Metrics for sqrtexp (problem 3.4.4)

analyze2.0ms (0%)

Memory

1.9MiB live, 1.9MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
50%	50%	50%	0%	0%	0%	0%	2
75%	75%	25%	0%	0%	0%	0%	3
87.5%	87.5%	12.5%	0%	0%	0%	0%	4
93.8%	93.7%	6.2%	0%	0%	0%	0%	5
96.9%	96.8%	3.1%	0%	0%	0%	0%	6
98.4%	98.4%	1.6%	0%	0%	0%	0%	7
99.2%	99.2%	0.8%	0%	0%	0%	0%	8
99.6%	99.6%	0.4%	0%	0%	0%	0%	9
99.8%	99.8%	0.2%	0%	0%	0%	0%	10
99.9%	99.9%	0.1%	0%	0%	0%	0%	11
100%	99.9%	0%	0%	0%	0%	0%	12

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample905.0ms (14.2%)

Memory

37.0MiB live, 916.7MiB allocated

Samples

462.0ms	8 256×	0	valid
134.0ms	2 551×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 369.0ms

ival-expm1: 126.0ms (34.1% of total)

ival-mult: 82.0ms (22.2% of total)

ival-div: 75.0ms (20.3% of total)

ival-sqrt: 68.0ms (18.4% of total)

ival-true: 8.0ms (2.2% of total)

exact: 6.0ms (1.6% of total)

ival-assert: 4.0ms (1.1% of total)

Bogosity

preprocess397.0ms (6.2%)

Memory

13.3MiB live, 365.9MiB allocated

Algorithm

1×	egg-herbie

Rules

15 394×	`lower-fma.f64`
15 394×	`lower-fma.f32`
2 850×	`lower--.f32`
2 846×	`lower--.f64`
2 458×	`lower-*.f32`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	12	29
1	32	27
2	55	27
3	89	27
4	143	13
5	250	13
6	513	13
7	2039	13
8	7136	13
0	10	12
0	17	12
1	29	12
2	35	12
3	47	12
4	73	7
5	126	5
6	203	5
7	606	5
8	2926	5
9	6783	5
0	8197	5

Stop Event

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

Calls

Call 1

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

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

explain194.0ms (3%)

Memory

-10.0MiB live, 156.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
175	0	-	-	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`
175	0	-	-	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
2	0	-	-	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
0	1	(124.83777898865645)	-	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(*.f64 #s(literal 2 binary64) x)`
0	0	-	-	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))`
0	0	-	-	`#s(literal 2 binary64)`
0	0	-	-	`(exp.f64 x)`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	cancellation	175	1
`-.f64`	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	cancellation	175	0
`/.f64`	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`	o/o	2	0
↳	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`	overflow	2
↳	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	overflow	2
↳	`(exp.f64 x)`	overflow	2
↳	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	overflow	2
`exp.f64`	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	177	0
-	1	78

Precision

0.9943820224719101

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	177	0	0
-	1	1	77

Precision?

0.9888268156424581

Recall?

1.0

Freqs

test

number	freq
0	78
1	3
2	175

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

39.0ms

512×

valid

Compiler

Compiled 120 to 44 computations (63.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-exp: 7.0ms (28.6% of total)

ival-expm1: 6.0ms (24.5% of total)

ival-mult: 4.0ms (16.3% of total)

ival-div: 3.0ms (12.3% of total)

ival-sqrt: 3.0ms (12.3% of total)

exact: 1.0ms (4.1% of total)

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

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

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	31.7%	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))

Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

localize39.0ms (0.6%)

Memory

-5.1MiB live, 36.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(exp.f64 x)
✓	accuracy	99.4%	(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
✓	accuracy	36.1%	(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
✓	accuracy	36.1%	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Samples

19.0ms

256×

valid

Compiler

Compiled 47 to 12 computations (74.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-exp: 3.0ms (25.2% of total)

ival-expm1: 3.0ms (25.2% of total)

ival-div: 2.0ms (16.8% of total)

ival-mult: 2.0ms (16.8% of total)

ival-sqrt: 2.0ms (16.8% 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

2.9MiB live, 2.9MiB allocated

Counts

4 → 48

Calls

Call 1

Inputs
#<alt (-.f64 (exp.f64 x) #s(literal 1 binary64))>
#<alt (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))>
#<alt (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))>
#<alt (exp.f64 x)>

Outputs
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (* 2 x)>
#<alt (* x (+ 2 (* 2 x)))>
#<alt (* x (+ 2 (* x (+ 2 (* 4/3 x)))))>
#<alt (* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
0.0ms	x	@	inf	(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
0.0ms	x	@	0	(- (exp x) 1)
0.0ms	x	@	0	(- (exp (* 2 x)) 1)
0.0ms	x	@	0	(/ (- (exp (* 2 x)) 1) (- (exp x) 1))

rewrite364.0ms (5.7%)

Memory

15.4MiB live, 331.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 402×	`lower-fma.f64`
5 402×	`lower-fma.f32`
4 492×	`lower-*.f32`
4 490×	`lower-*.f64`
2 532×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
0	15	23
1	56	16
2	378	16
3	4570	16
0	8200	12

Stop Event

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

Counts

4 → 631

Calls

Call 1

Inputs
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
(exp.f64 x)

Outputs
(exp.f64 (log.f64 (expm1.f64 x)))
(exp.f64 (*.f64 (neg.f64 (log.f64 (expm1.f64 x))) #s(literal -1 binary64)))
(+.f64 (exp.f64 x) #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) (exp.f64 x))
(+.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 x)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 x))))))
(+.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(+.f64 (neg.f64 (neg.f64 (exp.f64 x))) #s(literal -1 binary64))
(+.f64 (-.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 (exp.f64 x) (expm1.f64 (+.f64 x x)))) (/.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 x x))))
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(-.f64 #s(literal 0 binary64) (neg.f64 (expm1.f64 x)))
(-.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 x)))))
(-.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(-.f64 (/.f64 (/.f64 (exp.f64 (.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 (.f64 x #s(literal 4 binary64)))))) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 (*.f64 x #s(literal 4 binary64)))))) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(-.f64 (/.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (neg.f64 (expm1.f64 x)))
(-.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (neg.f64 (exp.f64 x))))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (neg.f64 (exp.f64 x))))))
(-.f64 (/.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
(-.f64 (/.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 x)))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 x)))) #s(literal 1 binary64)))
(fma.f64 (exp.f64 x) #s(literal 1 binary64) #s(literal -1 binary64))
(fma.f64 (exp.f64 x) (/.f64 (exp.f64 x) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(fma.f64 (exp.f64 x) (/.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 x)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 x))))))
(fma.f64 #s(literal 1 binary64) (exp.f64 x) #s(literal -1 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(fma.f64 (expm1.f64 x) (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 (+.f64 x x))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(fma.f64 (exp.f64 (+.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(fma.f64 (exp.f64 (+.f64 x x)) (/.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 x)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 x))))))
(fma.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 x)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 x))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(fma.f64 (*.f64 (expm1.f64 x) (exp.f64 (+.f64 x x))) (/.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 x x))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(fma.f64 (/.f64 (exp.f64 x) (expm1.f64 (+.f64 x x))) (/.f64 (exp.f64 x) (/.f64 #s(literal 1 binary64) (expm1.f64 x))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 x x))) (*.f64 (expm1.f64 x) (exp.f64 (+.f64 x x))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(fma.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(fma.f64 (exp.f64 (.f64 x #s(literal 3/2 binary64))) (/.f64 (exp.f64 (.f64 x #s(literal 3/2 binary64))) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 x)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 x))))))
(fma.f64 (exp.f64 (.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)))) (/.f64 (exp.f64 (.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)))) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(fma.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 (+.f64 x x))) (expm1.f64 x) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(fma.f64 (/.f64 (exp.f64 x) #s(literal 1 binary64)) (/.f64 (exp.f64 x) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(fma.f64 (/.f64 (exp.f64 x) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 (exp.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(fma.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 (.f64 x #s(literal 6 binary64)))) (.f64 (expm1.f64 x) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 (*.f64 x #s(literal 4 binary64)))))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(fma.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 (.f64 x #s(literal 4 binary64)))) (.f64 (expm1.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(fma.f64 (/.f64 (exp.f64 (.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)))) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 (exp.f64 (.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(fma.f64 (/.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(fma.f64 (/.f64 (exp.f64 (.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)))) (expm1.f64 (+.f64 x x))) (/.f64 (exp.f64 (.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (expm1.f64 x))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(fma.f64 (/.f64 (exp.f64 x) (/.f64 #s(literal 1 binary64) (expm1.f64 x))) (/.f64 (exp.f64 x) (expm1.f64 (+.f64 x x))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
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(pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) #s(literal -1 binary64))
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(*.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(*.f64 (expm1.f64 (+.f64 x x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))
(*.f64 (expm1.f64 (+.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal 1 binary64)))
(*.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (/.f64 #s(literal -1 binary64) (expm1.f64 x)))
(.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x)) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (expm1.f64 (+.f64 x x)))
(.f64 (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 x))) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (.f64 x #s(literal 3 binary64)))))
(.f64 (expm1.f64 (.f64 x #s(literal 6 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 (*.f64 x #s(literal 4 binary64)))))) (expm1.f64 x)))
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(*.f64 #s(literal -1 binary64) (neg.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
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(*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (/.f64 (expm1.f64 (+.f64 x x)) (.f64 (expm1.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))))))
(*.f64 (fma.f64 (expm1.f64 x) (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64)))
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(.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64))))
(.f64 (-.f64 (.f64 (exp.f64 (.f64 x #s(literal 6 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (.f64 (exp.f64 (.f64 x #s(literal 4 binary64))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64))))))
(*.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x)) (neg.f64 (expm1.f64 (+.f64 x x))))
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(.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (.f64 x #s(literal 3 binary64)))) (+.f64 (expm1.f64 (.f64 x #s(literal 4 binary64))) (.f64 (exp.f64 x) (expm1.f64 (+.f64 x x)))))
(.f64 (/.f64 (expm1.f64 (.f64 x #s(literal 6 binary64))) (expm1.f64 (+.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 (*.f64 x #s(literal 4 binary64)))))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(.f64 (/.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (expm1.f64 (.f64 x #s(literal 3 binary64)))) (/.f64 (expm1.f64 x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 x))))))
(.f64 (/.f64 (expm1.f64 (.f64 x #s(literal 4 binary64))) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 x))))))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (expm1.f64 x)) (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))))
(*.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 (expm1.f64 (+.f64 x x)))) (/.f64 #s(literal -1 binary64) (expm1.f64 x)))
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(.f64 (.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (expm1.f64 x))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (neg.f64 (expm1.f64 (+.f64 x x)))) (neg.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (expm1.f64 x) (expm1.f64 (.f64 x #s(literal 6 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 (*.f64 x #s(literal 4 binary64)))))))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (expm1.f64 x) (expm1.f64 (.f64 x #s(literal 4 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))))
(*.f64 (/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (expm1.f64 (+.f64 x x))) (neg.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(.f64 (/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (expm1.f64 (.f64 x #s(literal 3 binary64)))) (neg.f64 (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 x)))))
(.f64 (/.f64 (expm1.f64 (+.f64 x x)) (neg.f64 (expm1.f64 (.f64 x #s(literal 3 binary64))))) (neg.f64 (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 x)))))
(.f64 (/.f64 (/.f64 (expm1.f64 (.f64 x #s(literal 6 binary64))) (expm1.f64 x)) (+.f64 (exp.f64 (.f64 (+.f64 x x) #s(literal 6 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) #s(literal 3 binary64)))) (fma.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (-.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (exp.f64 (.f64 x #s(literal 4 binary64)))) (exp.f64 (*.f64 (+.f64 x x) #s(literal 4 binary64)))))
(.f64 (/.f64 (/.f64 (expm1.f64 (.f64 x #s(literal 6 binary64))) (expm1.f64 x)) (-.f64 (exp.f64 (.f64 (+.f64 x x) #s(literal 4 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) #s(literal 2 binary64)))) (-.f64 (expm1.f64 (.f64 x #s(literal 4 binary64))) (exp.f64 (+.f64 x x))))
(.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 6 binary64))))) (fma.f64 (exp.f64 (+.f64 x x)) (expm1.f64 (+.f64 x x)) #s(literal 1 binary64)))
(.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64))))) (neg.f64 (expm1.f64 (+.f64 x x))))
(exp.f64 x)
(exp.f64 (*.f64 x #s(literal 1 binary64)))
(pow.f64 (exp.f64 x) #s(literal 1 binary64))
(*.f64 (exp.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (exp.f64 x))

