Metrics for sqrtexp (problem 3.4.4)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze2.0ms (0%)

Memory

3.5MiB live, 3.5MiB 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)

sample934.0ms (14%)

Memory

27.3MiB live, 937.8MiB allocated

Samples

424.0ms	8 256×	0	valid
180.0ms	2 707×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 388.0ms

ival-expm1: 148.0ms (38.2% of total)

ival-mult: 80.0ms (20.6% of total)

ival-div: 73.0ms (18.8% of total)

ival-sqrt: 68.0ms (17.5% of total)

ival-true: 7.0ms (1.8% of total)

exact: 6.0ms (1.5% of total)

ival-assert: 4.0ms (1% of total)

Bogosity

explain120.0ms (1.8%)

Memory

10.3MiB live, 133.1MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	cancellation	161	0
`-.f64`	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	cancellation	161	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	1	0
↳	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`	overflow	1
↳	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	overflow	1
↳	`(exp.f64 x)`	overflow	1
↳	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	overflow	1

Confusion

	Predicted +	Predicted -
+	161	0
-	1	94

Precision

0.9938271604938271

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	161	0	0
-	1	0	94

Precision?

0.9938271604938271

Recall?

1.0

Freqs

test

number	freq
0	94
1	1
2	161

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 107 to 34 computations (68.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-exp: 8.0ms (31.6% of total)

ival-expm1: 6.0ms (23.7% of total)

ival-div: 3.0ms (11.8% of total)

ival-mult: 3.0ms (11.8% of total)

ival-sqrt: 3.0ms (11.8% of total)

exact: 1.0ms (3.9% of total)

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

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

preprocess209.0ms (3.1%)

Memory

28.2MiB live, 141.0MiB 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 (exp.f64 x) #s(literal -1 binary64)))

Compiler

Compiled 13 to 10 computations (23.1% saved)

eval0.0ms (0%)

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

prune3.0ms (0%)

Memory

-37.3MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	40.3%	(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)

simplify151.0ms (2.3%)

Memory

38.0MiB live, 111.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	128	(*.f64 #s(literal 2 binary64) x)
cost-diff	192	(-.f64 (exp.f64 x) #s(literal 1 binary64))
cost-diff	192	(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
cost-diff	7104	(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))

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: 0 (0.0ms)

Iter	Nodes	Cost
0	10	45
0	17	45
1	29	45
2	35	45
3	47	45
4	73	35
5	126	31
6	203	31
7	606	31
8	2926	31
9	6783	31
0	8197	27

Stop Event

1×	iter limit
1×	node limit
1×	iter 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))))
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
(exp.f64 (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
#s(literal 1 binary64)
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(exp.f64 x)

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 (exp.f64 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)))
(-.f64 (exp.f64 x) #s(literal -1 binary64))
(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
(expm1.f64 (+.f64 x x))
(exp.f64 (*.f64 #s(literal 2 binary64) x))
(exp.f64 (+.f64 x x))
(*.f64 #s(literal 2 binary64) x)
(+.f64 x x)
#s(literal 2 binary64)
x
#s(literal 1 binary64)
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(expm1.f64 x)
(exp.f64 x)

localize130.0ms (2%)

Memory

-10.3MiB live, 46.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(exp.f64 x)
accuracy	0.22103500976844204	(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
accuracy	36.33326807196	(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
accuracy	36.38716419134709	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Samples

123.0ms

256×

valid

Compiler

Compiled 47 to 12 computations (74.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 84.0ms

ival-expm1: 75.0ms (89.3% of total)

ival-exp: 3.0ms (3.6% of total)

ival-div: 2.0ms (2.4% of total)

ival-mult: 2.0ms (2.4% of total)

ival-sqrt: 2.0ms (2.4% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.1%)

Memory

-33.7MiB live, 6.1MiB allocated

Counts

5 → 60

Calls

Call 1

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

Outputs
#s(alt 2 (taylor 0 x) (#s(alt (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 2 x) (taylor 0 x) (#s(alt (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#s(alt (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) (taylor 0 x) (#s(alt (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2 (* 2 x))) (taylor 0 x) (#s(alt (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2 (* x (+ 2 (* 4/3 x))))) (taylor 0 x) (#s(alt (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x))))))) (taylor 0 x) (#s(alt (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 x))) (taylor 0 x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))) (taylor 0 x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x))))))) (taylor 0 x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) (taylor 0 x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (taylor inf x) (#s(alt (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (taylor inf x) (#s(alt (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (taylor inf x) (#s(alt (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (taylor inf x) (#s(alt (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (exp (* 2 x)) 1) (taylor inf x) (#s(alt (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* 2 x)) 1) (taylor inf x) (#s(alt (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* 2 x)) 1) (taylor inf x) (#s(alt (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* 2 x)) 1) (taylor inf x) (#s(alt (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor inf x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor inf x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor inf x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor inf x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (taylor -inf x) (#s(alt (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (taylor -inf x) (#s(alt (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (taylor -inf x) (#s(alt (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (taylor -inf x) (#s(alt (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (exp (* 2 x)) 1) (taylor -inf x) (#s(alt (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* 2 x)) 1) (taylor -inf x) (#s(alt (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* 2 x)) 1) (taylor -inf x) (#s(alt (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp (* 2 x)) 1) (taylor -inf x) (#s(alt (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor -inf x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor -inf x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor -inf x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (exp x) 1) (taylor -inf x) (#s(alt (-.f64 (exp.f64 x) #s(literal 1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor -inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor -inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor -inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor -inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	((/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (- (exp (* 2 x)) 1) (- (exp x) 1) (* 2 x) (exp x))
1.0ms	x	@	-inf	((/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (- (exp (* 2 x)) 1) (- (exp x) 1) (* 2 x) (exp x))
1.0ms	x	@	0	((/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (- (exp (* 2 x)) 1) (- (exp x) 1) (* 2 x) (exp x))

Time

Variable

Point

Expression

3.0ms

inf

((/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (- (exp (* 2 x)) 1) (- (exp x) 1) (* 2 x) (exp x))

1.0ms

-inf

((/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (- (exp (* 2 x)) 1) (- (exp x) 1) (* 2 x) (exp x))

1.0ms

((/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (- (exp (* 2 x)) 1) (- (exp x) 1) (* 2 x) (exp x))

simplify192.0ms (2.9%)

Memory

27.6MiB live, 176.5MiB 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	342
1	155	342
2	336	342
3	752	342
4	1208	302
5	1538	286
6	2035	286
7	2978	286
8	4658	286
0	8365	232

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 59

Calls

Call 1

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

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

rewrite168.0ms (2.5%)

Memory

7.4MiB live, 167.8MiB allocated

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	26
0	15	26
1	56	19
2	378	19
3	4533	19
0	8161	15

Stop Event

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

Counts

5 → 656

Calls

Call 1

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

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

eval173.0ms (2.6%)

Memory: -16.9MiB live, 134.8MiB allocated
Compiler: Compiled 16 883 to 2 358 computations (86% saved)

prune166.0ms (2.5%)

Memory

-1.4MiB live, 177.2MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	710	5	715
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	711	5	716

Accuracy

100.0%

Counts

716 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
▶	63.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
▶	64.5%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
▶	62.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64))))
▶	68.7%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))

Compiler

Compiled 78 to 56 computations (28.2% saved)

simplify169.0ms (2.5%)

Memory

4.3MiB live, 120.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
cost-diff	0	(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
cost-diff	0	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
cost-diff	0	(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
cost-diff	0	(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
cost-diff	0	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
cost-diff	0	(+.f64 x #s(literal 2 binary64))
cost-diff	0	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64)))
cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64))))
cost-diff	0	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
cost-diff	0	(exp.f64 x)
cost-diff	0	(-.f64 (exp.f64 x) #s(literal -1 binary64))
cost-diff	0	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))

Rules

14 808×	`lower-fma.f32`
14 798×	`lower-fma.f64`
2 514×	`lower--.f32`
2 512×	`lower--.f64`
2 236×	`lower-*.f64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	29	202
0	47	202
1	71	202
2	98	202
3	176	202
4	312	162
5	409	146
6	487	146
7	891	146
8	3237	146
9	7151	146
0	8176	146

Stop Event

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

Calls

Call 1

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

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

localize90.0ms (1.4%)

Memory

0.3MiB live, 38.3MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.0390625	(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
accuracy	0.046875	(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
accuracy	0.12109375	(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
accuracy	23.523794534384088	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
accuracy	0	(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
accuracy	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
accuracy	0.00390625	(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
accuracy	22.87821169070813	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
accuracy	0	(+.f64 x #s(literal 2 binary64))
accuracy	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64))))
accuracy	23.972905869556822	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64)))
accuracy	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
accuracy	20.54872627098806	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))
accuracy	0	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
accuracy	0	(exp.f64 x)
accuracy	0.0078125	(-.f64 (exp.f64 x) #s(literal -1 binary64))

Samples

75.0ms

256×

valid

Compiler

Compiled 163 to 27 computations (83.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 31.0ms

ival-mult: 9.0ms (29.4% of total)

ival-add: 6.0ms (19.6% of total)

ival-expm1: 3.0ms (9.8% of total)

const: 3.0ms (9.8% of total)

ival-sqrt: 3.0ms (9.8% of total)

ival-div: 2.0ms (6.5% of total)

ival-exp: 2.0ms (6.5% of total)

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

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

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

exact: 0.0ms (0% of total)

series12.0ms (0.2%)

