Metrics for sqrtexp (problem 3.4.4)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze2.0ms (0%)

Memory

5.2MiB live, 5.2MiB allocated

Algorithm

1×

Search

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

sample1.3s (20.5%)

Memory

29.3MiB live, 941.1MiB allocated

Samples

719.0ms	8 256×	0	valid
237.0ms	2 575×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 361.0ms

ival-expm1: 123.0ms (34.1% of total)

ival-mult: 77.0ms (21.3% of total)

ival-sqrt: 73.0ms (20.2% of total)

ival-div: 72.0ms (20% of total)

ival-true: 7.0ms (1.9% of total)

exact: 6.0ms (1.7% of total)

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

Bogosity

explain123.0ms (2%)

Memory

7.5MiB live, 131.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
161	0	-	-	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`
161	0	-	-	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
1	153	(2.333095018222388e-281)	-	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
0	1	(-351.3611993026807)	-	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(*.f64 #s(literal 2 binary64) x)`
0	0	-	-	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))`
0	0	-	-	`#s(literal 2 binary64)`
0	0	-	-	`(exp.f64 x)`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	cancellation	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)))`	u/u	153	0
↳	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`	underflow	92
↳	`(exp.f64 x)`	underflow	92
`/.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
`exp.f64`	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	161	0
-	2	93

Precision

0.9877300613496932

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	161	0	0
-	2	0	93

Precision?

0.9877300613496932

Recall?

1.0

Freqs

test

number	freq
0	93
1	2
2	8
3	153

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

44.0ms

512×

valid

Compiler

Compiled 151 to 67 computations (55.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 29.0ms

ival-exp: 13.0ms (44.2% of total)

ival-expm1: 6.0ms (20.4% of total)

ival-mult: 4.0ms (13.6% of total)

ival-div: 3.0ms (10.2% of total)

ival-sqrt: 3.0ms (10.2% of total)

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

exact: 0.0ms (0% of total)

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

preprocess202.0ms (3.2%)

Memory

22.0MiB live, 133.4MiB 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 12 to 10 computations (16.7% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	39.0%	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))

Compiler

Compiled 12 to 10 computations (16.7% saved)

simplify174.0ms (2.8%)

Memory

-0.2MiB live, 116.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	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))))
cost-diff	192	(-.f64 (exp.f64 x) #s(literal 1 binary64))
cost-diff	6336	(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
cost-diff	7232	(/.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 #s(literal 2 binary64)))
(exp.f64 (*.f64 #s(literal 2 binary64) x))
(pow.f64 (exp.f64 #s(literal 2 binary64)) x)
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
#s(literal 2 binary64)
x
#s(literal 1 binary64)
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(expm1.f64 x)
(exp.f64 x)

localize27.0ms (0.4%)

Memory

-11.2MiB live, 27.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
accuracy	0.21322250976844204	(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
accuracy	36.785880326683284	(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
accuracy	36.796072073342465	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Samples

20.0ms

256×

valid

Compiler

Compiled 47 to 12 computations (74.5% saved)

Precisions

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

ival-exp: 3.0ms (25.8% of total)

ival-expm1: 3.0ms (25.8% of total)

ival-div: 2.0ms (17.2% of total)

ival-mult: 2.0ms (17.2% of total)

ival-sqrt: 2.0ms (17.2% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0.1%)

Memory

4.2MiB live, 4.2MiB allocated

Counts

4 → 48

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

Calls

3 calls:

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

Time

Variable

Point

Expression

1.0ms

inf

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

1.0ms

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

1.0ms

-inf

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

simplify169.0ms (2.7%)

Memory

-1.9MiB live, 144.9MiB allocated

Algorithm

1×	egg-herbie

Rules

15 504×	`lower-fma.f64`
15 504×	`lower-fma.f32`
4 704×	`lower-*.f64`
4 704×	`lower-*.f32`
2 492×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	444
1	252	410
2	661	410
3	1434	404
4	2557	324
5	5968	289
0	8342	234

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 47

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)))))))
(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))))))
(/ (- (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)
(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))
(- (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)
(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)))

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

rewrite187.0ms (3%)

Memory

29.6MiB live, 193.6MiB allocated

Rules

4 562×	`lower-fma.f64`
4 562×	`lower-fma.f32`
3 484×	`lower-*.f32`
3 482×	`lower-*.f64`
2 734×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	33
0	17	33
1	63	19
2	429	19
3	4997	19
0	8103	15

