1	74	168
2	127	162
3	221	162
4	354	159
5	630	159
6	1845	159
7	5085	159
0	8049	159

Stop Event

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

Calls

Call 1

Inputs
#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) x)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) x))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) x)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) x))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 #s(literal -1 binary64) x)
#s(literal -1 binary64)
x
#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (/.f64 x (sqrt.f64 x))))
(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (/.f64 x (sqrt.f64 x)))
(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
(*.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
(/.f64 x (sqrt.f64 x))
(sqrt.f64 x)
#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))))
(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x))))
(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
(*.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
(*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))
(sqrt.f64 (sqrt.f64 x))
(sqrt.f64 x)
#s(approx (sqrt (* 2 (pow x 2))) (.f64 (/.f64 #s(literal -1 binary64) (.f64 (pow.f64 x #s(literal -3 binary64)) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 (pow.f64 x #s(literal -3 binary64)) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal -1 binary64) (.f64 (pow.f64 x #s(literal -3 binary64)) (.f64 x x)))
#s(literal -1 binary64)
(.f64 (pow.f64 x #s(literal -3 binary64)) (.f64 x x))
(pow.f64 x #s(literal -3 binary64))
x
#s(literal -3 binary64)
(*.f64 x x)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)

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

localize100.0ms (0.9%)

Memory

-4.4MiB live, 152.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.09765625	(/.f64 #s(literal -1 binary64) (.f64 (pow.f64 x #s(literal -3 binary64)) (.f64 x x)))
accuracy	0.203125	(.f64 (/.f64 #s(literal -1 binary64) (.f64 (pow.f64 x #s(literal -3 binary64)) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))
accuracy	24.484781266169765	(.f64 (pow.f64 x #s(literal -3 binary64)) (.f64 x x))
accuracy	33.690072915294	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (/.f64 #s(literal -1 binary64) (.f64 (pow.f64 x #s(literal -3 binary64)) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.0	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))))
accuracy	0.078125	(sqrt.f64 (sqrt.f64 x))
accuracy	0.1953125	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x))))
accuracy	0.26857377930532605	(*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))
accuracy	0.0	(sqrt.f64 x)
accuracy	0.0	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (/.f64 x (sqrt.f64 x))))
accuracy	0.1953125	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (/.f64 x (sqrt.f64 x)))
accuracy	0.28125	(/.f64 x (sqrt.f64 x))
accuracy	0.0	(/.f64 #s(literal -1 binary64) x)
accuracy	0.0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.234375	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) x))
accuracy	33.690072915294	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) x)))
accuracy	0.0	(/.f64 #s(literal 1 binary64) x)
accuracy	0.0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.0	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) x)))
accuracy	0.234375	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) x))

Samples

31.0ms	118×	0	invalid
30.0ms	138×	0	valid

Compiler

Compiled 362 to 60 computations (83.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 45.0ms

ival-mult: 17.0ms (37.7% of total)

ival-div: 10.0ms (22.2% of total)

ival-sqrt: 10.0ms (22.2% of total)

ival-pow: 4.0ms (8.9% of total)

ival-pow2: 3.0ms (6.7% of total)

exact: 1.0ms (2.2% of total)

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

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

series58.0ms (0.5%)

Memory

-15.0MiB live, 113.6MiB allocated

Counts

21 → 14

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) x))
#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) x)))
(sqrt.f64 #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) x)
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) x))
#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) x)))
(/.f64 #s(literal -1 binary64) x)
#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (/.f64 x (sqrt.f64 x))))
(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (/.f64 x (sqrt.f64 x)))
(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
(*.f64 x #s(literal 2 binary64))
(*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))
#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))))
(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x))))
(/.f64 #s(literal -1 binary64) (.f64 (pow.f64 x #s(literal -3 binary64)) (.f64 x x)))
(.f64 (pow.f64 x #s(literal -3 binary64)) (.f64 x x))
#s(approx (sqrt (* 2 (pow x 2))) (.f64 (/.f64 #s(literal -1 binary64) (.f64 (pow.f64 x #s(literal -3 binary64)) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 (pow.f64 x #s(literal -3 binary64)) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 x))
(sqrt.f64 x)
(sqrt.f64 (sqrt.f64 x))