Memory

9.6MiB live, 9.6MiB allocated

Counts

17 → 204

Calls

Call 1

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

Outputs
#s(alt (sqrt 2) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) (patch (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) (patch (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) (patch (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(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)))))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) (patch (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt 2 (taylor 0 x) (#s(alt (-.f64 (exp.f64 x) #s(literal -1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 2 x) (taylor 0 x) (#s(alt (-.f64 (exp.f64 x) #s(literal -1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#s(alt (-.f64 (exp.f64 x) #s(literal -1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) (taylor 0 x) (#s(alt (-.f64 (exp.f64 x) #s(literal -1 binary64)) (patch (-.f64 (exp.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) (taylor 0 x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt 2) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(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)))))) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt 2 (taylor 0 x) (#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 2 x) (taylor 0 x) (#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) (taylor 0 x) (#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt 2) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(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)))))) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt 2 (taylor 0 x) (#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 2 x) (taylor 0 x) (#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) (taylor 0 x) (#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt 2 (taylor 0 x) (#s(alt (+.f64 x #s(literal 2 binary64)) (patch (+.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 2 x) (taylor 0 x) (#s(alt (+.f64 x #s(literal 2 binary64)) (patch (+.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 2 x) (taylor 0 x) (#s(alt (+.f64 x #s(literal 2 binary64)) (patch (+.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 2 x) (taylor 0 x) (#s(alt (+.f64 x #s(literal 2 binary64)) (patch (+.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt 2) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(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)))))) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt 2 (taylor 0 x) (#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 2 x) (taylor 0 x) (#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) (taylor 0 x) (#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt 2 (taylor 0 x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 2 x) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt 2) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(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)))))) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt 2 (taylor 0 x) (#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 2 x) (taylor 0 x) (#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
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#s(alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (taylor -inf x) (#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (taylor -inf x) (#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (taylor -inf x) (#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (taylor -inf x) (#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (pow x 3)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/6 (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/6 (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/6 (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

inf

((sqrt (- (exp x) -1)) (- (exp x) -1) (exp x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ x 2) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* 1/2 x) 1) x) 2) (+ (* 1/2 x) 1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (+ (* (+ (* 1/6 x) 1/2) x) 1) (+ (* 1/6 x) 1/2))

2.0ms

((sqrt (- (exp x) -1)) (- (exp x) -1) (exp x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ x 2) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* 1/2 x) 1) x) 2) (+ (* 1/2 x) 1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (+ (* (+ (* 1/6 x) 1/2) x) 1) (+ (* 1/6 x) 1/2))

2.0ms

-inf

((sqrt (- (exp x) -1)) (- (exp x) -1) (exp x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ x 2) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* 1/2 x) 1) x) 2) (+ (* 1/2 x) 1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (+ (* (+ (* 1/6 x) 1/2) x) 1) (+ (* 1/6 x) 1/2))

simplify177.0ms (2.6%)

Memory

-12.5MiB live, 178.0MiB allocated

Algorithm

1×	egg-herbie

Rules

16 534×	`lower-fma.f64`
16 534×	`lower-fma.f32`
4 720×	`lower-*.f64`
4 720×	`lower-*.f32`
2 888×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	102	1818
1	322	1640
2	922	1632
3	3268	1602
4	6535	1602
0	8224	1222

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 202

Calls

Call 1

Inputs
(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))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 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))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 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))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
2
(+ 2 x)
(+ 2 x)
(+ 2 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))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* 1/2 x))))
1
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 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))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(exp x)
(exp x)
(exp x)
(exp x)
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (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))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (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))
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (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))
(* 1/2 (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 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (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))
(* 1/6 (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 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 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(exp x)
(exp x)
(exp x)
(exp x)
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (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))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (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))
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (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))
(* 1/2 (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 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (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))
(* 1/6 (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)))
(* 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 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))

Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (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))))))
(fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x #s(literal 2 binary64))
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(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 (*.f64 x x) #s(literal 1/2 binary64) x)
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x #s(literal 2 binary64))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x #s(literal 2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(* 1/6 (pow x 3))
(.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x)
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))

rewrite159.0ms (2.4%)

Memory

25.7MiB live, 218.9MiB allocated

Rules

5 474×	`lower-fma.f32`
5 464×	`lower-fma.f64`
4 092×	`lower-/.f64`
4 092×	`lower-/.f32`
3 562×	`lower-*.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	29	188
0	47	188
1	180	132
2	1264	132
0	8396	132