Stop Event

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

Counts

4 → 687

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))
(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
(.f64 (/.f64 (/.f64 (expm1.f64 (.f64 #s(literal 4 binary64) x)) (expm1.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 x) #s(literal 4 binary64)))) (neg.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64)))))
(.f64 (/.f64 (/.f64 (expm1.f64 (.f64 #s(literal 4 binary64) x)) (expm1.f64 x)) (+.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) #s(literal 1 binary64))) (fma.f64 #s(literal -1 binary64) (expm1.f64 (*.f64 x #s(literal 2 binary64))) (pow.f64 (exp.f64 x) #s(literal 4 binary64))))
(.f64 (/.f64 (/.f64 (expm1.f64 (.f64 #s(literal 6 binary64) x)) (expm1.f64 x)) (-.f64 (pow.f64 (exp.f64 x) #s(literal 8 binary64)) (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))) (-.f64 (expm1.f64 (*.f64 #s(literal 4 binary64) x)) (pow.f64 (exp.f64 #s(literal 2 binary64)) x)))
(.f64 (/.f64 (/.f64 (expm1.f64 (.f64 #s(literal 6 binary64) x)) (expm1.f64 x)) (+.f64 (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 (exp.f64 x) #s(literal 12 binary64)))) (fma.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (-.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) #s(literal 4 binary64))) (pow.f64 (exp.f64 x) #s(literal 8 binary64))))
(.f64 (/.f64 (expm1.f64 (.f64 x #s(literal 2 binary64))) (neg.f64 (expm1.f64 (*.f64 #s(literal 3 binary64) x)))) (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64)))))
(.f64 (pow.f64 (/.f64 (expm1.f64 x) (expm1.f64 (.f64 #s(literal 4 binary64) x))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (expm1.f64 x) (expm1.f64 (.f64 #s(literal 6 binary64) x))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 (neg.f64 (expm1.f64 (.f64 x #s(literal 2 binary64)))) (expm1.f64 (*.f64 #s(literal 3 binary64) x))) (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64)))))
(.f64 (/.f64 (neg.f64 (expm1.f64 (.f64 x #s(literal 2 binary64)))) (expm1.f64 (*.f64 x #s(literal 2 binary64)))) (fma.f64 #s(literal -1 binary64) (exp.f64 x) #s(literal -1 binary64)))
(.f64 (/.f64 (expm1.f64 (.f64 x #s(literal 2 binary64))) (neg.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))))) (fma.f64 #s(literal -1 binary64) (exp.f64 x) #s(literal -1 binary64)))
(.f64 (.f64 (pow.f64 (expm1.f64 x) #s(literal -1 binary64)) (-.f64 (exp.f64 x) #s(literal -1 binary64))) (expm1.f64 x))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 (expm1.f64 (.f64 x #s(literal 2 binary64))) (expm1.f64 (.f64 #s(literal 3 binary64) x)))) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))))) (/.f64 #s(literal -1 binary64) (expm1.f64 x)))
(.f64 (/.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (expm1.f64 x)) (/.f64 (expm1.f64 (.f64 x #s(literal 2 binary64))) (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64))))
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(-.f64 (/.f64 #s(literal 0 binary64) (fma.f64 #s(literal -1 binary64) (exp.f64 x) #s(literal -1 binary64))) (neg.f64 (expm1.f64 x)))
(-.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64))) (-.f64 (exp.f64 x) #s(literal -1 binary64))) (/.f64 (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (-.f64 (exp.f64 x) #s(literal -1 binary64))))
(-.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)))) (-.f64 (exp.f64 x) #s(literal -1 binary64))) (/.f64 (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) (-.f64 (exp.f64 x) #s(literal -1 binary64))))
(-.f64 (/.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64)))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64)))) (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 (expm1.f64 x)))
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(+.f64 (-.f64 (/.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) (/.f64 (exp.f64 x) (expm1.f64 (.f64 x #s(literal 2 binary64))))) (pow.f64 (expm1.f64 (.f64 x #s(literal 2 binary64))) #s(literal -1 binary64)))
(+.f64 (neg.f64 (neg.f64 (exp.f64 x))) #s(literal -1 binary64))
(+.f64 (/.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64))))
(+.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64)))) (neg.f64 (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) #s(literal -1 binary64))))
(+.f64 #s(literal -1 binary64) (exp.f64 x))
(+.f64 (exp.f64 x) #s(literal -1 binary64))
(exp.f64 (.f64 (.f64 (log.f64 (expm1.f64 x)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (neg.f64 (log.f64 (expm1.f64 x))) #s(literal -1 binary64)))
(.f64 (/.f64 (sqrt.f64 (expm1.f64 (.f64 x #s(literal 2 binary64)))) (sqrt.f64 (expm1.f64 (*.f64 #s(literal 3 binary64) x)))) (hypot.f64 (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) (exp.f64 x)))
(.f64 (sqrt.f64 (/.f64 (expm1.f64 (.f64 x #s(literal 2 binary64))) (expm1.f64 (*.f64 #s(literal 3 binary64) x)))) (hypot.f64 (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) (exp.f64 x)))
(*.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 1/4 binary64)))
(.f64 (neg.f64 (sqrt.f64 (expm1.f64 (.f64 x #s(literal 2 binary64))))) (pow.f64 (neg.f64 (sqrt.f64 (expm1.f64 x))) #s(literal -1 binary64)))
(.f64 (sqrt.f64 (neg.f64 (expm1.f64 (.f64 x #s(literal 2 binary64))))) (pow.f64 (neg.f64 (expm1.f64 x)) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #s(literal 1 binary64))
(.f64 (pow.f64 (expm1.f64 x) #s(literal -1/2 binary64)) (sqrt.f64 (expm1.f64 (.f64 x #s(literal 2 binary64)))))
(.f64 (sqrt.f64 (expm1.f64 (.f64 x #s(literal 2 binary64)))) (pow.f64 (expm1.f64 x) #s(literal -1/2 binary64)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))))
(pow.f64 (*.f64 #s(literal 1 binary64) (exp.f64 (log1p.f64 (exp.f64 x)))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (exp.f64 (log1p.f64 (exp.f64 x))) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (/.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) #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 -2 binary64)) #s(literal -1/4 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 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(literal -1 binary64))
(pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal -1/2 binary64))
(/.f64 (sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 4 binary64) x)) (expm1.f64 x))) (sqrt.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 6 binary64) x)) (expm1.f64 x))) (sqrt.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)))))
(/.f64 (.f64 (sqrt.f64 (expm1.f64 (.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)) (sqrt.f64 (expm1.f64 x)))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64)))))) (neg.f64 (neg.f64 (sqrt.f64 (expm1.f64 x)))))
(/.f64 (neg.f64 (sqrt.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64)))))) (neg.f64 (sqrt.f64 (neg.f64 (expm1.f64 x)))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) (pow.f64 (expm1.f64 x) #s(literal -2 binary64))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64)))) (sqrt.f64 (.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (pow.f64 (expm1.f64 x) #s(literal -1 binary64)))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) (pow.f64 (expm1.f64 x) #s(literal -3 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64)))) (sqrt.f64 (fma.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) (pow.f64 (expm1.f64 x) #s(literal -2 binary64)) (fma.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) x) (pow.f64 (expm1.f64 x) #s(literal -2 binary64)) (pow.f64 (expm1.f64 x) #s(literal -2 binary64))))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (fma.f64 (expm1.f64 x) (pow.f64 (exp.f64 #s(literal 2 binary64)) 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 (/.f64 #s(literal -1 binary64) (-.f64 (exp.f64 x) #s(literal -1 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))))) (neg.f64 (sqrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (expm1.f64 (.f64 #s(literal 4 binary64) x))) (sqrt.f64 (.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (expm1.f64 x))))
(/.f64 (sqrt.f64 (expm1.f64 (.f64 #s(literal 6 binary64) x))) (sqrt.f64 (.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64))) (expm1.f64 x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))))
(/.f64 (sqrt.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64)))) (sqrt.f64 (expm1.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))))) (sqrt.f64 (expm1.f64 x))))
(neg.f64 (/.f64 (sqrt.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64)))) (neg.f64 (sqrt.f64 (expm1.f64 x)))))
(sqrt.f64 (exp.f64 (log1p.f64 (exp.f64 x))))
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (neg.f64 (log1p.f64 (exp.f64 x))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log1p.f64 (exp.f64 x)))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (neg.f64 (log1p.f64 (exp.f64 x))) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/2 binary64)))

eval204.0ms (3.3%)

