Metrics for sqrtexp (problem 3.4.4)

analyze2.0ms (0%)

Memory

3.2MiB live, 3.2MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample896.0ms (11.5%)

Memory

43.7MiB live, 962.2MiB allocated

Samples

451.0ms	8 256×	0	valid
163.0ms	2 669×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 400.0ms

ival-expm1: 130.0ms (32.5% of total)

ival-div: 100.0ms (25% of total)

ival-mult: 76.0ms (19% of total)

ival-sqrt: 76.0ms (19% of total)

ival-true: 8.0ms (2% of total)

exact: 6.0ms (1.5% of total)

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

Bogosity

preprocess489.0ms (6.3%)

Memory

0.8MiB live, 446.1MiB allocated

Algorithm

2×	egg-herbie

Rules

15 394×	`accelerator-lowering-fma.f32`
15 394×	`accelerator-lowering-fma.f64`
2 850×	`--lowering--.f32`
2 850×	`--lowering--.f64`
2 458×	`-lowering-.f32`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	19	41
1	44	39
2	70	39
3	113	39
4	192	20
5	340	18
6	672	18
7	2570	18
0	10	12
1	22	12
2	28	12
3	40	12
4	66	7
5	119	5
6	195	5
7	593	5
8	2904	5
9	6743	5
0	8156	5

Stop Event

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

Calls

Call 1

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

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

Call 2

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

Outputs
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (+ 1 (exp x)))
(sqrt (/ (- (exp (* 2 (neg x))) 1) (- (exp (neg x)) 1)))
(sqrt (+ 1 (exp (neg x))))
(neg (sqrt (/ (- (exp (* 2 (neg x))) 1) (- (exp (neg x)) 1))))
(neg (sqrt (+ 1 (exp (neg x)))))

explain137.0ms (1.8%)

Memory

14.1MiB live, 167.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
156	-	-	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`
156	-	-	`(-.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	156	0
`-.f64`	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	cancellation	156	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 -
+	157	0
-	0	99

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	157	0	0
-	0	1	98

Precision?

0.9936708860759493

Recall?

1.0

Freqs

test

number	freq
0	99
1	1
2	156

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

44.0ms

512×

valid

Compiler

Compiled 120 to 44 computations (63.3% saved)

Precisions

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

ival-exp: 12.0ms (41.1% of total)

ival-expm1: 6.0ms (20.5% of total)

ival-mult: 4.0ms (13.7% of total)

ival-div: 3.0ms (10.3% of total)

ival-sqrt: 3.0ms (10.3% of total)

exact: 1.0ms (3.4% of total)

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

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

eval0.0ms (0%)

Memory: 0.6MiB live, 0.6MiB allocated
Compiler: Compiled 6 to 5 computations (16.7% saved)

prune1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify3.0ms (0%)

Memory

3.4MiB live, 3.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Program
✓	cost-diff	(exp.f64 x)
✓	cost-diff	(+.f64 #s(literal 1 binary64) (exp.f64 x))
✓	cost-diff	(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))

Rules

4×	`+-lowering-+.f64`
4×	`+-lowering-+.f32`
2×	`sqrt-lowering-sqrt.f64`
2×	`exp-lowering-exp.f32`
2×	`1-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	13
1	8	13
0	8	13

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
1
(exp x)
x

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

localize23.0ms (0.3%)

Memory

-15.0MiB live, 22.1MiB allocated

Localize:

Found 3 expressions of interest:

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

Samples

10.0ms

256×

valid

Compiler

Compiled 15 to 7 computations (53.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-exp: 2.0ms (38.2% of total)

ival-sqrt: 2.0ms (38.2% of total)

ival-add: 1.0ms (19.1% 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

2.4MiB live, 2.4MiB allocated

Counts

3 → 36

Calls

Call 1

Inputs
#<alt (sqrt (+ 1 (exp x)))>
#<alt (+ 1 (exp x))>
#<alt (exp x)>

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

Calls

9 calls:

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

rewrite92.0ms (1.2%)

Memory

-2.4MiB live, 80.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

508×	`/-lowering-/.f32`
508×	`/-lowering-/.f64`
482×	`accelerator-lowering-fma.f32`
482×	`accelerator-lowering-fma.f64`
446×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
1	23	11
2	143	11
0	1067	11

Stop Event

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

Counts

3 → 83

Calls

Call 1

Inputs
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
(exp x)

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

simplify446.0ms (5.7%)

Memory

-13.8MiB live, 474.7MiB allocated

Algorithm

1×	egg-herbie

Rules

15 182×	`accelerator-lowering-fma.f32`
15 182×	`accelerator-lowering-fma.f64`
5 376×	`-lowering-.f32`
5 376×	`-lowering-.f64`
1 938×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	224
1	156	190
2	454	190
3	920	184
4	1914	183
5	5027	181
0	8491	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))))))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)

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

eval12.0ms (0.2%)

Memory: 21.0MiB live, 20.9MiB allocated
Compiler: Compiled 1 665 to 324 computations (80.5% saved)

prune15.0ms (0.2%)

Memory

-9.6MiB live, 29.5MiB allocated

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	113	6	119
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	113	7	120

Accuracy

100.0%

Counts

120 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.1%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
	61.1%	(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
▶	60.9%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
▶	62.9%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))))
▶	60.6%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓	100.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
▶	68.1%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 114 to 87 computations (23.7% saved)

simplify15.0ms (0.2%)

Memory

13.8MiB live, 13.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

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

Rules

400×	`accelerator-lowering-fma.f32`
400×	`accelerator-lowering-fma.f64`
134×	`-lowering-.f32`
134×	`-lowering-.f64`
132×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	147
1	54	147
2	98	147
3	183	147
4	230	147
5	239	147
0	239	129

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize139.0ms (1.8%)

Memory

-17.1MiB live, 99.9MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
✓	accuracy	99.7%	(*.f64 x #s(literal 1/6 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) x)
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
✓	accuracy	100.0%	(+.f64 #s(literal 2 binary64) x)
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(exp.f64 x)
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (exp.f64 x))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))
✓	accuracy	99.1%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))

Samples

69.0ms	157×	0	valid
21.0ms	99×	0	invalid

Compiler

Compiled 149 to 27 computations (81.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 74.0ms

const: 43.0ms (57.8% of total)

ival-sqrt: 10.0ms (13.4% of total)

ival-add: 8.0ms (10.7% of total)

ival-mult: 7.0ms (9.4% of total)

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

ival-exp: 2.0ms (2.7% of total)

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

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

exact: 0.0ms (0% of total)

series16.0ms (0.2%)

Memory

29.6MiB live, 29.6MiB allocated

Counts

19 → 216

Calls

Call 1

Inputs
#<alt (/ 1 (sqrt (/ 1 (+ 1 (exp x)))))>
#<alt (sqrt (/ 1 (+ 1 (exp x))))>
#<alt (/ 1 (+ 1 (exp x)))>
#<alt (+ 1 (exp x))>
#<alt (sqrt 2)>
#<alt (sqrt (+ 2 x))>
#<alt (+ 2 x)>
#<alt (sqrt (+ 2 (* x (+ 1 (* 1/2 x)))))>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (+ 1 (* 1/2 x))>
#<alt (sqrt (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))>
#<alt (+ 1 (* x (+ 1/2 (* x 1/6))))>
#<alt (exp x)>
#<alt (* 1/2 x)>
#<alt (* x 1/6)>
#<alt (* x (+ 1/2 (* x 1/6)))>

Outputs
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (sqrt (/ 1 (+ 1 (exp x))))>
#<alt (sqrt (/ 1 (+ 1 (exp x))))>
#<alt (sqrt (/ 1 (+ 1 (exp x))))>
#<alt (sqrt (/ 1 (+ 1 (exp x))))>
#<alt (sqrt (/ 1 (+ 1 (exp x))))>
#<alt (sqrt (/ 1 (+ 1 (exp x))))>
#<alt (sqrt (/ 1 (+ 1 (exp x))))>
#<alt (sqrt (/ 1 (+ 1 (exp x))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))>
#<alt (+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* -1/480 (pow x 2)))) 1/4)))>
#<alt (/ 1 (+ 1 (exp x)))>
#<alt (/ 1 (+ 1 (exp x)))>
#<alt (/ 1 (+ 1 (exp x)))>
#<alt (/ 1 (+ 1 (exp x)))>
#<alt (/ 1 (+ 1 (exp x)))>
#<alt (/ 1 (+ 1 (exp x)))>
#<alt (/ 1 (+ 1 (exp x)))>
#<alt (/ 1 (+ 1 (exp x)))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* -1/8 (/ x (pow (sqrt 2) 3))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt 2) 5))) (* 1/8 (/ 1 (pow (sqrt 2) 3))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (sqrt (/ 1 (pow x 3)))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 5)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 7))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 x)>
#<alt (+ 2 x)>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))>
#<alt (* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))>
#<alt (* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))))>
#<alt (* -1 (* x (sqrt 1/2)))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>