simplify428.0ms (6.7%)

Memory

-11.1MiB live, 467.6MiB allocated

Algorithm

1×	egg-herbie

Rules

18 226×	`lower-fma.f64`
18 226×	`lower-fma.f32`
2 938×	`lower-+.f64`
2 938×	`lower-+.f32`
2 780×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	306
1	155	306
2	334	306
3	753	306
4	1205	266
5	1536	250
6	2032	250
7	2954	250
8	4636	250
0	8301	196

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 47

Calls

Call 1

Inputs
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(* 2 x)
(* x (+ 2 (* 2 x)))
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)

Outputs
x
(* x (+ 1 (* 1/2 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(* 2 x)
(+.f64 x x)
(* x (+ 2 (* 2 x)))
(*.f64 x (+.f64 x (+.f64 x #s(literal 2 binary64))))
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 4/3 binary64) #s(literal 2 binary64)) #s(literal 2 binary64)))
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 2/3 binary64) #s(literal 4/3 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)

eval104.0ms (1.6%)

Memory: 20.2MiB live, 131.1MiB allocated
Compiler: Compiled 16 245 to 2 236 computations (86.2% saved)

prune107.0ms (1.7%)

Memory

7.6MiB live, 166.0MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	673	5	678
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	674	5	679

Accuracy

100.0%

Counts

679 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	68.7%	(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
▶	70.2%	(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
▶	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
▶	68.6%	(sqrt.f64 (+.f64 x #s(literal 2 binary64)))
▶	74.4%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 70 to 56 computations (20% saved)

simplify0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

localize112.0ms (1.8%)

Memory

-22.5MiB live, 102.4MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
✓	accuracy	100.0%	(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
✓	accuracy	100.0%	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓	accuracy	100.0%	(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
✓	accuracy	100.0%	(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
✓	accuracy	100.0%	(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓	accuracy	100.0%	(+.f64 x #s(literal 2 binary64))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 x #s(literal 2 binary64)))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓	accuracy	100.0%	(exp.f64 x)
✓	accuracy	100.0%	(-.f64 (exp.f64 x) #s(literal -1 binary64))

Samples

32.0ms	179×	0	valid
19.0ms	77×	0	invalid

Compiler

Compiled 101 to 26 computations (74.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 39.0ms

ival-sqrt: 14.0ms (36% of total)

ival-mult: 8.0ms (20.6% of total)

ival-add: 7.0ms (18% of total)

ival-sub: 4.0ms (10.3% of total)

const: 4.0ms (10.3% of total)

ival-exp: 2.0ms (5.1% of total)

exact: 1.0ms (2.6% of total)

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

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

series11.0ms (0.2%)

Memory

14.5MiB live, 14.5MiB allocated

Counts

13 → 144

Calls

Call 1

Inputs
#<alt (-.f64 (exp.f64 x) #s(literal -1 binary64))>
#<alt (exp.f64 x)>
#<alt (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))>
#<alt (sqrt.f64 #s(literal 2 binary64))>
#<alt (sqrt.f64 (+.f64 x #s(literal 2 binary64)))>
#<alt (+.f64 x #s(literal 2 binary64))>
#<alt (sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))>
#<alt (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))>
#<alt (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))>
#<alt (sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))>
#<alt (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))>
#<alt (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))>
#<alt (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))>

Outputs
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* -1/8 (/ x (pow (sqrt 2) 3))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt 2) 5))) (* 1/8 (/ 1 (pow (sqrt 2) 3))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (sqrt (/ 1 (pow x 3)))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 5)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 7))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 x)>
#<alt (+ 2 x)>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))>
#<alt (* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))>
#<alt (* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))))>
#<alt (* -1 (* x (sqrt 1/2)))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))>

Calls

36 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(sqrt (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2))
1.0ms	x	@	-inf	(sqrt (+ x 2))
1.0ms	x	@	inf	(sqrt (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2))
1.0ms	x	@	inf	(sqrt (+ (* x (+ (* x 1/2) 1)) 2))
0.0ms	x	@	inf	(sqrt (+ x 2))

rewrite321.0ms (5%)

Memory

1.8MiB live, 511.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 484×	`lower-fma.f32`
4 474×	`lower-fma.f64`
4 300×	`lower-*.f64`
4 300×	`lower-*.f32`
4 238×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	71
0	37	71
1	155	71
2	1130	71
0	8234	71

Stop Event

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

Counts

13 → 456

Calls

Call 1

Inputs
(-.f64 (exp.f64 x) #s(literal -1 binary64))
(exp.f64 x)
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (+.f64 x #s(literal 2 binary64)))
(+.f64 x #s(literal 2 binary64))
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))