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

Calls

3 calls:

Time

Variable

Point

Expression

37.0ms

((/ (sqrt 2) (/ 1 x)) (sqrt (* 2 (pow x 2))) (sqrt 2) (/ 1 x) (/ (sqrt 2) (/ -1 x)) (sqrt (* 2 (pow x 2))) (/ -1 x) (sqrt (* 2 (pow x 2))) (* (sqrt (* x 2)) (/ x (sqrt x))) (sqrt (* x 2)) (* x 2) (* (sqrt (sqrt x)) (sqrt (sqrt x))) (sqrt (* 2 (pow x 2))) (* (sqrt (* x 2)) (* (sqrt (sqrt x)) (sqrt (sqrt x)))) (/ -1 (* (pow x -3) (* x x))) (* (pow x -3) (* x x)) (sqrt (* 2 (pow x 2))) (* (/ -1 (* (pow x -3) (* x x))) (sqrt 2)) (/ x (sqrt x)) (sqrt x) (sqrt (sqrt x)))

13.0ms

-inf

((/ (sqrt 2) (/ 1 x)) (sqrt (* 2 (pow x 2))) (sqrt 2) (/ 1 x) (/ (sqrt 2) (/ -1 x)) (sqrt (* 2 (pow x 2))) (/ -1 x) (sqrt (* 2 (pow x 2))) (* (sqrt (* x 2)) (/ x (sqrt x))) (sqrt (* x 2)) (* x 2) (* (sqrt (sqrt x)) (sqrt (sqrt x))) (sqrt (* 2 (pow x 2))) (* (sqrt (* x 2)) (* (sqrt (sqrt x)) (sqrt (sqrt x)))) (/ -1 (* (pow x -3) (* x x))) (* (pow x -3) (* x x)) (sqrt (* 2 (pow x 2))) (* (/ -1 (* (pow x -3) (* x x))) (sqrt 2)) (/ x (sqrt x)) (sqrt x) (sqrt (sqrt x)))

8.0ms

inf

((/ (sqrt 2) (/ 1 x)) (sqrt (* 2 (pow x 2))) (sqrt 2) (/ 1 x) (/ (sqrt 2) (/ -1 x)) (sqrt (* 2 (pow x 2))) (/ -1 x) (sqrt (* 2 (pow x 2))) (* (sqrt (* x 2)) (/ x (sqrt x))) (sqrt (* x 2)) (* x 2) (* (sqrt (sqrt x)) (sqrt (sqrt x))) (sqrt (* 2 (pow x 2))) (* (sqrt (* x 2)) (* (sqrt (sqrt x)) (sqrt (sqrt x)))) (/ -1 (* (pow x -3) (* x x))) (* (pow x -3) (* x x)) (sqrt (* 2 (pow x 2))) (* (/ -1 (* (pow x -3) (* x x))) (sqrt 2)) (/ x (sqrt x)) (sqrt x) (sqrt (sqrt x)))

simplify172.0ms (1.5%)

Memory

34.6MiB live, 73.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	32	63
1	66	63
2	184	63
3	360	63
4	584	63
5	975	63
6	1358	63
7	1723	62
8	2410	62
9	2579	62
10	2847	62
11	3024	62
12	3050	62
13	3054	62
14	3054	62
15	3217	62
16	3824	62
17	4029	62
18	4556	62
19	5155	62
20	5435	62
21	5462	62
22	5507	62
23	5581	62
24	5839	62
25	7026	62
26	7720	62
0	8073	62

Stop Event

1×	iter limit
1×	node limit

Counts

14 → 14

Calls

Call 1

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

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

rewrite141.0ms (1.2%)

Memory

-15.4MiB live, 170.6MiB allocated

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	31	172
0	49	131
1	136	94
2	519	94
3	4218	93
0	8498	93