Memory: -12.0MiB live, 151.4MiB allocated
Compiler: Compiled 16 704 to 2 386 computations (85.7% saved)

prune135.0ms (2.2%)

Memory

-13.3MiB live, 150.1MiB allocated

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	726	8	734
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	727	8	735

Accuracy

100.0%

Counts

735 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.0%	(pow.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
▶	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
	63.1%	(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))))
▶	64.6%	(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))))
	62.5%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64))))
▶	69.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
▶	64.4%	#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))))
	63.4%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (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))))

Compiler

Compiled 138 to 120 computations (13% saved)

simplify175.0ms (2.8%)

Memory

-3.3MiB live, 111.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(exp.f64 x)
cost-diff	0	(-.f64 (exp.f64 x) #s(literal -1 binary64))
cost-diff	0	(pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 1/4 binary64))
cost-diff	12288	(pow.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
cost-diff	0	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
cost-diff	0	(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)))
cost-diff	0	#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))))
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	#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

14 660×	`lower-fma.f32`
14 652×	`lower-fma.f64`
2 514×	`lower--.f32`
2 512×	`lower--.f64`
2 298×	`lower-*.f64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	30	168
0	47	165
1	71	165
2	98	165
3	171	165
4	266	140
5	360	130
6	495	130
7	899	130
8	3241	130
9	7173	130
0	8198	130

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)) (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)
#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 (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 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
#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))
#s(literal 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 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 1/4 binary64))
(-.f64 (exp.f64 x) #s(literal -1 binary64))
(exp.f64 x)
x
#s(literal -1 binary64)
#s(literal 1/4 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)) (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)
#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))))
#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 (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 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
#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))
#s(literal 2 binary64)
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 1/4 binary64))
(-.f64 (exp.f64 x) #s(literal -1 binary64))
(exp.f64 x)
x
#s(literal -1 binary64)
#s(literal 1/4 binary64)
#s(literal 2 binary64)

localize114.0ms (1.8%)

Memory

-6.5MiB live, 79.6MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0	(exp.f64 x)
accuracy	0.00390625	(pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 1/4 binary64))
accuracy	0.0078125	(-.f64 (exp.f64 x) #s(literal -1 binary64))
accuracy	0.6171875	(pow.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.07650375976844201	(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)))
accuracy	0.37109375	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	22.768037585576707	#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))))
accuracy	0	(fma.f64 (fma.f64 #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	0.00390625	(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	22.790652539315147	#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	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
accuracy	20.164676921986032	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))
accuracy	0	(exp.f64 x)
accuracy	0.00390625	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
accuracy	0.0078125	(-.f64 (exp.f64 x) #s(literal -1 binary64))

Samples

49.0ms	244×	0	valid
3.0ms	6×	2	valid
2.0ms	6×	1	valid

Compiler

Compiled 144 to 29 computations (79.9% saved)

Precisions

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

ival-mult: 10.0ms (25.9% of total)

ival-add: 5.0ms (12.9% of total)

ival-sqrt: 5.0ms (12.9% of total)

ival-pow: 5.0ms (12.9% of total)

ival-div: 3.0ms (7.8% of total)

ival-expm1: 3.0ms (7.8% of total)

ival-pow2: 3.0ms (7.8% of total)

ival-exp: 2.0ms (5.2% of total)

adjust: 1.0ms (2.6% of total)

ival-sub: 1.0ms (2.6% of total)

exact: 1.0ms (2.6% of total)

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

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

series71.0ms (1.1%)

Memory

14.9MiB live, 49.8MiB allocated

Counts

16 → 180

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

Calls

3 calls:

Time

Variable

Point

Expression

32.0ms

-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)) (+ (* (+ (* 1/2 x) 1) x) 2) (+ (* 1/2 x) 1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (+ (* 3/16 x) 1/2) (/ x (sqrt 2)) (pow (pow (- (exp x) -1) 1/4) 2) (pow (- (exp x) -1) 1/4) (sqrt 2))

31.0ms

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)) (+ (* (+ (* 1/2 x) 1) x) 2) (+ (* 1/2 x) 1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (+ (* 3/16 x) 1/2) (/ x (sqrt 2)) (pow (pow (- (exp x) -1) 1/4) 2) (pow (- (exp x) -1) 1/4) (sqrt 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)) (+ (* (+ (* 1/2 x) 1) x) 2) (+ (* 1/2 x) 1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (+ (* 3/16 x) 1/2) (/ x (sqrt 2)) (pow (pow (- (exp x) -1) 1/4) 2) (pow (- (exp x) -1) 1/4) (sqrt 2))

simplify203.0ms (3.2%)

Memory

13.0MiB live, 202.4MiB allocated

Algorithm

1×	egg-herbie

Rules

18 952×	`lower-fma.f64`
18 952×	`lower-fma.f32`
5 100×	`lower-*.f64`
5 100×	`lower-*.f32`
2 898×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	120	1669
1	372	1441
2	971	1388
3	3088	1371
4	7411	1371
0	8255	1108