Outputs
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (exp.f64 x))))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (exp.f64 x)) #s(literal -1 binary64)))
(+.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (neg.f64 (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))))
(+.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(-.f64 (exp.f64 x) #s(literal -1 binary64))
(-.f64 #s(literal 1 binary64) (neg.f64 (exp.f64 x)))
(-.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))))
(-.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))
(fma.f64 (exp.f64 x) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (neg.f64 (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))))
(fma.f64 (exp.f64 (+.f64 x x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(neg.f64 (/.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (neg.f64 (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))))
(neg.f64 (/.f64 (expm1.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))
(neg.f64 (/.f64 (neg.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))))
(neg.f64 (/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (expm1.f64 x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 1 binary64)))
(/.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (neg.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (neg.f64 (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))))
(/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (expm1.f64 x)))
(/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (neg.f64 (expm1.f64 x)))
(/.f64 (-.f64 (.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (.f64 (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))) #s(literal -1 binary64))) (.f64 (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))))
(/.f64 (-.f64 (.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (.f64 (expm1.f64 x) #s(literal 1 binary64))) (*.f64 (expm1.f64 x) (expm1.f64 x)))
(/.f64 (.f64 (+.f64 (exp.f64 (.f64 (.f64 x #s(literal 3 binary64)) #s(literal 3 binary64))) #s(literal 1 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 (exp.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64)))))) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))))
(/.f64 (.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))))
(/.f64 (.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) #s(literal 1 binary64)) (*.f64 (+.f64 (exp.f64 (+.f64 (+.f64 x x) (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (expm1.f64 x)))
(/.f64 (.f64 (expm1.f64 (+.f64 (+.f64 x x) (+.f64 x x))) #s(literal 1 binary64)) (.f64 (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)) (expm1.f64 x)))
(/.f64 (neg.f64 (neg.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))))
(/.f64 (neg.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (neg.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64))))) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (exp.f64 x)))))
(/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64)))) (+.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (+.f64 x x)) (.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) #s(literal 3 binary64))) (fma.f64 (/.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (/.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (fma.f64 (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal 3 binary64))) (fma.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (fma.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (*.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x))))))
(/.f64 (-.f64 (.f64 (/.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (/.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))) (.f64 (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))))) (+.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))))
(/.f64 (-.f64 (.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x))) (.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))) (+.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(.f64 (+.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))))
(*.f64 (expm1.f64 (+.f64 x x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))
(.f64 (neg.f64 (+.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))))
(*.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (expm1.f64 x))))
(exp.f64 x)
(pow.f64 (exp.f64 x) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 1 binary64)) x)
(*.f64 (exp.f64 x) #s(literal 1 binary64))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (sqrt.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 (+.f64 x x)))))
(/.f64 (sqrt.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))))
(/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 x)))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)))) (sqrt.f64 (neg.f64 (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))))
(/.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))))
(/.f64 (neg.f64 (sqrt.f64 (expm1.f64 (+.f64 x x)))) (neg.f64 (sqrt.f64 (expm1.f64 x))))
(pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log1p.f64 (exp.f64 x))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 1/4 binary64))
(.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))))
(.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (pow.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (expm1.f64 x))))
(*.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (+.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 x #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 (fma.f64 x x #s(literal 4 binary64)) (.f64 x #s(literal -2 binary64)))) (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 x #s(literal -2 binary64))) (sqrt.f64 (fma.f64 x x #s(literal -4 binary64)))))
(/.f64 (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 8 binary64))) (sqrt.f64 (+.f64 (fma.f64 x x #s(literal 4 binary64)) (.f64 x #s(literal -2 binary64)))))
(/.f64 (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 8 binary64))) (sqrt.f64 (+.f64 #s(literal 4 binary64) (fma.f64 x x (.f64 x #s(literal -2 binary64))))))
(/.f64 (sqrt.f64 (fma.f64 x x #s(literal -4 binary64))) (sqrt.f64 (+.f64 x #s(literal -2 binary64))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 x (.f64 x x) #s(literal 8 binary64)))) (sqrt.f64 (neg.f64 (+.f64 (fma.f64 x x #s(literal 4 binary64)) (.f64 x #s(literal -2 binary64))))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 x x #s(literal -4 binary64)))) (sqrt.f64 (+.f64 (neg.f64 x) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x))) (sqrt.f64 (-.f64 #s(literal 2 binary64) x)))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 8 binary64)))) (neg.f64 (sqrt.f64 (+.f64 (fma.f64 x x #s(literal 4 binary64)) (.f64 x #s(literal -2 binary64))))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x x #s(literal -4 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal -2 binary64)))))
(pow.f64 (+.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 x #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 x #s(literal 2 binary64)) (+.f64 x #s(literal 2 binary64))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (+.f64 x #s(literal 2 binary64)))) #s(literal 1/2 binary64))
(.f64 (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 8 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 x x #s(literal 4 binary64)) (*.f64 x #s(literal -2 binary64)))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 8 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 x x #s(literal 4 binary64)) (*.f64 x #s(literal -2 binary64))))))
(.f64 (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 8 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (fma.f64 x x #s(literal 4 binary64)) (*.f64 x #s(literal -2 binary64))))))
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal -4 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal -4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -2 binary64)))))
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal -4 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal -2 binary64)))))
(*.f64 (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 x #s(literal 2 binary64))
(+.f64 #s(literal 2 binary64) x)
(+.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal -2 binary64))) (neg.f64 (/.f64 #s(literal 4 binary64) (+.f64 x #s(literal -2 binary64)))))
(-.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal -2 binary64))) (/.f64 #s(literal 4 binary64) (+.f64 x #s(literal -2 binary64))))
(-.f64 (/.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) x)) (/.f64 (*.f64 x x) (-.f64 #s(literal 2 binary64) x)))
(fma.f64 x #s(literal 1 binary64) #s(literal 2 binary64))
(fma.f64 #s(literal 1 binary64) x #s(literal 2 binary64))
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -2 binary64))) (neg.f64 (/.f64 #s(literal 4 binary64) (+.f64 x #s(literal -2 binary64)))))
(neg.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 8 binary64)) (neg.f64 (+.f64 (fma.f64 x x #s(literal 4 binary64)) (.f64 x #s(literal -2 binary64))))))
(neg.f64 (/.f64 (fma.f64 x x #s(literal -4 binary64)) (+.f64 (neg.f64 x) #s(literal 2 binary64))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 x (.f64 x x) #s(literal 8 binary64))) (+.f64 (fma.f64 x x #s(literal 4 binary64)) (.f64 x #s(literal -2 binary64)))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 x x #s(literal -4 binary64))) (+.f64 x #s(literal -2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 4 binary64) (fma.f64 x x (.f64 x #s(literal -2 binary64)))) (fma.f64 x (.f64 x x) #s(literal 8 binary64))))
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(/.f64 (+.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x))) #s(literal 3 binary64)) (.f64 x (.f64 x x))) (fma.f64 (+.f64 #s(literal 2 binary64) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x))) (+.f64 #s(literal 2 binary64) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x))) (-.f64 (.f64 x x) (.f64 (+.f64 #s(literal 2 binary64) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x))) x))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal -2 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 4 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal -2 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal -2 binary64))) (/.f64 (.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal -2 binary64))) (fma.f64 (/.f64 #s(literal 4 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal -2 binary64))) (/.f64 #s(literal 4 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal -2 binary64))) (.f64 (/.f64 (.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal -2 binary64))) (/.f64 #s(literal 4 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal -2 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x))) (.f64 (+.f64 x #s(literal 2 binary64)) (+.f64 x #s(literal 2 binary64)))) (-.f64 (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)) (+.f64 x #s(literal 2 binary64))))
(/.f64 (-.f64 (.f64 (+.f64 #s(literal 2 binary64) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x))) (+.f64 #s(literal 2 binary64) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x)))) (.f64 x x)) (-.f64 (+.f64 #s(literal 2 binary64) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x))) x))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal -2 binary64))) (/.f64 (.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal -2 binary64)))) (.f64 (/.f64 #s(literal 4 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal -2 binary64))) (/.f64 #s(literal 4 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal -2 binary64))))) (+.f64 (/.f64 (.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal -2 binary64))) (/.f64 #s(literal 4 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal -2 binary64)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
(.f64 (fma.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x) (.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x)) #s(literal 8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (.f64 x (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x)) #s(literal 4 binary64)) (.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)))))
(.f64 (fma.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x) (.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x)) #s(literal 8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (fma.f64 x (.f64 (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x)) (.f64 (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (*.f64 x #s(literal -2 binary64)))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x) #s(literal -4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal -2 binary64))))
(.f64 (neg.f64 (fma.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x) (.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x)) #s(literal 8 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (.f64 x (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x)) #s(literal 4 binary64)) (.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x))))))
(.f64 (neg.f64 (fma.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x) #s(literal -4 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (neg.f64 (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal 2 binary64))))
(.f64 (-.f64 #s(literal 4 binary64) (.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x) x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x))))

simplify358.0ms (5.6%)

Memory

-7.1MiB live, 473.1MiB allocated

Algorithm

1×	egg-herbie

Rules

11 602×	`lower-fma.f64`
11 602×	`lower-fma.f32`
5 042×	`lower-*.f64`
5 042×	`lower-*.f32`
3 340×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	277	1514
1	881	1294
2	2974	1264
0	8381	1149

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 142

Calls

Call 1

Inputs
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* -1/8 (/ x (pow (sqrt 2) 3))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt 2) 5))) (* 1/8 (/ 1 (pow (sqrt 2) 3))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (sqrt (/ 1 (pow x 3)))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 5)))))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 7))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
2
(+ 2 x)
(+ 2 x)
(+ 2 x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* x (sqrt 1/2))
(* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))
(* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))
(* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))))
(* -1 (* x (sqrt 1/2)))
(* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
1
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* 1/2 x))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))

Outputs
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* 1/2 x))))
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1
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2
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1/2
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(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(* 1/6 (pow x 3))
(.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x)
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(* 1/6 (pow x 3))
(.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x)) x)) (neg.f64 (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal -2 binary64) (.f64 x x))) x)) (neg.f64 (.f64 x (.f64 x x))))

eval97.0ms (1.5%)

Memory: 13.9MiB live, 127.2MiB allocated
Compiler: Compiled 14 352 to 1 956 computations (86.4% saved)

prune76.0ms (1.2%)

Memory

-1.3MiB live, 146.4MiB allocated

Pruning

15 alts after pruning (10 fresh and 5 done)

	Pruned	Kept	Total
New	588	10	598
Fresh	0	0	0
Picked	0	5	5
Done	0	0	0
Total	588	15	603

Accuracy

100.0%

Counts

603 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
	68.9%	(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
▶	69.9%	(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
▶	67.7%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))))
	3.0%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
	68.7%	(sqrt.f64 (fma.f64 x (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64)) x) (/.f64 #s(literal -1 binary64) (fma.f64 x #s(literal -1/6 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓	68.7%	(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓	70.2%	(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
	2.5%	(sqrt.f64 (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))
▶	4.1%	(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓	68.6%	(sqrt.f64 (+.f64 x #s(literal 2 binary64)))
▶	3.4%	(sqrt.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
	2.3%	(sqrt.f64 (.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x))))
▶	2.5%	(sqrt.f64 x)
✓	74.4%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 273 to 186 computations (31.9% saved)

simplify0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

localize93.0ms (1.5%)

Memory

-5.8MiB live, 151.9MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
✓	accuracy	100.0%	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓	accuracy	99.4%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))))
✓	accuracy	100.0%	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
✓	accuracy	83.6%	(sqrt.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
✓	accuracy	100.0%	(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	100.0%	(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	99.4%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))

