Metrics for sqrtexp (problem 3.4.4)

analyze2.0ms (0%)

Memory

2.8MiB live, 2.8MiB 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)

sample916.0ms (17.3%)

Memory

44.9MiB live, 958.9MiB allocated

Samples

472.0ms	8 256×	0	valid
140.0ms	2 635×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 396.0ms

ival-expm1: 142.0ms (35.9% of total)

ival-mult: 86.0ms (21.7% of total)

ival-div: 78.0ms (19.7% of total)

ival-sqrt: 73.0ms (18.4% of total)

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

exact: 6.0ms (1.5% of total)

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

Bogosity

preprocess395.0ms (7.4%)

Memory

-13.9MiB live, 338.4MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 5 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

explain195.0ms (3.7%)

Memory

9.0MiB live, 140.7MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
256	-	76	(-9.791702008120803e+98)	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
256	-	256	(-8.515774434116377e-201)	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))`
256	-	76	(-9.791702008120803e+98)	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`
256	-	256	(-8.515774434116377e-201)	`(exp.f64 x)`
256	-	256	(-8.515774434116377e-201)	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
83	-	83	(-9.791702008120803e+98)	`(*.f64 #s(literal 2 binary64) x)`
0	-	0	-	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`
0	-	0	-	`#s(literal 1 binary64)`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	cancellation	180	0
`-.f64`	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	cancellation	180	0

Confusion

	Predicted +	Predicted -
+	179	0
-	1	76

Precision

0.9944444444444445

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	179	0	0
-	1	0	76

Precision?

0.9944444444444445

Recall?

1.0

Freqs

test

number	freq
0	76
2	180

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

43.0ms

512×

valid

Compiler

Compiled 166 to 54 computations (67.5% saved)

Precisions

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

ival-exp: 7.0ms (28.4% of total)

ival-expm1: 6.0ms (24.3% of total)

ival-div: 4.0ms (16.2% of total)

ival-mult: 4.0ms (16.2% of total)

ival-sqrt: 3.0ms (12.2% of total)

exact: 1.0ms (4.1% of total)

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

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	32.0%	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))

Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify415.0ms (7.8%)

Memory

12.0MiB live, 365.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

localize32.0ms (0.6%)

Memory

-3.3MiB live, 38.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	3.2%	(exp.f64 x)
✓	accuracy	3.0%	(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
✓	accuracy	2.8%	(-.f64 (exp.f64 x) #s(literal 1 binary64))
✓	accuracy	2.8%	(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))

Samples

20.0ms

256×

valid

Compiler

Compiled 93 to 22 computations (76.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-exp: 5.0ms (36.8% of total)

ival-expm1: 3.0ms (22.1% of total)

ival-div: 2.0ms (14.7% of total)

ival-mult: 2.0ms (14.7% of total)

ival-sqrt: 2.0ms (14.7% of total)

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

exact: 0.0ms (0% of total)

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

series8.0ms (0.1%)

Memory

-33.4MiB live, 5.4MiB allocated

Counts

5 → 60

Calls

Call 1

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

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

15 calls:

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

Compiler

Compiled 105 to 82 computations (21.9% saved)

rewrite363.0ms (6.8%)

Memory

3.2MiB live, 364.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	26
0	15	26
1	56	19
2	378	19
3	4533	19
0	8161	15

Stop Event

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

Counts

5 → 656

Calls

Call 1

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

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

simplify398.0ms (7.5%)

Memory

21.9MiB live, 418.9MiB allocated

Algorithm

1×	egg-herbie

Rules

12 518×	`lower-fma.f64`
12 518×	`lower-fma.f32`
3 984×	`lower-+.f64`
3 984×	`lower-+.f32`
2 820×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	330
1	158	330
2	339	330
3	763	330
4	1221	290
5	1557	274
6	2048	274
7	3388	274
8	6635	274
0	8418	220

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 55

Calls

Call 1

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

eval147.0ms (2.8%)

Memory: 22.5MiB live, 131.9MiB allocated
Compiler: Compiled 16 772 to 2 361 computations (85.9% saved)

prune87.0ms (1.6%)

Memory

-17.5MiB live, 183.4MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	705	6	711
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	706	6	712

