Metrics for sqrtexp (problem 3.4.4)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze2.0ms (0%)

Memory

2.0MiB live, 2.0MiB 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)

sample972.0ms (21.5%)

Memory

46.7MiB live, 925.4MiB allocated

Samples

488.0ms	8 256×	0	valid
145.0ms	2 621×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 407.0ms

ival-expm1: 130.0ms (31.9% of total)

ival-mult: 110.0ms (27% of total)

ival-div: 74.0ms (18.2% of total)

ival-sqrt: 73.0ms (17.9% of total)

ival-true: 9.0ms (2.2% of total)

exact: 7.0ms (1.7% of total)

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

Bogosity

explain157.0ms (3.5%)

Memory

1.5MiB live, 134.4MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	cancellation	165	0
`-.f64`	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	cancellation	165	0
`/.f64`	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`	o/o	1	0
↳	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`	overflow	1
↳	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	overflow	1
↳	`(exp.f64 x)`	overflow	1
↳	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	overflow	1

Confusion

	Predicted +	Predicted -
+	165	0
-	1	90

Precision

0.9939759036144579

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	165	0	0
-	1	0	90

Precision?

0.9939759036144579

Recall?

1.0

Freqs

test

number	freq
0	90
1	1
2	165

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

41.0ms

512×

valid

Compiler

Compiled 151 to 44 computations (70.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 26.0ms

ival-exp: 7.0ms (27.2% of total)

ival-expm1: 6.0ms (23.3% of total)

ival-div: 4.0ms (15.5% of total)

ival-mult: 4.0ms (15.5% of total)

ival-sqrt: 4.0ms (15.5% of total)

exact: 1.0ms (3.9% of total)

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

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

preprocess207.0ms (4.6%)

Memory

-6.2MiB live, 147.3MiB allocated

Algorithm

1×	egg-herbie

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

Compiler

Compiled 12 to 10 computations (16.7% saved)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 5 to 5 computations (0% saved)

prune1.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))

Compiler

Compiled 5 to 5 computations (0% saved)

simplify3.0ms (0.1%)

Memory

1.7MiB live, 1.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
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)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	13
0	8	13
1	11	13
2	14	13
0	14	13

Stop Event

1×	iter limit
1×	saturated
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)

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)

localize18.0ms (0.4%)

Memory

-23.0MiB live, 15.5MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(exp.f64 x)
accuracy	0.015625	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
accuracy	0.02734375	(-.f64 (exp.f64 x) #s(literal -1 binary64))

Samples

14.0ms

256×

valid

Compiler

Compiled 28 to 12 computations (57.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-sqrt: 4.0ms (51.4% of total)

ival-exp: 2.0ms (25.7% of total)

ival-sub: 1.0ms (12.9% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0%)

Memory

2.3MiB live, 2.3MiB allocated

Counts

3 → 36

Calls

Call 1

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

Inputs

#s(alt #<batchref> (patch (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #<representation binary64>) () ())

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

#s(alt #<batchref> (patch (exp.f64 x) #<representation binary64>) () ())

Outputs
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 (exp.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 (exp.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 (exp.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 (exp.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 (exp.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 (exp.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 (exp.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 (exp.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 (exp.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 (exp.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 (exp.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 (exp.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (exp.f64 x) #<representation binary64>) () ())) ())

Calls

3 calls:

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

simplify180.0ms (4%)

Memory

25.1MiB live, 140.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	224
1	156	190
2	455	190
3	921	184
4	1920	183
5	4949	181
0	8409	165

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

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 (+ 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 (+ 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)

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

rewrite61.0ms (1.4%)

Memory

0.1MiB live, 36.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
0	8	11
1	26	11
2	137	11
0	1185	11

Stop Event

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

Counts

3 → 97

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)

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>

eval22.0ms (0.5%)

Memory: -12.2MiB live, 25.1MiB allocated
Compiler: Compiled 2 159 to 384 computations (82.2% saved)

prune10.0ms (0.2%)

Memory

20.1MiB live, 20.1MiB allocated

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	123	10	133
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	123	11	134

Accuracy

100.0%

Counts

134 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	36.8%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))))))
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
	66.2%	(sqrt.f64 (-.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal -1 binary64)))
	64.1%	(sqrt.f64 (-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
▶	64.6%	(sqrt.f64 #s(approx (- (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))))
▶	66.2%	(sqrt.f64 #s(approx (- (exp x) -1) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
▶	64.1%	(sqrt.f64 #s(approx (- (exp x) -1) (+.f64 #s(literal 2 binary64) x)))
▶	70.3%	(sqrt.f64 #s(approx (- (exp x) -1) #s(literal 2 binary64)))
▶	65.9%	#s(approx (sqrt (- (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))))
	64.9%	#s(approx (sqrt (- (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))))
	64.5%	#s(approx (sqrt (- (exp x) -1)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 263 to 217 computations (17.5% saved)

simplify19.0ms (0.4%)

Memory

-23.8MiB live, 14.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	175
0	50	175
1	71	175
2	102	175
3	208	175
4	360	175
5	441	175
6	502	175
7	502	175
0	502	175

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize76.0ms (1.7%)

Memory

4.7MiB live, 90.0MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.078125	(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	0.515625	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	21.780967039947363	#s(approx (sqrt (- (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	0.03515625	(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64))
accuracy	0.046875	(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
accuracy	0.12890625	(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
accuracy	22.490129922326428	#s(approx (- (exp x) -1) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
accuracy	0	(fma.f64 (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	0.015625	(sqrt.f64 #s(approx (- (exp x) -1) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
accuracy	21.804642220320982	#s(approx (- (exp x) -1) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
accuracy	0	(+.f64 #s(literal 2 binary64) x)
accuracy	0.015625	(sqrt.f64 #s(approx (- (exp x) -1) (+.f64 #s(literal 2 binary64) x)))
accuracy	22.72931071386279	#s(approx (- (exp x) -1) (+.f64 #s(literal 2 binary64) x))
accuracy	0.015625	(sqrt.f64 #s(approx (- (exp x) -1) #s(literal 2 binary64)))
accuracy	19.483481610014152	#s(approx (- (exp x) -1) #s(literal 2 binary64))