Stop Event

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

Counts

17 → 436

Calls

Call 1

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

Outputs
(.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (.f64 x #s(literal 3 binary64))))) (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) (-.f64 (exp.f64 x) #s(literal -1 binary64)))))
(*.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))) (sqrt.f64 (expm1.f64 (+.f64 x x))))
(.f64 (pow.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)) (pow.f64 (+.f64 (exp.f64 (+.f64 x x)) (-.f64 (exp.f64 x) #s(literal -1 binary64))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (neg.f64 (expm1.f64 (+.f64 x x))) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 (expm1.f64 (+.f64 x x))))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (expm1.f64 x))))
(*.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))) (pow.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))))
(*.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)))
(.f64 (sqrt.f64 (-.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (neg.f64 (expm1.f64 x)) (exp.f64 (+.f64 x x))))))
(.f64 (sqrt.f64 (-.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (neg.f64 (expm1.f64 x)) (exp.f64 (+.f64 x x))))))
(.f64 (sqrt.f64 (-.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) #s(literal -1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (neg.f64 (expm1.f64 x)) (exp.f64 (+.f64 x x)))) #s(literal 1/2 binary64)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log1p.f64 (exp.f64 x))) #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 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.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 (neg.f64 (sqrt.f64 (expm1.f64 (+.f64 x x)))) (neg.f64 (sqrt.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 (neg.f64 (expm1.f64 x)) (exp.f64 (+.f64 x x))))))
(/.f64 (sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) (+.f64 x x))) (expm1.f64 x))) (sqrt.f64 (-.f64 (exp.f64 (+.f64 x x)) #s(literal -1 binary64))))
(/.f64 (sqrt.f64 (/.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) (expm1.f64 x))) (sqrt.f64 (+.f64 (+.f64 (exp.f64 (.f64 #s(literal 2 binary64) (+.f64 x x))) #s(literal 1 binary64)) (exp.f64 (+.f64 x x)))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x))) (-.f64 (exp.f64 x) #s(literal -1 binary64)))) (sqrt.f64 (+.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (exp.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64)))) (sqrt.f64 (fma.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (+.f64 x x))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64)) (+.f64 (pow.f64 (expm1.f64 x) #s(literal -2 binary64)) (/.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (expm1.f64 x))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (+.f64 x x)) (exp.f64 x)))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)))) (sqrt.f64 (+.f64 (neg.f64 (exp.f64 (+.f64 x x))) (expm1.f64 x))))
(/.f64 (sqrt.f64 (fma.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x) (neg.f64 (expm1.f64 x)))) (sqrt.f64 (pow.f64 (expm1.f64 x) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64))))))
(/.f64 (sqrt.f64 (expm1.f64 (.f64 #s(literal 2 binary64) (+.f64 x x)))) (sqrt.f64 (.f64 (-.f64 (exp.f64 (+.f64 x x)) #s(literal -1 binary64)) (expm1.f64 x))))
(/.f64 (sqrt.f64 (expm1.f64 (.f64 #s(literal 2 binary64) (+.f64 x x)))) (sqrt.f64 (.f64 (expm1.f64 x) (-.f64 (exp.f64 (+.f64 x x)) #s(literal -1 binary64)))))
(/.f64 (sqrt.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 3 binary64)))) (sqrt.f64 (.f64 (+.f64 (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (+.f64 x x))) #s(literal 1 binary64)) (exp.f64 (+.f64 x x))) (expm1.f64 x))))
(/.f64 (sqrt.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 3 binary64)))) (sqrt.f64 (.f64 (expm1.f64 x) (+.f64 (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (+.f64 x x))) #s(literal 1 binary64)) (exp.f64 (+.f64 x x))))))
(/.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 x)))
(/.f64 (sqrt.f64 (-.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal -1 binary64))) (sqrt.f64 (+.f64 (neg.f64 (expm1.f64 x)) (exp.f64 (+.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 (+.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 (neg.f64 (expm1.f64 x)) (exp.f64 (+.f64 x x)))) (sqrt.f64 (-.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64)))))
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/2 binary64)))
(.f64 (/.f64 (expm1.f64 (+.f64 x x)) (/.f64 (expm1.f64 (+.f64 x x)) (-.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (neg.f64 (expm1.f64 x)) (exp.f64 (+.f64 x x)))))
(*.f64 (/.f64 (-.f64 (exp.f64 (+.f64 x x)) #s(literal -1 binary64)) (expm1.f64 x)) (/.f64 (expm1.f64 (+.f64 x x)) (-.f64 (exp.f64 (+.f64 x x)) #s(literal -1 binary64))))
(.f64 (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) (+.f64 x x))) (/.f64 (expm1.f64 (+.f64 x x)) (-.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (+.f64 x x)) #s(literal -1 binary64))) (+.f64 (neg.f64 (expm1.f64 x)) (exp.f64 (+.f64 x x)))))
(.f64 (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) (+.f64 x x))) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (+.f64 x x)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 (exp.f64 x) #s(literal -1 binary64))))))
(.f64 (/.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) (/.f64 (expm1.f64 (+.f64 x x)) (-.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (exp.f64 (.f64 #s(literal 2 binary64) (+.f64 x x))) #s(literal 1 binary64)) (exp.f64 (+.f64 x x)))) (+.f64 (neg.f64 (expm1.f64 x)) (exp.f64 (+.f64 x x)))))
(.f64 (/.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) (/.f64 (expm1.f64 (+.f64 x x)) (-.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)))) (/.f64 (expm1.f64 x) (+.f64 (neg.f64 (expm1.f64 x)) (exp.f64 (+.f64 x x)))))
(.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 (exp.f64 (+.f64 x x)) (-.f64 (exp.f64 x) #s(literal -1 binary64))))))
(.f64 (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) (+.f64 x x))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (+.f64 x x)) #s(literal -1 binary64))) (expm1.f64 x)))
(.f64 (/.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (+.f64 x x))) #s(literal 1 binary64)) (exp.f64 (+.f64 x x)))) (expm1.f64 x)))
(*.f64 (/.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 1 binary64)) (/.f64 (expm1.f64 x) (expm1.f64 x)))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))
(.f64 (/.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) (expm1.f64 (+.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (+.f64 x x))) #s(literal 1 binary64)) (exp.f64 (+.f64 x x)))) (/.f64 #s(literal 1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64)))))
(.f64 (pow.f64 (/.f64 (expm1.f64 x) (expm1.f64 (.f64 #s(literal 2 binary64) (+.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (+.f64 x x)) #s(literal -1 binary64))))
(.f64 (pow.f64 (/.f64 (expm1.f64 x) (expm1.f64 (.f64 (+.f64 x x) #s(literal 3 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (+.f64 x x))) #s(literal 1 binary64)) (exp.f64 (+.f64 x x)))))
(.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 (exp.f64 x) #s(literal -1 binary64))))))
(.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (.f64 x #s(literal 3 binary64)))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 (exp.f64 x) #s(literal -1 binary64))))
(.f64 (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) (+.f64 x x))) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (+.f64 x x)) #s(literal -1 binary64))))
(.f64 (/.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (+.f64 x x))) #s(literal 1 binary64)) (exp.f64 (+.f64 x x)))))
(.f64 (.f64 (+.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x))) (-.f64 (exp.f64 x) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))))
(.f64 (-.f64 (.f64 (exp.f64 (.f64 (+.f64 x x) #s(literal 3 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 (exp.f64 (.f64 #s(literal 2 binary64) (+.f64 x x))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64)) (+.f64 (pow.f64 (expm1.f64 x) #s(literal -2 binary64)) (/.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (expm1.f64 x))))))
(.f64 (+.f64 #s(literal 1 binary64) (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)))))
(.f64 (neg.f64 (-.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (+.f64 (neg.f64 (expm1.f64 x)) (exp.f64 (+.f64 x x)))))
(*.f64 (fma.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x) (neg.f64 (expm1.f64 x))) (/.f64 #s(literal 1 binary64) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))))
(*.f64 (-.f64 (exp.f64 (+.f64 x x)) #s(literal -1 binary64)) (/.f64 (/.f64 #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)))))
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(/.f64 (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal -1 binary64)) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))) (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))) (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x))))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))) (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))) (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x))) (fma.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))) (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))))
(fma.f64 (.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 x x) #s(literal -1/4 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))) #s(literal 1 binary64))
(fma.f64 (.f64 (fma.f64 #s(literal 1/216 binary64) (.f64 (.f64 x x) x) #s(literal 1/8 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/12 binary64))))) #s(literal 1 binary64))
(fma.f64 (.f64 x (fma.f64 #s(literal 1/36 binary64) (.f64 x x) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))) #s(literal 1 binary64))
(fma.f64 (.f64 x (fma.f64 #s(literal 1/216 binary64) (.f64 (.f64 x x) x) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/12 binary64))))) #s(literal 1 binary64))
(fma.f64 (.f64 (.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)))))
(fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64))
(fma.f64 x (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x))) (/.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x))))
(-.f64 (/.f64 (.f64 (.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64))))
(+.f64 (/.f64 (.f64 (.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)))))
(+.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x))
(.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/36 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/6 binary64) x))))
(.f64 (neg.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 x x) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64))))
(.f64 (neg.f64 (fma.f64 #s(literal 1/216 binary64) (.f64 (.f64 x x) x) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/12 binary64)))))))
(.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 x x) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))))
(.f64 (fma.f64 #s(literal 1/216 binary64) (.f64 (.f64 x x) x) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (*.f64 x #s(literal -1/12 binary64))))))
(.f64 (fma.f64 #s(literal 1/216 binary64) (.f64 (.f64 x x) x) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/12 binary64))))))
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 #s(literal 1/36 binary64) (.f64 x x)) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))) (/.f64 (.f64 #s(literal 1/36 binary64) (.f64 x x)) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64)))) (.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64))))) (+.f64 (/.f64 (.f64 #s(literal 1/36 binary64) (.f64 x x)) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/36 binary64) (.f64 x x)) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 #s(literal 1/36 binary64) (.f64 x x)) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))) (/.f64 (.f64 #s(literal 1/36 binary64) (.f64 x x)) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))) (fma.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64))) (.f64 (/.f64 (.f64 #s(literal 1/36 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/36 binary64) (.f64 x x)))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) x))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/36 binary64) (*.f64 x x) #s(literal -1/4 binary64)))) (neg.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/216 binary64) (.f64 (.f64 x x) x) #s(literal 1/8 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/36 binary64) (.f64 x x)) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))) (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64)) #s(literal 1/4 binary64))) (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64)) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/36 binary64) (.f64 x x))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) x)))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/36 binary64) (*.f64 x x) #s(literal -1/4 binary64))) (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/216 binary64) (.f64 (.f64 x x) x) #s(literal 1/8 binary64))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (.f64 x #s(literal -1/12 binary64))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/216 binary64) (.f64 (.f64 x x) x) #s(literal 1/8 binary64))) (neg.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64))))))
(/.f64 (fma.f64 #s(literal 1/36 binary64) (*.f64 x x) #s(literal -1/4 binary64)) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64)))
(/.f64 (fma.f64 #s(literal 1/216 binary64) (.f64 (.f64 x x) x) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (.f64 x #s(literal -1/12 binary64)))))
(/.f64 (fma.f64 #s(literal 1/216 binary64) (.f64 (.f64 x x) x) #s(literal 1/8 binary64)) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/6 binary64) x)) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/36 binary64) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (.f64 x #s(literal -1/12 binary64)))) (fma.f64 #s(literal 1/216 binary64) (.f64 (.f64 x x) x) #s(literal 1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)))))
(fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)))))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/6 binary64) x))) (/.f64 (.f64 #s(literal 1/36 binary64) (.f64 x x)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/6 binary64) x))))
(-.f64 (/.f64 (.f64 #s(literal 1/36 binary64) (.f64 x x)) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))) (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64))))
(+.f64 (/.f64 (.f64 #s(literal 1/36 binary64) (.f64 x x)) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)))))
(+.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) x))

eval135.0ms (2%)

Memory: -2.9MiB live, 160.7MiB allocated
Compiler: Compiled 12 669 to 1 617 computations (87.2% saved)

prune87.0ms (1.3%)

Memory

-25.3MiB live, 181.3MiB allocated

Pruning

13 alts after pruning (8 fresh and 5 done)

	Pruned	Kept	Total
New	630	8	638
Fresh	0	0	0
Picked	0	5	5
Done	0	0	0
Total	630	13	643

Accuracy

100.0%

Counts

643 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓	63.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
	63.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 1/36 binary64) (*.f64 x x) #s(literal -1/4 binary64)) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
✓	64.5%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
✓	62.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64))))
▶	2.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x))))
	3.4%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))))
▶	2.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64)))))
	3.9%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) x))))
▶	5.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
✓	68.7%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
▶	63.3%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64))))
▶	64.3%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 253 to 154 computations (39.1% saved)

simplify140.0ms (2.1%)

Memory

35.0MiB live, 108.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	(fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64))))
cost-diff	1344	(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
cost-diff	0	(fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x)
cost-diff	0	#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x))
cost-diff	0	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x)))
cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x))))
cost-diff	0	(.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64))
cost-diff	0	#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64)))
cost-diff	0	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64))))
cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64)))))
cost-diff	0	(.f64 (.f64 x x) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
cost-diff	0	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))
cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))

Rules

12 754×	`lower-fma.f32`
12 740×	`lower-fma.f64`
2 220×	`lower-*.f32`
2 210×	`lower-*.f64`
2 206×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	423
0	74	417
1	133	407
2	251	407
3	376	405
4	676	365
5	905	345
6	1190	345
7	1622	345
8	3838	345
9	7386	345
0	8282	330

Stop Event

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

Calls

Call 1

Inputs
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
#s(literal 3/16 binary64)
#s(literal 1/2 binary64)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))
#s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(*.f64 x x)
x
#s(literal 1/2 binary64)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64)))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64))))
#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64)))
(.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64))
(.f64 (.f64 x x) x)
(*.f64 x x)
x
#s(literal 1/6 binary64)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x)))
#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x))
(fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x)
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
#s(literal 1/6 binary64)
x
#s(literal 1/2 binary64)
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
#s(literal 7/192 binary64)
#s(literal 3/16 binary64)
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
#s(literal 1/2 binary64)

Outputs
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
#s(literal 3/16 binary64)
#s(literal 1/2 binary64)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))
#s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(*.f64 x x)
x
#s(literal 1/2 binary64)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64)))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64))))
#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64)))
(.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64))
(.f64 (.f64 x x) x)
(*.f64 x x)
x
#s(literal 1/6 binary64)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x)))
#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x))
(fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x)
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
#s(literal 1/6 binary64)
x
#s(literal 1/2 binary64)
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
#s(literal 7/192 binary64)
#s(literal 3/16 binary64)
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
#s(literal 1/2 binary64)

localize142.0ms (2.1%)

Memory

0.3MiB live, 119.7MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.1953125	(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
accuracy	0.5	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	1.0	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
accuracy	23.507022720355103	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.05859375	(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
accuracy	0.12109375	(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
accuracy	23.523794534384088	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x)))
accuracy	39.07421553823167	#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x))
accuracy	0.10546875	(.f64 (.f64 x x) x)
accuracy	0.140625	(.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64))
accuracy	23.523794534384088	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64))))
accuracy	39.938028777125155	#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64)))
accuracy	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
accuracy	0.01171875	(.f64 (.f64 x x) #s(literal 1/2 binary64))
accuracy	22.87821169070813	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))
accuracy	39.45485591825946	#s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.08203125	(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.5	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	22.83464961300175	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))