Accuracy

100.0%

Counts

712 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	70.4%	(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
▶	71.8%	(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
	100.0%	(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
▶	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
▶	70.2%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
▶	75.6%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 88 to 68 computations (22.7% saved)

simplify16.0ms (0.3%)

Memory

-15.7MiB live, 21.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

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

Rules

400×	`lower-fma.f32`
390×	`lower-fma.f64`
134×	`lower-*.f64`
134×	`lower-*.f32`
132×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	85
0	37	85
1	67	85
2	113	85
3	202	85
4	249	85
5	255	85
0	255	85

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize73.0ms (1.4%)

Memory

18.2MiB live, 138.2MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓	accuracy	99.1%	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
✓	accuracy	99.1%	(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
✓	accuracy	99.1%	(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
✓	accuracy	100.0%	(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
✓	accuracy	44.3%	(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
✓	accuracy	32.3%	(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓	accuracy	43.7%	(+.f64 #s(literal 2 binary64) x)
✓	accuracy	43.7%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓	accuracy	43.7%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	42.9%	(exp.f64 x)
✓	accuracy	32.2%	(-.f64 (exp.f64 x) #s(literal -1 binary64))
✓	accuracy	30.8%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))

Samples

37.0ms	180×	0	valid
14.0ms	76×	0	invalid

Compiler

Compiled 187 to 45 computations (75.9% saved)

Precisions

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

ival-mult: 11.0ms (29.6% of total)

ival-sqrt: 8.0ms (21.5% of total)

ival-add: 7.0ms (18.8% of total)

const: 7.0ms (18.8% of total)

ival-exp: 2.0ms (5.4% of total)

ival-sub: 1.0ms (2.7% of total)

exact: 1.0ms (2.7% of total)

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

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

series15.0ms (0.3%)

Memory

-13.5MiB live, 22.8MiB allocated

Counts

13 → 144

Calls

Call 1

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

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

Calls

36 calls:

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

Compiler

Compiled 357 to 282 computations (21% saved)

rewrite328.0ms (6.2%)

Memory

16.7MiB live, 497.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 428×	`lower-fma.f32`
4 418×	`lower-fma.f64`
4 328×	`lower-*.f64`
4 328×	`lower-*.f32`
4 210×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	71
0	37	71
1	155	71
2	1136	71
0	8248	71

Stop Event

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

Counts

13 → 442

Calls

Call 1

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

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

simplify324.0ms (6.1%)

Memory

-6.0MiB live, 378.8MiB allocated

Algorithm

1×	egg-herbie

Rules

8 922×	`lower-fma.f64`
8 922×	`lower-fma.f32`
4 724×	`lower-*.f64`
4 724×	`lower-*.f32`
3 044×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	289	1461
1	895	1276
2	2822	1232
3	7753	1232
0	8047	1129