Calls

54 calls:

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

rewrite379.0ms (4.9%)

Memory

-12.6MiB live, 539.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 476×	`/-lowering-/.f32`
4 476×	`/-lowering-/.f64`
4 100×	`-lowering-.f32`
4 100×	`-lowering-.f64`
2 904×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	128
1	157	123
2	1306	123
0	8310	105

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 656

Calls

Call 1

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

Outputs
(exp.f64 (.f64 (.f64 #s(literal -1/2 binary64) (log1p.f64 (exp.f64 x))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (-.f64 #s(literal 0 binary64) (log1p.f64 (exp.f64 x))) #s(literal -1/2 binary64)))
(exp.f64 (neg.f64 (*.f64 #s(literal -1/2 binary64) (log1p.f64 (exp.f64 x)))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (exp.f64 x) (expm1.f64 x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))))))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/2 binary64))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 1 binary64))
(/.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (exp.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64)))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (exp.f64 x) (expm1.f64 x)))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64))))) (sqrt.f64 (+.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64))))) (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))) #s(literal -1 binary64))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64)))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 (exp.f64 x) (expm1.f64 x))))))
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(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (+.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) (.f64 #s(literal 1/6 binary64) (.f64 x x))) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 #s(literal 1/6 binary64) (.f64 x x))))))
(/.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) (.f64 #s(literal 1/6 binary64) (.f64 x x)))) (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 #s(literal 1/6 binary64) (.f64 x x))))
(/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x #s(literal 1/6 binary64)) (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)))))
(/.f64 (.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/6 binary64) x)))
(/.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))) x) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x #s(literal 1/6 binary64)) (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64))) x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/6 binary64) x)))
(/.f64 (neg.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))))) (neg.f64 (+.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) (.f64 #s(literal 1/6 binary64) (.f64 x x))) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 #s(literal 1/6 binary64) (.f64 x x)))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) (.f64 #s(literal 1/6 binary64) (.f64 x x))))) (neg.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 #s(literal 1/6 binary64) (.f64 x x)))))
(/.f64 (neg.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x #s(literal 1/6 binary64)) (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64))))))
(/.f64 (neg.f64 (.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/6 binary64) x))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))) x)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x #s(literal 1/6 binary64)) (+.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64))))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64))) x)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/6 binary64) x))))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))) (+.f64 (.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) (.f64 #s(literal 1/6 binary64) (.f64 x x))) (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) (.f64 #s(literal 1/6 binary64) (.f64 x x))) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (-.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))
(.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) x)
(.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) #s(literal 1 binary64))
(.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (-.f64 (.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) (.f64 #s(literal 1/6 binary64) (.f64 x x))) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 #s(literal 1/6 binary64) (*.f64 x x)))))))
(.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) (.f64 #s(literal 1/6 binary64) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 #s(literal 1/6 binary64) (*.f64 x x)))))
(.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x #s(literal 1/6 binary64)) (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64))))))
(.f64 (.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/6 binary64) x))))
(.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x #s(literal 1/6 binary64)) (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64))))))
(.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64))) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/6 binary64) x))))

simplify601.0ms (7.7%)

Memory

30.5MiB live, 662.1MiB allocated

Algorithm

1×	egg-herbie

Rules

12 296×	`accelerator-lowering-fma.f32`
12 296×	`accelerator-lowering-fma.f64`
5 502×	`-lowering-.f32`
5 502×	`-lowering-.f64`
3 626×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	318	2081
1	975	1825
2	3204	1769
0	8492	1627

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))))))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))
(sqrt (/ 1 (+ 1 (exp x))))
(sqrt (/ 1 (+ 1 (exp x))))
(sqrt (/ 1 (+ 1 (exp x))))
(sqrt (/ 1 (+ 1 (exp x))))
(sqrt (/ 1 (+ 1 (exp x))))
(sqrt (/ 1 (+ 1 (exp x))))
(sqrt (/ 1 (+ 1 (exp x))))
(sqrt (/ 1 (+ 1 (exp x))))
1/2
(+ 1/2 (* -1/4 x))
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))
(+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* -1/480 (pow x 2)))) 1/4)))
(/ 1 (+ 1 (exp x)))
(/ 1 (+ 1 (exp x)))
(/ 1 (+ 1 (exp x)))
(/ 1 (+ 1 (exp x)))
(/ 1 (+ 1 (exp x)))
(/ 1 (+ 1 (exp x)))
(/ 1 (+ 1 (exp x)))
(/ 1 (+ 1 (exp x)))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* -1/8 (/ x (pow (sqrt 2) 3))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt 2) 5))) (* 1/8 (/ 1 (pow (sqrt 2) 3))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (sqrt (/ 1 (pow x 3)))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 5)))))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 7))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
2
(+ 2 x)
(+ 2 x)
(+ 2 x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* x (sqrt 1/2))
(* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))
(* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))
(* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))))
(* -1 (* x (sqrt 1/2)))
(* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* 1/2 x))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* 1/2 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
1
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/2 x)
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))

Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal 3/16 binary64) x) (sqrt.f64 #s(literal 2 binary64))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 x (+.f64 (/.f64 (*.f64 #s(literal 7/192 binary64) x) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))))))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 #s(literal -1/8 binary64) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 x (+.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1/64 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
(+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))
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(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
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#s(literal 2 binary64)
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x
(* x (+ 1 (* 2 (/ 1 x))))
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x
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(sqrt 2)
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#s(literal 2 binary64)
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(* 1/2 (pow x 2))
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(* (pow x 2) (+ 1/2 (/ 1 x)))
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(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
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(* 1/2 (pow x 2))
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(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
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x
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(* 1/2 (pow x 2))
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(* (pow x 2) (+ 1/2 (/ 1 x)))
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(* (pow x 2) (+ 1/2 (/ 1 x)))
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(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
(* 1/2 (pow x 2))
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(* (pow x 2) (+ 1/2 (/ 1 x)))
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(* (pow x 2) (+ 1/2 (/ 1 x)))
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(* (pow x 2) (+ 1/2 (/ 1 x)))
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1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
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(+ 1 (* 1/2 x))
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(sqrt 2)
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(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) (.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (+.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(+.f64 (.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))))) (.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1/6 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (.f64 x #s(literal 1/16 binary64)) #s(literal -1/6 binary64))) (sqrt.f64 #s(literal -1/6 binary64))))))) x)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(* 1/6 (pow x 3))
(.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)) (.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 2 binary64) (.f64 x (.f64 x x))) #s(literal 1/6 binary64)))))
(* 1/6 (pow x 3))
(.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal -2 binary64) (.f64 x x))) x)) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))))
x
(* x (+ 1 (* 1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* 1/6 (pow x 3))
(.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* 1/6 (pow x 3))
(.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* 1/2 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/6 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* x (+ 1/2 (* 1/6 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* x (+ 1/2 (* 1/6 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))

eval130.0ms (1.7%)

Memory: -24.2MiB live, 242.2MiB allocated
Compiler: Compiled 21 375 to 2 891 computations (86.5% saved)

prune207.0ms (2.7%)

Memory

-30.9MiB live, 251.3MiB allocated

Pruning

13 alts after pruning (8 fresh and 5 done)

	Pruned	Kept	Total
New	864	8	872
Fresh	1	0	1
Picked	1	4	5
Done	0	1	1
Total	866	13	879

Accuracy

100.0%

Counts

879 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(pow.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (exp.f64 x))) #s(literal -1/2 binary64))
▶	62.7%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))
▶	67.1%	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
	2.8%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
✓	60.9%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
✓	62.9%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))))
✓	60.6%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓	100.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
	3.1%	(sqrt.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
▶	2.1%	(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
	2.0%	(sqrt.f64 (.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x))))
▶	2.1%	(sqrt.f64 x)
✓	68.1%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 168 to 133 computations (20.8% saved)

simplify17.0ms (0.2%)

Memory

24.0MiB live, 24.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

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

Rules

232×	`accelerator-lowering-fma.f32`
232×	`accelerator-lowering-fma.f64`
154×	`-lowering-.f32`
154×	`-lowering-.f64`
88×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	111
1	47	111
2	87	111
3	176	111
4	229	111
5	241	111
6	255	111
7	269	111
8	273	111
9	275	111
10	278	111
11	281	111
0	281	100