Samples

97.0ms	231×	0	valid
8.0ms	11×	2	valid
8.0ms	14×	1	valid

Compiler

Compiled 266 to 43 computations (83.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 77.0ms

ival-add: 29.0ms (37.7% of total)

ival-mult: 26.0ms (33.8% of total)

const: 7.0ms (9.1% of total)

ival-div: 5.0ms (6.5% of total)

adjust: 3.0ms (3.9% of total)

ival-sqrt: 3.0ms (3.9% of total)

ival-expm1: 3.0ms (3.9% of total)

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

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

exact: 0.0ms (0% of total)

series34.0ms (0.5%)

Memory

-10.8MiB live, 24.9MiB allocated

Counts

24 → 264

Calls

Call 1

Inputs
#s(alt #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (patch (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(literal 2 binary64)) (patch (sqrt.f64 #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (patch #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (.f64 x x) x) #s(literal 1/6 binary64))))) (patch (sqrt.f64 #s(approx (/ (- (exp ( 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64))))) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (.f64 x x) x) #s(literal 1/6 binary64)))) (patch #s(approx (/ (- (exp ( 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (.f64 x x) x) #s(literal 1/6 binary64))) (patch #s(approx (+ ( (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (.f64 x x) x) #s(literal 1/6 binary64)) (patch (.f64 (.f64 (.f64 x x) x) #s(literal 1/6 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x)))) (patch (sqrt.f64 #s(approx (/ (- (exp ( 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x)))) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x))) (patch #s(approx (/ (- (exp ( 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x)) (patch #s(approx (+ ( (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x) (patch (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x) #<representation binary64>) () ())
#s(alt (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (patch (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64))) (patch (fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (patch (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (sqrt 2) (taylor 0 x) (#s(alt #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
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#s(alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))) (taylor 0 x) (#s(alt #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(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)))))) (taylor 0 x) (#s(alt #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt 2) (taylor 0 x) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (patch (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) (taylor 0 x) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (patch (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))) (taylor 0 x) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (patch (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))) (taylor 0 x) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (patch (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ x (sqrt 2)) (taylor 0 x) (#s(alt (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ x (sqrt 2)) (taylor 0 x) (#s(alt (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ x (sqrt 2)) (taylor 0 x) (#s(alt (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ x (sqrt 2)) (taylor 0 x) (#s(alt (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (sqrt 2) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(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)))))) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt 2 (taylor 0 x) (#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 2 x) (taylor 0 x) (#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) (taylor 0 x) (#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt 2 (taylor 0 x) (#s(alt #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (patch #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 2 x) (taylor 0 x) (#s(alt #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (patch #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#s(alt #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (patch #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#s(alt #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (patch #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (.f64 x x) #s(literal 1/2 binary64)) (patch (.f64 (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt 2) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (.f64 x x) x) #s(literal 1/6 binary64))))) (patch (sqrt.f64 #s(approx (/ (- (exp ( 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2)))) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (.f64 x x) x) #s(literal 1/6 binary64))))) (patch (sqrt.f64 #s(approx (/ (- (exp ( 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (.f64 x x) x) #s(literal 1/6 binary64))))) (patch (sqrt.f64 #s(approx (/ (- (exp ( 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64))))) #<representation binary64>) () ())) ())
#s(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)))))) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (.f64 x x) x) #s(literal 1/6 binary64))))) (patch (sqrt.f64 #s(approx (/ (- (exp ( 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64))))) #<representation binary64>) () ())) ())
#s(alt 2 (taylor 0 x) (#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (.f64 x x) x) #s(literal 1/6 binary64)))) (patch #s(approx (/ (- (exp ( 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 2 x) (taylor 0 x) (#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (.f64 x x) x) #s(literal 1/6 binary64)))) (patch #s(approx (/ (- (exp ( 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (.f64 x x) x) #s(literal 1/6 binary64)))) (patch #s(approx (/ (- (exp ( 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) (taylor 0 x) (#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (.f64 x x) x) #s(literal 1/6 binary64)))) (patch #s(approx (/ (- (exp ( 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64)))) #<representation binary64>) () ())) ())
#s(alt 2 (taylor 0 x) (#s(alt #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (.f64 x x) x) #s(literal 1/6 binary64))) (patch #s(approx (+ ( (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 2 x) (taylor 0 x) (#s(alt #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (.f64 x x) x) #s(literal 1/6 binary64))) (patch #s(approx (+ ( (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x)) (patch #s(approx (+ ( (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6))) (taylor -inf x) (#s(alt #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x)) (patch #s(approx (+ ( (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (pow x 3)) (taylor -inf x) (#s(alt (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x) (patch (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x) (patch (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x) (patch (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x) (patch (fma.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x) #<representation binary64>) () ())) ())
#s(alt (* 7/192 (/ (pow x 2) (sqrt 2))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (patch (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (patch (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2)))))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (patch (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2)))))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (patch (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 7/192 (/ (pow x 3) (sqrt 2))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64))) (patch (fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64))) (patch (fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2)))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64))) (patch (fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2)))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64))) (patch (fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/6 (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/6 (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/6 (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor -inf x) (#s(alt (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 7/192 x) (taylor -inf x) (#s(alt (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (patch (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 7/192 (* 3/16 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (patch (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 7/192 (* 3/16 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (patch (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 7/192 (* 3/16 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (patch (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

15.0ms

inf

((sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (sqrt 2)) (/ x (sqrt 2)) (sqrt 2) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* 1/2 x) 1) x) 2) (* (* x x) 1/2) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (* (* (* x x) x) 1/6) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (+ (* (* (+ (* 1/6 x) 1/2) x) x) x) (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (* (* x x) x) (+ (* 1/6 x) 1/2) (* (+ (* 1/6 x) 1/2) x) (/ 1/2 (sqrt 2)) (+ (* 7/192 x) 3/16))

4.0ms

-inf

((sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (sqrt 2)) (/ x (sqrt 2)) (sqrt 2) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* 1/2 x) 1) x) 2) (* (* x x) 1/2) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (* (* (* x x) x) 1/6) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (+ (* (* (+ (* 1/6 x) 1/2) x) x) x) (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (* (* x x) x) (+ (* 1/6 x) 1/2) (* (+ (* 1/6 x) 1/2) x) (/ 1/2 (sqrt 2)) (+ (* 7/192 x) 3/16))

4.0ms

((sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (sqrt 2)) (/ x (sqrt 2)) (sqrt 2) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* 1/2 x) 1) x) 2) (* (* x x) 1/2) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (* (* (* x x) x) 1/6) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (+ (* (* (+ (* 1/6 x) 1/2) x) x) x) (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (* (* x x) x) (+ (* 1/6 x) 1/2) (* (+ (* 1/6 x) 1/2) x) (/ 1/2 (sqrt 2)) (+ (* 7/192 x) 3/16))

simplify410.0ms (6.2%)

Memory

-11.2MiB live, 136.7MiB allocated

Algorithm

1×	egg-herbie

Rules

20 158×	`lower-fma.f64`
20 158×	`lower-fma.f32`
5 028×	`lower-*.f64`
5 028×	`lower-*.f32`
3 404×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	162	2698
1	540	2475
2	1635	2364
3	4902	2332
0	8143	1927

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 263

Calls

Call 1

Inputs
(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 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))))))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 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))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* 1/2 x))))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (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))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(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))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(/ 1/2 (sqrt 2))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))
(+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 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 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(* 1/2 x)
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
3/16
(+ 3/16 (* 7/192 x))
(+ 3/16 (* 7/192 x))
(+ 3/16 (* 7/192 x))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(* 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)))))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (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))
(* 1/2 (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))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (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))
(* 1/6 (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))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (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))
(* 1/6 (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))))
(* (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)))))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* 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 (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))))
(* 7/192 x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(* 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)))))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (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))
(* 1/2 (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))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (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))
(* 1/6 (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)))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (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))
(* 1/6 (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)))
(* 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)) x)) 1/6)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* 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 (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))))
(* 7/192 x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))

Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (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))))))
(fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 #s(literal 3/16 binary64) x #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 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (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))))))
(fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x #s(literal 2 binary64))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (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))))))
(fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(* 1/6 (pow x 3))
(.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64))
(* 1/6 (pow x 3))
(.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64))
(* 1/6 (pow x 3))
(.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64))
(* 1/6 (pow x 3))
(.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (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))))))
(fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
x
(* x (+ 1 (* 1/2 x)))
(fma.f64 (*.f64 x x) #s(literal 1/2 binary64) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)
(/ 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 (fma.f64 #s(literal 3/8 binary64) x #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))
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(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(* 1/6 (pow x 3))
(.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(.f64 (.f64 (*.f64 (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) x) #s(literal -1/6 binary64)) x) x) x)
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(.f64 (.f64 (.f64 (-.f64 (/.f64 (+.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) x)) x) #s(literal -1/6 binary64)) x) x) x)
(* 1/6 (pow x 3))
(.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64))
(* 1/6 (pow x 3))
(.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64))
(* 1/6 (pow x 3))
(.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64))
(* 1/6 (pow x 3))
(.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(* 1/6 (pow x 3))
(.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(.f64 (.f64 (*.f64 (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) x) #s(literal -1/6 binary64)) x) x) x)
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(.f64 (.f64 (.f64 (-.f64 (/.f64 (+.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) x)) x) #s(literal -1/6 binary64)) x) x) x)
(* 1/6 (pow x 3))
(.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(.f64 (.f64 (*.f64 (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) x) #s(literal -1/6 binary64)) x) x) x)
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(.f64 (.f64 (*.f64 (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) x) #s(literal -1/6 binary64)) x) x) x)
(* 7/192 (/ (pow x 2) (sqrt 2)))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 7/192 binary64))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) x)) x) x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) x)) x) x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(.f64 (.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 7/192 binary64)) x)
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(.f64 (.f64 (-.f64 (/.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) x) (/.f64 #s(literal -7/192 binary64) (sqrt.f64 #s(literal 2 binary64)))) x) (*.f64 x x))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(.f64 (.f64 (-.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x x))) x) (/.f64 #s(literal -7/192 binary64) (sqrt.f64 #s(literal 2 binary64)))) x) (*.f64 x x))
(pow x 3)
(.f64 (.f64 x x) x)
(pow x 3)
(.f64 (.f64 x x) x)
(pow x 3)
(.f64 (.f64 x x) x)
(pow x 3)
(.f64 (.f64 x x) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
(* 7/192 x)
(*.f64 #s(literal 7/192 binary64) x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))

rewrite229.0ms (3.4%)