Samples

51.0ms	247×	0	valid
2.0ms	5×	2	valid
2.0ms	4×	1	valid

Compiler

Compiled 302 to 58 computations (80.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 40.0ms

ival-add: 15.0ms (37.2% of total)

ival-mult: 11.0ms (27.3% of total)

ival-sqrt: 4.0ms (9.9% of total)

const: 4.0ms (9.9% of total)

ival-div: 2.0ms (5% of total)

ival-exp: 2.0ms (5% of total)

adjust: 1.0ms (2.5% of total)

ival-sub: 1.0ms (2.5% of total)

exact: 1.0ms (2.5% of total)

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

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

series12.0ms (0.3%)

Memory

16.0MiB live, 16.0MiB allocated

Counts

19 → 216

Calls

Call 1

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

Outputs
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sqrt.f64 #s(approx (- (exp x) -1) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sqrt.f64 #s(approx (- (exp x) -1) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sqrt.f64 #s(approx (- (exp x) -1) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sqrt.f64 #s(approx (- (exp x) -1) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (exp x) -1) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (exp x) -1) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (exp x) -1) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (exp x) -1) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sqrt.f64 #s(approx (- (exp x) -1) (+.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sqrt.f64 #s(approx (- (exp x) -1) (+.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sqrt.f64 #s(approx (- (exp x) -1) (+.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sqrt.f64 #s(approx (- (exp x) -1) (+.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (exp x) -1) (+.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (exp x) -1) (+.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (exp x) -1) (+.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (exp x) -1) (+.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sqrt.f64 #s(approx (- (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 #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sqrt.f64 #s(approx (- (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 #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sqrt.f64 #s(approx (- (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 #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sqrt.f64 #s(approx (- (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 #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (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 #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (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 #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (- (exp x) -1) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
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Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	((sqrt (- (exp x) -1)) (- (exp x) -1) (sqrt (- (exp x) -1)) (- (exp x) -1) (+ 2 x) (sqrt (- (exp x) -1)) (- (exp x) -1) (+ (* (+ (* 1/2 x) 1) x) 2) (+ (* 1/2 x) 1) (sqrt (- (exp 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)) (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (+ (* 3/16 x) 1/2) (/ x (sqrt 2)) (+ (* 1/6 x) 1/2) (sqrt 2))
2.0ms	x	@	-inf	((sqrt (- (exp x) -1)) (- (exp x) -1) (sqrt (- (exp x) -1)) (- (exp x) -1) (+ 2 x) (sqrt (- (exp x) -1)) (- (exp x) -1) (+ (* (+ (* 1/2 x) 1) x) 2) (+ (* 1/2 x) 1) (sqrt (- (exp 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)) (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (+ (* 3/16 x) 1/2) (/ x (sqrt 2)) (+ (* 1/6 x) 1/2) (sqrt 2))
2.0ms	x	@	0	((sqrt (- (exp x) -1)) (- (exp x) -1) (sqrt (- (exp x) -1)) (- (exp x) -1) (+ 2 x) (sqrt (- (exp x) -1)) (- (exp x) -1) (+ (* (+ (* 1/2 x) 1) x) 2) (+ (* 1/2 x) 1) (sqrt (- (exp 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)) (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (+ (* 3/16 x) 1/2) (/ x (sqrt 2)) (+ (* 1/6 x) 1/2) (sqrt 2))

Time

Variable

Point

Expression

3.0ms

inf

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

2.0ms

-inf

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

2.0ms

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

simplify276.0ms (6.1%)

Memory

10.3MiB live, 171.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	122	1573
1	399	1373
2	1146	1320
3	4203	1303
4	7841	1303
0	8430	1169

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 216

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))))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
2
(+ 2 x)
(+ 2 x)
(+ 2 x)
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* 1/2 x))))
1
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(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))
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(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))
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(* 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 (+ 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))
(* 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)))
(* 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))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(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))
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(* 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 (+ 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))
(* 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)))
(* 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))
(* 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.f64 #s(literal 2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))
#s(literal 2 binary64)
(+.f64 #s(literal 2 binary64) x)
(fma.f64 (fma.f64 #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))
(sqrt.f64 #s(literal 2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))
#s(literal 2 binary64)
(+.f64 #s(literal 2 binary64) x)
(fma.f64 (fma.f64 #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))
#s(literal 2 binary64)
(+.f64 #s(literal 2 binary64) x)
(+.f64 #s(literal 2 binary64) x)
(+.f64 #s(literal 2 binary64) x)
(sqrt.f64 #s(literal 2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))
#s(literal 2 binary64)
(+.f64 #s(literal 2 binary64) x)
(fma.f64 (fma.f64 #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))
#s(literal 2 binary64)
(+.f64 #s(literal 2 binary64) x)
(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))
#s(literal 1 binary64)
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(sqrt.f64 #s(literal 2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))
#s(literal 2 binary64)
(+.f64 #s(literal 2 binary64) x)
(fma.f64 (fma.f64 #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))
#s(literal 2 binary64)
(+.f64 #s(literal 2 binary64) x)
(fma.f64 (fma.f64 #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))
#s(literal 1 binary64)
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(sqrt.f64 #s(literal 2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
#s(literal 1/2 binary64)
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 3/16 binary64) x #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)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
#s(literal 1/2 binary64)
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
x
(+.f64 #s(literal 2 binary64) x)
(+.f64 #s(literal 2 binary64) x)
(+.f64 #s(literal 2 binary64) x)
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
(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))
(*.f64 #s(literal 1/2 binary64) x)
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
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(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64))
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x 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))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) 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))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(*.f64 (fma.f64 (fma.f64 #s(literal 3/8 binary64) x #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)) x)
(*.f64 (fma.f64 (fma.f64 #s(literal 3/8 binary64) x #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)) x)
(*.f64 #s(literal 3/16 binary64) x)
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 3/16 binary64) x #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)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(*.f64 #s(literal 1/6 binary64) x)
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
x
(+.f64 #s(literal 2 binary64) x)
(+.f64 #s(literal 2 binary64) x)
(+.f64 #s(literal 2 binary64) x)
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
(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))
(*.f64 #s(literal 1/2 binary64) x)
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64))
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(*.f64 (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) x) #s(literal -1/6 binary64)) (pow.f64 x #s(literal 3 binary64)))
(.f64 (-.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) x (/.f64 (+.f64 #s(literal 2 binary64) x) x)) (.f64 x x)) #s(literal -1/6 binary64)) (pow.f64 x #s(literal 3 binary64)))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) 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))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(*.f64 (fma.f64 (fma.f64 #s(literal 3/8 binary64) x #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)) x)
(*.f64 (fma.f64 (fma.f64 #s(literal 3/8 binary64) x #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)) x)
(*.f64 #s(literal 3/16 binary64) x)
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 3/16 binary64) x #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)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(*.f64 #s(literal 1/6 binary64) x)
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))

rewrite198.0ms (4.4%)