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 142

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

Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(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))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* -1/8 (/ x (pow (sqrt 2) 3))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/16 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt 2) 5))) (* 1/8 (/ 1 (pow (sqrt 2) 3))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (sqrt (/ 1 (pow x 3)))))
(.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 5)))))))
(.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 7))))))))
(.f64 x (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 x))
(* -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))))))
(neg.f64 (.f64 x (+.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))))
(* -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)))))))
(.f64 x (neg.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(+ (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))))))
(fma.f64 x (fma.f64 x (*.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1 binary64)) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt x) (sqrt 3/2))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 3/2 binary64)))
(* x (+ (* (sqrt (/ 1 x)) (sqrt 3/2)) (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 3/2)))))
(.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 3/2 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 #s(literal 3/2 binary64)))))
(* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 3/2) 3)))) (+ (* (sqrt (/ 1 x)) (sqrt 3/2)) (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 3/2))))))
(.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal -1/3 binary64) (sqrt.f64 #s(literal 3/2 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 3/2 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 #s(literal 3/2 binary64))))))
(* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 3/2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 3/2) 5)))) (+ (* (sqrt (/ 1 x)) (sqrt 3/2)) (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 3/2)))))))
(.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sqrt.f64 #s(literal 3/2 binary64)) #s(literal 5 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal -1/3 binary64) (sqrt.f64 #s(literal 3/2 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 3/2 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 #s(literal 3/2 binary64)))))))
(* -1 (* x (sqrt 1/2)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (neg.f64 x))
(* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))
(fma.f64 x (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* -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)))))
(-.f64 (+.f64 (/.f64 #s(literal -3/4 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(* -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)))))
(-.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 3/4 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) x) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(* 3/2 x)
(*.f64 x #s(literal 3/2 binary64))
(* x (+ 3/2 (* 2 (/ 1 x))))
(fma.f64 x #s(literal 3/2 binary64) #s(literal 2 binary64))
(* x (+ 3/2 (* 2 (/ 1 x))))
(fma.f64 x #s(literal 3/2 binary64) #s(literal 2 binary64))
(* x (+ 3/2 (* 2 (/ 1 x))))
(fma.f64 x #s(literal 3/2 binary64) #s(literal 2 binary64))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 4) (sqrt 1/6))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal 1/6 binary64)))
(* (pow x 4) (sqrt 1/6))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal 1/6 binary64)))
(* (pow x 4) (+ (sqrt 1/6) (* 3/4 (/ 1 (* (pow x 7) (sqrt 1/6))))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 (sqrt.f64 #s(literal 1/6 binary64)) (/.f64 #s(literal 3/4 binary64) (.f64 (pow.f64 x #s(literal 7 binary64)) (sqrt.f64 #s(literal 1/6 binary64))))))
(* (pow x 4) (+ (sqrt 1/6) (+ (/ 3/4 (* (pow x 7) (sqrt 1/6))) (/ 1 (* (pow x 8) (sqrt 1/6))))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 (sqrt.f64 #s(literal 1/6 binary64)) (+.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (pow.f64 x #s(literal 7 binary64)) (sqrt.f64 #s(literal 1/6 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/6 binary64)) (pow.f64 x #s(literal 8 binary64)))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(.f64 (.f64 (sqrt.f64 (.f64 x (.f64 x x))) (sqrt.f64 #s(literal -1/6 binary64))) (sqrt.f64 #s(literal -1 binary64)))
(* (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) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (.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))))))
(* (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) (fma.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 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))))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (/.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 x #s(literal -3/8 binary64) #s(literal 2 binary64))) (sqrt.f64 #s(literal -1/6 binary64)))) x) (.f64 (.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (.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)))))))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(* 1/6 (pow x 8))
(*.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 8 binary64)))
(* 1/6 (pow x 8))
(*.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 8 binary64)))
(* (pow x 8) (+ 1/6 (* 3/2 (/ 1 (pow x 7)))))
(*.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 3/2 binary64) (pow.f64 x #s(literal 7 binary64)))))
(* (pow x 8) (+ 1/6 (+ (* 3/2 (/ 1 (pow x 7))) (/ 2 (pow x 8)))))
(*.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (/.f64 #s(literal 3/2 binary64) (pow.f64 x #s(literal 7 binary64))) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 8 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 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (neg.f64 (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(neg.f64 (.f64 (.f64 x (.f64 x x)) (+.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))))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* 1/6 (pow x 3))
(.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 (pow x 2))) (/ 1 (pow x 3)))))
(fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 (pow x 2))) (/ 1 (pow x 3)))))
(fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) #s(literal 1 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 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/6 x))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* 1/6 x))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* 1/6 x))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))

eval78.0ms (1.5%)

Memory: -12.6MiB live, 141.7MiB allocated
Compiler: Compiled 13 916 to 1 938 computations (86.1% saved)

prune61.0ms (1.1%)

Memory

19.5MiB live, 139.0MiB allocated

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	582	2	584
Fresh	1	0	1
Picked	0	5	5
Done	0	0	0
Total	583	7	590

Accuracy

100.0%

Counts

590 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	2.8%	(fma.f64 x (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
✓	70.4%	(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓	71.8%	(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
▶	69.5%	(sqrt.f64 (fma.f64 x #s(literal 3/2 binary64) #s(literal 2 binary64)))
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓	70.2%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓	75.6%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 51 to 40 computations (21.6% saved)

simplify23.0ms (0.4%)

Memory

-24.0MiB live, 15.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Program
✓	cost-diff	(/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
✓	cost-diff	(sqrt.f64 #s(literal 1/2 binary64))
✓	cost-diff	(neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))
✓	cost-diff	(fma.f64 x (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
✓	cost-diff	(fma.f64 x #s(literal 3/2 binary64) #s(literal 2 binary64))
✓	cost-diff	(sqrt.f64 (fma.f64 x #s(literal 3/2 binary64) #s(literal 2 binary64)))