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize104.0ms (1.3%)

Memory

-8.3MiB live, 107.9MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
✓	accuracy	99.9%	(*.f64 x #s(literal 1/6 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))
✓	accuracy	100.0%	(*.f64 x #s(literal -1/4 binary64))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/2 binary64))
✓	accuracy	99.5%	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(pow.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (exp.f64 x))) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(exp.f64 x)
✓	accuracy	100.0%	(-.f64 #s(literal -1 binary64) (exp.f64 x))
✓	accuracy	100.0%	(/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (exp.f64 x)))

Samples

53.0ms	179×	0	invalid
15.0ms	77×	0	valid

Compiler

Compiled 113 to 26 computations (77% saved)

Precisions

Click to see histograms. Total time spent on operations: 53.0ms

ival-add: 21.0ms (39.7% of total)

ival-mult: 6.0ms (11.3% of total)

ival-sqrt: 6.0ms (11.3% of total)

ival-div: 5.0ms (9.4% of total)

ival-pow: 5.0ms (9.4% of total)

const: 4.0ms (7.6% of total)

ival-exp: 2.0ms (3.8% of total)

ival-sub: 1.0ms (1.9% of total)

ival-true: 1.0ms (1.9% of total)

exact: 1.0ms (1.9% of total)

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

series14.0ms (0.2%)

Memory

-22.4MiB live, 18.2MiB allocated

Counts

16 → 168

Calls

Call 1

Inputs
#<alt (pow (/ -1 (- -1 (exp x))) -1/2)>
#<alt (/ -1 (- -1 (exp x)))>
#<alt (- -1 (exp x))>
#<alt (exp x)>
#<alt (sqrt x)>
#<alt (/ 1 (sqrt 1/2))>
#<alt (sqrt 1/2)>
#<alt (/ 1 (sqrt (+ 1/2 (* x -1/4))))>
#<alt (sqrt (+ 1/2 (* x -1/4)))>
#<alt (+ 1/2 (* x -1/4))>
#<alt (* x -1/4)>
#<alt (sqrt (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))>
#<alt (+ 1 (* x (+ 1/2 (* x 1/6))))>
#<alt (* x (+ 1/2 (* x 1/6)))>
#<alt (* x 1/6)>

Outputs
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))>
#<alt (+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* -1/480 (pow x 2)))) 1/4)))>
#<alt (/ 1 (+ 1 (exp x)))>
#<alt (/ 1 (+ 1 (exp x)))>
#<alt (/ 1 (+ 1 (exp x)))>
#<alt (/ 1 (+ 1 (exp x)))>
#<alt (/ 1 (+ 1 (exp x)))>
#<alt (/ 1 (+ 1 (exp x)))>
#<alt (/ 1 (+ 1 (exp x)))>
#<alt (/ 1 (+ 1 (exp x)))>
#<alt -2>
#<alt (- (* -1 x) 2)>
#<alt (- (* x (- (* -1/2 x) 1)) 2)>
#<alt (- (* x (- (* x (- (* -1/6 x) 1/2)) 1)) 2)>
#<alt (* -1 (+ 1 (exp x)))>
#<alt (* -1 (+ 1 (exp x)))>
#<alt (* -1 (+ 1 (exp x)))>
#<alt (* -1 (+ 1 (exp x)))>
#<alt (* -1 (+ 1 (exp x)))>
#<alt (* -1 (+ 1 (exp x)))>
#<alt (* -1 (+ 1 (exp x)))>
#<alt (* -1 (+ 1 (exp x)))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/4 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* (sqrt (/ 1 x)) (sqrt -4))>
#<alt (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))>
#<alt (+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4))))>
#<alt (+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 32 (* 16 (/ x (pow (sqrt -4) 2)))) (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))))>
#<alt (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))>
#<alt (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1))))>
#<alt (+ (* -4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ 32 (* -4 x))))) (* 4 (* (sqrt x) (sqrt -1)))) (pow x 3))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (* x (- (* x (- (* -1/1024 (/ x (pow (sqrt 1/2) 5))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (* (sqrt x) (sqrt -1/4))>
#<alt (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))>
#<alt (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4)))))>
#<alt (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1/4) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))))>
#<alt (* -1/2 (* (sqrt x) (sqrt -1)))>
#<alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))>
#<alt (* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1)))))))>
#<alt (* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (* -1/4 x)>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/4))>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/4))>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/4))>
#<alt (* -1/4 x)>
#<alt (* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (sqrt x)>
#<alt (+ (sqrt x) (* 1/4 (sqrt (pow x 3))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* 1/12 (sqrt x)) (* 1/4 (sqrt (/ 1 x))))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* 1/4 (sqrt (/ 1 x))) (* x (+ (* -1/32 (sqrt (/ 1 x))) (* 1/12 (sqrt (/ 1 x))))))))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* (sqrt (pow x 3)) (* (pow (sqrt -1) 2) (sqrt 1/6)))>
#<alt (* (pow x 2) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6))))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* 1/32 (* (sqrt x) (/ (pow (sqrt -1) 2) (pow (sqrt 1/6) 3)))) (* 1/2 (* (sqrt x) (/ (pow (sqrt -1) 2) (sqrt 1/6))))) (pow x 3))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>

Calls

42 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(+ 1/2 (* x -1/4))
1.0ms	x	@	-inf	(sqrt (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))
1.0ms	x	@	inf	(/ 1 (sqrt (+ 1/2 (* x -1/4))))
1.0ms	x	@	inf	(sqrt (+ 1/2 (* x -1/4)))
1.0ms	x	@	-inf	(sqrt (+ 1/2 (* x -1/4)))

rewrite338.0ms (4.4%)

Memory

46.0MiB live, 478.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 922×	`accelerator-lowering-fma.f32`
5 922×	`accelerator-lowering-fma.f64`
4 766×	`-lowering-.f32`
4 766×	`-lowering-.f64`
3 192×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	92
1	129	90
2	899	88
0	8101	77

Stop Event

1×	iter limit
1×	node limit

Counts

16 → 596

Calls

Call 1

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

Outputs
(exp.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (log1p.f64 (exp.f64 x)))))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal -2 binary64))) #s(literal -1/4 binary64)))
(exp.f64 (.f64 (neg.f64 (.f64 (log1p.f64 (exp.f64 x)) #s(literal -1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (+.f64 (neg.f64 (.f64 (log1p.f64 (exp.f64 x)) #s(literal -1/4 binary64))) (neg.f64 (.f64 (log1p.f64 (exp.f64 x)) #s(literal -1/4 binary64)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal -1/2 binary64))
(pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal -2 binary64)) #s(literal -1/4 binary64))
(pow.f64 (exp.f64 #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) (log1p.f64 (exp.f64 x))))
(*.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 #s(literal -1 binary64) #s(literal -1/4 binary64)) (.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (exp.f64 x)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64)) (pow.f64 (-.f64 #s(literal -1 binary64) (exp.f64 x)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (exp.f64 x)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/8 binary64)) (.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/8 binary64)) (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64))))) #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (*.f64 (exp.f64 x) (+.f64 #s(literal -1 binary64) (exp.f64 x)))) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64))))) #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal -1 binary64) (exp.f64 x)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 #s(literal -1 binary64) #s(literal -1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (-.f64 #s(literal -1 binary64) (exp.f64 x)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal -1/4 binary64))) (pow.f64 (-.f64 #s(literal -1 binary64) (exp.f64 x)) #s(literal 1/4 binary64)))
(.f64 (.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/8 binary64))) (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/8 binary64)))
(+.f64 (.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64))))) #s(literal 1 binary64)) (.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64))))) (*.f64 (exp.f64 x) (+.f64 #s(literal -1 binary64) (exp.f64 x)))))
(+.f64 (.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64))))) (.f64 (exp.f64 x) (+.f64 #s(literal -1 binary64) (exp.f64 x)))) (.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64))))) #s(literal 1 binary64)))
(+.f64 (.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64))))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64))))) (.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64))))) (-.f64 #s(literal 0 binary64) (exp.f64 x))))
(+.f64 (.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64))))) #s(literal -1 binary64)) (.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64))))) (exp.f64 x)))
(+.f64 (.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64))))) (exp.f64 x)) (.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64))))) #s(literal -1 binary64)))
(+.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64)))))) (.f64 (.f64 (exp.f64 x) (+.f64 #s(literal -1 binary64) (exp.f64 x))) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64)))))))
(+.f64 (.f64 (.f64 (exp.f64 x) (+.f64 #s(literal -1 binary64) (exp.f64 x))) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64)))))) (.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64)))))))
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(/.f64 (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/36 binary64))) #s(literal -1/4 binary64))) (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)))
(/.f64 (.f64 (+.f64 #s(literal -1/8 binary64) (neg.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) x) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 x (-.f64 (.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64))))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/36 binary64)))) x) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(/.f64 (.f64 (+.f64 (.f64 x (.f64 x #s(literal 1/36 binary64))) #s(literal -1/4 binary64)) x) (+.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) x)
(.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) #s(literal 1 binary64))
(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 x (-.f64 (*.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64))))) x))
(.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))) (/.f64 x (+.f64 #s(literal 1/4 binary64) (.f64 x (-.f64 (.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64))))))
(.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/36 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))) x))
(.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/36 binary64))) (/.f64 x (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(.f64 (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (-.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x #s(literal 1/2 binary64)))))))
(.f64 (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (.f64 x (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))) (/.f64 #s(literal 1 binary64) (.f64 x (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))))
(.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 x (-.f64 (*.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64))))))
(.f64 (.f64 x (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/36 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(.f64 (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 x (-.f64 (.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64))) (.f64 (.f64 x (-.f64 (.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64))) (.f64 x (-.f64 (.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64))))))) (+.f64 #s(literal 1/16 binary64) (.f64 (.f64 x (-.f64 (.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64))) (-.f64 (.f64 x (-.f64 (.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64))) #s(literal 1/4 binary64)))))
(.f64 (/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (-.f64 #s(literal 1/16 binary64) (.f64 (.f64 x (-.f64 (.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64))) (.f64 x (-.f64 (.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64)))))) (-.f64 #s(literal 1/4 binary64) (.f64 x (-.f64 (.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64)))))
(.f64 (/.f64 (.f64 x (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/36 binary64)))) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/36 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(.f64 (/.f64 (.f64 x (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/36 binary64)))) (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 1/36 binary64)) #s(literal 1/12 binary64)))))
(*.f64 x #s(literal 1/6 binary64))
(.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/6 binary64)))
(*.f64 #s(literal 1/6 binary64) x)
(.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1 binary64))