Memory

-18.9MiB live, 141.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	159
0	50	159
1	189	159
2	1358	159
0	8327	159

Stop Event

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

Counts

19 → 390

Calls

Call 1

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

Outputs
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eval101.0ms (2.2%)

Memory: 21.6MiB live, 96.3MiB allocated
Compiler: Compiled 15 104 to 1 942 computations (87.1% saved)

prune57.0ms (1.3%)

Memory

-29.1MiB live, 53.9MiB allocated

Pruning

18 alts after pruning (12 fresh and 6 done)

	Pruned	Kept	Total
New	612	9	621
Fresh	2	3	5
Picked	0	5	5
Done	0	1	1
Total	614	18	632

Accuracy

100.0%

Counts

632 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
▶	66.2%	(sqrt.f64 (-.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal -1 binary64)))
	64.1%	(sqrt.f64 (-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
✓	64.6%	(sqrt.f64 #s(approx (- (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))))
✓	66.2%	(sqrt.f64 #s(approx (- (exp x) -1) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
▶	64.1%	(sqrt.f64 #s(approx (- (exp x) -1) (/.f64 (fma.f64 x x #s(literal -4 binary64)) (-.f64 x #s(literal 2 binary64)))))
✓	64.1%	(sqrt.f64 #s(approx (- (exp x) -1) (+.f64 #s(literal 2 binary64) x)))
	2.7%	(sqrt.f64 #s(approx (- (exp x) -1) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x))))
▶	3.4%	(sqrt.f64 #s(approx (- (exp x) -1) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))))
	4.5%	(sqrt.f64 #s(approx (- (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))))
▶	5.1%	(sqrt.f64 #s(approx (- (exp x) -1) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
▶	2.7%	(sqrt.f64 #s(approx (- (exp x) -1) #s(approx (+ 2 x) x)))
✓	70.3%	(sqrt.f64 #s(approx (- (exp x) -1) #s(literal 2 binary64)))
	65.0%	#s(approx (sqrt (- (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)))))
✓	65.9%	#s(approx (sqrt (- (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))))
	64.9%	#s(approx (sqrt (- (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))))
	4.2%	#s(approx (sqrt (- (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)))))
	4.3%	#s(approx (sqrt (- (exp x) -1)) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)))

Compiler

Compiled 555 to 445 computations (19.8% saved)

simplify11.0ms (0.2%)

Memory

6.6MiB live, 6.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(fma.f64 x x #s(literal -4 binary64))
cost-diff	0	(/.f64 (fma.f64 x x #s(literal -4 binary64)) (-.f64 x #s(literal 2 binary64)))
cost-diff	0	#s(approx (- (exp x) -1) (/.f64 (fma.f64 x x #s(literal -4 binary64)) (-.f64 x #s(literal 2 binary64))))
cost-diff	0	(sqrt.f64 #s(approx (- (exp x) -1) (/.f64 (fma.f64 x x #s(literal -4 binary64)) (-.f64 x #s(literal 2 binary64)))))
cost-diff	0	(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
cost-diff	0	#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))
cost-diff	0	#s(approx (- (exp x) -1) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)))
cost-diff	0	(sqrt.f64 #s(approx (- (exp x) -1) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))))
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 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 x) -1) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
cost-diff	0	#s(approx (+ 2 x) x)
cost-diff	0	#s(approx (- (exp x) -1) #s(approx (+ 2 x) x))
cost-diff	0	(sqrt.f64 #s(approx (- (exp x) -1) #s(approx (+ 2 x) x)))
cost-diff	0	(fma.f64 (fma.f64 #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 #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 #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 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal -1 binary64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	280
0	61	280
1	87	280
2	110	280
3	166	280
4	305	280
5	359	280
6	363	280
0	363	271

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize79.0ms (1.7%)

Memory

18.3MiB live, 90.9MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	(-.f64 x #s(literal 2 binary64))
accuracy	0.015625	(sqrt.f64 #s(approx (- (exp x) -1) (/.f64 (fma.f64 x x #s(literal -4 binary64)) (-.f64 x #s(literal 2 binary64)))))
accuracy	10.454392034032919	(/.f64 (fma.f64 x x #s(literal -4 binary64)) (-.f64 x #s(literal 2 binary64)))
accuracy	22.72931071386279	#s(approx (- (exp x) -1) (/.f64 (fma.f64 x x #s(literal -4 binary64)) (-.f64 x #s(literal 2 binary64))))
accuracy	0.05859375	(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
accuracy	0.12890625	(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
accuracy	22.490129922326428	#s(approx (- (exp x) -1) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)))
accuracy	39.88109429724827	#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))
accuracy	0	(*.f64 x x)
accuracy	0.015625	(sqrt.f64 #s(approx (- (exp x) -1) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
accuracy	21.804642220320982	#s(approx (- (exp x) -1) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))
accuracy	40.181697549439384	#s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
accuracy	0.015625	(sqrt.f64 #s(approx (- (exp x) -1) #s(approx (+ 2 x) x)))
accuracy	22.72931071386279	#s(approx (- (exp x) -1) #s(approx (+ 2 x) x))
accuracy	40.23325751756271	#s(approx (+ 2 x) x)
accuracy	0	(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
accuracy	0.015625	(sqrt.f64 (-.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal -1 binary64)))
accuracy	0.02734375	(-.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal -1 binary64))
accuracy	22.313136531519664	#s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))

Samples

58.0ms

256×

valid

Compiler

Compiled 433 to 79 computations (81.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 42.0ms

ival-add: 13.0ms (30.8% of total)

ival-mult: 12.0ms (28.4% of total)

ival-exp: 6.0ms (14.2% of total)

const: 4.0ms (9.5% of total)

ival-sub: 3.0ms (7.1% of total)

ival-div: 2.0ms (4.7% of total)

ival-sqrt: 2.0ms (4.7% of total)

exact: 1.0ms (2.4% of total)

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

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

series34.0ms (0.7%)