Samples

38.0ms	160×	0	invalid
21.0ms	96×	0	valid

Compiler

Compiled 181 to 31 computations (82.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 44.0ms

ival-add: 13.0ms (29.8% of total)

ival-mult: 12.0ms (27.5% of total)

ival-sqrt: 8.0ms (18.3% of total)

ival-div: 6.0ms (13.8% of total)

const: 4.0ms (9.2% of total)

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

exact: 0.0ms (0% of total)

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

series17.0ms (0.3%)

Memory

-26.9MiB live, 11.7MiB allocated

Counts

15 → 156

Calls

Call 1

Inputs
#<alt (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (sqrt.f64 #s(literal 2 binary64))>
#<alt (sqrt.f64 x)>
#<alt (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)>
#<alt (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))>
#<alt (*.f64 x x)>
#<alt (sqrt.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))>
#<alt (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))>
#<alt (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))>
#<alt (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))>
#<alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))))>
#<alt (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))>
#<alt (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))>

Outputs
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))>
#<alt (* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))>
#<alt (/ 1/2 (sqrt 2))>
#<alt (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))>
#<alt (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))>
#<alt (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))>
#<alt (* 3/16 (/ x (sqrt 2)))>
#<alt (* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* 3/16 (/ x (sqrt 2)))>
#<alt (* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (sqrt x)>
#<alt (+ (sqrt x) (* 1/4 (sqrt (pow x 3))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* -1/32 (sqrt x)) (* 1/4 (sqrt (/ 1 x))))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* 1/4 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/32 (sqrt (/ 1 (pow x 3)))) (* 1/128 (sqrt (/ 1 x))))))))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))>
#<alt (* x (- (+ (sqrt 1/2) (/ 1/2 (* x (sqrt 1/2)))) (/ 1/8 (* (pow x 2) (pow (sqrt 1/2) 3)))))>
#<alt (* x (- (+ (sqrt 1/2) (+ (/ 1/2 (* x (sqrt 1/2))) (* 1/16 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5)))))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))))>
#<alt (* -1 (* x (sqrt 1/2)))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* 1/8 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 (* x (pow (sqrt 1/2) 5)))) (* 1/8 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* x (sqrt 1/2))>
#<alt (* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))>
#<alt (* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2)))))))>
#<alt (* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2)))))))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* 1/6 x)))>
#<alt (* (pow x 2) (+ 1/2 (* 1/6 x)))>
#<alt (* (pow x 2) (+ 1/2 (* 1/6 x)))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))>
#<alt (+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* 1/96 x))) 1/4)))>
#<alt (/ 6 (pow x 3))>
#<alt (/ (- 6 (* 18 (/ 1 x))) (pow x 3))>
#<alt (/ (- (+ 6 (/ 18 (pow x 2))) (* 18 (/ 1 x))) (pow x 3))>
#<alt (/ (- (+ 6 (/ 18 (pow x 2))) (+ (* 18 (/ 1 x)) (* 18 (/ 1 (pow x 3))))) (pow x 3))>
#<alt (/ 6 (pow x 3))>
#<alt (* -1 (/ (- (* 18 (/ 1 x)) 6) (pow x 3)))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 18 (/ 1 x)) 18) x)) 6) (pow x 3)))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 18 (/ 1 x)) 18) x)) 18) x)) 6) (pow x 3)))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>

Calls

39 calls:

Time	Variable		Point	Expression
7.0ms	x	@	inf	(+ (* x (+ (* x 1/6) 1/2)) 1)
1.0ms	x	@	-inf	(sqrt (* x (* x (+ (* x 1/6) 1/2))))
1.0ms	x	@	inf	(sqrt (* x (* x (+ (* x 1/6) 1/2))))
1.0ms	x	@	0	(+ (* x (+ (* x (/ 3/16 (sqrt 2))) (/ 1/2 (sqrt 2)))) (sqrt 2))
0.0ms	x	@	0	(sqrt (* x (* x (+ (* x 1/6) 1/2))))

rewrite359.0ms (5.6%)

Memory

37.4MiB live, 474.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 676×	`lower-fma.f32`
5 664×	`lower-fma.f64`
3 868×	`lower-/.f32`
3 860×	`lower-/.f64`
3 708×	`lower-*.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	24	109
0	47	109
1	198	105
2	1460	100
0	8259	100

Stop Event

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

Counts

15 → 561

Calls

Call 1

Inputs
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 x)
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
(*.f64 x x)
(sqrt.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
(.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))

Outputs
(exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))) #s(literal 3 binary64)) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))) #s(literal 3 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(neg.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal -1/2 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(pow.f64 #s(literal 2 binary64) #s(literal -3/2 binary64))
(pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -3 binary64))
(pow.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3 binary64))
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))))
(*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/4 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64))))
(+.f64 (.f64 x (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+.f64 (/.f64 (.f64 x x) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (/.f64 (.f64 x (.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) (.f64 x (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64))))) (fma.f64 x (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (neg.f64 (/.f64 #s(literal 2 binary64) (fma.f64 x (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))))
(+.f64 (+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 x x) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64)))) (/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(-.f64 (/.f64 (.f64 x (.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) (.f64 x (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64))))) (fma.f64 x (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 #s(literal 2 binary64) (fma.f64 x (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(-.f64 (/.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64))))) (/.f64 (.f64 x (.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) (.f64 x (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64))))) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64))))))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64) (.f64 x (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64))))
(fma.f64 x (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x x) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (*.f64 x x) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64))))
(fma.f64 (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))) x (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 x (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64))))
(fma.f64 (.f64 x (.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) (.f64 x (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64))))) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (neg.f64 (/.f64 #s(literal 2 binary64) (fma.f64 x (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))))
(fma.f64 (fma.f64 (/.f64 (.f64 x x) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 9/512 binary64))) (/.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 8 binary64) (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 9/512 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) (.f64 (/.f64 (.f64 x x) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))) (/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 9/512 binary64))) (.f64 (.f64 x x) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (*.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 x (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64))))
(fma.f64 (.f64 x (.f64 x #s(literal 3/16 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 x (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 27/4096 binary64)) (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64))) #s(literal 8 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 x x) #s(literal 9/512 binary64) #s(literal 1/8 binary64)) (.f64 (.f64 x #s(literal 3/16 binary64)) #s(literal 1/4 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal 9/512 binary64) #s(literal -1/8 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (.f64 (.f64 x #s(literal 3/16 binary64)) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 27/4096 binary64)) (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64))) #s(literal 8 binary64)) x) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 x x) #s(literal 9/512 binary64) #s(literal 1/8 binary64)) (.f64 (.f64 x #s(literal 3/16 binary64)) #s(literal 1/4 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 9/512 binary64) #s(literal -1/8 binary64)) x) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 (*.f64 x #s(literal 3/16 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (*.f64 x #s(literal 3/16 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (-.f64 (.f64 x (.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) (.f64 x (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64))))) (.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) (.f64 x (sqrt.f64 #s(literal 2 binary64)))))) (fma.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 x (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64))) #s(literal 3 binary64)))))
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(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/36 binary64))) (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))) (-.f64 (.f64 (*.f64 x x) #s(literal 1/6 binary64)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))))
(/.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64)))) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (-.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))) (.f64 #s(literal 1/2 binary64) x)))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (/.f64 (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))))) (+.f64 (/.f64 (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) #s(literal 1 binary64)) (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))))
(.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))))
(.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))))
(.f64 (neg.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) #s(literal 1 binary64)) (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))))
(.f64 (neg.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))))

simplify556.0ms (8.7%)

Memory

21.3MiB live, 552.0MiB allocated

Algorithm

1×	egg-herbie

Rules

9 576×	`lower-fma.f64`
9 576×	`lower-fma.f32`
4 780×	`lower-*.f64`
4 780×	`lower-*.f32`
3 312×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	324	1768
1	1025	1683
2	3195	1625
3	7526	1625
0	8214	1499

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 155

Calls

Call 1

Inputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(/ 1/2 (sqrt 2))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(* 3/16 (/ x (sqrt 2)))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* 3/16 (/ x (sqrt 2)))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* 1/2 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(sqrt x)
(+ (sqrt x) (* 1/4 (sqrt (pow x 3))))
(+ (sqrt x) (* (pow x 2) (+ (* -1/32 (sqrt x)) (* 1/4 (sqrt (/ 1 x))))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/4 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/32 (sqrt (/ 1 (pow x 3)))) (* 1/128 (sqrt (/ 1 x))))))))
(* x (sqrt 1/2))
(* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))
(* x (- (+ (sqrt 1/2) (/ 1/2 (* x (sqrt 1/2)))) (/ 1/8 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(* x (- (+ (sqrt 1/2) (+ (/ 1/2 (* x (sqrt 1/2))) (* 1/16 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5)))))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))))
(* -1 (* x (sqrt 1/2)))
(* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* 1/8 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 (* x (pow (sqrt 1/2) 5)))) (* 1/8 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* x (sqrt 1/2))
(* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))
(* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2)))))))
(* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2)))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/2 x)
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
1/2
(+ 1/2 (* -1/4 x))
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))
(+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* 1/96 x))) 1/4)))
(/ 6 (pow x 3))
(/ (- 6 (* 18 (/ 1 x))) (pow x 3))
(/ (- (+ 6 (/ 18 (pow x 2))) (* 18 (/ 1 x))) (pow x 3))
(/ (- (+ 6 (/ 18 (pow x 2))) (+ (* 18 (/ 1 x)) (* 18 (/ 1 (pow x 3))))) (pow x 3))
(/ 6 (pow x 3))
(* -1 (/ (- (* 18 (/ 1 x)) 6) (pow x 3)))
(* -1 (/ (- (* -1 (/ (- (* 18 (/ 1 x)) 18) x)) 6) (pow x 3)))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 18 (/ 1 x)) 18) x)) 18) x)) 6) (pow x 3)))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))

Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(.f64 #s(literal 3/16 binary64) (.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (.f64 (.f64 x x) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (.f64 (.f64 x x) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(.f64 #s(literal 3/16 binary64) (.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(fma.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)) x (.f64 #s(literal 3/16 binary64) (.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(fma.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)) x (.f64 #s(literal 3/16 binary64) (.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(/ 1/2 (sqrt 2))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* 3/16 (/ x (sqrt 2)))
(/.f64 (*.f64 x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* 3/16 (/ x (sqrt 2)))
(/.f64 (*.f64 x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
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(.f64 x (.f64 x (fma.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(fma.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (.f64 (fma.f64 x #s(literal -3/8 binary64) #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 #s(literal -1/6 binary64))) (/.f64 (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1/6 binary64))))) x) (.f64 (.f64 x x) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 #s(literal -1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/4 x))
(fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))
(fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* 1/96 x))) 1/4)))
(fma.f64 x (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/96 binary64) #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))
(/ 6 (pow x 3))
(/.f64 #s(literal 6 binary64) (.f64 x (.f64 x x)))
(/ (- 6 (* 18 (/ 1 x))) (pow x 3))
(/.f64 (+.f64 #s(literal 6 binary64) (/.f64 #s(literal -18 binary64) x)) (.f64 x (.f64 x x)))
(/ (- (+ 6 (/ 18 (pow x 2))) (* 18 (/ 1 x))) (pow x 3))
(/.f64 (+.f64 #s(literal 6 binary64) (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) x) #s(literal -18 binary64)) x)) (.f64 x (.f64 x x)))
(/ (- (+ 6 (/ 18 (pow x 2))) (+ (* 18 (/ 1 x)) (* 18 (/ 1 (pow x 3))))) (pow x 3))
(/.f64 (+.f64 (+.f64 #s(literal 6 binary64) (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) x) #s(literal -18 binary64)) x)) (/.f64 #s(literal -18 binary64) (.f64 x (.f64 x x)))) (.f64 x (.f64 x x)))
(/ 6 (pow x 3))
(/.f64 #s(literal 6 binary64) (.f64 x (.f64 x x)))
(* -1 (/ (- (* 18 (/ 1 x)) 6) (pow x 3)))
(/.f64 (+.f64 #s(literal 6 binary64) (/.f64 #s(literal -18 binary64) x)) (.f64 x (.f64 x x)))
(* -1 (/ (- (* -1 (/ (- (* 18 (/ 1 x)) 18) x)) 6) (pow x 3)))
(/.f64 (+.f64 (/.f64 (+.f64 #s(literal 18 binary64) (/.f64 #s(literal -18 binary64) x)) x) #s(literal -6 binary64)) (neg.f64 (.f64 x (.f64 x x))))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 18 (/ 1 x)) 18) x)) 18) x)) 6) (pow x 3)))
(/.f64 (-.f64 #s(literal -6 binary64) (/.f64 (+.f64 (/.f64 (+.f64 #s(literal 18 binary64) (/.f64 #s(literal -18 binary64) x)) x) #s(literal -18 binary64)) x)) (neg.f64 (.f64 x (.f64 x x))))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))

eval219.0ms (3.4%)

Memory: -4.7MiB live, 169.7MiB allocated
Compiler: Compiled 19 068 to 2 519 computations (86.8% saved)

prune168.0ms (2.6%)

Memory

-32.5MiB live, 169.8MiB allocated

Pruning

21 alts after pruning (15 fresh and 6 done)

	Pruned	Kept	Total
New	781	12	793
Fresh	2	3	5
Picked	4	1	5
Done	0	5	5
Total	787	21	808

Accuracy

100.0%

Counts

808 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
	69.9%	(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
▶	69.9%	(fma.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) x (sqrt.f64 #s(literal 2 binary64)))
	1.3%	(fma.f64 (.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal -1/32 binary64) (.f64 x x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/128 binary64) (*.f64 x x) #s(literal 1/4 binary64)))) (sqrt.f64 x))
	68.9%	(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
	68.9%	(fma.f64 x (fma.f64 x (.f64 #s(literal 7/192 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
	69.9%	(fma.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
▶	67.7%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))
▶	69.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))))
▶	73.3%	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
	69.9%	(+.f64 (.f64 x (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
	4.0%	(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
	2.7%	(*.f64 (sqrt.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x)
▶	3.0%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
	4.2%	(.f64 #s(literal 3/16 binary64) (.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
✓	68.7%	(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓	70.2%	(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
	2.5%	(sqrt.f64 (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓	68.6%	(sqrt.f64 (+.f64 x #s(literal 2 binary64)))
✓	2.5%	(sqrt.f64 x)
✓	74.4%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 448 to 302 computations (32.6% saved)

simplify0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

localize93.0ms (1.5%)

Memory

5.4MiB live, 161.2MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x #s(literal 3/16 binary64))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x #s(literal 3/16 binary64))))
✓	accuracy	99.4%	(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x #s(literal 3/16 binary64)))
✓	accuracy	100.0%	(fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64))
✓	accuracy	100.0%	(sqrt.f64 (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))
✓	accuracy	99.6%	(*.f64 x #s(literal 1/48 binary64))
✓	accuracy	99.0%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))
✓	accuracy	99.0%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/2 binary64))
✓	accuracy	99.5%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/2 binary64))
✓	accuracy	98.9%	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))

Samples

38.0ms	176×	0	valid
16.0ms	80×	0	invalid

Compiler

Compiled 150 to 31 computations (79.3% saved)

Precisions

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

ival-mult: 14.0ms (38.1% of total)

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

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

const: 5.0ms (13.6% of total)

ival-div: 4.0ms (10.9% of total)

exact: 1.0ms (2.7% of total)

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

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

series15.0ms (0.2%)

Memory

29.1MiB live, 29.1MiB allocated

Counts

14 → 132

Calls

Call 1

Inputs
#<alt (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))>
#<alt (sqrt.f64 #s(literal 1/2 binary64))>
#<alt (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))>
#<alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))))>
#<alt (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))>
#<alt (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))>
#<alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))>
#<alt (*.f64 x #s(literal 1/48 binary64))>
#<alt (sqrt.f64 (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))>
#<alt (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64))>
#<alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x #s(literal 3/16 binary64)))>
#<alt (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x #s(literal 3/16 binary64))))>
#<alt (sqrt.f64 #s(literal 2 binary64))>
#<alt (*.f64 x #s(literal 3/16 binary64))>

Outputs
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/4 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* (sqrt (/ 1 x)) (sqrt -4))>
#<alt (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))>
#<alt (+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4))))>
#<alt (+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 32 (* 16 (/ x (pow (sqrt -4) 2)))) (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))))>
#<alt (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))>
#<alt (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1))))>
#<alt (+ (* -4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ 32 (* -4 x))))) (* 4 (* (sqrt x) (sqrt -1)))) (pow x 3))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (* x (- (* x (- (* -1/1024 (/ x (pow (sqrt 1/2) 5))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (* (sqrt x) (sqrt -1/4))>
#<alt (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))>
#<alt (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4)))))>
#<alt (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1/4) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))))>
#<alt (* -1/2 (* (sqrt x) (sqrt -1)))>
#<alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))>
#<alt (* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1)))))))>
#<alt (* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (* -1/4 x)>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/4))>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/4))>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/4))>
#<alt (* -1/4 x)>
#<alt (* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* (sqrt (/ 1 (pow x 3))) (sqrt 48))>
#<alt (/ (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48))) x)>
#<alt (/ (+ (* -576 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 48)))) (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48)))) x)>
#<alt (/ (+ (* -576 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 48)))) (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (+ (* 3456 (* (sqrt (/ 1 (pow x 9))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48))))) x)>
#<alt (* -1 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -48) (sqrt -1))))>
#<alt (* -1 (/ (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -48)))) (* (sqrt (/ 1 x)) (* (sqrt -48) (sqrt -1)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -288 (* (sqrt x) (/ (sqrt -1) (sqrt -48)))) (* 576 (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt -48))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -48) (sqrt -1)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -288 (* (sqrt x) (/ (sqrt -1) (sqrt -48)))) (* -1 (/ (+ (* -576 (* (sqrt x) (/ (sqrt -1) (sqrt -48)))) (* 3456 (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt -48))))) x))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -48) (sqrt -1)))) x))>
#<alt (* 1/48 x)>
#<alt (* 1/48 x)>
#<alt (* 1/48 x)>
#<alt (* 1/48 x)>
#<alt (* 1/48 x)>
#<alt (* 1/48 x)>
#<alt (* 1/48 x)>
#<alt (* 1/48 x)>
#<alt (* 1/48 x)>
#<alt (* 1/48 x)>
#<alt (* 1/48 x)>
#<alt (* 1/48 x)>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/48))>
#<alt (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/48)))) (* (sqrt (/ 1 x)) (sqrt 1/48))))>
#<alt (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/48)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 1/48)))) (* (sqrt (/ 1 x)) (sqrt 1/48)))))>
#<alt (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/48)))) (+ (* -1/128 (* (sqrt (/ 1 (pow x 9))) (/ 1 (pow (sqrt 1/48) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 1/48)))) (* (sqrt (/ 1 x)) (sqrt 1/48))))))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/48)))>
#<alt (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/48)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/48)))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt -1/48)))) (* 1/8 (* (sqrt x) (/ (sqrt -1) (sqrt -1/48))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/48)))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/128 (* (sqrt (/ 1 x)) (/ (sqrt -1) (pow (sqrt -1/48) 3)))) (* 1/4 (* (sqrt x) (/ (sqrt -1) (sqrt -1/48))))) x)) (* 1/8 (* (sqrt x) (/ (sqrt -1) (sqrt -1/48))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/48)))))>
#<alt -1/4>
#<alt (- (* 1/48 (pow x 2)) 1/4)>
#<alt (- (* 1/48 (pow x 2)) 1/4)>
#<alt (- (* 1/48 (pow x 2)) 1/4)>
#<alt (* 1/48 (pow x 2))>
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* 1/48 (pow x 2))>
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* 3/16 (* x (sqrt 2)))>
#<alt (* 3/16 (* x (sqrt 2)))>
#<alt (* 3/16 (* x (sqrt 2)))>
#<alt (* 3/16 (* x (sqrt 2)))>
#<alt (* 3/16 (* x (sqrt 2)))>
#<alt (* 3/16 (* x (sqrt 2)))>
#<alt (* 3/16 (* x (sqrt 2)))>
#<alt (* 3/16 (* x (sqrt 2)))>
#<alt (* 3/16 (* x (sqrt 2)))>
#<alt (* 3/16 (* x (sqrt 2)))>
#<alt (* 3/16 (* x (sqrt 2)))>
#<alt (* 3/16 (* x (sqrt 2)))>
#<alt (* 1/2 (sqrt 2))>
#<alt (+ (* 3/16 (* x (sqrt 2))) (* 1/2 (sqrt 2)))>
#<alt (+ (* 3/16 (* x (sqrt 2))) (* 1/2 (sqrt 2)))>
#<alt (+ (* 3/16 (* x (sqrt 2))) (* 1/2 (sqrt 2)))>
#<alt (* 3/16 (* x (sqrt 2)))>
#<alt (* x (+ (* 3/16 (sqrt 2)) (* 1/2 (/ (sqrt 2) x))))>
#<alt (* x (+ (* 3/16 (sqrt 2)) (* 1/2 (/ (sqrt 2) x))))>
#<alt (* x (+ (* 3/16 (sqrt 2)) (* 1/2 (/ (sqrt 2) x))))>
#<alt (* 3/16 (* x (sqrt 2)))>
#<alt (* -1 (* x (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2)))))>
#<alt (* -1 (* x (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2)))))>
#<alt (* -1 (* x (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2)))))>
#<alt (* 3/16 x)>
#<alt (* 3/16 x)>
#<alt (* 3/16 x)>
#<alt (* 3/16 x)>
#<alt (* 3/16 x)>
#<alt (* 3/16 x)>
#<alt (* 3/16 x)>
#<alt (* 3/16 x)>
#<alt (* 3/16 x)>
#<alt (* 3/16 x)>
#<alt (* 3/16 x)>
#<alt (* 3/16 x)>