Stop Event

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

Counts

21 → 1 754

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) x))
#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) x)))
(sqrt.f64 #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) x)
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) x))
#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) x)))
(/.f64 #s(literal -1 binary64) x)
#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (/.f64 x (sqrt.f64 x))))
(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (/.f64 x (sqrt.f64 x)))
(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
(*.f64 x #s(literal 2 binary64))
(*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))
#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))))
(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x))))
(/.f64 #s(literal -1 binary64) (.f64 (pow.f64 x #s(literal -3 binary64)) (.f64 x x)))
(.f64 (pow.f64 x #s(literal -3 binary64)) (.f64 x x))
#s(approx (sqrt (* 2 (pow x 2))) (.f64 (/.f64 #s(literal -1 binary64) (.f64 (pow.f64 x #s(literal -3 binary64)) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 (pow.f64 x #s(literal -3 binary64)) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 x))
(sqrt.f64 x)
(sqrt.f64 (sqrt.f64 x))

Outputs
(.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x x)) (.f64 x x)) x)
(.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x x)) (pow.f64 x #s(literal 3 binary64))) (.f64 x x))
(.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x)) (pow.f64 x #s(literal -2 binary64))) (pow.f64 x #s(literal -3 binary64)))
(.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x)) #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64)))
(.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x)) #s(literal 1 binary64)) (pow.f64 x #s(literal -1 binary64)))
(.f64 (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 3/4 binary64)))
(.f64 (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 x)) (sqrt.f64 x))
(.f64 (.f64 #s(literal -1 binary64) (pow.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))) (pow.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal -1 binary64) (*.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 #s(literal -2 binary64) x))) (sqrt.f64 x))
(.f64 (.f64 (*.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 1/8 binary64)))
(.f64 (.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))) (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))) (pow.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (neg.f64 (pow.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))) (pow.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(.f64 (neg.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 (.f64 (sqrt.f64 x) (pow.f64 (.f64 #s(literal -2 binary64) x) #s(literal 1/4 binary64))) (pow.f64 (.f64 #s(literal -2 binary64) x) #s(literal 1/4 binary64)))
(.f64 (/.f64 (sqrt.f64 (.f64 #s(literal -2 binary64) x)) #s(literal -1 binary64)) (sqrt.f64 x))
(.f64 (/.f64 (pow.f64 (.f64 #s(literal -2 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (/.f64 (pow.f64 (*.f64 #s(literal -2 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal -3/4 binary64))))
(.f64 (/.f64 (pow.f64 (.f64 #s(literal -2 binary64) x) #s(literal 1/4 binary64)) (sqrt.f64 x)) (/.f64 (pow.f64 (*.f64 #s(literal -2 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (pow.f64 x #s(literal -3/2 binary64))) (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sqrt.f64 x)))
(*.f64 (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (pow.f64 x #s(literal -1/2 binary64))) (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (pow.f64 x #s(literal -1/2 binary64))))
(.f64 (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 x x)) (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (pow.f64 x #s(literal -3 binary64))))
(.f64 (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (pow.f64 x #s(literal -3 binary64))) (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 x x)))
(*.f64 (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (pow.f64 x #s(literal -2 binary64))) (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x))
(*.f64 (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (pow.f64 x #s(literal -1 binary64))) (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (pow.f64 x #s(literal -1 binary64))) (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal -3/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sqrt.f64 x)) (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (pow.f64 x #s(literal -3/2 binary64))))
(*.f64 (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (pow.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x) (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (pow.f64 x #s(literal -2 binary64))))
(*.f64 (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (pow.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 5/4 binary64)))
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(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/8 binary64) (log.f64 x)) #s(literal 2 binary64)))
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(exp.f64 (*.f64 (neg.f64 (log.f64 x)) #s(literal -1/4 binary64)))
(exp.f64 (.f64 (.f64 #s(literal -1/2 binary64) (log.f64 x)) #s(literal -1/2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/4 binary64) (log.f64 x)) #s(literal 1 binary64)))
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(exp.f64 (*.f64 #s(literal 1/4 binary64) (log.f64 x)))

eval132.0ms (1.1%)