simplify447.0ms (5.8%)

Memory

-20.7MiB live, 574.8MiB allocated

Algorithm

1×	egg-herbie

Rules

12 844×	`accelerator-lowering-fma.f32`
12 844×	`accelerator-lowering-fma.f64`
5 706×	`-lowering-.f32`
5 706×	`-lowering-.f64`
3 386×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	300	1698
1	878	1525
2	2789	1473
3	5735	1422
0	8216	1310

Stop Event

1×	iter limit
1×	node limit

Counts

168 → 168

Calls

Call 1

Inputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
1/2
(+ 1/2 (* -1/4 x))
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))
(+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* -1/480 (pow x 2)))) 1/4)))
(/ 1 (+ 1 (exp x)))
(/ 1 (+ 1 (exp x)))
(/ 1 (+ 1 (exp x)))
(/ 1 (+ 1 (exp x)))
(/ 1 (+ 1 (exp x)))
(/ 1 (+ 1 (exp x)))
(/ 1 (+ 1 (exp x)))
(/ 1 (+ 1 (exp x)))
-2
(- (* -1 x) 2)
(- (* x (- (* -1/2 x) 1)) 2)
(- (* x (- (* x (- (* -1/6 x) 1/2)) 1)) 2)
(* -1 (+ 1 (exp x)))
(* -1 (+ 1 (exp x)))
(* -1 (+ 1 (exp x)))
(* -1 (+ 1 (exp x)))
(* -1 (+ 1 (exp x)))
(* -1 (+ 1 (exp x)))
(* -1 (+ 1 (exp x)))
(* -1 (+ 1 (exp x)))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/4 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* (sqrt (/ 1 x)) (sqrt -4))
(+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4))))
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 32 (* 16 (/ x (pow (sqrt -4) 2)))) (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))))
(* 2 (* (sqrt (/ 1 x)) (sqrt -1)))
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1))))
(+ (* -4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ 32 (* -4 x))))) (* 4 (* (sqrt x) (sqrt -1)))) (pow x 3))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (- (* x (- (* -1/1024 (/ x (pow (sqrt 1/2) 5))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))
(* (sqrt x) (sqrt -1/4))
(* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4)))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1/4) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))))
(* -1/2 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1)))))))
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))))
1/2
(+ 1/2 (* -1/4 x))
(+ 1/2 (* -1/4 x))
(+ 1/2 (* -1/4 x))
(* -1/4 x)
(* x (- (* 1/2 (/ 1 x)) 1/4))
(* x (- (* 1/2 (/ 1 x)) 1/4))
(* x (- (* 1/2 (/ 1 x)) 1/4))
(* -1/4 x)
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(sqrt x)
(+ (sqrt x) (* 1/4 (sqrt (pow x 3))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/12 (sqrt x)) (* 1/4 (sqrt (/ 1 x))))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/4 (sqrt (/ 1 x))) (* x (+ (* -1/32 (sqrt (/ 1 x))) (* 1/12 (sqrt (/ 1 x))))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* (sqrt (pow x 3)) (* (pow (sqrt -1) 2) (sqrt 1/6)))
(* (pow x 2) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6)))))
(* (pow x 2) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6))))))
(* (pow x 2) (+ (* -1 (/ (+ (* 1/32 (* (sqrt x) (/ (pow (sqrt -1) 2) (pow (sqrt 1/6) 3)))) (* 1/2 (* (sqrt x) (/ (pow (sqrt -1) 2) (sqrt 1/6))))) (pow x 3))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6))))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/2 x)
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)

Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal 3/16 binary64) x) (sqrt.f64 #s(literal 2 binary64))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 x (+.f64 (*.f64 #s(literal 7/192 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))))))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/4 x))
(-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64)))
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 x (*.f64 x #s(literal 1/48 binary64))))))
(+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* -1/480 (pow x 2)))) 1/4)))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/48 binary64) (.f64 (*.f64 x x) #s(literal -1/480 binary64)))))))
(/ 1 (+ 1 (exp x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(/ 1 (+ 1 (exp x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(/ 1 (+ 1 (exp x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(/ 1 (+ 1 (exp x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(/ 1 (+ 1 (exp x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(/ 1 (+ 1 (exp x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(/ 1 (+ 1 (exp x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(/ 1 (+ 1 (exp x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))
-2
#s(literal -2 binary64)
(- (* -1 x) 2)
(-.f64 #s(literal -2 binary64) x)
(- (* x (- (* -1/2 x) 1)) 2)
(+.f64 #s(literal -2 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x #s(literal -1/2 binary64)))))
(- (* x (- (* x (- (* -1/6 x) 1/2)) 1)) 2)
(+.f64 #s(literal -2 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal -1/6 binary64)))))))
(* -1 (+ 1 (exp x)))
(-.f64 #s(literal -1 binary64) (exp.f64 x))
(* -1 (+ 1 (exp x)))
(-.f64 #s(literal -1 binary64) (exp.f64 x))
(* -1 (+ 1 (exp x)))
(-.f64 #s(literal -1 binary64) (exp.f64 x))
(* -1 (+ 1 (exp x)))
(-.f64 #s(literal -1 binary64) (exp.f64 x))
(* -1 (+ 1 (exp x)))
(-.f64 #s(literal -1 binary64) (exp.f64 x))
(* -1 (+ 1 (exp x)))
(-.f64 #s(literal -1 binary64) (exp.f64 x))
(* -1 (+ 1 (exp x)))
(-.f64 #s(literal -1 binary64) (exp.f64 x))
(* -1 (+ 1 (exp x)))
(-.f64 #s(literal -1 binary64) (exp.f64 x))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* 1/2 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal 3/16 binary64) x) (sqrt.f64 #s(literal 2 binary64))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/4 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 x (+.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 #s(literal 5/64 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))))))
(* (sqrt (/ 1 x)) (sqrt -4))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64)))
(+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))
(+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal -4 binary64) (sqrt.f64 #s(literal -4 binary64)))))
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4))))
(+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64))) (/.f64 (+.f64 (.f64 #s(literal -8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (.f64 #s(literal -4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))) (sqrt.f64 #s(literal -4 binary64))))
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 32 (* 16 (/ x (pow (sqrt -4) 2)))) (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))))
(+.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 (.f64 (+.f64 #s(literal 32 binary64) (.f64 x #s(literal -4 binary64))) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -4 binary64))))) (/.f64 (+.f64 (.f64 #s(literal -8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (.f64 #s(literal -4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (sqrt.f64 #s(literal -4 binary64))))
(* 2 (* (sqrt (/ 1 x)) (sqrt -1)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 #s(literal -2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))))
(+ (* -4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (+.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 #s(literal -2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/4 binary64))))
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ 32 (* -4 x))))) (* 4 (* (sqrt x) (sqrt -1)))) (pow x 3))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))
(-.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 #s(literal -2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))))) (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 32 binary64) (.f64 x #s(literal -4 binary64)))) (.f64 (sqrt.f64 x) #s(literal 4 binary64)))) (.f64 x (.f64 x x))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 x #s(literal -1/8 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 x (+.f64 (.f64 x (/.f64 #s(literal -1/64 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
(+ (sqrt 1/2) (* x (- (* x (- (* -1/1024 (/ x (pow (sqrt 1/2) 5))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 x (+.f64 (.f64 x (+.f64 (/.f64 (*.f64 x #s(literal -1/1024 binary64)) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -1/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
(* (sqrt x) (sqrt -1/4))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1/4 binary64)))
(* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))
(.f64 x (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -1/4 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1/4 binary64)))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4)))))
(.f64 x (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -1/4 binary64)))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1/4 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1/4 binary64)))))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1/4) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))))
(.f64 x (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -1/4 binary64)))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/128 binary64) (pow.f64 (sqrt.f64 #s(literal -1/4 binary64)) #s(literal 5 binary64)))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1/4 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1/4 binary64))))))))
(* -1/2 (* (sqrt x) (sqrt -1)))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))
(.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))))
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1)))))))
(.f64 x (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) (+.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))))))
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))))
(.f64 x (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (+.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))) #s(literal -1 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/4 x))
(-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64)))
(+ 1/2 (* -1/4 x))
(-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64)))
(+ 1/2 (* -1/4 x))
(-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64)))
(* -1/4 x)
(/.f64 x #s(literal -4 binary64))
(* x (- (* 1/2 (/ 1 x)) 1/4))
(-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64)))
(* x (- (* 1/2 (/ 1 x)) 1/4))
(-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64)))
(* x (- (* 1/2 (/ 1 x)) 1/4))
(-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64)))
(* -1/4 x)
(/.f64 x #s(literal -4 binary64))
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64)))
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64)))
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64)))
(* -1/4 x)
(/.f64 x #s(literal -4 binary64))
(* -1/4 x)
(/.f64 x #s(literal -4 binary64))
(* -1/4 x)
(/.f64 x #s(literal -4 binary64))
(* -1/4 x)
(/.f64 x #s(literal -4 binary64))
(* -1/4 x)
(/.f64 x #s(literal -4 binary64))
(* -1/4 x)
(/.f64 x #s(literal -4 binary64))
(* -1/4 x)
(/.f64 x #s(literal -4 binary64))
(* -1/4 x)
(/.f64 x #s(literal -4 binary64))
(* -1/4 x)
(/.f64 x #s(literal -4 binary64))
(* -1/4 x)
(/.f64 x #s(literal -4 binary64))
(* -1/4 x)
(/.f64 x #s(literal -4 binary64))
(* -1/4 x)
(/.f64 x #s(literal -4 binary64))
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* 1/4 (sqrt (pow x 3))))
(+.f64 (sqrt.f64 x) (.f64 #s(literal 1/4 binary64) (sqrt.f64 (.f64 x (*.f64 x x)))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/12 (sqrt x)) (* 1/4 (sqrt (/ 1 x))))))
(+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/4 binary64) (.f64 x x))) (.f64 (sqrt.f64 x) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/12 binary64) (.f64 x x)))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/4 (sqrt (/ 1 x))) (* x (+ (* -1/32 (sqrt (/ 1 x))) (* 1/12 (sqrt (/ 1 x))))))))
(+.f64 (sqrt.f64 x) (.f64 (.f64 x x) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal 5/96 binary64) x)))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(.f64 (.f64 x x) (+.f64 (.f64 #s(literal 1/4 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal 1/6 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64))) (/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))) (sqrt.f64 #s(literal 1/6 binary64)))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(.f64 (.f64 x x) (+.f64 (.f64 #s(literal 1/4 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal 1/6 binary64)))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64))) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 #s(literal 1/6 binary64))) #s(literal 5/16 binary64)))))
(* (sqrt (pow x 3)) (* (pow (sqrt -1) 2) (sqrt 1/6)))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/6 binary64))))
(* (pow x 2) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6)))))
(.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/4 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal 1/6 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64)))))
(* (pow x 2) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6))))))
(.f64 (.f64 x x) (-.f64 (/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (sqrt.f64 #s(literal 1/6 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64)))))
(* (pow x 2) (+ (* -1 (/ (+ (* 1/32 (* (sqrt x) (/ (pow (sqrt -1) 2) (pow (sqrt 1/6) 3)))) (* 1/2 (* (sqrt x) (/ (pow (sqrt -1) 2) (sqrt 1/6))))) (pow x 3))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6))))))
(+.f64 (.f64 (.f64 x x) (-.f64 (.f64 #s(literal 1/4 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal 1/6 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64))))) (/.f64 (*.f64 (/.f64 (sqrt.f64 x) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/6 binary64)))) #s(literal 11/16 binary64)) (-.f64 #s(literal 0 binary64) x)))
x
(* x (+ 1 (* 1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* 1/6 (pow x 3))
(.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* 1/6 (pow x 3))
(.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/6 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* x (+ 1/2 (* 1/6 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* x (+ 1/2 (* 1/6 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))

eval89.0ms (1.1%)

Memory: 35.7MiB live, 185.1MiB allocated
Compiler: Compiled 16 827 to 2 399 computations (85.7% saved)

prune85.0ms (1.1%)

Memory

-11.5MiB live, 185.2MiB allocated

Pruning

13 alts after pruning (6 fresh and 7 done)

	Pruned	Kept	Total
New	760	4	764
Fresh	1	2	3
Picked	1	4	5
Done	2	3	5
Total	764	13	777

Accuracy

100.0%

Counts

777 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(pow.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (exp.f64 x))) #s(literal -1/2 binary64))
▶	63.6%	(pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64))
	61.7%	(pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 x (*.f64 x #s(literal 1/48 binary64)))))) #s(literal -1/2 binary64))
▶	62.7%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))))
✓	67.1%	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
▶	2.8%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
✓	60.6%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓	100.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
✓	2.1%	(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
▶	3.1%	(sqrt.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
▶	2.0%	(sqrt.f64 (.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x))))
✓	2.1%	(sqrt.f64 x)
✓	68.1%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 164 to 128 computations (22% saved)

simplify22.0ms (0.3%)

Memory

-9.8MiB live, 30.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))))
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))))))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))))
✓	cost-diff	256	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
✓	cost-diff	0	(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
✓	cost-diff	0	(sqrt.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 #s(literal 1/6 binary64) (.f64 x x))
✓	cost-diff	0	(.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
✓	cost-diff	0	(sqrt.f64 (.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x))))
✓	cost-diff	0	(sqrt.f64 #s(literal 1/2 binary64))
✓	cost-diff	0	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
✓	cost-diff	0	(/.f64 x #s(literal 4 binary64))
✓	cost-diff	0	(-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64)))
✓	cost-diff	0	(pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64))

Rules

242×	`accelerator-lowering-fma.f32`
242×	`accelerator-lowering-fma.f64`
166×	`-lowering-.f32`
166×	`-lowering-.f64`
96×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	127
1	54	127
2	103	123
3	122	123
4	134	123
5	196	123
6	241	123
7	299	123
8	365	123
9	402	123
10	412	123
11	417	123
12	419	123
0	419	112

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize98.0ms (1.3%)

Memory

-24.4MiB live, 149.6MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))))))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))))
✓	accuracy	100.0%	(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
✓	accuracy	99.9%	(*.f64 x #s(literal 1/6 binary64))
✓	accuracy	86.9%	(sqrt.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
✓	accuracy	99.9%	(.f64 #s(literal 1/6 binary64) (.f64 x x))
✓	accuracy	90.1%	(sqrt.f64 (.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/2 binary64))
✓	accuracy	99.8%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(/.f64 x #s(literal 4 binary64))
✓	accuracy	100.0%	(-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64)))

Samples

41.0ms	179×	0	invalid
17.0ms	77×	0	valid

Compiler

Compiled 141 to 29 computations (79.4% saved)

Precisions

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

ival-mult: 15.0ms (35.8% of total)

ival-div: 7.0ms (16.7% of total)

ival-sqrt: 6.0ms (14.3% of total)

ival-pow: 5.0ms (11.9% of total)

ival-sub: 3.0ms (7.2% of total)

const: 3.0ms (7.2% of total)

ival-add: 2.0ms (4.8% of total)

exact: 1.0ms (2.4% of total)