Calls

33 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(* x (sqrt 1/2))
1.0ms	x	@	inf	(/ 1 (sqrt (+ (* x -1/4) 1/2)))
1.0ms	x	@	-inf	(/ 1 (sqrt (+ (* x (+ (* x (* x 1/48)) -1/4)) 1/2)))
1.0ms	x	@	inf	(sqrt (+ (* x -1/4) 1/2))
1.0ms	x	@	inf	(/ 1 (sqrt (+ (* x (+ (* x (* x 1/48)) -1/4)) 1/2)))

rewrite363.0ms (5.7%)

Memory

5.0MiB live, 479.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

8 948×	`lower-fma.f32`
8 940×	`lower-fma.f64`
5 708×	`lower-*.f32`
5 700×	`lower-*.f64`
3 096×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	78
0	41	78
1	139	73
2	827	73
0	8363	72

Stop Event

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

Counts

14 → 447

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 1/2 binary64))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))))
(sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))
(fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))
(*.f64 x #s(literal 1/48 binary64))
(sqrt.f64 (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))
(fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x #s(literal 3/16 binary64)))
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x #s(literal 3/16 binary64))))
(sqrt.f64 #s(literal 2 binary64))
(*.f64 x #s(literal 3/16 binary64))

Outputs
(exp.f64 (.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 1/2 binary64)))))
(exp.f64 (*.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))
(exp.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 1/2 binary64)))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)))
(pow.f64 #s(literal 1/2 binary64) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1/2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal -1/4 binary64)) (pow.f64 #s(literal 1/2 binary64) #s(literal -1/4 binary64)))
(.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal -1/4 binary64)) (.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal -1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1 binary64))
(*.f64 (pow.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 #s(literal 1/2 binary64) #s(literal -1/4 binary64))) (pow.f64 #s(literal 1/2 binary64) #s(literal -1/4 binary64)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 1/2 binary64))))
(exp.f64 (neg.f64 (.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 1/2 binary64))))))
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt.f64 #s(literal 1/2 binary64))
(neg.f64 (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 1/2 binary64) #s(literal -1/4 binary64))) (pow.f64 #s(literal 1/2 binary64) #s(literal -1/4 binary64)))
(pow.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1 binary64))
(pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 #s(literal 1/2 binary64))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1 binary64))
(*.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)))
(.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (/.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(/.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal 1 binary64))
(/.f64 (*.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 (*.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 (*.f64 x (neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(/.f64 (*.f64 (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) x) #s(literal -1 binary64))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)
(.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) x))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal 1 binary64))
(.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) x))
(.f64 (.f64 x (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)))
(exp.f64 (.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (log.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))))))
(exp.f64 (*.f64 (log.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))) #s(literal -1/2 binary64)))
(exp.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))) (pow.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))
(pow.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))))
(*.f64 (pow.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) #s(literal -1/4 binary64)) (pow.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) #s(literal -1/4 binary64)))
(.f64 (pow.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) #s(literal -1/4 binary64)) (.f64 (pow.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(.f64 (pow.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 (.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/4 binary64))) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (fma.f64 x (.f64 x #s(literal 1/16 binary64)) #s(literal -1/4 binary64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/2 binary64))) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) #s(literal -1/4 binary64))) (pow.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)) #s(literal -1/4 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 x (.f64 x x)) #s(literal 1/8 binary64)))) (sqrt.f64 (fma.f64 x (-.f64 (.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/4 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (.f64 x #s(literal 1/16 binary64)) #s(literal -1/4 binary64)))) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/2 binary64))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))))
(exp.f64 (neg.f64 (.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (log.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))))))
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))))
(sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))
(neg.f64 (neg.f64 (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 x (-.f64 (.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/4 binary64))) (sqrt.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 x (*.f64 x x)) #s(literal 1/8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/2 binary64))) (sqrt.f64 (fma.f64 x (*.f64 x #s(literal 1/16 binary64)) #s(literal -1/4 binary64)))))
(/.f64 (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(/.f64 (sqrt.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 x (.f64 x x)) #s(literal 1/8 binary64))) (sqrt.f64 (fma.f64 x (-.f64 (*.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/4 binary64))))
(/.f64 (sqrt.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 x (.f64 x x)) #s(literal 1/8 binary64))) (.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (-.f64 (.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/4 binary64)))))
(/.f64 (sqrt.f64 (fma.f64 x (*.f64 x #s(literal 1/16 binary64)) #s(literal -1/4 binary64))) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/2 binary64))))
(/.f64 (sqrt.f64 (fma.f64 x (.f64 x #s(literal 1/16 binary64)) #s(literal -1/4 binary64))) (.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/2 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 x (.f64 x x)) #s(literal 1/8 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 x (-.f64 (*.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/4 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 x (*.f64 x #s(literal 1/16 binary64)) #s(literal -1/4 binary64)))) (sqrt.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/16 binary64) (.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/4 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 #s(literal -1/64 binary64) (.f64 x (.f64 x x)) #s(literal 1/8 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 x (-.f64 (*.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/4 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x (*.f64 x #s(literal 1/16 binary64)) #s(literal -1/4 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/2 binary64)))))
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(.f64 (fma.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 9/256 binary64)) (fma.f64 x #s(literal -3/16 binary64) #s(literal 1/2 binary64))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 9/256 binary64)) (fma.f64 x #s(literal -3/16 binary64) #s(literal 1/2 binary64)))))
(.f64 (fma.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -9/256 binary64) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 3/16 binary64))))))
(.f64 (neg.f64 (.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 27/4096 binary64) (.f64 x (.f64 x x)) #s(literal 1/8 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(literal 2 binary64) (.f64 (*.f64 x x) #s(literal 9/256 binary64)) (fma.f64 x #s(literal -3/16 binary64) #s(literal 1/2 binary64))))))
(.f64 (neg.f64 (fma.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -9/256 binary64) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 3/16 binary64)))))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 9/256 binary64)) (fma.f64 x #s(literal -3/16 binary64) #s(literal 1/2 binary64)))) (.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 27/4096 binary64) (.f64 x (*.f64 x x)) #s(literal 1/8 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 3/16 binary64))))) (fma.f64 (.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal -9/256 binary64) #s(literal 1/2 binary64)))
(.f64 (fma.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 9/256 binary64) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (*.f64 x #s(literal 3/16 binary64)) #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)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))))
(*.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 3/16 binary64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 3/16 binary64)))))
(.f64 (/.f64 (fma.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -9/256 binary64) #s(literal 1/2 binary64)) (fma.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -9/256 binary64) #s(literal 1/2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))))
(.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 27/4096 binary64) (.f64 x (.f64 x x)) #s(literal 1/8 binary64))) (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 9/256 binary64)) (.f64 x #s(literal -3/16 binary64))) (.f64 (fma.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 9/256 binary64)) (.f64 x #s(literal -3/16 binary64))) (fma.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 9/256 binary64)) (.f64 x #s(literal -3/16 binary64)))) #s(literal 1/8 binary64))) (fma.f64 (fma.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 9/256 binary64)) (.f64 x #s(literal -3/16 binary64))) (-.f64 (fma.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 9/256 binary64)) (*.f64 x #s(literal -3/16 binary64))) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))
(.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 27/4096 binary64) (.f64 x (.f64 x x)) #s(literal 1/8 binary64))) (-.f64 #s(literal 1/4 binary64) (.f64 (fma.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 9/256 binary64)) (.f64 x #s(literal -3/16 binary64))) (fma.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 9/256 binary64)) (.f64 x #s(literal -3/16 binary64)))))) (+.f64 (fma.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -9/256 binary64) #s(literal 1/2 binary64)) (*.f64 x #s(literal 3/16 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -9/256 binary64) #s(literal 1/2 binary64)) (.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1/8 binary64) (.f64 #s(literal 27/4096 binary64) (.f64 x (.f64 x x)))))) (fma.f64 (.f64 x #s(literal 3/16 binary64)) (fma.f64 #s(literal 2 binary64) (.f64 x #s(literal 3/16 binary64)) #s(literal 1 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))))
(sqrt.f64 #s(literal 2 binary64))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(.f64 #s(literal 1 binary64) (.f64 x #s(literal 3/16 binary64)))
(.f64 #s(literal 1/2 binary64) (.f64 #s(literal 2 binary64) (*.f64 x #s(literal 3/16 binary64))))
(*.f64 x #s(literal 3/16 binary64))
(.f64 x (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 #s(literal 3/32 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 #s(literal 3/16 binary64) x)
(.f64 #s(literal 3/16 binary64) (.f64 #s(literal 1 binary64) x))
(.f64 (.f64 x #s(literal 3/16 binary64)) #s(literal 1 binary64))
(.f64 (.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64))))
(.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (.f64 #s(literal 3/16 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 #s(literal 3/32 binary64) (.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)) (.f64 x (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (.f64 #s(literal 1 binary64) x) #s(literal 3/16 binary64))
(.f64 (.f64 #s(literal 2 binary64) (*.f64 x #s(literal 3/16 binary64))) #s(literal 1/2 binary64))
(.f64 (.f64 #s(literal 3/32 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)))
(.f64 (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) (.f64 x (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64))) x)
(.f64 (.f64 (.f64 #s(literal 3/32 binary64) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))