Memory

-33.6MiB live, 15.5MiB allocated

Counts

24 → 288

Calls

Call 1

Inputs
#s(alt #<batchref> (patch (sqrt.f64 (-.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (-.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 #s(approx (- (exp x) -1) #s(approx (+ 2 x) x))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (exp x) -1) #s(approx (+ 2 x) x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (+ 2 x) x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 #s(approx (- (exp x) -1) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (exp x) -1) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 #s(approx (- (exp x) -1) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (exp x) -1) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 #s(approx (- (exp x) -1) (/.f64 (fma.f64 x x #s(literal -4 binary64)) (-.f64 x #s(literal 2 binary64))))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (- (exp x) -1) (/.f64 (fma.f64 x x #s(literal -4 binary64)) (-.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 (fma.f64 x x #s(literal -4 binary64)) (-.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 x x #s(literal -4 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (-.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())

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

Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

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

2.0ms

-inf

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

2.0ms

inf

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

simplify266.0ms (5.9%)

Memory

42.0MiB live, 270.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	112	1748
1	356	1570
2	1015	1562
3	3680	1532
4	6866	1532
0	8263	1382

Stop Event

1×	iter limit
1×	node limit

Counts

288 → 288

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

Outputs
(sqrt.f64 #s(literal 2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))
#s(literal 2 binary64)
(+.f64 #s(literal 2 binary64) x)
(fma.f64 (fma.f64 #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))
#s(literal 1 binary64)
(+.f64 #s(literal 1 binary64) x)
(fma.f64 (fma.f64 #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(literal 1 binary64)
(+.f64 #s(literal 1 binary64) x)
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(sqrt.f64 #s(literal 2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))
#s(literal 2 binary64)
(+.f64 #s(literal 2 binary64) x)
(fma.f64 (fma.f64 #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))
#s(literal 2 binary64)
(+.f64 #s(literal 2 binary64) x)
(+.f64 #s(literal 2 binary64) x)
(+.f64 #s(literal 2 binary64) x)
(sqrt.f64 #s(literal 2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))
#s(literal 2 binary64)
(+.f64 #s(literal 2 binary64) x)
(fma.f64 (fma.f64 #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))
#s(literal 2 binary64)
(+.f64 #s(literal 2 binary64) x)
(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))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))
#s(literal 2 binary64)
(+.f64 #s(literal 2 binary64) x)
(fma.f64 (fma.f64 #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))
#s(literal 2 binary64)
(+.f64 #s(literal 2 binary64) x)
(fma.f64 (fma.f64 #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))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(sqrt.f64 #s(literal 2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) x (sqrt.f64 #s(literal 2 binary64)))
#s(literal 2 binary64)
(+.f64 #s(literal 2 binary64) x)
(fma.f64 (fma.f64 #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))
#s(literal 2 binary64)
(+.f64 #s(literal 2 binary64) x)
(+.f64 #s(literal 2 binary64) x)
(+.f64 #s(literal 2 binary64) x)
#s(literal -4 binary64)
(fma.f64 x x #s(literal -4 binary64))
(fma.f64 x x #s(literal -4 binary64))
(fma.f64 x x #s(literal -4 binary64))
#s(literal 1 binary64)
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
#s(literal 1/2 binary64)
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
#s(literal -2 binary64)
(-.f64 x #s(literal 2 binary64))
(-.f64 x #s(literal 2 binary64))
(-.f64 x #s(literal 2 binary64))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(exp.f64 x)
(exp.f64 x)
(exp.f64 x)
(exp.f64 x)
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/2 binary64) x)
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
x
(+.f64 #s(literal 2 binary64) x)
(+.f64 #s(literal 2 binary64) x)
(+.f64 #s(literal 2 binary64) x)
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/2 binary64) x)
(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))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64))
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) 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))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64))
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
x
(+.f64 #s(literal 2 binary64) x)
(+.f64 #s(literal 2 binary64) x)
(+.f64 #s(literal 2 binary64) x)
(*.f64 x x)
(fma.f64 x x #s(literal -4 binary64))
(fma.f64 x x #s(literal -4 binary64))
(fma.f64 x x #s(literal -4 binary64))
(*.f64 #s(literal 1/2 binary64) x)
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(*.f64 #s(literal 1/6 binary64) x)
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
x
(-.f64 x #s(literal 2 binary64))
(-.f64 x #s(literal 2 binary64))
(-.f64 x #s(literal 2 binary64))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(exp.f64 x)
(exp.f64 x)
(exp.f64 x)
(exp.f64 x)
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/2 binary64) x)
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
x
(+.f64 #s(literal 2 binary64) x)
(+.f64 #s(literal 2 binary64) x)
(+.f64 #s(literal 2 binary64) x)
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/2 binary64) x)
(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))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64))
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) 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))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64))
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
x
(+.f64 #s(literal 2 binary64) x)
(+.f64 #s(literal 2 binary64) x)
(+.f64 #s(literal 2 binary64) x)
(*.f64 x x)
(fma.f64 x x #s(literal -4 binary64))
(fma.f64 x x #s(literal -4 binary64))
(fma.f64 x x #s(literal -4 binary64))
(*.f64 #s(literal 1/2 binary64) x)
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(*.f64 x x)
(*.f64 #s(literal 1/6 binary64) x)
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
x
(-.f64 x #s(literal 2 binary64))
(-.f64 x #s(literal 2 binary64))
(-.f64 x #s(literal 2 binary64))

rewrite222.0ms (4.9%)

Memory

-26.6MiB live, 214.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	267
0	61	267
1	222	252
2	1465	252
0	8420	243

Stop Event

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

Counts

24 → 469

Calls

Call 1

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

Outputs
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eval136.0ms (3%)

Memory: 30.0MiB live, 138.2MiB allocated
Compiler: Compiled 19 669 to 2 506 computations (87.3% saved)

prune37.0ms (0.8%)

Memory

-18.7MiB live, 63.1MiB allocated

Pruning

19 alts after pruning (9 fresh and 10 done)

	Pruned	Kept	Total
New	754	3	757
Fresh	1	6	7
Picked	1	4	5
Done	0	6	6
Total	756	19	775