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

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

series11.0ms (0.1%)

Memory

8.0MiB live, 8.0MiB allocated

Counts

18 → 204

Calls

Call 1

Inputs
#<alt (pow (- 1/2 (/ x 4)) -1/2)>
#<alt (- 1/2 (/ x 4))>
#<alt (/ x 4)>
#<alt (* x (sqrt 1/2))>
#<alt (sqrt 1/2)>
#<alt (sqrt (* x (* 1/6 (* x x))))>
#<alt (* x (* 1/6 (* x x)))>
#<alt (* 1/6 (* x x))>
#<alt (* x x)>
#<alt (sqrt (* x (* x (+ 1/2 (* x 1/6)))))>
#<alt (* x (* x (+ 1/2 (* x 1/6))))>
#<alt (* x (+ 1/2 (* x 1/6)))>
#<alt (+ 1/2 (* x 1/6))>
#<alt (/ 1 (/ 1 (+ 1/2 (* x -1/4))))>
#<alt (/ 1 (sqrt (/ 1 (/ 1 (+ 1/2 (* x -1/4))))))>
#<alt (sqrt (/ 1 (/ 1 (+ 1/2 (* x -1/4)))))>
#<alt (/ 1 (+ 1/2 (* x -1/4)))>
#<alt (* x 1/6)>

Outputs
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/4 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* (sqrt (/ 1 x)) (sqrt -4))>
#<alt (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))>
#<alt (+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4))))>
#<alt (+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 32 (* 16 (/ x (pow (sqrt -4) 2)))) (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))))>
#<alt (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))>
#<alt (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1))))>
#<alt (+ (* -4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ 32 (* -4 x))))) (* 4 (* (sqrt x) (sqrt -1)))) (pow x 3))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (* -1/4 x)>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/4))>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/4))>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/4))>
#<alt (* -1/4 x)>
#<alt (* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* x (sqrt 1/2))>
#<alt (* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))>
#<alt (* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2)))))))>
#<alt (* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2)))))))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* 1/6 x)))>
#<alt (* (pow x 2) (+ 1/2 (* 1/6 x)))>
#<alt (* (pow x 2) (+ 1/2 (* 1/6 x)))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (* -1/4 x)>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/4))>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/4))>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/4))>
#<alt (* -1/4 x)>
#<alt (* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/4 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* (sqrt (/ 1 x)) (sqrt -4))>
#<alt (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))>
#<alt (+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4))))>
#<alt (+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 32 (* 16 (/ x (pow (sqrt -4) 2)))) (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))))>
#<alt (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))>
#<alt (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1))))>
#<alt (+ (* -4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ 32 (* -4 x))))) (* 4 (* (sqrt x) (sqrt -1)))) (pow x 3))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (* x (- (* x (- (* -1/1024 (/ x (pow (sqrt 1/2) 5))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (* (sqrt x) (sqrt -1/4))>
#<alt (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))>
#<alt (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4)))))>
#<alt (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1/4) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))))>
#<alt (* -1/2 (* (sqrt x) (sqrt -1)))>
#<alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))>
#<alt (* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1)))))))>
#<alt (* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/4 x))))))>
#<alt (/ -4 x)>
#<alt (* -1 (/ (+ 4 (* 8 (/ 1 x))) x))>
#<alt (/ (- (* -1 (/ (+ 8 (* 16 (/ 1 x))) x)) 4) x)>
#<alt (/ (- (* -1 (/ (+ 16 (* 32 (/ 1 x))) (pow x 2))) (+ 4 (* 8 (/ 1 x)))) x)>
#<alt (/ -4 x)>
#<alt (* -1 (/ (+ 4 (* 8 (/ 1 x))) x))>
#<alt (* -1 (/ (+ 4 (+ (* 8 (/ 1 x)) (/ 16 (pow x 2)))) x))>
#<alt (* -1 (/ (+ 4 (* -1 (/ (- (* -1 (/ (+ 16 (* 32 (/ 1 x))) x)) 8) x))) x))>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>

Calls

51 calls:

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

rewrite630.0ms (8.1%)

Memory

30.2MiB live, 618.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 726×	`accelerator-lowering-fma.f32`
4 726×	`accelerator-lowering-fma.f64`
3 522×	`-lowering-.f32`
3 522×	`-lowering-.f64`
2 338×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	103
1	137	103
2	858	97
3	7060	97
0	8866	87

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 762

Calls

Call 1

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

Outputs
(exp.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))))))
(exp.f64 (.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64)))))))
(exp.f64 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64)))))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))))) #s(literal -1/4 binary64)))
(exp.f64 (.f64 (.f64 #s(literal -1/4 binary64) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))))) #s(literal 2 binary64)))
(exp.f64 (+.f64 (.f64 #s(literal -1/4 binary64) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))))) (.f64 #s(literal -1/4 binary64) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64)))))))
(fabs.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64)))))
(neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64)))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (+.f64 (/.f64 x #s(literal 4 binary64)) #s(literal -1/2 binary64))))
(/.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64))) #s(literal -1 binary64))
(/.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 (+.f64 (/.f64 x #s(literal 4 binary64)) #s(literal -1/2 binary64)))))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (+.f64 (/.f64 x #s(literal 4 binary64)) #s(literal -1/2 binary64))))
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 (/.f64 x #s(literal 4 binary64)) #s(literal -1/2 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64))) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64)))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64)))) #s(literal -1/4 binary64))
(pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64)))))
(*.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64)))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(*.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/4 binary64)) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/4 binary64)))
(.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/4 binary64)) (.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/4 binary64)) (/.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64)))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64)) (.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64)) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/4 binary64))))
(*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64))) #s(literal -1 binary64))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64)) (pow.f64 (+.f64 (/.f64 x #s(literal 4 binary64)) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 #s(literal 1/64 binary64) (.f64 x x)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64))))) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) #s(literal -16 binary64))) #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 #s(literal 1/64 binary64) (.f64 x x))))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64))))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) #s(literal -16 binary64)))) #s(literal 1/2 binary64)) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64))) (sqrt.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 #s(literal 1/64 binary64) (.f64 x x)))))) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) #s(literal -16 binary64))))) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/4 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/4 binary64))) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/4 binary64)))
(.f64 (.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/4 binary64)) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64))) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64)))) #s(literal 1/2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 #s(literal 1/64 binary64) (.f64 x x)))))) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) #s(literal -16 binary64))))) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64)))
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64)))
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -4 binary64)))
(+.f64 (/.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64))
(+.f64 (/.f64 x #s(literal -4 binary64)) #s(literal 1/2 binary64))
(+.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64)))) (neg.f64 (/.f64 (.f64 x x) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal 16 binary64)))))
(+.f64 (/.f64 #s(literal 1/8 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64))))) (neg.f64 (/.f64 (.f64 x (.f64 #s(literal 1/64 binary64) (.f64 x x))) (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))))))
(exp.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64)))))
(exp.f64 (*.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64)))) #s(literal 1 binary64)))
(-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64)))
(-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -4 binary64)))
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(.f64 (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 #s(literal 1/64 binary64) (.f64 x x))))))
(.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/4 binary64)) (.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/4 binary64)) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64))))
(*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 #s(literal 1/64 binary64) (.f64 x x))))) (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 #s(literal 1/64 binary64) (.f64 x x))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64))))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 #s(literal 1/64 binary64) (.f64 x x))))) (/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) #s(literal -16 binary64)))) (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 #s(literal 1/64 binary64) (.f64 x x))))) #s(literal 1 binary64)) (pow.f64 (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) #s(literal -16 binary64)))) #s(literal 1 binary64)) (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))))
(.f64 (.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/4 binary64))) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/4 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 #s(literal 1/64 binary64) (.f64 x x))))) (+.f64 #s(literal -1/4 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))))
(.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x x) #s(literal -16 binary64)))) (+.f64 (/.f64 x #s(literal 4 binary64)) #s(literal -1/2 binary64)))
(.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 1/64 binary64) (.f64 #s(literal 1/4096 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (+.f64 #s(literal 1/16 binary64) (.f64 (/.f64 x (/.f64 #s(literal 16 binary64) x)) (+.f64 #s(literal 1/4 binary64) (/.f64 x (/.f64 #s(literal 16 binary64) x))))))
(.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1/16 binary64) (.f64 #s(literal 1/256 binary64) (.f64 (.f64 x x) (*.f64 x x))))) (+.f64 #s(literal 1/4 binary64) (/.f64 x (/.f64 #s(literal 16 binary64) x))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 #s(literal 1/64 binary64) (.f64 x x))) #s(literal -1/8 binary64))) (+.f64 #s(literal -1/4 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/4 binary64) (/.f64 x (/.f64 #s(literal 16 binary64) x)))) (+.f64 (/.f64 x #s(literal 4 binary64)) #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x (/.f64 #s(literal 16 binary64) x)) #s(literal -1/4 binary64))) (+.f64 (/.f64 x #s(literal 4 binary64)) #s(literal -1/2 binary64)))
(.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))) (+.f64 #s(literal 1/512 binary64) (.f64 (.f64 x (.f64 #s(literal 1/64 binary64) (.f64 x x))) (.f64 #s(literal 1/4096 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))))) (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 x (.f64 #s(literal 1/64 binary64) (.f64 x x))) (-.f64 (.f64 x (.f64 #s(literal 1/64 binary64) (.f64 x x))) #s(literal 1/8 binary64)))))
(.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))) (+.f64 #s(literal 1/64 binary64) (.f64 #s(literal 1/4096 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 #s(literal 1/64 binary64) (.f64 x x)))))
(.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 x (+.f64 (.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))) (-.f64 #s(literal 1/512 binary64) (.f64 (.f64 x (.f64 #s(literal 1/64 binary64) (.f64 x x))) (.f64 #s(literal 1/4096 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))))) (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 x (.f64 #s(literal 1/64 binary64) (.f64 x x))) (+.f64 #s(literal 1/8 binary64) (.f64 x (.f64 #s(literal 1/64 binary64) (.f64 x x)))))))
(*.f64 x #s(literal 1/6 binary64))
(*.f64 #s(literal 1/6 binary64) x)