Memory: 5.1MiB live, 122.8MiB allocated
Compiler: Compiled 16 427 to 2 696 computations (83.6% saved)

prune36.0ms (0.3%)

Memory

21.7MiB live, 60.2MiB allocated

Pruning

17 alts after pruning (8 fresh and 9 done)

	Pruned	Kept	Total
New	848	3	851
Fresh	3	5	8
Picked	1	4	5
Done	0	5	5
Total	852	17	869

Accuracy

100.0%

Counts

869 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	54.6%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
	51.2%	(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 (.f64 (neg.f64 x) x) (.f64 x (/.f64 #s(literal -1 binary64) x))))))
✓	51.2%	(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
✓	5.3%	(sqrt.f64 #s(literal 2 binary64))
	47.0%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64))) (/.f64 #s(literal -1 binary64) x)))
	26.6%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))
✓	54.5%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) x)))
✓	47.0%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) x)))
	53.5%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (neg.f64 (sqrt.f64 (*.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))
	54.5%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 x (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64))))
	47.0%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))
	47.1%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 #s(literal -1 binary64) (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) x)))
	47.1%	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (neg.f64 x))))
✓	53.5%	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (/.f64 x (sqrt.f64 x))))
✓	53.4%	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))))
✓	53.6%	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)))
✓	47.0%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 646 to 308 computations (52.3% saved)

regimes50.0ms (0.4%)

Memory

-12.2MiB live, 34.5MiB allocated

Counts

31 → 2

Calls

Call 1

Inputs
(sqrt.f64 #s(literal 2 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)))
#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) x)))
#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))
#s(approx (sqrt (* 2 (pow x 2))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (/.f64 x (sqrt.f64 x))))
(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 (.f64 (neg.f64 x) x) (.f64 x (/.f64 #s(literal -1 binary64) x))))))
#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (neg.f64 (sqrt.f64 (*.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))
#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))))
#s(approx (sqrt (* 2 (pow x 2))) (/.f64 x (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
#s(approx (sqrt (* 2 (pow x 2))) (/.f64 x (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal -1 binary64))))
#s(approx (sqrt (* 2 (pow x 2))) (/.f64 #s(literal -1 binary64) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) x)))
#s(approx (sqrt (* 2 (pow x 2))) (/.f64 #s(literal -1 binary64) (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) x)))
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (pow x 2) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (pow x 2) (/.f64 (pow.f64 x #s(literal 3 binary64)) x))))
(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 x x)))))
#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64))) (/.f64 #s(literal -1 binary64) x)))
#s(approx (sqrt (* 2 (pow x 2))) (.f64 (/.f64 #s(literal -1 binary64) (.f64 (pow.f64 x #s(literal -3 binary64)) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))))
(*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x)
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64))))
#s(approx (sqrt (* 2 (pow x 2))) (.f64 (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x) (neg.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)))))
#s(approx (sqrt (* 2 (pow x 2))) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (neg.f64 x))))
#s(approx (sqrt (* 2 (pow x 2))) (*.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 -1 binary64) x))))

Outputs

#s(approx (sqrt (* 2 (pow x 2))) (/.f64 #s(literal -1 binary64) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) x)))

#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (sqrt.f64 (*.f64 x #s(literal 2 binary64))) (sqrt.f64 x)))

Calls

4 calls:

26.0ms	(pow.f64 x #s(literal 2 binary64))
8.0ms	x
7.0ms	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
7.0ms	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
99.4%	2	`x`
78.4%	3	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
78.4%	3	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
78.4%	3	`(pow.f64 x #s(literal 2 binary64))`

Compiler

Compiled 15 to 13 computations (13.3% saved)

regimes6.0ms (0.1%)