Memory

-3.8MiB live, 310.2MiB allocated

Rules

5 018×	`lower-*.f32`
5 008×	`lower-*.f64`
3 900×	`lower-/.f32`
3 896×	`lower-/.f64`
3 614×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	391
0	74	375
1	311	319
2	2600	315
0	8683	303

Stop Event

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

Counts

24 → 596

Calls

Call 1

Inputs
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))
#s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64)))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64))))
#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64)))
(.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x)))
#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x))
(fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x)
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))
(.f64 (.f64 x x) x)
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))

Outputs
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x) (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x)) #s(literal 1/2 binary64) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x) (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x)) (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x)) #s(literal 1/2 binary64) #s(literal 4 binary64)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x) (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x)) #s(literal 1/2 binary64) (-.f64 #s(literal 2 binary64) (.f64 (*.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))))))
(pow.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x) (*.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x)) #s(literal 1/2 binary64) #s(literal -2 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x) (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x)) #s(literal 1/2 binary64) (-.f64 #s(literal 2 binary64) (.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (fma.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x) (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x)) (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x)) #s(literal 1/2 binary64) #s(literal 4 binary64)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x) (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x)) #s(literal 1/2 binary64)) (fma.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (.f64 (fma.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))) (*.f64 (fma.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (-.f64 #s(literal 2 binary64) (.f64 (.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x) (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x)) #s(literal 1/2 binary64))) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x) (*.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x)) #s(literal 1/2 binary64) #s(literal -2 binary64))) (neg.f64 (fma.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (neg.f64 (/.f64 (fma.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x) (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x)) (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x)) #s(literal 1/2 binary64) #s(literal 4 binary64)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64)))) (neg.f64 (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x) (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x)) #s(literal 1/2 binary64) (-.f64 #s(literal 2 binary64) (.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))))))
(/.f64 (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x) (*.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x)) #s(literal 1/2 binary64) #s(literal -2 binary64)) (fma.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (/.f64 (fma.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x) (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x)) (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x)) #s(literal 1/2 binary64) #s(literal 4 binary64)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))) (+.f64 #s(literal 2 binary64) (-.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x) (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x)) #s(literal 1/2 binary64)) (.f64 (*.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (/.f64 (fma.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x) (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x)) (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x)) #s(literal 1/2 binary64) #s(literal 4 binary64)) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))) (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x) (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x)) #s(literal 1/2 binary64) (-.f64 #s(literal 2 binary64) (.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))))
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(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)))
(.f64 (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) #s(literal -9/256 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 7/192 binary64) x #s(literal -3/16 binary64))))
(.f64 (fma.f64 #s(literal 343/7077888 binary64) (.f64 (.f64 x x) x) #s(literal 27/4096 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) (-.f64 #s(literal 9/256 binary64) (*.f64 x #s(literal 7/1024 binary64))))))
(pow.f64 (/.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal -3/16 binary64)) (fma.f64 #s(literal 49/36864 binary64) (*.f64 x x) #s(literal -9/256 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) (-.f64 #s(literal 9/256 binary64) (.f64 x #s(literal 7/1024 binary64)))) (fma.f64 #s(literal 343/7077888 binary64) (.f64 (.f64 x x) x) #s(literal 27/4096 binary64))) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 49/36864 binary64) (.f64 x x)) (fma.f64 #s(literal 7/192 binary64) x #s(literal -3/16 binary64))) (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal -3/16 binary64)) #s(literal 9/256 binary64))) (*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal -3/16 binary64)) (fma.f64 #s(literal 7/192 binary64) x #s(literal -3/16 binary64))))
(/.f64 (-.f64 #s(literal 9/256 binary64) (.f64 #s(literal 49/36864 binary64) (.f64 x x))) (-.f64 #s(literal 3/16 binary64) (*.f64 #s(literal 7/192 binary64) x)))
(/.f64 (neg.f64 (fma.f64 #s(literal 49/36864 binary64) (*.f64 x x) #s(literal -9/256 binary64))) (neg.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal -3/16 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 343/7077888 binary64) (.f64 (.f64 x x) x) #s(literal 27/4096 binary64))) (neg.f64 (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) (-.f64 #s(literal 9/256 binary64) (.f64 x #s(literal 7/1024 binary64))))))
(/.f64 (fma.f64 #s(literal 49/36864 binary64) (*.f64 x x) #s(literal -9/256 binary64)) (fma.f64 #s(literal 7/192 binary64) x #s(literal -3/16 binary64)))
(/.f64 (fma.f64 #s(literal 343/7077888 binary64) (.f64 (.f64 x x) x) #s(literal 27/4096 binary64)) (+.f64 #s(literal 9/256 binary64) (-.f64 (.f64 #s(literal 49/36864 binary64) (.f64 x x)) (*.f64 x #s(literal 7/1024 binary64)))))
(/.f64 (fma.f64 #s(literal 343/7077888 binary64) (.f64 (.f64 x x) x) #s(literal 27/4096 binary64)) (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) (-.f64 #s(literal 9/256 binary64) (.f64 x #s(literal 7/1024 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal -3/16 binary64)) (fma.f64 #s(literal 49/36864 binary64) (*.f64 x x) #s(literal -9/256 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) (-.f64 #s(literal 9/256 binary64) (.f64 x #s(literal 7/1024 binary64)))) (fma.f64 #s(literal 343/7077888 binary64) (.f64 (.f64 x x) x) #s(literal 27/4096 binary64))))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(-.f64 (/.f64 (.f64 #s(literal 49/36864 binary64) (.f64 x x)) (fma.f64 #s(literal 7/192 binary64) x #s(literal -3/16 binary64))) (/.f64 #s(literal 9/256 binary64) (fma.f64 #s(literal 7/192 binary64) x #s(literal -3/16 binary64))))
(+.f64 (*.f64 #s(literal 7/192 binary64) x) #s(literal 3/16 binary64))
(+.f64 #s(literal 3/16 binary64) (*.f64 #s(literal 7/192 binary64) x))

eval160.0ms (2.4%)

Memory: 23.2MiB live, 291.9MiB allocated
Compiler: Compiled 26 104 to 2 491 computations (90.5% saved)

prune291.0ms (4.4%)

Memory

1.9MiB live, 257.8MiB allocated

Pruning

18 alts after pruning (11 fresh and 7 done)

	Pruned	Kept	Total
New	906	10	916
Fresh	2	1	3
Picked	3	2	5
Done	0	5	5
Total	911	18	929

Accuracy

100.0%

Counts

929 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓	63.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
✓	64.5%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
✓	62.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64))))
▶	2.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x))))
▶	3.9%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) x x))))
	3.4%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))))
✓	2.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64)))))
✓	5.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
✓	68.7%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
	63.3%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) x (sqrt.f64 #s(literal 2 binary64))))
	63.3%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (.f64 (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) #s(literal -9/256 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal -3/16 binary64)) #s(literal 1/2 binary64))) (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal -3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64))))
▶	63.3%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
	61.5%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 #s(approx (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))) x (sqrt.f64 #s(literal 2 binary64))))
▶	3.9%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))))
	4.4%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (sqrt 2)) (.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)))
▶	3.2%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))))
	2.4%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 7/192 binary64)) x)))

Compiler

Compiled 409 to 243 computations (40.6% saved)

simplify152.0ms (2.3%)

Memory

-3.3MiB live, 153.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
cost-diff	0	(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
cost-diff	0	#s(approx (+ (* (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))))
cost-diff	0	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))))
cost-diff	0	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
cost-diff	0	#s(approx (+ (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))))
cost-diff	0	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))))
cost-diff	0	(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x)
cost-diff	0	#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x))
cost-diff	0	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x)))
cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x))))
cost-diff	0	(fma.f64 (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) x x)
cost-diff	0	#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) x x))
cost-diff	0	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) x x)))
cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) x x))))
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	(fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
cost-diff	320	(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))

Rules

12 778×	`lower-fma.f32`
12 764×	`lower-fma.f64`
2 256×	`lower-*.f32`
2 244×	`lower-*.f64`
2 182×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	500
0	88	500
1	170	488
2	385	478
3	778	478
4	1218	443
5	1344	429
6	1421	429
7	1818	429
8	4032	429
9	7606	429
0	8130	421

Stop Event

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

Calls

Call 1

Inputs
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
#s(literal 1 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64))
x
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
#s(literal 7/192 binary64)
#s(literal 3/16 binary64)
#s(literal 1/2 binary64)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) x x))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) x x)))
#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) x x))
(fma.f64 (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) x x)
(.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x)
#s(approx (+ (* 1/6 x) 1/2) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
x
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x)))
#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x)
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
#s(literal 1/6 binary64)
x
#s(literal 1/2 binary64)
(*.f64 x x)
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))))
#s(approx (+ (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
#s(literal 3/16 binary64)
#s(literal 1/2 binary64)
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))))
#s(approx (+ (* (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
#s(literal 7/192 binary64)
#s(literal 3/16 binary64)