simplify505.0ms (6.5%)

Memory

-14.5MiB live, 780.7MiB allocated

Algorithm

1×	egg-herbie

Rules

13 172×	`accelerator-lowering-fma.f32`
13 172×	`accelerator-lowering-fma.f64`
5 100×	`-lowering-.f32`
5 100×	`-lowering-.f64`
3 316×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	293	2073
1	872	1909
2	2605	1866
3	5494	1835
0	8082	1714

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 204

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 (- 1/4 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* (sqrt (/ 1 x)) (sqrt -4))
(+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4))))
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 32 (* 16 (/ x (pow (sqrt -4) 2)))) (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))))
(* 2 (* (sqrt (/ 1 x)) (sqrt -1)))
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1))))
(+ (* -4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ 32 (* -4 x))))) (* 4 (* (sqrt x) (sqrt -1)))) (pow x 3))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))
1/2
(+ 1/2 (* -1/4 x))
(+ 1/2 (* -1/4 x))
(+ 1/2 (* -1/4 x))
(* -1/4 x)
(* x (- (* 1/2 (/ 1 x)) 1/4))
(* x (- (* 1/2 (/ 1 x)) 1/4))
(* x (- (* 1/2 (/ 1 x)) 1/4))
(* -1/4 x)
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* x (sqrt 1/2))
(* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))
(* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2)))))))
(* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2)))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/2 x)
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
1/2
(+ 1/2 (* -1/4 x))
(+ 1/2 (* -1/4 x))
(+ 1/2 (* -1/4 x))
(* -1/4 x)
(* x (- (* 1/2 (/ 1 x)) 1/4))
(* x (- (* 1/2 (/ 1 x)) 1/4))
(* x (- (* 1/2 (/ 1 x)) 1/4))
(* -1/4 x)
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/4 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* (sqrt (/ 1 x)) (sqrt -4))
(+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4))))
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 32 (* 16 (/ x (pow (sqrt -4) 2)))) (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))))
(* 2 (* (sqrt (/ 1 x)) (sqrt -1)))
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1))))
(+ (* -4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ 32 (* -4 x))))) (* 4 (* (sqrt x) (sqrt -1)))) (pow x 3))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (- (* x (- (* -1/1024 (/ x (pow (sqrt 1/2) 5))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))
(* (sqrt x) (sqrt -1/4))
(* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4)))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1/4) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))))
(* -1/2 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1)))))))
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/4 x))))))
(/ -4 x)
(* -1 (/ (+ 4 (* 8 (/ 1 x))) x))
(/ (- (* -1 (/ (+ 8 (* 16 (/ 1 x))) x)) 4) x)
(/ (- (* -1 (/ (+ 16 (* 32 (/ 1 x))) (pow x 2))) (+ 4 (* 8 (/ 1 x)))) x)
(/ -4 x)
(* -1 (/ (+ 4 (* 8 (/ 1 x))) x))
(* -1 (/ (+ 4 (+ (* 8 (/ 1 x)) (/ 16 (pow x 2)))) x))
(* -1 (/ (+ 4 (* -1 (/ (- (* -1 (/ (+ 16 (* 32 (/ 1 x))) x)) 8) x))) x))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)

Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 #s(literal 2 binary64))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3/16 binary64) x))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/4 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 3/16 binary64) (*.f64 #s(literal 5/64 binary64) x))))))
(* (sqrt (/ 1 x)) (sqrt -4))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64)))
(+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))
(+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal -4 binary64) (sqrt.f64 #s(literal -4 binary64)))))
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4))))
(+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64))) (/.f64 (+.f64 (.f64 #s(literal -4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (*.f64 #s(literal -8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (sqrt.f64 #s(literal -4 binary64))))
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 32 (* 16 (/ x (pow (sqrt -4) 2)))) (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))))
(+.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 (.f64 (+.f64 #s(literal 32 binary64) (.f64 x #s(literal -4 binary64))) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -4 binary64))))) (/.f64 (+.f64 (.f64 #s(literal -4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 #s(literal -8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (sqrt.f64 #s(literal -4 binary64))))
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(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -4 binary64)))
(* x (- (* 1/2 (/ 1 x)) 1/4))
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -4 binary64)))
(* -1/4 x)
(/.f64 x #s(literal -4 binary64))
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -4 binary64)))
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -4 binary64)))
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal -4 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 #s(literal 2 binary64))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3/16 binary64) x))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/4 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 3/16 binary64) (*.f64 #s(literal 5/64 binary64) x))))))
(* (sqrt (/ 1 x)) (sqrt -4))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64)))
(+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))
(+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal -4 binary64) (sqrt.f64 #s(literal -4 binary64)))))
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4))))
(+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64))) (/.f64 (+.f64 (.f64 #s(literal -4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (*.f64 #s(literal -8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (sqrt.f64 #s(literal -4 binary64))))
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 32 (* 16 (/ x (pow (sqrt -4) 2)))) (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))))
(+.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 (.f64 (+.f64 #s(literal 32 binary64) (.f64 x #s(literal -4 binary64))) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -4 binary64))))) (/.f64 (+.f64 (.f64 #s(literal -4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 #s(literal -8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (sqrt.f64 #s(literal -4 binary64))))
(* 2 (* (sqrt (/ 1 x)) (sqrt -1)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -2 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(+ (* -4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -2 binary64)) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/4 binary64))))
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ 32 (* -4 x))))) (* 4 (* (sqrt x) (sqrt -1)))) (pow x 3))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))
(-.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -2 binary64)) (.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 32 binary64) (.f64 x #s(literal -4 binary64)))) (.f64 #s(literal 4 binary64) (sqrt.f64 x)))) (.f64 x (.f64 x x))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1/8 binary64)))
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 x (+.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1/64 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
(+ (sqrt 1/2) (* x (- (* x (- (* -1/1024 (/ x (pow (sqrt 1/2) 5))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 x (+.f64 (.f64 x (+.f64 (/.f64 (*.f64 x #s(literal -1/1024 binary64)) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -1/64 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
(* (sqrt x) (sqrt -1/4))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1/4 binary64)))
(* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))
(.f64 x (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal -1/4 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1/4 binary64)))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4)))))
(.f64 x (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1/4 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1/4 binary64))) (+.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/32 binary64)) #s(literal -1/4 binary64))))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1/4) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1/4) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1/4)))) (* (sqrt (/ 1 x)) (sqrt -1/4))))))
(.f64 x (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1/4 binary64))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/128 binary64) (pow.f64 (sqrt.f64 #s(literal -1/4 binary64)) #s(literal 5 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1/4 binary64))) (+.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/32 binary64)) #s(literal -1/4 binary64)))))))
(* -1/2 (* (sqrt x) (sqrt -1)))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))
(.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))))
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1)))))))
(.f64 x (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) (+.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/4 binary64)))))
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 x)) (sqrt -1))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))))))))
(.f64 x (-.f64 #s(literal 0 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (+.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/4 binary64)))))))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/4 x))))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64)))))))
(/ -4 x)
(/.f64 #s(literal -4 binary64) x)
(* -1 (/ (+ 4 (* 8 (/ 1 x))) x))
(/.f64 (+.f64 #s(literal -4 binary64) (/.f64 #s(literal -8 binary64) x)) x)
(/ (- (* -1 (/ (+ 8 (* 16 (/ 1 x))) x)) 4) x)
(/.f64 (-.f64 #s(literal -4 binary64) (/.f64 (+.f64 #s(literal 8 binary64) (/.f64 #s(literal 16 binary64) x)) x)) x)
(/ (- (* -1 (/ (+ 16 (* 32 (/ 1 x))) (pow x 2))) (+ 4 (* 8 (/ 1 x)))) x)
(/.f64 (+.f64 #s(literal -4 binary64) (/.f64 (+.f64 #s(literal -8 binary64) (/.f64 (+.f64 #s(literal -16 binary64) (/.f64 #s(literal -32 binary64) x)) x)) x)) x)
(/ -4 x)
(/.f64 #s(literal -4 binary64) x)
(* -1 (/ (+ 4 (* 8 (/ 1 x))) x))
(/.f64 (+.f64 #s(literal -4 binary64) (/.f64 #s(literal -8 binary64) x)) x)
(* -1 (/ (+ 4 (+ (* 8 (/ 1 x)) (/ 16 (pow x 2)))) x))
(/.f64 (-.f64 #s(literal -4 binary64) (/.f64 (+.f64 #s(literal 8 binary64) (/.f64 #s(literal 16 binary64) x)) x)) x)
(* -1 (/ (+ 4 (* -1 (/ (- (* -1 (/ (+ 16 (* 32 (/ 1 x))) x)) 8) x))) x))
(/.f64 (+.f64 #s(literal -4 binary64) (/.f64 (+.f64 #s(literal -8 binary64) (/.f64 (+.f64 #s(literal -16 binary64) (/.f64 #s(literal -32 binary64) x)) x)) x)) x)
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))