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

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 (+ 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))))))
(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
(+ 1/2 (* 3/16 x))
(+ 1/2 (* 3/16 x))
(+ 1/2 (* 3/16 x))
(/ 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))))))
(pow 2 1/4)
(+ (* 1/8 (* (pow 2 1/4) x)) (pow 2 1/4))
(+ (* x (+ (* 5/128 (* (pow 2 1/4) x)) (* 1/8 (pow 2 1/4)))) (pow 2 1/4))
(+ (* x (+ (* 1/8 (pow 2 1/4)) (* x (+ (* 13/3072 (* (pow 2 1/4) x)) (* 5/128 (pow 2 1/4)))))) (pow 2 1/4))
(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))
(* 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)))
(* 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 x)
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(pow (* 1 (+ 1 (exp x))) 1/4)
(pow (* 1 (+ 1 (exp x))) 1/4)
(pow (* 1 (+ 1 (exp x))) 1/4)
(pow (* 1 (+ 1 (exp x))) 1/4)
(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))
(* 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)))
(* 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 x)
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(pow (* 1 (+ 1 (exp x))) 1/4)
(pow (* 1 (+ 1 (exp x))) 1/4)
(pow (* 1 (+ 1 (exp x))) 1/4)
(pow (* 1 (+ 1 (exp x))) 1/4)

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))
(+ 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
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) #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))
(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))
(+ 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))
(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))
(+ 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
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(+ 1 (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(+ 1 (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 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 (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)))
(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)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 3/16 x))
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
(+ 1/2 (* 3/16 x))
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
(+ 1/2 (* 3/16 x))
(fma.f64 #s(literal 3/16 binary64) x #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 #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)))
(pow 2 1/4)
(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
(+ (* 1/8 (* (pow 2 1/4) x)) (pow 2 1/4))
(*.f64 (fma.f64 #s(literal 1/8 binary64) x #s(literal 1 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(+ (* x (+ (* 5/128 (* (pow 2 1/4) x)) (* 1/8 (pow 2 1/4)))) (pow 2 1/4))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (fma.f64 (.f64 #s(literal 5/128 binary64) x) x (fma.f64 #s(literal 1/8 binary64) x #s(literal 1 binary64))))
(+ (* x (+ (* 1/8 (pow 2 1/4)) (* x (+ (* 13/3072 (* (pow 2 1/4) x)) (* 5/128 (pow 2 1/4)))))) (pow 2 1/4))
(fma.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (fma.f64 x (.f64 #s(literal 13/3072 binary64) x) (fma.f64 #s(literal 5/128 binary64) x #s(literal 1/8 binary64)))) x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 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 #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (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 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 x)
(*.f64 #s(literal 3/16 binary64) x)
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 3/16 binary64) x #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 (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(pow (* 1 (+ 1 (exp x))) 1/4)
(pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64))
(pow (* 1 (+ 1 (exp x))) 1/4)
(pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64))
(pow (* 1 (+ 1 (exp x))) 1/4)
(pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64))
(pow (* 1 (+ 1 (exp x))) 1/4)
(pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 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 #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (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 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(fma.f64 (/.f64 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)))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 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)))
(* 3/16 x)
(*.f64 #s(literal 3/16 binary64) x)
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 3/16 binary64) x #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 (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(pow (* 1 (+ 1 (exp x))) 1/4)
(pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64))
(pow (* 1 (+ 1 (exp x))) 1/4)
(pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64))
(pow (* 1 (+ 1 (exp x))) 1/4)
(pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64))
(pow (* 1 (+ 1 (exp x))) 1/4)
(pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64))

rewrite167.0ms (2.7%)

Memory

1.7MiB live, 200.6MiB allocated

Rules

5 020×	`lower-fma.f32`
5 012×	`lower-fma.f64`
3 924×	`lower-/.f32`
3 922×	`lower-/.f64`
3 642×	`lower-*.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	147
0	47	144
1	184	109
2	1270	109
0	8390	109

Stop Event

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

Counts

16 → 509

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)) (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(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 (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 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
(/.f64 x (sqrt.f64 #s(literal 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 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 1/4 binary64))
(sqrt.f64 #s(literal 2 binary64))

Outputs
(.f64 (sqrt.f64 (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (hypot.f64 (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) (exp.f64 x)))
(*.f64 (pow.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 3/8 binary64)) #s(literal 1 binary64)) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 1/8 binary64)))
(.f64 (pow.f64 (sqrt.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x))) #s(literal 1 binary64)) (pow.f64 (pow.f64 (expm1.f64 x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)) (hypot.f64 (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) (exp.f64 x)))
(*.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 3/8 binary64)) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 1/8 binary64)))
(.f64 (neg.f64 (sqrt.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (expm1.f64 x)))))
(.f64 (sqrt.f64 (neg.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (expm1.f64 x)))))
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(pow.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 1/8 binary64)) #s(literal 4 binary64))
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal -1/2 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/4 binary64)))
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #s(literal 1 binary64))
(pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x))))) (neg.f64 (neg.f64 (sqrt.f64 (expm1.f64 x)))))
(/.f64 (neg.f64 (sqrt.f64 (neg.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x))))) (neg.f64 (sqrt.f64 (neg.f64 (expm1.f64 x)))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) #s(literal -1 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 #s(literal -1 binary64) (expm1.f64 x) (pow.f64 (exp.f64 x) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) (expm1.f64 x))) (sqrt.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) #s(literal 1 binary64)) (expm1.f64 x))) (sqrt.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) (pow.f64 (expm1.f64 x) #s(literal -2 binary64))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64)))) (sqrt.f64 (+.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (expm1.f64 x)) (pow.f64 (expm1.f64 x) #s(literal -1 binary64)))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) (pow.f64 (expm1.f64 x) #s(literal -3 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64)))) (sqrt.f64 (fma.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) (pow.f64 (expm1.f64 x) #s(literal -2 binary64)) (+.f64 (pow.f64 (expm1.f64 x) #s(literal -2 binary64)) (/.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (expm1.f64 x)) (expm1.f64 x))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 x) #s(literal 3 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (exp.f64 x)))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) #s(literal -1 binary64)))) (sqrt.f64 (fma.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64) (expm1.f64 x))))
(/.f64 (sqrt.f64 (fma.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (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 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)))) (neg.f64 (sqrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (neg.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) #s(literal -1 binary64))) (sqrt.f64 (fma.f64 #s(literal -1 binary64) (expm1.f64 x) (pow.f64 (exp.f64 x) #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (expm1.f64 x))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (expm1.f64 x) (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) #s(literal 2 binary64))) (expm1.f64 x))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (expm1.f64 x) (+.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x))) (sqrt.f64 (expm1.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 #s(literal -1 binary64) (expm1.f64 x) (pow.f64 (exp.f64 x) #s(literal 2 binary64)))) (sqrt.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) #s(literal -1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))))))
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))) #s(literal 1 binary64)))
(exp.f64 (log.f64 (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))))
(exp.f64 (.f64 (.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (exp.f64 x) #s(literal -1 binary64))) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 (fma.f64 #s(literal -1 binary64) (expm1.f64 x) (pow.f64 (exp.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (neg.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x))) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (pow.f64 (expm1.f64 x) #s(literal -1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 (expm1.f64 x) #s(literal -1 binary64)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #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 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 1/8 binary64)) (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 1/8 binary64)))
(*.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 1/4 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 #s(literal 1/4 binary64)) (log1p.f64 (exp.f64 x)))
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64)) #s(literal 1/8 binary64))
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 1/8 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal -1/4 binary64))
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 1/4 binary64)) #s(literal 1 binary64))
(pow.f64 (sqrt.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 1/4 binary64))
(exp.f64 (.f64 (.f64 #s(literal 1/8 binary64) (log1p.f64 (exp.f64 x))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 2 binary64))) #s(literal 1/8 binary64)))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(pow.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 #s(literal 2 binary64))
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(exp.f64 (log.f64 (sqrt.f64 #s(literal 2 binary64))))