Accuracy

100.0%

Counts

775 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓	66.2%	(sqrt.f64 (-.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal -1 binary64)))
▶	64.1%	(sqrt.f64 (-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
✓	64.6%	(sqrt.f64 #s(approx (- (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))))
✓	66.2%	(sqrt.f64 #s(approx (- (exp x) -1) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
▶	66.9%	(sqrt.f64 #s(approx (- (exp x) -1) (/.f64 #s(approx (+ (* x x) -4) #s(literal -4 binary64)) (-.f64 x #s(literal 2 binary64)))))
✓	64.1%	(sqrt.f64 #s(approx (- (exp x) -1) (+.f64 #s(literal 2 binary64) x)))
	2.7%	(sqrt.f64 #s(approx (- (exp x) -1) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x))))
✓	3.4%	(sqrt.f64 #s(approx (- (exp x) -1) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))))
▶	2.4%	(sqrt.f64 #s(approx (- (exp x) -1) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 #s(approx (+ (* 1/6 x) 1/2) (*.f64 #s(literal 1/6 binary64) x)) x) x))))
	4.5%	(sqrt.f64 #s(approx (- (exp x) -1) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) x))))
✓	5.1%	(sqrt.f64 #s(approx (- (exp x) -1) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
✓	2.7%	(sqrt.f64 #s(approx (- (exp x) -1) #s(approx (+ 2 x) x)))
✓	70.3%	(sqrt.f64 #s(approx (- (exp x) -1) #s(literal 2 binary64)))
	65.0%	#s(approx (sqrt (- (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)))))
✓	65.9%	#s(approx (sqrt (- (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))))
▶	64.9%	#s(approx (sqrt (- (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))))
	4.2%	#s(approx (sqrt (- (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)))))
▶	4.3%	#s(approx (sqrt (- (exp x) -1)) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)))

Compiler

Compiled 554 to 435 computations (21.5% saved)

simplify29.0ms (0.6%)

Memory

5.0MiB live, 43.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 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)))
cost-diff	0	#s(approx (sqrt (- (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))))
cost-diff	0	(*.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
cost-diff	0	(.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)
cost-diff	0	#s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x))
cost-diff	0	#s(approx (sqrt (- (exp x) -1)) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)))
cost-diff	0	(.f64 (.f64 #s(approx (+ (* 1/6 x) 1/2) (*.f64 #s(literal 1/6 binary64) x)) x) x)
cost-diff	0	#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 #s(approx (+ (* 1/6 x) 1/2) (*.f64 #s(literal 1/6 binary64) x)) x) x))
cost-diff	0	#s(approx (- (exp x) -1) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 #s(approx (+ (* 1/6 x) 1/2) (*.f64 #s(literal 1/6 binary64) x)) x) x)))
cost-diff	0	(sqrt.f64 #s(approx (- (exp x) -1) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 #s(approx (+ (* 1/6 x) 1/2) (*.f64 #s(literal 1/6 binary64) x)) x) x))))
cost-diff	0	(+.f64 #s(literal 1 binary64) x)
cost-diff	0	#s(approx (exp x) (+.f64 #s(literal 1 binary64) x))
cost-diff	0	(-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
cost-diff	0	(sqrt.f64 (-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
cost-diff	0	#s(approx (+ (* x x) -4) #s(literal -4 binary64))
cost-diff	0	(/.f64 #s(approx (+ (* x x) -4) #s(literal -4 binary64)) (-.f64 x #s(literal 2 binary64)))
cost-diff	0	#s(approx (- (exp x) -1) (/.f64 #s(approx (+ (* x x) -4) #s(literal -4 binary64)) (-.f64 x #s(literal 2 binary64))))
cost-diff	0	(sqrt.f64 #s(approx (- (exp x) -1) (/.f64 #s(approx (+ (* x x) -4) #s(literal -4 binary64)) (-.f64 x #s(literal 2 binary64)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	345
0	75	345
1	123	345
2	215	345
3	392	345
4	713	345
5	933	345
6	1122	345
7	1122	345
0	1122	322

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

Outputs
(sqrt.f64 #s(approx (- (exp x) -1) (/.f64 #s(approx (+ (* x x) -4) #s(literal -4 binary64)) (-.f64 x #s(literal 2 binary64)))))
#s(approx (- (exp x) -1) (/.f64 #s(approx (+ (* x x) -4) #s(literal -4 binary64)) (-.f64 x #s(literal 2 binary64))))
(/.f64 #s(approx (+ (* x x) -4) #s(literal -4 binary64)) (-.f64 x #s(literal 2 binary64)))
#s(approx (+ (* x x) -4) #s(literal -4 binary64))
#s(literal -4 binary64)
(-.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
(sqrt.f64 (-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
(-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
#s(approx (exp x) (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(literal -1 binary64)
(sqrt.f64 #s(approx (- (exp x) -1) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 #s(approx (+ ( 1/6 x) 1/2) (.f64 #s(literal 1/6 binary64) x)) (.f64 x x)))))
#s(approx (- (exp x) -1) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 #s(approx (+ ( 1/6 x) 1/2) (.f64 #s(literal 1/6 binary64) x)) (.f64 x x))))
#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 #s(approx (+ ( 1/6 x) 1/2) (.f64 #s(literal 1/6 binary64) x)) (.f64 x x)))
(.f64 #s(approx (+ ( 1/6 x) 1/2) (.f64 #s(literal 1/6 binary64) x)) (.f64 x x))
(.f64 #s(approx (+ ( 1/6 x) 1/2) (*.f64 #s(literal 1/6 binary64) x)) x)
#s(approx (+ (* 1/6 x) 1/2) (*.f64 #s(literal 1/6 binary64) x))
(*.f64 #s(literal 1/6 binary64) x)
#s(literal 1/6 binary64)
x
#s(approx (sqrt (- (exp x) -1)) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)))
#s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x))
(.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)
(*.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
(/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))
#s(literal 3/16 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
x
#s(approx (sqrt (- (exp x) -1)) (fma.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
#s(literal 7/192 binary64)
#s(literal 3/16 binary64)
#s(literal 1/2 binary64)

localize143.0ms (3.2%)

Memory

17.5MiB live, 188.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.05859375	(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)))
accuracy	0.140625	(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
accuracy	0.515625	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	21.983788432783793	#s(approx (sqrt (- (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))))
accuracy	0.09765625	(.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)
accuracy	0.546875	(*.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
accuracy	21.334420435694753	#s(approx (sqrt (- (exp x) -1)) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)))
accuracy	39.930718996607496	#s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x))
accuracy	0.3828125	(*.f64 #s(literal 1/6 binary64) x)
accuracy	21.99763951248248	#s(approx (- (exp x) -1) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 #s(approx (+ (* 1/6 x) 1/2) (*.f64 #s(literal 1/6 binary64) x)) x) x)))
accuracy	39.76585813143366	#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 #s(approx (+ (* 1/6 x) 1/2) (*.f64 #s(literal 1/6 binary64) x)) x) x))
accuracy	39.981004029514864	#s(approx (+ (* 1/6 x) 1/2) (*.f64 #s(literal 1/6 binary64) x))
accuracy	0	(+.f64 #s(literal 1 binary64) x)
accuracy	0.015625	(sqrt.f64 (-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
accuracy	0.02734375	(-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
accuracy	22.00758150472509	#s(approx (exp x) (+.f64 #s(literal 1 binary64) x))
accuracy	0.015625	(sqrt.f64 #s(approx (- (exp x) -1) (/.f64 #s(approx (+ (* x x) -4) #s(literal -4 binary64)) (-.f64 x #s(literal 2 binary64)))))
accuracy	10.454392034032919	(/.f64 #s(approx (+ (* x x) -4) #s(literal -4 binary64)) (-.f64 x #s(literal 2 binary64)))
accuracy	22.237024112277076	#s(approx (- (exp x) -1) (/.f64 #s(approx (+ (* x x) -4) #s(literal -4 binary64)) (-.f64 x #s(literal 2 binary64))))
accuracy	22.301960693699925	#s(approx (+ (* x x) -4) #s(literal -4 binary64))