simplify367.0ms (5.8%)

Memory

-13.7MiB live, 519.4MiB allocated

Algorithm

1×	egg-herbie

Rules

10 796×	`lower-fma.f64`
10 796×	`lower-fma.f32`
6 328×	`lower-*.f64`
6 328×	`lower-*.f32`
2 886×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	335	1723
1	933	1538
2	2860	1493
3	5904	1480
0	8152	1392

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

Calls

Call 1

Inputs
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/4 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* (sqrt (/ 1 x)) (sqrt -4))
(+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4))))
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 32 (* 16 (/ x (pow (sqrt -4) 2)))) (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))))
(* 2 (* (sqrt (/ 1 x)) (sqrt -1)))
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1))))
(+ (* -4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ 32 (* -4 x))))) (* 4 (* (sqrt x) (sqrt -1)))) (pow x 3))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (- (* x (- (* -1/1024 (/ x (pow (sqrt 1/2) 5))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))
(* (sqrt x) (sqrt -1/4))
(* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4)))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1/4) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))))
(* -1/2 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1)))))))
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))))
1/2
(+ 1/2 (* -1/4 x))
(+ 1/2 (* -1/4 x))
(+ 1/2 (* -1/4 x))
(* -1/4 x)
(* x (- (* 1/2 (/ 1 x)) 1/4))
(* x (- (* 1/2 (/ 1 x)) 1/4))
(* x (- (* 1/2 (/ 1 x)) 1/4))
(* -1/4 x)
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* (sqrt (/ 1 (pow x 3))) (sqrt 48))
(/ (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48))) x)
(/ (+ (* -576 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 48)))) (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48)))) x)
(/ (+ (* -576 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 48)))) (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (+ (* 3456 (* (sqrt (/ 1 (pow x 9))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48))))) x)
(* -1 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -48) (sqrt -1))))
(* -1 (/ (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -48)))) (* (sqrt (/ 1 x)) (* (sqrt -48) (sqrt -1)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -288 (* (sqrt x) (/ (sqrt -1) (sqrt -48)))) (* 576 (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt -48))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -48) (sqrt -1)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -288 (* (sqrt x) (/ (sqrt -1) (sqrt -48)))) (* -1 (/ (+ (* -576 (* (sqrt x) (/ (sqrt -1) (sqrt -48)))) (* 3456 (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt -48))))) x))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -48) (sqrt -1)))) x))
(* 1/48 x)
(* 1/48 x)
(* 1/48 x)
(* 1/48 x)
(* 1/48 x)
(* 1/48 x)
(* 1/48 x)
(* 1/48 x)
(* 1/48 x)
(* 1/48 x)
(* 1/48 x)
(* 1/48 x)
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))
(* (sqrt (pow x 3)) (sqrt 1/48))
(* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/48)))) (* (sqrt (/ 1 x)) (sqrt 1/48))))
(* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/48)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 1/48)))) (* (sqrt (/ 1 x)) (sqrt 1/48)))))
(* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/48)))) (+ (* -1/128 (* (sqrt (/ 1 (pow x 9))) (/ 1 (pow (sqrt 1/48) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 1/48)))) (* (sqrt (/ 1 x)) (sqrt 1/48))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/48)))
(* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/48)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/48)))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt -1/48)))) (* 1/8 (* (sqrt x) (/ (sqrt -1) (sqrt -1/48))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/48)))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/128 (* (sqrt (/ 1 x)) (/ (sqrt -1) (pow (sqrt -1/48) 3)))) (* 1/4 (* (sqrt x) (/ (sqrt -1) (sqrt -1/48))))) x)) (* 1/8 (* (sqrt x) (/ (sqrt -1) (sqrt -1/48))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/48)))))
-1/4
(- (* 1/48 (pow x 2)) 1/4)
(- (* 1/48 (pow x 2)) 1/4)
(- (* 1/48 (pow x 2)) 1/4)
(* 1/48 (pow x 2))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(* 1/48 (pow x 2))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(* 3/16 (* x (sqrt 2)))
(* 3/16 (* x (sqrt 2)))
(* 3/16 (* x (sqrt 2)))
(* 3/16 (* x (sqrt 2)))
(* 3/16 (* x (sqrt 2)))
(* 3/16 (* x (sqrt 2)))
(* 3/16 (* x (sqrt 2)))
(* 3/16 (* x (sqrt 2)))
(* 3/16 (* x (sqrt 2)))
(* 3/16 (* x (sqrt 2)))
(* 3/16 (* x (sqrt 2)))
(* 3/16 (* x (sqrt 2)))
(* 1/2 (sqrt 2))
(+ (* 3/16 (* x (sqrt 2))) (* 1/2 (sqrt 2)))
(+ (* 3/16 (* x (sqrt 2))) (* 1/2 (sqrt 2)))
(+ (* 3/16 (* x (sqrt 2))) (* 1/2 (sqrt 2)))
(* 3/16 (* x (sqrt 2)))
(* x (+ (* 3/16 (sqrt 2)) (* 1/2 (/ (sqrt 2) x))))
(* x (+ (* 3/16 (sqrt 2)) (* 1/2 (/ (sqrt 2) x))))
(* x (+ (* 3/16 (sqrt 2)) (* 1/2 (/ (sqrt 2) x))))
(* 3/16 (* x (sqrt 2)))
(* -1 (* x (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2)))))
(* -1 (* x (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2)))))
(* -1 (* x (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2)))))
(* 3/16 x)
(* 3/16 x)
(* 3/16 x)
(* 3/16 x)
(* 3/16 x)
(* 3/16 x)
(* 3/16 x)
(* 3/16 x)
(* 3/16 x)
(* 3/16 x)
(* 3/16 x)
(* 3/16 x)