eval129.0ms (2.1%)

Memory: 8.7MiB live, 250.8MiB allocated
Compiler: Compiled 15 932 to 2 103 computations (86.8% saved)

prune169.0ms (2.7%)

Memory

-41.2MiB live, 153.1MiB allocated

Pruning

14 alts after pruning (10 fresh and 4 done)

	Pruned	Kept	Total
New	863	7	870
Fresh	0	3	3
Picked	1	4	5
Done	0	0	0
Total	864	14	878

Accuracy

100.0%

Counts

878 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
	63.1%	(sqrt.f64 (-.f64 #s(approx (exp 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))) #s(literal -1 binary64)))
	63.1%	(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))))
✓	64.6%	(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))))
▶	62.5%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64))))
▶	3.8%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x))))
	4.9%	(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)))))
✓	69.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
	63.4%	#s(approx (pow (pow (- (exp x) -1) 1/4) 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))))
▶	63.5%	#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))) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))))
✓	64.4%	#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))))
	63.4%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (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))))
▶	3.8%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 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)))))
▶	4.1%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))

Compiler

Compiled 263 to 218 computations (17.1% saved)

simplify155.0ms (2.5%)

Memory

1.8MiB live, 116.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Rules

14 758×	`lower-fma.f32`
14 752×	`lower-fma.f64`
2 494×	`lower--.f64`
2 494×	`lower--.f32`
2 300×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	345
0	62	342
1	102	342
2	157	342
3	205	342
4	299	307
5	399	293
6	515	293
7	911	293
8	3227	293
9	7106	293
0	8148	286

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

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

localize116.0ms (1.9%)

Memory

-4.6MiB live, 102.1MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.08431625976844201	(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
accuracy	0.37109375	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	22.768037585576707	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 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	39.497505176281436	#s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 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	0.13671875	(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))
accuracy	0.37109375	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	22.768037585576707	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))
accuracy	39.55100669218335	#s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64)))
accuracy	0.00390625	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x))))
accuracy	0.01171875	(*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x)
accuracy	22.790652539315147	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x)))
accuracy	39.47151210320368	#s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x))
accuracy	0	(+.f64 x #s(literal 2 binary64))
accuracy	0.00390625	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64))))
accuracy	23.759370242442735	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64)))
accuracy	0.07650375976844201	(fma.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
accuracy	0.37109375	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	1.0	(/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
accuracy	22.768037585576707	#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))) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))))

Samples

88.0ms	244×	0	valid
3.0ms	6×	2	valid
2.0ms	6×	1	valid

Compiler

Compiled 228 to 33 computations (85.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 75.0ms

ival-mult: 51.0ms (67.7% of total)

ival-add: 8.0ms (10.6% of total)

ival-div: 5.0ms (6.6% of total)

ival-pow: 4.0ms (5.3% of total)

ival-expm1: 3.0ms (4% of total)

ival-sqrt: 3.0ms (4% of total)

adjust: 1.0ms (1.3% of total)

exact: 1.0ms (1.3% of total)

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

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

series16.0ms (0.3%)

Memory

34.1MiB live, 34.1MiB allocated

Counts

19 → 216

Calls

Call 1

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

Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

inf

((sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (/ 1 (pow 2 -1/2))) (+ (* 3/16 x) 1/2) (/ x (sqrt 2)) (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) (* (+ (* x 1/2) 1) x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (* (* (/ x (sqrt 2)) x) 3/16) (* (/ x (sqrt 2)) x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (/ 1 (pow 2 -1/2)))

2.0ms

-inf

((sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (/ 1 (pow 2 -1/2))) (+ (* 3/16 x) 1/2) (/ x (sqrt 2)) (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) (* (+ (* x 1/2) 1) x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (* (* (/ x (sqrt 2)) x) 3/16) (* (/ x (sqrt 2)) x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (/ 1 (pow 2 -1/2)))

2.0ms

((sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (/ 1 (pow 2 -1/2))) (+ (* 3/16 x) 1/2) (/ x (sqrt 2)) (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) (* (+ (* x 1/2) 1) x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (* (* (/ x (sqrt 2)) x) 3/16) (* (/ x (sqrt 2)) x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (* (/ x (sqrt 2)) (+ (* 3/16 x) 1/2)) (/ 1 (pow 2 -1/2)))

simplify193.0ms (3.1%)