Memory

5.2MiB live, 5.2MiB allocated

Counts

17 → 2

Calls

Call 1

Inputs
(sqrt.f64 #s(literal 2 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)))
#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) x)))
#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (.f64 (.f64 x #s(literal 2 binary64)) x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))
#s(approx (sqrt (* 2 (pow x 2))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (/.f64 x (sqrt.f64 x))))
(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 (.f64 (neg.f64 x) x) (.f64 x (/.f64 #s(literal -1 binary64) x))))))
#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (neg.f64 (sqrt.f64 (*.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))
#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))))
#s(approx (sqrt (* 2 (pow x 2))) (/.f64 x (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
#s(approx (sqrt (* 2 (pow x 2))) (/.f64 x (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal -1 binary64))))

Outputs
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)))

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
99.4%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes2.0ms (0%)

Memory

2.7MiB live, 2.7MiB allocated

Counts

4 → 2

Calls

Call 1

Inputs
(sqrt.f64 #s(literal 2 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))

Outputs
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
99.3%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes17.0ms (0.1%)

Memory

-31.6MiB live, 7.4MiB allocated

Counts

2 → 2

Calls

Call 1

Inputs
(sqrt.f64 #s(literal 2 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)

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

Calls

4 calls:

13.0ms	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
1.0ms	x
1.0ms	(pow.f64 x #s(literal 2 binary64))
1.0ms	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
54.6%	1	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
54.6%	1	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
54.6%	1	`(pow.f64 x #s(literal 2 binary64))`
56.4%	2	`x`

Compiler

Compiled 15 to 13 computations (13.3% saved)

regimes5.0ms (0%)

Memory

9.5MiB live, 9.5MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(sqrt.f64 #s(literal 2 binary64))

Outputs
(sqrt.f64 #s(literal 2 binary64))

Calls

4 calls:

1.0ms	x
1.0ms	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
1.0ms	(pow.f64 x #s(literal 2 binary64))
1.0ms	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
5.3%	1	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
5.3%	1	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
5.3%	1	`(pow.f64 x #s(literal 2 binary64))`
5.3%	1	`x`

Compiler

Compiled 15 to 13 computations (13.3% saved)

bsearch13.0ms (0.1%)

Memory

16.0MiB live, 16.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	-1.1408794145084892e-303	2.775688416298775e-307

Samples

6.0ms

144×

valid

Compiler

Compiled 261 to 234 computations (10.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-pow2: 2.0ms (55.3% of total)

ival-mult: 1.0ms (27.6% of total)

ival-sqrt: 1.0ms (27.6% of total)

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

exact: 0.0ms (0% of total)

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

bsearch1.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	-1.1408794145084892e-303	2.775688416298775e-307

Compiler

Compiled 243 to 216 computations (11.1% saved)

bsearch1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	-1.1408794145084892e-303	2.775688416298775e-307

Compiler

Compiled 153 to 153 computations (0% saved)

bsearch19.0ms (0.2%)

Memory

-15.1MiB live, 20.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
18.0ms	-1.0110502917071796e-197	-2.520308784259226e-208

Samples

12.0ms

160×

valid

Compiler

Compiled 69 to 99 computations (-43.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-pow2: 2.0ms (48.3% of total)

ival-mult: 1.0ms (24.2% of total)

ival-sqrt: 1.0ms (24.2% of total)

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

exact: 0.0ms (0% of total)

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

simplify65.0ms (0.6%)

Memory

24.6MiB live, 60.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	94
1	37	94
2	49	94
3	59	94
4	68	94
5	74	94
6	93	94
7	214	94
8	3788	94

Stop Event

1×	node limit

Calls

Call 1

Inputs
(if (<=.f64 x #s(literal -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (/.f64 #s(literal -1 binary64) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) x))) #s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))))
(if (<=.f64 x #s(literal -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt ( 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))))
(if (<=.f64 x #s(literal -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(if (<=.f64 x #s(literal -7229475734293037/180736893357325919804742965901096183254486650358500961579737723575212405143116703993975930943694719806137463391890175780999890999416217020648099397663164550811570949854893831716648452639533025774320471006645409943407034368 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(sqrt.f64 #s(literal 2 binary64))