Outputs
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/4 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
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(.f64 (.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/48 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64)) (sqrt.f64 #s(literal -1/48 binary64))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/4 (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt -1/48)))) (* 1/8 (* (sqrt x) (/ (sqrt -1) (sqrt -1/48))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/48)))))
(fma.f64 #s(literal 1 binary64) (/.f64 (.f64 (neg.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/48 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/4 binary64) (.f64 (sqrt.f64 x) #s(literal 1/8 binary64)))) x) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/48 binary64))) (.f64 x x))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/128 (* (sqrt (/ 1 x)) (/ (sqrt -1) (pow (sqrt -1/48) 3)))) (* 1/4 (* (sqrt x) (/ (sqrt -1) (sqrt -1/48))))) x)) (* 1/8 (* (sqrt x) (/ (sqrt -1) (sqrt -1/48))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/48)))))
(fma.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)) (sqrt.f64 #s(literal -1/48 binary64))) (/.f64 (fma.f64 #s(literal 3/8 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1/48 binary64))) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -1/48 binary64))))) x)) x) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/48 binary64))) (.f64 x x))))
-1/4
#s(literal -1/4 binary64)
(- (* 1/48 (pow x 2)) 1/4)
(fma.f64 #s(literal 1/48 binary64) (*.f64 x x) #s(literal -1/4 binary64))
(- (* 1/48 (pow x 2)) 1/4)
(fma.f64 #s(literal 1/48 binary64) (*.f64 x x) #s(literal -1/4 binary64))
(- (* 1/48 (pow x 2)) 1/4)
(fma.f64 #s(literal 1/48 binary64) (*.f64 x x) #s(literal -1/4 binary64))
(* 1/48 (pow x 2))
(.f64 #s(literal 1/48 binary64) (.f64 x x))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/48 binary64) (*.f64 x x) #s(literal -1/4 binary64))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/48 binary64) (*.f64 x x) #s(literal -1/4 binary64))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/48 binary64) (*.f64 x x) #s(literal -1/4 binary64))
(* 1/48 (pow x 2))
(.f64 #s(literal 1/48 binary64) (.f64 x x))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/48 binary64) (*.f64 x x) #s(literal -1/4 binary64))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/48 binary64) (*.f64 x x) #s(literal -1/4 binary64))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/48 binary64) (*.f64 x x) #s(literal -1/4 binary64))
(* 3/16 (* x (sqrt 2)))
(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)))
(* 3/16 (* x (sqrt 2)))
(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)))
(* 3/16 (* x (sqrt 2)))
(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)))
(* 3/16 (* x (sqrt 2)))
(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)))
(* 3/16 (* x (sqrt 2)))
(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)))
(* 3/16 (* x (sqrt 2)))
(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)))
(* 3/16 (* x (sqrt 2)))
(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)))
(* 3/16 (* x (sqrt 2)))
(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)))
(* 3/16 (* x (sqrt 2)))
(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)))
(* 3/16 (* x (sqrt 2)))
(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)))
(* 3/16 (* x (sqrt 2)))
(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)))
(* 3/16 (* x (sqrt 2)))
(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)))
(* 1/2 (sqrt 2))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* 3/16 (* x (sqrt 2))) (* 1/2 (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(+ (* 3/16 (* x (sqrt 2))) (* 1/2 (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(+ (* 3/16 (* x (sqrt 2))) (* 1/2 (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* 3/16 (* x (sqrt 2)))
(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)))
(* x (+ (* 3/16 (sqrt 2)) (* 1/2 (/ (sqrt 2) x))))
(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(* x (+ (* 3/16 (sqrt 2)) (* 1/2 (/ (sqrt 2) x))))
(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(* x (+ (* 3/16 (sqrt 2)) (* 1/2 (/ (sqrt 2) x))))
(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(* 3/16 (* x (sqrt 2)))
(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)))
(* -1 (* x (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2)))))
(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(* -1 (* x (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2)))))
(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(* -1 (* x (+ (* -1/2 (/ (sqrt 2) x)) (* -3/16 (sqrt 2)))))
(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/2 binary64) x))))
(* 3/16 x)
(*.f64 x #s(literal 3/16 binary64))
(* 3/16 x)
(*.f64 x #s(literal 3/16 binary64))
(* 3/16 x)
(*.f64 x #s(literal 3/16 binary64))
(* 3/16 x)
(*.f64 x #s(literal 3/16 binary64))
(* 3/16 x)
(*.f64 x #s(literal 3/16 binary64))
(* 3/16 x)
(*.f64 x #s(literal 3/16 binary64))
(* 3/16 x)
(*.f64 x #s(literal 3/16 binary64))
(* 3/16 x)
(*.f64 x #s(literal 3/16 binary64))
(* 3/16 x)
(*.f64 x #s(literal 3/16 binary64))
(* 3/16 x)
(*.f64 x #s(literal 3/16 binary64))
(* 3/16 x)
(*.f64 x #s(literal 3/16 binary64))
(* 3/16 x)
(*.f64 x #s(literal 3/16 binary64))

eval95.0ms (1.5%)

Memory: -5.6MiB live, 108.4MiB allocated
Compiler: Compiled 13 571 to 2 046 computations (84.9% saved)

prune90.0ms (1.4%)

Memory

18.1MiB live, 132.3MiB allocated

Pruning

20 alts after pruning (10 fresh and 10 done)

	Pruned	Kept	Total
New	613	3	616
Fresh	3	7	10
Picked	1	4	5
Done	0	6	6
Total	617	20	637

Accuracy

100.0%

Counts

637 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
	69.9%	(fma.f64 (.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)) x (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)) x (sqrt.f64 #s(literal 2 binary64)))
	69.9%	(fma.f64 (.f64 (.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64)) x (sqrt.f64 #s(literal 2 binary64)))
	1.3%	(fma.f64 (.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal -1/32 binary64) (.f64 x x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/128 binary64) (*.f64 x x) #s(literal 1/4 binary64)))) (sqrt.f64 x))
	68.9%	(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 5/64 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
	68.9%	(fma.f64 x (fma.f64 x (.f64 #s(literal 7/192 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
✓	67.7%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))
✓	69.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))))
✓	73.3%	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
	69.9%	(+.f64 (.f64 x (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
	4.0%	(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
	2.7%	(*.f64 (sqrt.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x)
✓	3.0%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
	4.2%	(.f64 #s(literal 3/16 binary64) (.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
✓	68.7%	(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓	70.2%	(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
	2.5%	(sqrt.f64 (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓	68.6%	(sqrt.f64 (+.f64 x #s(literal 2 binary64)))
✓	2.5%	(sqrt.f64 x)
✓	74.4%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 588 to 275 computations (53.2% saved)

regimes27.0ms (0.4%)

Memory

-15.4MiB live, 28.0MiB allocated

Counts

31 → 1

Calls

Call 1

Inputs
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 x)
(sqrt.f64 (+.f64 x #s(literal 2 binary64)))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
(*.f64 (sqrt.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x)
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
(sqrt.f64 (.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x))))
(sqrt.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
(sqrt.f64 (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))))
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
(.f64 #s(literal 3/16 binary64) (.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))
(fma.f64 (.f64 (.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64)) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))))
(sqrt.f64 (fma.f64 x (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64)) x) (/.f64 #s(literal -1 binary64) (fma.f64 x #s(literal -1/6 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64)))
(fma.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)) x (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)) x (sqrt.f64 #s(literal 2 binary64)))
(+.f64 (.f64 x (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (fma.f64 x (.f64 #s(literal 7/192 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 5/64 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal -1/32 binary64) (.f64 x x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/128 binary64) (*.f64 x x) #s(literal 1/4 binary64)))) (sqrt.f64 x))
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))

Outputs
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))

Calls

3 calls:

10.0ms

(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))

8.0ms

7.0ms

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

Results

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

Compiler

Compiled 27 to 20 computations (25.9% saved)

regimes24.0ms (0.4%)

Memory

3.8MiB live, 40.7MiB allocated

Accuracy

Total -47.1b remaining (-287.1%)

Threshold costs -47.1b (-287.1%)

Counts

29 → 1

Calls

Call 1

Inputs
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 x)
(sqrt.f64 (+.f64 x #s(literal 2 binary64)))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
(*.f64 (sqrt.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x)
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
(sqrt.f64 (.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x))))
(sqrt.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
(sqrt.f64 (fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))))
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
(.f64 #s(literal 3/16 binary64) (.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))))
(fma.f64 (.f64 (.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64)) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))))
(sqrt.f64 (fma.f64 x (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64)) x) (/.f64 #s(literal -1 binary64) (fma.f64 x #s(literal -1/6 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64)))
(fma.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64)) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/16 binary64)) x (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)) x (sqrt.f64 #s(literal 2 binary64)))
(+.f64 (.f64 x (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x #s(literal 3/16 binary64)))) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (fma.f64 x (.f64 #s(literal 7/192 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 5/64 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal -1/32 binary64) (.f64 x x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/128 binary64) (*.f64 x x) #s(literal 1/4 binary64)))) (sqrt.f64 x))

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

Calls

3 calls:

9.0ms

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

8.0ms

6.0ms

(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))

Results

Accuracy	Segments	Branch
74.4%	1	`x`
74.4%	1	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))`
74.4%	1	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`

Compiler

Compiled 27 to 20 computations (25.9% saved)

simplify5.0ms (0.1%)

Memory

10.6MiB live, 10.6MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	7
1	9	7
2	13	7
3	14	7
4	15	7

Stop Event

1×

saturated

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(sqrt.f64 #s(literal 2 binary64))

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

soundness318.0ms (5%)

Memory

-39.4MiB live, 164.4MiB allocated

Rules

18 226×	`lower-fma.f64`
18 226×	`lower-fma.f32`
5 402×	`lower-fma.f64`
5 402×	`lower-fma.f32`
4 492×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	306
1	155	306
2	334	306
3	753	306
4	1205	266
5	1536	250
6	2032	250
7	2954	250
8	4636	250
0	8301	196
0	9	23
0	15	23
1	56	16
2	378	16
3	4570	16
0	8200	12

Stop Event

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

Compiler

Compiled 17 to 15 computations (11.8% saved)

preprocess37.0ms (0.6%)

Memory: 10.8MiB live, 48.6MiB allocated
Compiler: Compiled 42 to 34 computations (19% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze2.0ms (0%)

sample905.0ms (14.2%)

preprocess397.0ms (6.2%)

explain194.0ms (3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify0.0ms (0%)

localize39.0ms (0.6%)

series3.0ms (0%)

rewrite364.0ms (5.7%)

simplify428.0ms (6.7%)

eval104.0ms (1.6%)

prune107.0ms (1.7%)

simplify0.0ms (0%)

localize112.0ms (1.8%)

series11.0ms (0.2%)

rewrite321.0ms (5%)

simplify358.0ms (5.6%)

eval97.0ms (1.5%)

prune76.0ms (1.2%)

simplify0.0ms (0%)

localize93.0ms (1.5%)

series17.0ms (0.3%)

rewrite359.0ms (5.6%)

simplify556.0ms (8.7%)

eval219.0ms (3.4%)

prune168.0ms (2.6%)

simplify0.0ms (0%)

localize93.0ms (1.5%)

series15.0ms (0.2%)

rewrite363.0ms (5.7%)

simplify367.0ms (5.8%)

eval95.0ms (1.5%)

prune90.0ms (1.4%)

regimes27.0ms (0.4%)

regimes24.0ms (0.4%)

simplify5.0ms (0.1%)

soundness318.0ms (5%)

preprocess37.0ms (0.6%)

end0.0ms (0%)

Profiling