Memory

-6.5MiB live, 149.8MiB allocated

Algorithm

1×	egg-herbie

Rules

13 946×	`lower-fma.f64`
13 946×	`lower-fma.f32`
4 636×	`lower-*.f64`
4 636×	`lower-*.f32`
1 646×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	105	2292
1	328	2014
2	890	1900
3	2114	1885
4	6117	1605
0	8167	1479

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 213

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))))))
(/ 1 (sqrt 1/2))
(+ (* 1/2 (/ x (sqrt 2))) (/ 1 (sqrt 1/2)))
(+ (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))) (/ 1 (sqrt 1/2)))
(+ (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))) (/ 1 (sqrt 1/2)))
1/2
(+ 1/2 (* 3/16 x))
(+ 1/2 (* 3/16 x))
(+ 1/2 (* 3/16 x))
(/ 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)
(+ 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))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* 1/2 x)))
(* 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))))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (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 (+ (* 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)))))
(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))) (/ 1 (* (pow x 2) (sqrt 1/2))))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ 1 (* (pow x 2) (sqrt 1/2))))))
(* 3/16 x)
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(/ 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))
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 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(sqrt (/ (- (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)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (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)))
(* 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))))))
(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))) (/ 1 (* (pow x 2) (sqrt 1/2))))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ 1 (* (pow x 2) (sqrt 1/2))))))
(* 3/16 x)
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(/ 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))
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 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(sqrt (/ (- (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)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (sqrt 2))
(/ (pow x 2) (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)))
(* 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))))))

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

rewrite240.0ms (3.8%)

Memory

14.2MiB live, 330.9MiB allocated

Rules

4 600×	`lower-/.f32`
4 596×	`lower-/.f64`
4 098×	`lower-*.f32`
4 090×	`lower-*.f64`
3 850×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	302
0	62	286
1	232	237
2	1621	237
0	8314	234

Stop Event

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

Counts

19 → 732

Calls

Call 1

Inputs
#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))) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #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))) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))))
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
(/.f64 x (sqrt.f64 #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)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x)))
#s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x))
(*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x)
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))
#s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64)))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 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 (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 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 #s(literal 1 binary64) (pow.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))))
(.f64 (/.f64 (fma.f64 (pow.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (pow.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64))))
(.f64 (/.f64 (fma.f64 (pow.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal -3/4 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal 3/4 binary64))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (pow.f64 (-.f64 (fma.f64 (pow.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 2 binary64)) (/.f64 (.f64 (*.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64))))
(.f64 (fma.f64 (pow.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal -2 binary64)) (pow.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1 binary64)))
(.f64 (fma.f64 (pow.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal -3/4 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal 3/4 binary64))) (pow.f64 (-.f64 (fma.f64 (pow.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 2 binary64)) (/.f64 (.f64 (*.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal -2 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (fma.f64 (pow.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 2 binary64)) (/.f64 (.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) #s(literal 1 binary64))) (fma.f64 (pow.f64 (.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal -3/4 binary64)) (pow.f64 #s(literal 4 binary64) #s(literal 3/4 binary64)))) #s(literal -1 binary64))
(/.f64 (+.f64 (pow.f64 (+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))) #s(literal 3 binary64)) (pow.f64 (.f64 x (pow.f64 #s(literal 4 binary64) #s(literal -3/4 binary64))) #s(literal 3 binary64))) (fma.f64 (+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))) (-.f64 (pow.f64 (.f64 x (pow.f64 #s(literal 4 binary64) #s(literal -3/4 binary64))) #s(literal 2 binary64)) (.f64 (+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))) (.f64 x (pow.f64 #s(literal 4 binary64) #s(literal -3/4 binary64)))))))
(/.f64 (fma.f64 (pow.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3 binary64)) #s(literal 27/4096 binary64) (pow.f64 (fma.f64 x (pow.f64 #s(literal 4 binary64) #s(literal -3/4 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64)) #s(literal 2 binary64)) (-.f64 (.f64 (fma.f64 x (pow.f64 #s(literal 4 binary64) #s(literal -3/4 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (pow.f64 #s(literal 4 binary64) #s(literal -3/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64)) (fma.f64 x (pow.f64 #s(literal 4 binary64) #s(literal -3/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))))))
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eval159.0ms (2.5%)

Memory: 1.8MiB live, 262.3MiB allocated
Compiler: Compiled 22 508 to 3 360 computations (85.1% saved)

prune259.0ms (4.1%)

Memory

-33.5MiB live, 263.4MiB allocated

Pruning

15 alts after pruning (7 fresh and 8 done)

	Pruned	Kept	Total
New	1 062	2	1 064
Fresh	0	5	5
Picked	1	4	5
Done	0	4	4
Total	1 063	15	1 078

Accuracy

100.0%

Counts

1 078 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
▶	63.1%	(sqrt.f64 (-.f64 #s(approx (exp 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))) #s(literal -1 binary64)))
▶	63.1%	(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))))
✓	64.6%	(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))))
✓	62.5%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64))))
✓	3.8%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x))))
▶	4.9%	(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)))))
✓	69.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
	63.4%	#s(approx (pow (pow (- (exp x) -1) 1/4) 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))))
✓	64.4%	#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))))
	63.4%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (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))))
▶	62.0%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (/ 1 (pow 2 -1/2))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
▶	68.3%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
✓	3.8%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 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)))))
✓	4.1%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))

Compiler

Compiled 234 to 196 computations (16.2% saved)

simplify162.0ms (2.6%)

Memory

20.0MiB live, 212.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

15 254×	`lower-fma.f32`
15 244×	`lower-fma.f64`
2 496×	`lower--.f32`
2 494×	`lower--.f64`
2 420×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	377
0	69	377
1	105	377
2	145	377
3	265	377
4	490	347
5	651	335
6	799	335
7	1198	335
8	3503	335
9	7361	335
0	8387	321

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

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

localize265.0ms (4.2%)