Outputs
(if (<=.f64 x #s(literal -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (/.f64 #s(literal -1 binary64) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) x))) #s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))))
(if (<=.f64 x #s(literal -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt ( 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))))
(if (<=.f64 x #s(literal -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(if (<=.f64 x #s(literal -7229475734293037/180736893357325919804742965901096183254486650358500961579737723575212405143116703993975930943694719806137463391890175780999890999416217020648099397663164550811570949854893831716648452639533025774320471006645409943407034368 binary64)) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(sqrt.f64 #s(literal 2 binary64))

soundness8.6s (73.9%)

Memory

-34.1MiB live, 346.9MiB allocated

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	29	152
0	45	143
1	121	106
2	430	106
0	3285	106
0	8	17
1	15	17
2	32	17
3	38	17
4	42	17
5	54	17
6	66	17
7	77	17
8	97	17
9	102	17
0	102	17
0	5	14
0	8	14
1	22	12
2	57	12
3	186	12
4	765	4
5	6179	4
0	9030	4
0	14	54
0	21	55
1	46	53
2	112	53
3	469	53
4	3782	49
0	8402	49

Stop Event

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

Compiler

Compiled 158 to 87 computations (44.9% saved)

preprocess128.0ms (1.1%)

Memory: -8.3MiB live, 67.0MiB allocated
Compiler: Compiled 200 to 70 computations (65% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	7	15
1	15	13
2	34	13
3	124	13
4	250	13
5	276	13
6	286	13
0	5	6
0	8	6
1	10	6
2	14	6
3	16	6
0	16	6

Iter	Nodes	Cost
0	14	65
0	21	65
1	31	65
2	44	65
3	56	65
4	62	65
5	73	65
6	98	65
7	107	65
8	113	65
9	113	65
0	113	65

Iter	Nodes	Cost
0	7	15
1	15	13
2	34	13
3	124	13
4	250	13
5	276	13
6	286	13
0	5	6
0	8	6
1	10	6
2	14	6
3	16	6
0	16	6

Iter	Nodes	Cost
0	14	65
0	21	65
1	31	65
2	44	65
3	56	65
4	62	65
5	73	65
6	98	65
7	107	65
8	113	65
9	113	65
0	113	65

start0.0ms (0%)

analyze0.0ms (0%)

sample694.0ms (6%)

explain63.0ms (0.5%)

preprocess14.0ms (0.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify47.0ms (0.4%)

localize17.0ms (0.1%)

series3.0ms (0%)

simplify7.0ms (0.1%)

rewrite145.0ms (1.2%)

eval6.0ms (0.1%)

prune2.0ms (0%)

simplify11.0ms (0.1%)

localize41.0ms (0.4%)

series6.0ms (0%)

simplify4.0ms (0%)

rewrite130.0ms (1.1%)

eval59.0ms (0.5%)

prune21.0ms (0.2%)

simplify201.0ms (1.7%)

localize71.0ms (0.6%)

series18.0ms (0.2%)

simplify207.0ms (1.8%)

rewrite129.0ms (1.1%)

eval89.0ms (0.8%)

prune22.0ms (0.2%)

simplify80.0ms (0.7%)

localize100.0ms (0.9%)

series58.0ms (0.5%)

simplify172.0ms (1.5%)

rewrite141.0ms (1.2%)

eval132.0ms (1.1%)

prune36.0ms (0.3%)

regimes50.0ms (0.4%)

regimes6.0ms (0.1%)

regimes2.0ms (0%)

regimes17.0ms (0.1%)

regimes5.0ms (0%)

bsearch13.0ms (0.1%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch19.0ms (0.2%)

simplify65.0ms (0.6%)

soundness8.6s (73.9%)

preprocess128.0ms (1.1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	7	15
1	15	13
2	34	13
3	124	13
4	250	13
5	276	13
6	286	13
0	5	6
0	8	6
1	10	6
2	14	6
3	16	6
0	16	6

Iter	Nodes	Cost
0	14	65
0	21	65
1	31	65
2	44	65
3	56	65
4	62	65
5	73	65
6	98	65
7	107	65
8	113	65
9	113	65
0	113	65