Outputs
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 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 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
#s(literal 1 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64))
(fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64))
x
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
#s(literal 7/192 binary64)
#s(literal 3/16 binary64)
#s(literal 1/2 binary64)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) x x))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) x x)))
#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) x x))
(fma.f64 (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) x x)
(.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x)
#s(approx (+ (* 1/6 x) 1/2) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
x
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 x x) (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x)))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 x x) (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)))
#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x))
#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 x x) (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x)
(fma.f64 (*.f64 x x) (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
#s(literal 1/6 binary64)
x
#s(literal 1/2 binary64)
(*.f64 x x)
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (sqrt 2)) (*.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))))
#s(approx (+ (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (sqrt 2)) (*.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(*.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
#s(literal 3/16 binary64)
#s(literal 1/2 binary64)
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))) x)))
#s(approx (+ (* (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))))
#s(approx (+ (* (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))) x))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))) x)
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
#s(literal 7/192 binary64)
#s(literal 3/16 binary64)

localize156.0ms (2.3%)

Memory

-33.2MiB live, 194.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.1953125	(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
accuracy	0.5	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	23.507022720355103	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))))
accuracy	38.91264876162589	#s(approx (+ (* (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))))
accuracy	0.1015625	(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
accuracy	0.5	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	22.83464961300175	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))))
accuracy	39.21220643462701	#s(approx (+ (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))))
accuracy	0.03515625	(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x)
accuracy	0.12109375	(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
accuracy	23.523794534384088	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x)))
accuracy	39.07421553823167	#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x))
accuracy	0.05859375	(.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x)
accuracy	23.523794534384088	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) x x)))
accuracy	24.606393497006856	#s(approx (+ (* 1/6 x) 1/2) #s(literal 1/2 binary64))
accuracy	39.07421553823167	#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) x x))
accuracy	0.07421875	(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
accuracy	0.1953125	(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
accuracy	1.0	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
accuracy	23.507022720355103	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))

Samples

86.0ms	231×	0	valid
10.0ms	14×	1	valid
9.0ms	11×	2	valid

Compiler

Compiled 307 to 46 computations (85% saved)

Precisions

Click to see histograms. Total time spent on operations: 84.0ms

ival-mult: 30.0ms (35.9% of total)

const: 22.0ms (26.3% of total)

ival-add: 15.0ms (17.9% of total)

ival-div: 7.0ms (8.4% of total)

adjust: 3.0ms (3.6% of total)

ival-sqrt: 3.0ms (3.6% of total)

ival-expm1: 3.0ms (3.6% of total)

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

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

exact: 0.0ms (0% of total)

series26.0ms (0.4%)

Memory

8.6MiB live, 45.8MiB allocated

Counts

24 → 276

Calls

Call 1

Inputs
#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (/ (- (exp ( 2 x)) 1) (- (exp x) 1))) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) x (sqrt.f64 #s(literal 2 binary64))) (patch (fma.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) x x)))) (patch (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) x x)))) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) x x))) (patch #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) x x))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) x x)) (patch #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) x x)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) x x) (patch (fma.f64 (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) x x) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (.f64 x x) x)))) (patch (sqrt.f64 #s(approx (/ (- (exp ( 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x)))) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (.f64 x x) x))) (patch #s(approx (/ (- (exp ( 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (.f64 x x) x)) (patch #s(approx (+ ( (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x)) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (.f64 x x) x) (patch (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (.f64 x x) x) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (sqrt 2)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))))) (patch #s(approx (sqrt (/ (- (exp ( 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (sqrt 2)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))) (patch #s(approx (+ ( (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) (patch (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))))) (patch #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))) (patch #s(approx (+ (* (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))) (patch (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (patch (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (patch (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (+ (* 1/6 x) 1/2) #s(literal 1/2 binary64)) (patch #s(approx (+ (* 1/6 x) 1/2) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) (patch (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (/ 1/2 (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
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#s(alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) (taylor -inf x) (#s(alt (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))) (patch (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2)))))) (taylor -inf x) (#s(alt (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))) (patch (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (pow x 2) (sqrt 2)) (taylor -inf x) (#s(alt (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (patch (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (/ (pow x 2) (sqrt 2)) (taylor -inf x) (#s(alt (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (patch (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (/ (pow x 2) (sqrt 2)) (taylor -inf x) (#s(alt (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (patch (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (/ (pow x 2) (sqrt 2)) (taylor -inf x) (#s(alt (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (patch (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* 7/192 x) (taylor -inf x) (#s(alt (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (patch (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 7/192 (* 3/16 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (patch (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 7/192 (* 3/16 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (patch (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 7/192 (* 3/16 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (patch (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor -inf x) (#s(alt #s(approx (+ (* 1/6 x) 1/2) #s(literal 1/2 binary64)) (patch #s(approx (+ (* 1/6 x) 1/2) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/6 (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt #s(approx (+ (* 1/6 x) 1/2) #s(literal 1/2 binary64)) (patch #s(approx (+ (* 1/6 x) 1/2) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/6 (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt #s(approx (+ (* 1/6 x) 1/2) #s(literal 1/2 binary64)) (patch #s(approx (+ (* 1/6 x) 1/2) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/6 (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt #s(approx (+ (* 1/6 x) 1/2) #s(literal 1/2 binary64)) (patch #s(approx (+ (* 1/6 x) 1/2) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) (patch (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) (patch (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) (patch (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) (patch (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/6 (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/6 (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/6 (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

5.0ms

-inf

((* (/ 1 (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (* (/ 1 (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) x) (sqrt 2)) (/ 1 (sqrt 2)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (+ (* (* (+ (* 1/6 x) 1/2) x) x) x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (+ (* (+ (* 1/6 x) 1/2) (* x x)) x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (sqrt 2)) (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (/ x (sqrt 2)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (* (* (/ x (sqrt 2)) x) (+ (* 7/192 x) 3/16)) (* (/ x (sqrt 2)) x) (+ (* 7/192 x) 3/16) (+ (* 1/6 x) 1/2) (* (+ (* 1/6 x) 1/2) x) (+ (* 1/6 x) 1/2))

3.0ms

inf

((* (/ 1 (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (* (/ 1 (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) x) (sqrt 2)) (/ 1 (sqrt 2)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (+ (* (* (+ (* 1/6 x) 1/2) x) x) x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (+ (* (+ (* 1/6 x) 1/2) (* x x)) x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (sqrt 2)) (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (/ x (sqrt 2)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (* (* (/ x (sqrt 2)) x) (+ (* 7/192 x) 3/16)) (* (/ x (sqrt 2)) x) (+ (* 7/192 x) 3/16) (+ (* 1/6 x) 1/2) (* (+ (* 1/6 x) 1/2) x) (+ (* 1/6 x) 1/2))

2.0ms

((* (/ 1 (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (* (/ 1 (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) x) (sqrt 2)) (/ 1 (sqrt 2)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (+ (* (* (+ (* 1/6 x) 1/2) x) x) x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (+ (* (+ (* 1/6 x) 1/2) (* x x)) x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (sqrt 2)) (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (/ x (sqrt 2)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (* (* (/ x (sqrt 2)) x) (+ (* 7/192 x) 3/16)) (* (/ x (sqrt 2)) x) (+ (* 7/192 x) 3/16) (+ (* 1/6 x) 1/2) (* (+ (* 1/6 x) 1/2) x) (+ (* 1/6 x) 1/2))

simplify182.0ms (2.7%)

Memory

23.4MiB live, 177.2MiB allocated

Algorithm

1×	egg-herbie

Rules

20 608×	`lower-fma.f64`
20 608×	`lower-fma.f32`
4 978×	`lower-*.f64`
4 978×	`lower-*.f32`
3 360×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	160	3090
1	530	2832
2	1600	2659
3	4773	2604
0	8054	2198

Stop Event

1×	iter limit
1×	node limit

Counts

276 → 274

Calls

Call 1

Inputs
(/ 1/2 (sqrt 2))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))
(+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 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 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 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))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 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))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 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 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))))))
(* 1/2 (/ x (sqrt 2)))
(* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))
(* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))
(* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 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 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
3/16
(+ 3/16 (* 7/192 x))
(+ 3/16 (* 7/192 x))
(+ 3/16 (* 7/192 x))
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(* 1/2 x)
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (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))
(* 1/6 (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))))
(* (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)))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (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))
(* 1/6 (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))))
(* (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)))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(* 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) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(* 7/192 x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 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))))
(* 1/6 (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 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (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))
(* 1/6 (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)))
(* 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)) x)) 1/6)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (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))
(* 1/6 (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)))
(* 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)) x)) 1/6)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(* 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)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(* 7/192 x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 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))))
(* 1/6 (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 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))