Samples

70.0ms	246×	0	valid
5.0ms	2×	1	valid
5.0ms	6×	2	valid
2.0ms	2×	5	exit

Compiler

Compiled 529 to 101 computations (80.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 58.0ms

ival-mult: 19.0ms (32.9% of total)

ival-add: 12.0ms (20.8% of total)

const: 8.0ms (13.9% of total)

ival-div: 8.0ms (13.9% of total)

ival-sqrt: 4.0ms (6.9% of total)

ival-exp: 3.0ms (5.2% of total)

ival-sub: 3.0ms (5.2% of total)

adjust: 2.0ms (3.5% of total)

exact: 1.0ms (1.7% of total)

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

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

series19.0ms (0.4%)

Memory

-20.4MiB live, 17.6MiB allocated

Counts

23 → 264

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

6.0ms

((sqrt (- (exp x) -1)) (- (exp x) -1) (/ (+ (* x x) -4) (- x 2)) (+ (* x x) -4) (sqrt (- (exp x) -1)) (- (exp x) -1) (exp x) (+ 1 x) (sqrt (- (exp x) -1)) (- (exp x) -1) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (* (* (+ (* 1/6 x) 1/2) x) x) (sqrt (- (exp x) -1)) (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (* (* (/ 3/16 (sqrt 2)) x) x) (* (/ 3/16 (sqrt 2)) x) (sqrt (- (exp x) -1)) (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (/ x (sqrt 2)) (sqrt 2) (+ (* 1/6 x) 1/2) (* 1/6 x) (+ (* 7/192 x) 3/16))

3.0ms

-inf

((sqrt (- (exp x) -1)) (- (exp x) -1) (/ (+ (* x x) -4) (- x 2)) (+ (* x x) -4) (sqrt (- (exp x) -1)) (- (exp x) -1) (exp x) (+ 1 x) (sqrt (- (exp x) -1)) (- (exp x) -1) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (* (* (+ (* 1/6 x) 1/2) x) x) (sqrt (- (exp x) -1)) (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (* (* (/ 3/16 (sqrt 2)) x) x) (* (/ 3/16 (sqrt 2)) x) (sqrt (- (exp x) -1)) (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (/ x (sqrt 2)) (sqrt 2) (+ (* 1/6 x) 1/2) (* 1/6 x) (+ (* 7/192 x) 3/16))

3.0ms

inf

((sqrt (- (exp x) -1)) (- (exp x) -1) (/ (+ (* x x) -4) (- x 2)) (+ (* x x) -4) (sqrt (- (exp x) -1)) (- (exp x) -1) (exp x) (+ 1 x) (sqrt (- (exp x) -1)) (- (exp x) -1) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (* (* (+ (* 1/6 x) 1/2) x) x) (sqrt (- (exp x) -1)) (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (* (* (/ 3/16 (sqrt 2)) x) x) (* (/ 3/16 (sqrt 2)) x) (sqrt (- (exp x) -1)) (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (/ x (sqrt 2)) (sqrt 2) (+ (* 1/6 x) 1/2) (* 1/6 x) (+ (* 7/192 x) 3/16))

simplify242.0ms (5.4%)

Memory

9.6MiB live, 157.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	165	1953
1	531	1730
2	1576	1646
3	4822	1631
0	8149	1509

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 264

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))))))
2
(+ 2 x)
(+ 2 x)
(+ 2 x)
-4
(- (pow x 2) 4)
(- (pow x 2) 4)
(- (pow x 2) 4)
(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 x)
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(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)))
(* 3/16 (/ x (sqrt 2)))
(* 3/16 (/ x (sqrt 2)))
(* 3/16 (/ x (sqrt 2)))
(* 3/16 (/ x (sqrt 2)))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
3/16
(+ 3/16 (* 7/192 x))
(+ 3/16 (* 7/192 x))
(+ 3/16 (* 7/192 x))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(pow x 2)
(* (pow x 2) (- 1 (* 4 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 4 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 4 (/ 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)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(* 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)))
(* 3/16 (/ x (sqrt 2)))
(* 3/16 (/ x (sqrt 2)))
(* 3/16 (/ x (sqrt 2)))
(* 3/16 (/ x (sqrt 2)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 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))))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 7/192 x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(sqrt (+ 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))
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(pow x 2)
(* (pow x 2) (- 1 (* 4 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 4 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 4 (/ 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)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(* 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)))
(* 3/16 (/ x (sqrt 2)))
(* 3/16 (/ x (sqrt 2)))
(* 3/16 (/ x (sqrt 2)))
(* 3/16 (/ x (sqrt 2)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 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))))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 7/192 x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))