Memory

-15.6MiB live, 188.7MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	1.0	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
accuracy	1.0	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
accuracy	22.768037585576707	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (/ 1 (pow 2 -1/2))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
accuracy	23.833853544259092	#s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (/ 1 (pow 2 -1/2))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
accuracy	0.02734375	(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))
accuracy	0.03125	(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
accuracy	0.1171875	(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
accuracy	23.246464018538745	#s(approx (exp 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)))
accuracy	0.02734375	(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	0.03125	(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
accuracy	0.1171875	(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
accuracy	23.465167461880586	#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	(*.f64 x x)
accuracy	0.00390625	(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	22.790652539315147	#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	39.54020900405604	#s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
accuracy	0	(sqrt.f64 #s(literal 1/2 binary64))
accuracy	1.0	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
accuracy	22.768037585576707	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
accuracy	23.489079463098737	#s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))

Samples

79.0ms

256×

valid

Compiler

Compiled 233 to 44 computations (81.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 61.0ms

ival-mult: 19.0ms (31.1% of total)

ival-div: 10.0ms (16.4% of total)

ival-add: 10.0ms (16.4% of total)

ival-sqrt: 6.0ms (9.8% of total)

const: 5.0ms (8.2% of total)

ival-pow: 4.0ms (6.5% of total)

ival-expm1: 3.0ms (4.9% of total)

ival-exp: 2.0ms (3.3% of total)

ival-sub: 1.0ms (1.6% of total)

exact: 1.0ms (1.6% of total)

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

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

series16.0ms (0.3%)

Memory

15.3MiB live, 15.3MiB allocated

Counts

22 → 228

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

-inf

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

2.0ms

inf

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

2.0ms

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

simplify195.0ms (3.1%)

Memory

5.8MiB live, 122.5MiB allocated

Algorithm

1×	egg-herbie

Rules

14 592×	`lower-fma.f64`
14 592×	`lower-fma.f32`
4 154×	`lower-*.f64`
4 154×	`lower-*.f32`
2 582×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	135	2167
1	417	1997
2	1226	1902
3	3506	1887
4	6459	1647
0	8315	1486

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 228

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))))))
(/ 1 (sqrt 1/2))
(+ (* 1/2 (/ x (sqrt 2))) (/ 1 (sqrt 1/2)))
(+ (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))) (/ 1 (sqrt 1/2)))
(+ (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))) (/ 1 (sqrt 1/2)))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 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
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/6 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))))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* 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))))))
(/ 1 (sqrt 1/2))
(+ (* 1/2 (/ x (sqrt 2))) (/ 1 (sqrt 1/2)))
(+ (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))) (/ 1 (sqrt 1/2)))
(+ (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))) (/ 1 (sqrt 1/2)))
(/ 1 (sqrt 1/2))
(+ (* 1/2 (/ x (sqrt 2))) (/ 1 (sqrt 1/2)))
(+ (* 1/2 (/ x (sqrt 2))) (/ 1 (sqrt 1/2)))
(+ (* 1/2 (/ x (sqrt 2))) (/ 1 (sqrt 1/2)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 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))) (/ 1 (* (pow x 2) (sqrt 1/2))))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ 1 (* (pow x 2) (sqrt 1/2))))))
(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 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)))))
(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)
(* 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)) (/ 1 (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)))
(* 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))) (/ 1 (* (pow x 2) (sqrt 1/2))))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ 1 (* (pow x 2) (sqrt 1/2))))))
(* 1/2 (/ x (sqrt 2)))
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ 1 (* x (sqrt 1/2)))))
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ 1 (* x (sqrt 1/2)))))
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ 1 (* x (sqrt 1/2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(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 (/ (- (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))) (/ 1 (* (pow x 2) (sqrt 1/2))))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ 1 (* (pow x 2) (sqrt 1/2))))))
(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 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)))))
(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)
(* 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) (/ 1 (pow x 2)))) 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) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ 1 (* (pow x 2) (sqrt 1/2))))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ 1 (* (pow x 2) (sqrt 1/2))))))
(* 1/2 (/ x (sqrt 2)))
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ 1 (* x (sqrt 1/2)))))
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ 1 (* x (sqrt 1/2)))))
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ 1 (* x (sqrt 1/2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(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)))
(/ 1 (sqrt 1/2))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (* 1/2 (/ x (sqrt 2))) (/ 1 (sqrt 1/2)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))) (/ 1 (sqrt 1/2)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))) (/ 1 (sqrt 1/2)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #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 (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))
(+ 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 (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))
(+ 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
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 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 (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))
(+ 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
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) #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))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) #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))
(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)))
(/ 1 (sqrt 1/2))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (* 1/2 (/ x (sqrt 2))) (/ 1 (sqrt 1/2)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))) (/ 1 (sqrt 1/2)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))) (/ 1 (sqrt 1/2)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(/ 1 (sqrt 1/2))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (* 1/2 (/ x (sqrt 2))) (/ 1 (sqrt 1/2)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* 1/2 (/ x (sqrt 2))) (/ 1 (sqrt 1/2)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* 1/2 (/ x (sqrt 2))) (/ 1 (sqrt 1/2)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x 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))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)
(* (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 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ 1 (* (pow x 2) (sqrt 1/2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ 1 (* (pow x 2) (sqrt 1/2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 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 (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 (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
(* 1/6 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (.f64 x x))
(* (pow x 3) (+ 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)) (*.f64 x x) x)
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(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))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(* 1/6 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (.f64 x x))
(* (pow x 3) (+ 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)) (*.f64 x x) x)
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (/ 1 (pow x 3))))))
(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))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)
(* (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 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ 1 (* (pow x 2) (sqrt 1/2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ 1 (* (pow x 2) (sqrt 1/2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* 1/2 (/ x (sqrt 2)))
(*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ 1 (* x (sqrt 1/2)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ 1 (* x (sqrt 1/2)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ 1 (* x (sqrt 1/2)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 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))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)
(* (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 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ 1 (* (pow x 2) (sqrt 1/2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ 1 (* (pow x 2) (sqrt 1/2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 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 (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 (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
(* 1/6 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (.f64 x x))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 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))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(* 1/6 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (.f64 x x))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (*.f64 x x) x)
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 1 (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 1 binary64))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)
(* (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 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ 1 (* (pow x 2) (sqrt 1/2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ 1 (* (pow x 2) (sqrt 1/2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* 1/2 (/ x (sqrt 2)))
(*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ 1 (* x (sqrt 1/2)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ 1 (* x (sqrt 1/2)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ 1 (* x (sqrt 1/2)))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 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))

rewrite246.0ms (3.9%)