Outputs
(/ 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 (fma.f64 #s(literal 3/8 binary64) x #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 (/.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 (+ (* 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))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 (/.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 (+ (* 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))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
x
(* x (+ 1 (* 1/2 x)))
(fma.f64 (*.f64 x x) #s(literal 1/2 binary64) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 (/.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 (+ (* 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))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
x
(* x (+ 1 (* 1/2 x)))
(fma.f64 (*.f64 x x) #s(literal 1/2 binary64) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 (/.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 (+ (* 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))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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)))
(* 1/2 (/ x (sqrt 2)))
(*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
(* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 (/.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 (+ (* 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))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (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 (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) 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 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
(/ (pow x 2) (sqrt 2))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
(/ (pow x 2) (sqrt 2))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
(/ (pow x 2) (sqrt 2))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
(/ (pow x 2) (sqrt 2))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
3/16
#s(literal 3/16 binary64)
(+ 3/16 (* 7/192 x))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(+ 3/16 (* 7/192 x))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(+ 3/16 (* 7/192 x))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/6 x))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(+ 1/2 (* 1/6 x))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(+ 1/2 (* 1/6 x))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/6 x)))
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* 1/6 x)))
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* 1/6 x)))
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/6 x))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(+ 1/2 (* 1/6 x))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(+ 1/2 (* 1/6 x))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 7/192 binary64))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
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(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(* 1/6 (pow x 3))
(.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(.f64 (.f64 (*.f64 (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) x) #s(literal -1/6 binary64)) x) x) x)
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(.f64 (.f64 (.f64 (-.f64 (/.f64 (+.f64 (+.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) x)) x) #s(literal -1/6 binary64)) x) x) x)
(* 1/6 (pow x 3))
(.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(.f64 (.f64 (*.f64 (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) x) #s(literal -1/6 binary64)) x) x) x)
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(.f64 (.f64 (*.f64 (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) x) #s(literal -1/6 binary64)) x) x) x)
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 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)))))
(.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x x)) x (*.f64 (fma.f64 #s(literal 3/8 binary64) x #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))) x)
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x x)) x (*.f64 (fma.f64 #s(literal 3/8 binary64) x #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))) x)
(* 3/16 (/ (pow x 2) (sqrt 2)))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 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) (+ (* 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) (+ (* 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)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(.f64 (.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) x) #s(literal 7/192 binary64))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(.f64 (.f64 (-.f64 (/.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) x) (/.f64 #s(literal -7/192 binary64) (sqrt.f64 #s(literal 2 binary64)))) x) (*.f64 x x))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(.f64 (.f64 (-.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x x))) x) (/.f64 #s(literal -7/192 binary64) (sqrt.f64 #s(literal 2 binary64)))) x) (*.f64 x x))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(.f64 (.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) x) #s(literal 7/192 binary64))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
(/ (pow x 2) (sqrt 2))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
(/ (pow x 2) (sqrt 2))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
(/ (pow x 2) (sqrt 2))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
(/ (pow x 2) (sqrt 2))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
(* 7/192 x)
(*.f64 #s(literal 7/192 binary64) x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))

rewrite172.0ms (2.6%)

Memory

14.8MiB live, 207.8MiB allocated

Rules

5 540×	`lower-*.f32`
5 528×	`lower-*.f64`
3 324×	`lower-/.f32`
3 320×	`lower-/.f64`
2 806×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	453
0	88	453
1	360	381
2	3069	381
0	8721	373

Stop Event

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

Counts

24 → 354

Calls

Call 1

Inputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) x x))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) x x)))
#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) x x))
(fma.f64 (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) x x)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x)))
#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x)
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))))
#s(approx (+ (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))))
#s(approx (+ (* (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
#s(approx (+ (* 1/6 x) 1/2) #s(literal 1/2 binary64))
(.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x)
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))

Outputs
(.f64 (fma.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))) #s(literal 1/2 binary64) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))) #s(literal 1/2 binary64)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))) (.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))) #s(literal 1/2 binary64) (-.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) #s(literal 1/2 binary64)) #s(literal 2 binary64))))))
(*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #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))) (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(pow.f64 (/.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 (.f64 (*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))) #s(literal 1/2 binary64) #s(literal -1/8 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))) #s(literal 1/2 binary64) (-.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) #s(literal 1/2 binary64)) #s(literal 2 binary64)))) (fma.f64 (.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))) #s(literal 1/2 binary64)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))) (*.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64))) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))) #s(literal 1/2 binary64)) (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64))) (*.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) (*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal -1/2 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))) (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) #s(literal 1/2 binary64)))))
(/.f64 (*.f64 #s(literal -1 binary64) (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
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(/.f64 (.f64 (.f64 x x) (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) #s(literal -9/256 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 7/192 binary64) x #s(literal -3/16 binary64))))
(/.f64 (.f64 (.f64 x x) (fma.f64 #s(literal 343/7077888 binary64) (.f64 (.f64 x x) x) #s(literal 27/4096 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) (-.f64 #s(literal 9/256 binary64) (*.f64 x #s(literal 7/1024 binary64))))))
(/.f64 (.f64 (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) #s(literal -9/256 binary64)) (.f64 x x)) (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal -3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 (fma.f64 #s(literal 343/7077888 binary64) (.f64 (.f64 x x) x) #s(literal 27/4096 binary64)) (.f64 x x)) (.f64 (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) (-.f64 #s(literal 9/256 binary64) (*.f64 x #s(literal 7/1024 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) x) #s(literal 7/192 binary64) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) x))
(fma.f64 (.f64 (.f64 #s(literal 3/16 binary64) x) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) x) #s(literal 7/192 binary64)))
(fma.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) x (.f64 (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) x) #s(literal 7/192 binary64)))
(fma.f64 (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 7/192 binary64)) x (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) x))
(fma.f64 (.f64 (.f64 #s(literal 7/192 binary64) x) x) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) x))
(fma.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (.f64 #s(literal 7/192 binary64) x) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) x))
(fma.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64) (.f64 (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) x) #s(literal 7/192 binary64)))
(fma.f64 (.f64 #s(literal 7/192 binary64) x) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) x))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal 7/192 binary64) x) x) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) x))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (.f64 #s(literal 3/16 binary64) x) (.f64 (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) x) #s(literal 7/192 binary64)))
(fma.f64 (.f64 #s(literal 3/16 binary64) x) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) x) #s(literal 7/192 binary64)))
(fma.f64 #s(literal 3/16 binary64) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (.f64 (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) x) #s(literal 7/192 binary64)))
(fma.f64 #s(literal 7/192 binary64) (.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) x))
(fma.f64 x (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 #s(literal 3/16 binary64) x)) (.f64 (.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) x) #s(literal 7/192 binary64)))
(fma.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) (.f64 (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) x) #s(literal 7/192 binary64)))
(fma.f64 x (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 7/192 binary64)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) x))
(+.f64 (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) x) (.f64 (.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) x) #s(literal 7/192 binary64)))
(+.f64 (.f64 (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) x) #s(literal 7/192 binary64)) (.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) x))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
(.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x)) #s(literal -1 binary64))
(/.f64 (*.f64 x (neg.f64 x)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(/.f64 (*.f64 x #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(/.f64 (*.f64 (neg.f64 x) x) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (*.f64 x x)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (/.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x)))
(exp.f64 (-.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) (.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64))))
(.f64 (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) #s(literal -9/256 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 7/192 binary64) x #s(literal -3/16 binary64))))
(.f64 (fma.f64 #s(literal 343/7077888 binary64) (.f64 (.f64 x x) x) #s(literal 27/4096 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) (-.f64 #s(literal 9/256 binary64) (*.f64 x #s(literal 7/1024 binary64))))))
(pow.f64 (/.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal -3/16 binary64)) (fma.f64 #s(literal 49/36864 binary64) (*.f64 x x) #s(literal -9/256 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) (-.f64 #s(literal 9/256 binary64) (.f64 x #s(literal 7/1024 binary64)))) (fma.f64 #s(literal 343/7077888 binary64) (.f64 (.f64 x x) x) #s(literal 27/4096 binary64))) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 49/36864 binary64) (.f64 x x)) (fma.f64 #s(literal 7/192 binary64) x #s(literal -3/16 binary64))) (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal -3/16 binary64)) #s(literal 9/256 binary64))) (*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal -3/16 binary64)) (fma.f64 #s(literal 7/192 binary64) x #s(literal -3/16 binary64))))
(/.f64 (-.f64 #s(literal 9/256 binary64) (.f64 #s(literal 49/36864 binary64) (.f64 x x))) (-.f64 #s(literal 3/16 binary64) (*.f64 #s(literal 7/192 binary64) x)))
(/.f64 (neg.f64 (fma.f64 #s(literal 49/36864 binary64) (*.f64 x x) #s(literal -9/256 binary64))) (neg.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal -3/16 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 343/7077888 binary64) (.f64 (.f64 x x) x) #s(literal 27/4096 binary64))) (neg.f64 (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) (-.f64 #s(literal 9/256 binary64) (.f64 x #s(literal 7/1024 binary64))))))
(/.f64 (fma.f64 #s(literal 49/36864 binary64) (*.f64 x x) #s(literal -9/256 binary64)) (fma.f64 #s(literal 7/192 binary64) x #s(literal -3/16 binary64)))
(/.f64 (fma.f64 #s(literal 343/7077888 binary64) (.f64 (.f64 x x) x) #s(literal 27/4096 binary64)) (+.f64 #s(literal 9/256 binary64) (-.f64 (.f64 #s(literal 49/36864 binary64) (.f64 x x)) (*.f64 x #s(literal 7/1024 binary64)))))
(/.f64 (fma.f64 #s(literal 343/7077888 binary64) (.f64 (.f64 x x) x) #s(literal 27/4096 binary64)) (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) (-.f64 #s(literal 9/256 binary64) (.f64 x #s(literal 7/1024 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal -3/16 binary64)) (fma.f64 #s(literal 49/36864 binary64) (*.f64 x x) #s(literal -9/256 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) (-.f64 #s(literal 9/256 binary64) (.f64 x #s(literal 7/1024 binary64)))) (fma.f64 #s(literal 343/7077888 binary64) (.f64 (.f64 x x) x) #s(literal 27/4096 binary64))))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(-.f64 (/.f64 (.f64 #s(literal 49/36864 binary64) (.f64 x x)) (fma.f64 #s(literal 7/192 binary64) x #s(literal -3/16 binary64))) (/.f64 #s(literal 9/256 binary64) (fma.f64 #s(literal 7/192 binary64) x #s(literal -3/16 binary64))))
(+.f64 (*.f64 #s(literal 7/192 binary64) x) #s(literal 3/16 binary64))
(+.f64 #s(literal 3/16 binary64) (*.f64 #s(literal 7/192 binary64) x))
#s(approx (+ (* 1/6 x) 1/2) #s(literal 1/2 binary64))
(.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x)
(.f64 x #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)))
(.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 x x) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))))
(.f64 (fma.f64 #s(literal 1/216 binary64) (.f64 (.f64 x x) x) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/12 binary64))))))
(pow.f64 (/.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64)) (fma.f64 #s(literal 1/36 binary64) (*.f64 x x) #s(literal -1/4 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64)))) (fma.f64 #s(literal 1/216 binary64) (.f64 (.f64 x x) x) #s(literal 1/8 binary64))) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/36 binary64) (.f64 x x)) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))) (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64)) #s(literal 1/4 binary64))) (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64)) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/36 binary64) (.f64 x x))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) x)))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/36 binary64) (*.f64 x x) #s(literal -1/4 binary64))) (neg.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/216 binary64) (.f64 (.f64 x x) x) #s(literal 1/8 binary64))) (neg.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64))))))
(/.f64 (fma.f64 #s(literal 1/36 binary64) (*.f64 x x) #s(literal -1/4 binary64)) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64)))
(/.f64 (fma.f64 #s(literal 1/216 binary64) (.f64 (.f64 x x) x) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 x x)) (*.f64 x #s(literal 1/12 binary64)))))
(/.f64 (fma.f64 #s(literal 1/216 binary64) (.f64 (.f64 x x) x) #s(literal 1/8 binary64)) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64)) (fma.f64 #s(literal 1/36 binary64) (*.f64 x x) #s(literal -1/4 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/12 binary64)))) (fma.f64 #s(literal 1/216 binary64) (.f64 (.f64 x x) x) #s(literal 1/8 binary64))))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(-.f64 (/.f64 (.f64 #s(literal 1/36 binary64) (.f64 x x)) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))))
(+.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/6 binary64) x))