eval109.0ms (1.4%)

Memory: 31.0MiB live, 178.5MiB allocated
Compiler: Compiled 18 199 to 2 470 computations (86.4% saved)

prune101.0ms (1.3%)

Memory

4.8MiB live, 206.8MiB allocated

Pruning

14 alts after pruning (4 fresh and 10 done)

	Pruned	Kept	Total
New	963	3	966
Fresh	0	1	1
Picked	2	3	5
Done	0	7	7
Total	965	14	979

Accuracy

100.0%

Counts

979 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(pow.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (exp.f64 x))) #s(literal -1/2 binary64))
✓	63.6%	(pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64))
	61.7%	(pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 x (*.f64 x #s(literal 1/48 binary64)))))) #s(literal -1/2 binary64))
✓	62.7%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))))
	60.1%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))))))))))
✓	67.1%	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
	2.3%	(.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) x)
	1.4%	(.f64 (pow.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) x)
✓	2.8%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
✓	60.6%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓	100.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
✓	2.1%	(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
✓	2.1%	(sqrt.f64 x)
✓	68.1%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 319 to 180 computations (43.6% saved)

regimes32.0ms (0.4%)

Memory

-14.3MiB live, 24.8MiB allocated

Counts

23 → 1

Calls

Call 1

Inputs
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 x)
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(.f64 (pow.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) x)
(pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64))
(sqrt.f64 (.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))
(.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) x)
(sqrt.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(sqrt.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))))
(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 x (*.f64 x #s(literal 1/48 binary64)))))) #s(literal -1/2 binary64))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))))))))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(pow.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (exp.f64 x))) #s(literal -1/2 binary64))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(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
(pow.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (exp.f64 x))) #s(literal -1/2 binary64))

Calls

3 calls:

18.0ms

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

Compiler

Compiled 27 to 20 computations (25.9% saved)

regimes7.0ms (0.1%)

Memory

9.0MiB live, 9.0MiB allocated

Counts

19 → 1

Calls

Call 1

Inputs
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 x)
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(.f64 (pow.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) x)
(pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64))
(sqrt.f64 (.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))
(.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) x)
(sqrt.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(sqrt.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))))
(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 x (*.f64 x #s(literal 1/48 binary64)))))) #s(literal -1/2 binary64))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))))))))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))

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

Calls

1 calls:

6.0ms

Results

Accuracy	Segments	Branch
100.0%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes6.0ms (0.1%)

Memory

7.4MiB live, 7.4MiB allocated

Accuracy

Total -42.7b remaining (-208.9%)

Threshold costs -42.7b (-208.9%)

Counts

18 → 1

Calls

Call 1

Inputs
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 x)
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(.f64 (pow.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) x)
(pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64))
(sqrt.f64 (.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))
(.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) x)
(sqrt.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(sqrt.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))))
(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))))))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 x (*.f64 x #s(literal 1/48 binary64)))))) #s(literal -1/2 binary64))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 x #s(literal 4 binary64))))))))))

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

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
68.1%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify16.0ms (0.2%)

Memory

-31.0MiB live, 8.3MiB allocated

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`1-exp_binary64`
2×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	15
1	18	15
2	21	15
3	23	15
4	24	15

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.5s (19.1%)

Memory

19.9MiB live, 2 020.4MiB allocated

Rules

15 394×	`accelerator-lowering-fma.f32`
15 394×	`accelerator-lowering-fma.f64`
15 182×	`accelerator-lowering-fma.f32`
15 182×	`accelerator-lowering-fma.f64`
5 376×	`-lowering-.f32`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	52	224
1	156	190
2	454	190
3	920	184
4	1914	183
5	5027	181
0	8491	165
0	10	12
1	22	12
2	28	12
3	40	12
4	66	7
5	119	5
6	195	5
7	593	5
8	2904	5
9	6743	5
0	8156	5
0	25	128
1	157	123
2	1306	123
0	8310	105
0	5	11
1	23	11
2	143	11
0	1067	11

Stop Event

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

Compiler

Compiled 56 to 44 computations (21.4% saved)

preprocess51.0ms (0.7%)

Memory: -20.7MiB live, 57.6MiB allocated
Compiler: Compiled 58 to 44 computations (24.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	24	111
1	47	111
2	87	111
3	176	111
4	229	111
5	241	111
6	255	111
7	269	111
8	273	111
9	275	111
10	278	111
11	281	111
0	281	100

Iter	Nodes	Cost
0	27	127
1	54	127
2	103	123
3	122	123
4	134	123
5	196	123
6	241	123
7	299	123
8	365	123
9	402	123
10	412	123
11	417	123
12	419	123
0	419	112

Iter	Nodes	Cost
0	24	111
1	47	111
2	87	111
3	176	111
4	229	111
5	241	111
6	255	111
7	269	111
8	273	111
9	275	111
10	278	111
11	281	111
0	281	100

Iter	Nodes	Cost
0	27	127
1	54	127
2	103	123
3	122	123
4	134	123
5	196	123
6	241	123
7	299	123
8	365	123
9	402	123
10	412	123
11	417	123
12	419	123
0	419	112

analyze2.0ms (0%)

sample896.0ms (11.5%)

preprocess489.0ms (6.3%)

explain137.0ms (1.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0%)

localize23.0ms (0.3%)

series2.0ms (0%)

rewrite92.0ms (1.2%)

simplify446.0ms (5.7%)

eval12.0ms (0.2%)

prune15.0ms (0.2%)

simplify15.0ms (0.2%)

localize139.0ms (1.8%)

series16.0ms (0.2%)

rewrite379.0ms (4.9%)

simplify601.0ms (7.7%)

eval130.0ms (1.7%)

prune207.0ms (2.7%)

simplify17.0ms (0.2%)

localize104.0ms (1.3%)

series14.0ms (0.2%)

rewrite338.0ms (4.4%)

simplify447.0ms (5.8%)

eval89.0ms (1.1%)

prune85.0ms (1.1%)

simplify22.0ms (0.3%)

localize98.0ms (1.3%)

series11.0ms (0.1%)

rewrite630.0ms (8.1%)

simplify505.0ms (6.5%)

eval109.0ms (1.4%)

prune101.0ms (1.3%)

regimes32.0ms (0.4%)

regimes7.0ms (0.1%)

regimes6.0ms (0.1%)

simplify16.0ms (0.2%)

soundness1.5s (19.1%)

preprocess51.0ms (0.7%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	24	111
1	47	111
2	87	111
3	176	111
4	229	111
5	241	111
6	255	111
7	269	111
8	273	111
9	275	111
10	278	111
11	281	111
0	281	100

Iter	Nodes	Cost
0	27	127
1	54	127
2	103	123
3	122	123
4	134	123
5	196	123
6	241	123
7	299	123
8	365	123
9	402	123
10	412	123
11	417	123
12	419	123
0	419	112