Outputs
(sqrt.f64 #s(literal 2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
#s(literal 2 binary64)
(+.f64 #s(literal 2 binary64) x)
(fma.f64 (fma.f64 #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))
#s(literal 2 binary64)
(+.f64 #s(literal 2 binary64) x)
(+.f64 #s(literal 2 binary64) x)
(+.f64 #s(literal 2 binary64) x)
#s(literal -4 binary64)
(fma.f64 x x #s(literal -4 binary64))
(fma.f64 x x #s(literal -4 binary64))
(fma.f64 x x #s(literal -4 binary64))
(sqrt.f64 #s(literal 2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
#s(literal 2 binary64)
(+.f64 #s(literal 2 binary64) x)
(fma.f64 (fma.f64 #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))
#s(literal 1 binary64)
(+.f64 #s(literal 1 binary64) x)
(fma.f64 (fma.f64 #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(literal 1 binary64)
(+.f64 #s(literal 1 binary64) x)
(+.f64 #s(literal 1 binary64) x)
(+.f64 #s(literal 1 binary64) x)
(sqrt.f64 #s(literal 2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
#s(literal 2 binary64)
(+.f64 #s(literal 2 binary64) x)
(fma.f64 (fma.f64 #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))
#s(literal 2 binary64)
(+.f64 #s(literal 2 binary64) x)
(fma.f64 (fma.f64 #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))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(sqrt.f64 #s(literal 2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)
(.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)
(.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)
(.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)
(*.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
(*.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
(*.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
(*.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
(sqrt.f64 #s(literal 2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
#s(literal 1/2 binary64)
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(*.f64 #s(literal 1/6 binary64) x)
(*.f64 #s(literal 1/6 binary64) x)
(*.f64 #s(literal 1/6 binary64) x)
(*.f64 #s(literal 1/6 binary64) x)
#s(literal 3/16 binary64)
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
x
(+.f64 #s(literal 2 binary64) x)
(+.f64 #s(literal 2 binary64) x)
(+.f64 #s(literal 2 binary64) x)
(*.f64 x x)
(fma.f64 x x #s(literal -4 binary64))
(fma.f64 x x #s(literal -4 binary64))
(fma.f64 x x #s(literal -4 binary64))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(exp.f64 x)
(exp.f64 x)
(exp.f64 x)
(exp.f64 x)
x
(+.f64 #s(literal 1 binary64) x)
(+.f64 #s(literal 1 binary64) x)
(+.f64 #s(literal 1 binary64) x)
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64))
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) 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))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64))
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(.f64 (fma.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) x (.f64 (fma.f64 #s(literal 3/8 binary64) x #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))) x)
(.f64 (fma.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) x (.f64 (fma.f64 #s(literal 3/8 binary64) x #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))) x)
(.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)
(.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)
(.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)
(.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)
(*.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
(*.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
(*.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
(*.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(*.f64 (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 3 binary64)))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
(.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 x #s(literal 3 binary64)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(*.f64 #s(literal 1/6 binary64) x)
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(*.f64 #s(literal 1/6 binary64) x)
(*.f64 #s(literal 1/6 binary64) x)
(*.f64 #s(literal 1/6 binary64) x)
(*.f64 #s(literal 1/6 binary64) x)
(*.f64 #s(literal 7/192 binary64) x)
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
x
(+.f64 #s(literal 2 binary64) x)
(+.f64 #s(literal 2 binary64) x)
(+.f64 #s(literal 2 binary64) x)
(*.f64 x x)
(fma.f64 x x #s(literal -4 binary64))
(fma.f64 x x #s(literal -4 binary64))
(fma.f64 x x #s(literal -4 binary64))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(exp.f64 x)
(exp.f64 x)
(exp.f64 x)
(exp.f64 x)
x
(+.f64 #s(literal 1 binary64) x)
(+.f64 #s(literal 1 binary64) x)
(+.f64 #s(literal 1 binary64) x)
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64))
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(*.f64 (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) x) #s(literal -1/6 binary64)) (pow.f64 x #s(literal 3 binary64)))
(*.f64 (-.f64 (/.f64 (fma.f64 (+.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) x) #s(literal -1/6 binary64)) (pow.f64 x #s(literal 3 binary64)))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64))
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(.f64 (fma.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) x (.f64 (fma.f64 #s(literal 3/8 binary64) x #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))) x)
(.f64 (fma.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) x (.f64 (fma.f64 #s(literal 3/8 binary64) x #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))) x)
(.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)
(.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)
(.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)
(.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)
(*.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
(*.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
(*.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
(*.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(*.f64 (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 3 binary64)))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))
(.f64 (-.f64 (/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3/16 binary64))) x) (/.f64 #s(literal -7/192 binary64) (sqrt.f64 #s(literal 2 binary64)))) (pow.f64 x #s(literal 3 binary64)))
(*.f64 (-.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3/16 binary64)) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) x)) x) (/.f64 #s(literal -7/192 binary64) (sqrt.f64 #s(literal 2 binary64)))) (pow.f64 x #s(literal 3 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(*.f64 #s(literal 1/6 binary64) x)
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(*.f64 #s(literal 1/6 binary64) x)
(*.f64 #s(literal 1/6 binary64) x)
(*.f64 #s(literal 1/6 binary64) x)
(*.f64 #s(literal 1/6 binary64) x)
(*.f64 #s(literal 7/192 binary64) x)
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))

rewrite215.0ms (4.8%)

Memory

10.8MiB live, 220.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	302
0	75	302
1	299	302
2	2175	302
0	9055	280

Stop Event

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

Counts

23 → 286

Calls

Call 1

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

Outputs
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eval105.0ms (2.3%)

Memory: -18.2MiB live, 160.2MiB allocated
Compiler: Compiled 14 768 to 1 444 computations (90.2% saved)

prune56.0ms (1.2%)

Memory

-15.0MiB live, 58.6MiB allocated

Pruning

20 alts after pruning (7 fresh and 13 done)

	Pruned	Kept	Total
New	561	3	564
Fresh	0	4	4
Picked	1	4	5
Done	1	9	10
Total	563	20	583

Accuracy

100.0%

Counts

583 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓	66.2%	(sqrt.f64 (-.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal -1 binary64)))
✓	64.1%	(sqrt.f64 (-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
✓	64.6%	(sqrt.f64 #s(approx (- (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))))
✓	66.2%	(sqrt.f64 #s(approx (- (exp x) -1) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
✓	66.9%	(sqrt.f64 #s(approx (- (exp x) -1) (/.f64 #s(approx (+ (* x x) -4) #s(literal -4 binary64)) (-.f64 x #s(literal 2 binary64)))))
✓	64.1%	(sqrt.f64 #s(approx (- (exp x) -1) (+.f64 #s(literal 2 binary64) x)))
	2.7%	(sqrt.f64 #s(approx (- (exp x) -1) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x))))
✓	3.4%	(sqrt.f64 #s(approx (- (exp x) -1) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))))
✓	2.4%	(sqrt.f64 #s(approx (- (exp x) -1) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 #s(approx (+ (* 1/6 x) 1/2) (*.f64 #s(literal 1/6 binary64) x)) x) x))))
	4.5%	(sqrt.f64 #s(approx (- (exp x) -1) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) x))))
✓	5.1%	(sqrt.f64 #s(approx (- (exp x) -1) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
✓	2.7%	(sqrt.f64 #s(approx (- (exp x) -1) #s(approx (+ 2 x) x)))
✓	70.3%	(sqrt.f64 #s(approx (- (exp x) -1) #s(literal 2 binary64)))
	65.0%	#s(approx (sqrt (- (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)))))
✓	64.9%	#s(approx (sqrt (- (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))))
	3.1%	#s(approx (sqrt (- (exp x) -1)) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))))))
	3.1%	#s(approx (sqrt (- (exp x) -1)) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))))
	4.3%	#s(approx (sqrt (- (exp x) -1)) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (/.f64 (.f64 x x) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64)))))
	4.2%	#s(approx (sqrt (- (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)))))