Rules

224×	`lower-fma.f32`
220×	`lower-fma.f64`
144×	`lower-*.f64`
144×	`lower-*.f32`
72×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	33
0	19	33
1	29	33
2	41	33
3	57	33
4	69	33
5	95	33
6	146	33
7	190	33
8	263	33
9	275	33
10	292	33
11	324	33
12	334	33
13	347	33
14	361	33
15	369	33
16	378	33
17	382	33
0	382	33

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(sqrt.f64 (fma.f64 x #s(literal 3/2 binary64) #s(literal 2 binary64)))
(fma.f64 x #s(literal 3/2 binary64) #s(literal 2 binary64))
x
#s(literal 3/2 binary64)
#s(literal 2 binary64)
(fma.f64 x (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
x
(neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
#s(literal -1/2 binary64)

Outputs
(sqrt.f64 (fma.f64 x #s(literal 3/2 binary64) #s(literal 2 binary64)))
(fma.f64 x #s(literal 3/2 binary64) #s(literal 2 binary64))
x
#s(literal 3/2 binary64)
#s(literal 2 binary64)
(fma.f64 x (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(-.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
x
(neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
#s(literal -1/2 binary64)

localize34.0ms (0.6%)

Memory

15.2MiB live, 53.2MiB allocated

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))
✓	accuracy	99.1%	(fma.f64 x (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
✓	accuracy	32.3%	(sqrt.f64 #s(literal 1/2 binary64))
✓	accuracy	30.8%	(/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
✓	accuracy	44.0%	(fma.f64 x #s(literal 3/2 binary64) #s(literal 2 binary64))
✓	accuracy	43.7%	(sqrt.f64 (fma.f64 x #s(literal 3/2 binary64) #s(literal 2 binary64)))

Samples

17.0ms	180×	0	valid
6.0ms	76×	0	invalid

Compiler

Compiled 72 to 26 computations (63.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-mult: 5.0ms (34% of total)

ival-sqrt: 4.0ms (27.2% of total)

ival-div: 2.0ms (13.6% of total)

ival-add: 2.0ms (13.6% of total)

ival-neg: 1.0ms (6.8% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0.1%)

Memory

5.0MiB live, 5.0MiB allocated

Counts

6 → 36

Calls

Call 1

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

Outputs
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 3/4 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* -9/32 (/ x (pow (sqrt 2) 3))) (* 3/4 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (- (* 27/128 (/ x (pow (sqrt 2) 5))) (* 9/32 (/ 1 (pow (sqrt 2) 3))))) (* 3/4 (/ 1 (sqrt 2))))))>
#<alt (* (sqrt x) (sqrt 3/2))>
#<alt (* x (+ (* (sqrt (/ 1 x)) (sqrt 3/2)) (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 3/2)))))>
#<alt (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 3/2) 3)))) (+ (* (sqrt (/ 1 x)) (sqrt 3/2)) (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 3/2))))))>
#<alt (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 3/2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 3/2) 5)))) (+ (* (sqrt (/ 1 x)) (sqrt 3/2)) (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 3/2)))))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -3/2) (sqrt -1))))>
#<alt (* -1 (* x (+ (* (sqrt (/ 1 x)) (* (sqrt -3/2) (sqrt -1))) (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -3/2))))))>
#<alt (* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -3/2) 3)))) (+ (* (sqrt (/ 1 x)) (* (sqrt -3/2) (sqrt -1))) (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -3/2)))))))>
#<alt (* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -3/2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -3/2) 5)))) (+ (* (sqrt (/ 1 x)) (* (sqrt -3/2) (sqrt -1))) (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -3/2))))))))>
#<alt 2>
#<alt (+ 2 (* 3/2 x))>
#<alt (+ 2 (* 3/2 x))>
#<alt (+ 2 (* 3/2 x))>
#<alt (* 3/2 x)>
#<alt (* x (+ 3/2 (* 2 (/ 1 x))))>
#<alt (* x (+ 3/2 (* 2 (/ 1 x))))>
#<alt (* x (+ 3/2 (* 2 (/ 1 x))))>
#<alt (* 3/2 x)>
#<alt (* x (+ 3/2 (* 2 (/ 1 x))))>
#<alt (* x (+ 3/2 (* 2 (/ 1 x))))>
#<alt (* x (+ 3/2 (* 2 (/ 1 x))))>
#<alt (/ -1/2 (sqrt 1/2))>
#<alt (- (* -1 (* x (sqrt 1/2))) (* 1/2 (/ 1 (sqrt 1/2))))>
#<alt (- (* -1 (* x (sqrt 1/2))) (* 1/2 (/ 1 (sqrt 1/2))))>
#<alt (- (* -1 (* x (sqrt 1/2))) (* 1/2 (/ 1 (sqrt 1/2))))>
#<alt (* -1 (* x (sqrt 1/2)))>
#<alt (* x (- (* -1 (sqrt 1/2)) (* 1/2 (/ 1 (* x (sqrt 1/2))))))>
#<alt (* x (- (* -1 (sqrt 1/2)) (* 1/2 (/ 1 (* x (sqrt 1/2))))))>
#<alt (* x (- (* -1 (sqrt 1/2)) (* 1/2 (/ 1 (* 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) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))>