eval83.0ms (1.2%)

Memory: 0.6MiB live, 153.0MiB allocated
Compiler: Compiled 13 337 to 1 180 computations (91.2% saved)

prune179.0ms (2.7%)

Memory

-16.6MiB live, 233.7MiB allocated

Pruning

19 alts after pruning (8 fresh and 11 done)

	Pruned	Kept	Total
New	683	6	689
Fresh	4	2	6
Picked	1	4	5
Done	0	7	7
Total	688	19	707

Accuracy

100.0%

Counts

707 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓	63.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
✓	64.5%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
✓	62.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64))))
✓	2.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x))))
✓	3.9%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) x x))))
	3.4%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))))
✓	2.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64)))))
✓	5.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
✓	68.7%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
	63.3%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
	63.3%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 4 binary64)) x (sqrt.f64 #s(literal 2 binary64))))
	63.1%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))) #s(literal 1/2 binary64))) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x)) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64))))
	63.3%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 7/192 binary64))) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
	61.5%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 #s(approx (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))) x (sqrt.f64 #s(literal 2 binary64))))
✓	3.9%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))))
	4.4%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))
✓	3.2%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))))
	2.4%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) x) #s(literal 7/192 binary64))))

Compiler

Compiled 674 to 266 computations (60.5% saved)

regimes24.0ms (0.4%)

Memory

15.0MiB live, 15.0MiB allocated

Counts

30 → 1

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) x x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64)))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (sqrt 2)) (.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 7/192 binary64)) x)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) x) #s(literal 7/192 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 #s(approx (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 1/36 binary64) (*.f64 x x) #s(literal -1/4 binary64)) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 4 binary64)) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))) #s(literal 1/2 binary64))) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x)) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 7/192 binary64))) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (.f64 (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) #s(literal -9/256 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal -3/16 binary64)) #s(literal 1/2 binary64))) (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal -3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64))))
(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:

8.0ms

7.0ms

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

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)

regimes54.0ms (0.8%)

Memory

-15.6MiB live, 23.0MiB allocated

Counts

28 → 2

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) x x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64)))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (sqrt 2)) (.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 7/192 binary64)) x)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) x) #s(literal 7/192 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 #s(approx (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (/.f64 (fma.f64 #s(literal 1/36 binary64) (*.f64 x x) #s(literal -1/4 binary64)) (fma.f64 #s(literal 1/6 binary64) x #s(literal -1/2 binary64))) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 4 binary64)) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))) #s(literal 1/2 binary64))) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x)) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 7/192 binary64))) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (.f64 (fma.f64 #s(literal 49/36864 binary64) (.f64 x x) #s(literal -9/256 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal -3/16 binary64)) #s(literal 1/2 binary64))) (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal -3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64))))

Outputs

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

#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))

Calls

3 calls:

38.0ms

(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

7.0ms

(/.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
70.5%	2	`x`
70.5%	2	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))`
70.5%	2	`(/.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)

regimes20.0ms (0.3%)

Memory

-10.1MiB live, 26.5MiB allocated

Counts

19 → 2

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (.f64 #s(approx (+ ( 1/6 x) 1/2) #s(literal 1/2 binary64)) x) x x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (*.f64 x x) x) #s(literal 1/6 binary64)))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (sqrt 2)) (.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (sqrt 2)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 7/192 binary64)) x)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) x) #s(literal 7/192 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 #s(approx (+ (* (/ x (sqrt 2)) (+ (* 7/192 x) 3/16)) (/ 1/2 (sqrt 2))) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))) x (sqrt.f64 #s(literal 2 binary64))))

Outputs

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

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

Calls

3 calls:

9.0ms

5.0ms

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

5.0ms

(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
70.5%	2	`x`
70.5%	2	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))`
70.5%	2	`(/.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)

regimes10.0ms (0.1%)

Memory

15.5MiB live, 15.5MiB allocated

Counts

10 → 2

Calls

Call 1

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

Outputs

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

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

Calls

3 calls:

3.0ms

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

3.0ms

(/.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
70.3%	2	`x`
70.3%	2	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))`
70.3%	2	`(/.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)

regimes6.0ms (0.1%)

Memory

10.6MiB live, 10.6MiB allocated

Accuracy

Total -43.0b remaining (-214.4%)

Threshold costs -43b (-214.4%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

3 calls:

2.0ms

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

2.0ms

(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
68.7%	1	`x`
68.7%	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))))`
68.7%	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)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0	1.999939102319364

Compiler

Compiled 16 to 14 computations (12.5% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0	1.999939102319364

Compiler

Compiled 16 to 14 computations (12.5% saved)

bsearch0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0	1.999939102319364

Compiler

Compiled 16 to 14 computations (12.5% saved)

simplify9.0ms (0.1%)

Memory

-25.7MiB live, 10.9MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	173
1	54	173
2	61	173
3	69	173
4	70	173

Stop Event

1×

saturated

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(if (<=.f64 (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 3/2 binary64)) (sqrt.f64 #s(approx (/ (- (exp ( 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))) #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 3/2 binary64)) (sqrt.f64 #s(approx (/ (- (exp ( 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))) (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)))))
(if (<=.f64 (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 3/2 binary64)) (sqrt.f64 #s(approx (/ (- (exp ( 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))) (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))

Outputs
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(if (<=.f64 (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 3/2 binary64)) (sqrt.f64 #s(approx (/ (- (exp ( 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))) #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 3/2 binary64)) (sqrt.f64 #s(approx (/ (- (exp ( 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))) (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)))))
(if (<=.f64 (/.f64 (-.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 3/2 binary64)) (sqrt.f64 #s(approx (/ (- (exp ( 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))) (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))

soundness1.0s (15.5%)

Memory

24.4MiB live, 609.0MiB allocated

Rules

20 158×	`lower-fma.f64`
20 158×	`lower-fma.f32`
18 226×	`lower-fma.f64`
18 226×	`lower-fma.f32`
16 534×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	162	2698
1	540	2475
2	1635	2364
3	4902	2332
0	8143	1927
0	61	453
0	88	453
1	360	381
2	3069	381
0	8721	373
0	9	26
0	15	26
1	56	19
2	378	19
3	4533	19
0	8161	15
0	102	1818
1	322	1640
2	922	1632
3	3268	1602
4	6535	1602
0	8224	1222
0	49	342
1	155	342
2	336	342
3	752	342
4	1208	302
5	1538	286
6	2035	286
7	2978	286
8	4658	286
0	8365	232

Stop Event

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

Compiler

Compiled 169 to 90 computations (46.7% saved)

preprocess65.0ms (1%)

Memory: -5.6MiB live, 73.7MiB allocated
Compiler: Compiled 218 to 86 computations (60.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze2.0ms (0%)

sample934.0ms (14%)

explain120.0ms (1.8%)

preprocess209.0ms (3.1%)

eval0.0ms (0%)

prune3.0ms (0%)

simplify151.0ms (2.3%)

localize130.0ms (2%)

series6.0ms (0.1%)

simplify192.0ms (2.9%)

rewrite168.0ms (2.5%)

eval173.0ms (2.6%)

prune166.0ms (2.5%)

simplify169.0ms (2.5%)

localize90.0ms (1.4%)

series12.0ms (0.2%)

simplify177.0ms (2.6%)

rewrite159.0ms (2.4%)

eval135.0ms (2%)

prune87.0ms (1.3%)

simplify140.0ms (2.1%)

localize142.0ms (2.1%)

series34.0ms (0.5%)

simplify410.0ms (6.2%)

rewrite229.0ms (3.4%)

eval160.0ms (2.4%)

prune291.0ms (4.4%)

simplify152.0ms (2.3%)

localize156.0ms (2.3%)

series26.0ms (0.4%)

simplify182.0ms (2.7%)

rewrite172.0ms (2.6%)

eval83.0ms (1.2%)

prune179.0ms (2.7%)

regimes24.0ms (0.4%)

regimes54.0ms (0.8%)

regimes20.0ms (0.3%)

regimes10.0ms (0.1%)

regimes6.0ms (0.1%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify9.0ms (0.1%)

soundness1.0s (15.5%)

preprocess65.0ms (1%)

end0.0ms (0%)

Profiling