Compiler

Compiled 924 to 481 computations (47.9% saved)

regimes25.0ms (0.5%)

Memory

15.3MiB live, 52.0MiB allocated

Counts

27 → 1

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (- (exp x) -1) #s(literal 2 binary64)))
(sqrt.f64 #s(approx (- (exp x) -1) #s(approx (+ 2 x) x)))
(sqrt.f64 #s(approx (- (exp x) -1) (+.f64 #s(literal 2 binary64) x)))
(sqrt.f64 (-.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
(sqrt.f64 #s(approx (- (exp x) -1) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
(sqrt.f64 #s(approx (- (exp x) -1) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))))
(sqrt.f64 #s(approx (- (exp x) -1) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) x))))
(sqrt.f64 #s(approx (- (exp 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 x) -1) (/.f64 #s(approx (+ (* x x) -4) #s(literal -4 binary64)) (-.f64 x #s(literal 2 binary64)))))
(sqrt.f64 #s(approx (- (exp x) -1) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 #s(approx (+ (* 1/6 x) 1/2) (*.f64 #s(literal 1/6 binary64) x)) x) x))))
(sqrt.f64 (-.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal -1 binary64)))
(sqrt.f64 #s(approx (- (exp x) -1) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))))
(sqrt.f64 #s(approx (- (exp x) -1) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x x))))
(sqrt.f64 #s(approx (- (exp 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))))
(sqrt.f64 #s(approx (- (exp x) -1) (/.f64 (fma.f64 x x #s(literal -4 binary64)) (-.f64 x #s(literal 2 binary64)))))
#s(approx (sqrt (- (exp x) -1)) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (.f64 (.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x) x)))
#s(approx (sqrt (- (exp x) -1)) #s(approx (+ (* (+ (* 3/16 x) 1/2) (/ x (sqrt 2))) (sqrt 2)) (/.f64 (.f64 x x) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64)))))
#s(approx (sqrt (- (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 x) -1)) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)))))
#s(approx (sqrt (- (exp x) -1)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (- (exp x) -1)) #s(approx (+ (* (/ x (sqrt 2)) (+ (* x (+ (* 7/192 x) 3/16)) 1/2)) (sqrt 2)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 7/192 binary64) x) x (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))))))
#s(approx (sqrt (- (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 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))))
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
#s(approx (sqrt (- (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))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))))))

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

Calls

3 calls:

9.0ms

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

8.0ms

6.0ms

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

Results

Accuracy	Segments	Branch
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)

regimes28.0ms (0.6%)

Memory

10.1MiB live, 51.2MiB allocated

Accuracy

Total -43.9b remaining (-231.1%)

Threshold costs -43.9b (-231.1%)

Counts

23 → 1

Calls

Call 1

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

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

Calls

3 calls:

15.0ms

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

7.0ms

6.0ms

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

Results

Accuracy	Segments	Branch
70.3%	1	`x`
70.3%	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))))`
70.3%	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)

simplify27.0ms (0.6%)

Memory

-29.8MiB live, 84.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	12
1	12	12
2	16	12
3	17	12
4	18	12

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness438.0ms (9.7%)

Memory

24.6MiB live, 232.4MiB allocated

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	52	224
1	156	190
2	455	190
3	921	184
4	1920	183
5	4949	181
0	8409	165
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×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit

Compiler

Compiled 48 to 40 computations (16.7% saved)

preprocess31.0ms (0.7%)

Memory: -9.9MiB live, 68.2MiB allocated
Compiler: Compiled 48 to 42 computations (12.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	29	175
0	50	175
1	71	175
2	102	175
3	208	175
4	360	175
5	441	175
6	502	175
7	502	175
0	502	175

Iter	Nodes	Cost
0	44	280
0	61	280
1	87	280
2	110	280
3	166	280
4	305	280
5	359	280
6	363	280
0	363	271

Iter	Nodes	Cost
0	29	175
0	50	175
1	71	175
2	102	175
3	208	175
4	360	175
5	441	175
6	502	175
7	502	175
0	502	175

Iter	Nodes	Cost
0	44	280
0	61	280
1	87	280
2	110	280
3	166	280
4	305	280
5	359	280
6	363	280
0	363	271

start0.0ms (0%)

analyze2.0ms (0%)

sample972.0ms (21.5%)

explain157.0ms (3.5%)

preprocess207.0ms (4.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0.1%)

localize18.0ms (0.4%)

series2.0ms (0%)

simplify180.0ms (4%)

rewrite61.0ms (1.4%)

eval22.0ms (0.5%)

prune10.0ms (0.2%)

simplify19.0ms (0.4%)

localize76.0ms (1.7%)

series12.0ms (0.3%)

simplify276.0ms (6.1%)

rewrite198.0ms (4.4%)

eval101.0ms (2.2%)

prune57.0ms (1.3%)

simplify11.0ms (0.2%)

localize79.0ms (1.7%)

series34.0ms (0.7%)

simplify266.0ms (5.9%)

rewrite222.0ms (4.9%)

eval136.0ms (3%)

prune37.0ms (0.8%)

simplify29.0ms (0.6%)

localize143.0ms (3.2%)

series19.0ms (0.4%)

simplify242.0ms (5.4%)

rewrite215.0ms (4.8%)

eval105.0ms (2.3%)

prune56.0ms (1.2%)

regimes25.0ms (0.5%)

regimes28.0ms (0.6%)

simplify27.0ms (0.6%)

soundness438.0ms (9.7%)

preprocess31.0ms (0.7%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	29	175
0	50	175
1	71	175
2	102	175
3	208	175
4	360	175
5	441	175
6	502	175
7	502	175
0	502	175

Iter	Nodes	Cost
0	44	280
0	61	280
1	87	280
2	110	280
3	166	280
4	305	280
5	359	280
6	363	280
0	363	271