Memory

-1.9MiB live, 117.7MiB allocated

Rules

3 938×	`lower-/.f32`
3 934×	`lower-/.f64`
3 730×	`lower-*.f32`
3 726×	`lower-*.f64`
3 488×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	340
0	69	328
1	289	280
2	2253	270
0	8663	256

Stop Event

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

Counts

22 → 374

Calls

Call 1

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

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

eval102.0ms (1.6%)

Memory: 16.5MiB live, 90.6MiB allocated
Compiler: Compiled 12 822 to 2 225 computations (82.6% saved)

prune121.0ms (1.9%)

Memory

-8.5MiB live, 113.9MiB allocated

Pruning

17 alts after pruning (5 fresh and 12 done)

	Pruned	Kept	Total
New	736	3	739
Fresh	0	2	2
Picked	1	4	5
Done	0	8	8
Total	737	17	754

Accuracy

100.0%

Counts

754 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓	63.1%	(sqrt.f64 (-.f64 #s(approx (exp 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))) #s(literal -1 binary64)))
✓	63.1%	(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))))
✓	64.6%	(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))))
✓	62.5%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 x #s(literal 2 binary64))))
	2.0%	(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))))
	3.1%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (.f64 x x)))))
✓	3.8%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x))))
✓	4.9%	(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)))))
✓	69.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
	63.4%	#s(approx (pow (pow (- (exp x) -1) 1/4) 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))))
✓	64.4%	#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))))
	63.4%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (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))))
	62.0%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (/ 1 (pow 2 -1/2))) (fma.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) x (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
✓	68.3%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
✓	3.8%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 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)))))
✓	4.1%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))

Compiler

Compiled 391 to 235 computations (39.9% saved)

regimes72.0ms (1.1%)

Memory

-9.5MiB live, 27.1MiB allocated

Counts

21 → 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)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #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 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) 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 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (.f64 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 (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))
(sqrt.f64 (-.f64 #s(approx (exp 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))) #s(literal -1 binary64)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 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 (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (/ 1 (pow 2 -1/2))) (fma.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) x (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 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))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (/ 1 (pow 2 -1/2))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (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))))
#s(approx (pow (pow (- (exp x) -1) 1/4) 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))))
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 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))) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 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))))
(pow.f64 (pow.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))

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

Calls

3 calls:

59.0ms

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

6.0ms

5.0ms

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

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 24 to 20 computations (16.7% saved)

regimes15.0ms (0.2%)

Memory

19.0MiB live, 19.0MiB allocated

Accuracy

Total -43.5b remaining (-221.4%)

Threshold costs -43.5b (-221.4%)

Counts

17 → 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)))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (/ 1 (pow 2 -1/2))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #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 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) 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 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) (.f64 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 (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))
(sqrt.f64 (-.f64 #s(approx (exp 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))) #s(literal -1 binary64)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 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 (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (/ 1 (pow 2 -1/2))) (fma.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) x (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 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))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (/ 1 (pow 2 -1/2))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (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))))
#s(approx (pow (pow (- (exp x) -1) 1/4) 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))))

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

Calls

3 calls:

5.0ms

4.0ms

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

4.0ms

(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
69.3%	1	`x`
69.3%	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))))`
69.3%	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 24 to 20 computations (16.7% saved)

simplify68.0ms (1.1%)

Memory

-25.1MiB live, 23.1MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative-binary64-+.f64`
4×	`sub-neg-binary64-neg.f64-+.f64--.f64`
2×	`1-exp-binary32-exp.f32`
2×	`1-exp-binary64-exp.f64`
2×	`neg-sub0-binary64--.f64-neg.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	19
1	20	19
2	23	19
3	24	19
4	25	19

Stop Event

1×

saturated

Calls

Call 1

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

soundness301.0ms (4.8%)

Memory

14.1MiB live, 169.5MiB allocated

Rules

15 504×	`lower-fma.f64`
15 504×	`lower-fma.f32`
4 704×	`lower-*.f64`
4 704×	`lower-*.f32`
4 562×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	444
1	252	410
2	661	410
3	1434	404
4	2557	324
5	5968	289
0	8342	234
0	10	33
0	17	33
1	63	19
2	429	19
3	4997	19
0	8103	15

Stop Event

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

Compiler

Compiled 27 to 24 computations (11.1% saved)

preprocess22.0ms (0.3%)

Memory: 12.5MiB live, 50.9MiB allocated
Compiler: Compiled 40 to 36 computations (10% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze2.0ms (0%)

sample1.3s (20.5%)

explain123.0ms (2%)

preprocess202.0ms (3.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify174.0ms (2.8%)

localize27.0ms (0.4%)

series4.0ms (0.1%)

simplify169.0ms (2.7%)

rewrite187.0ms (3%)

eval204.0ms (3.3%)

prune135.0ms (2.2%)

simplify175.0ms (2.8%)

localize114.0ms (1.8%)

series71.0ms (1.1%)

simplify203.0ms (3.2%)

rewrite167.0ms (2.7%)

eval129.0ms (2.1%)

prune169.0ms (2.7%)

simplify155.0ms (2.5%)

localize116.0ms (1.9%)

series16.0ms (0.3%)

simplify193.0ms (3.1%)

rewrite240.0ms (3.8%)

eval159.0ms (2.5%)

prune259.0ms (4.1%)

simplify162.0ms (2.6%)

localize265.0ms (4.2%)

series16.0ms (0.3%)

simplify195.0ms (3.1%)

rewrite246.0ms (3.9%)

eval102.0ms (1.6%)

prune121.0ms (1.9%)

regimes72.0ms (1.1%)

regimes15.0ms (0.2%)

simplify68.0ms (1.1%)

soundness301.0ms (4.8%)

preprocess22.0ms (0.3%)

end0.0ms (0%)

Profiling