Calls

9 calls:

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

Compiler

Compiled 87 to 69 computations (20.7% saved)

rewrite55.0ms (1%)

Memory

-11.3MiB live, 28.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

274×	`lower-fma.f32`
270×	`lower-fma.f64`
262×	`lower-*.f64`
262×	`lower-*.f32`
180×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	27
0	19	27
1	65	27
0	452	27

Stop Event

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

Counts

6 → 67

Calls

Call 1

Inputs
(sqrt.f64 (fma.f64 x #s(literal 3/2 binary64) #s(literal 2 binary64)))
(fma.f64 x #s(literal 3/2 binary64) #s(literal 2 binary64))
(fma.f64 x (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(neg.f64 (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 1/2 binary64))
(/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))

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

simplify432.0ms (8.1%)

Memory

28.1MiB live, 620.7MiB allocated

Algorithm

1×	egg-herbie

Rules

16 480×	`lower-fma.f64`
16 480×	`lower-fma.f32`
5 382×	`lower-*.f64`
5 382×	`lower-*.f32`
2 086×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	115	466
1	318	450
2	940	433
3	2741	412
4	6173	412
0	8384	386

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

Calls

Call 1

Inputs
(sqrt 2)
(+ (sqrt 2) (* 3/4 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* -9/32 (/ x (pow (sqrt 2) 3))) (* 3/4 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (- (* 27/128 (/ x (pow (sqrt 2) 5))) (* 9/32 (/ 1 (pow (sqrt 2) 3))))) (* 3/4 (/ 1 (sqrt 2))))))
(* (sqrt x) (sqrt 3/2))
(* x (+ (* (sqrt (/ 1 x)) (sqrt 3/2)) (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 3/2)))))
(* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 3/2) 3)))) (+ (* (sqrt (/ 1 x)) (sqrt 3/2)) (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 3/2))))))
(* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 3/2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 3/2) 5)))) (+ (* (sqrt (/ 1 x)) (sqrt 3/2)) (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 3/2)))))))
(* -1 (* (sqrt x) (* (sqrt -3/2) (sqrt -1))))
(* -1 (* x (+ (* (sqrt (/ 1 x)) (* (sqrt -3/2) (sqrt -1))) (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -3/2))))))
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -3/2) 3)))) (+ (* (sqrt (/ 1 x)) (* (sqrt -3/2) (sqrt -1))) (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -3/2)))))))
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -3/2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -3/2) 5)))) (+ (* (sqrt (/ 1 x)) (* (sqrt -3/2) (sqrt -1))) (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -3/2))))))))
2
(+ 2 (* 3/2 x))
(+ 2 (* 3/2 x))
(+ 2 (* 3/2 x))
(* 3/2 x)
(* x (+ 3/2 (* 2 (/ 1 x))))
(* x (+ 3/2 (* 2 (/ 1 x))))
(* x (+ 3/2 (* 2 (/ 1 x))))
(* 3/2 x)
(* x (+ 3/2 (* 2 (/ 1 x))))
(* x (+ 3/2 (* 2 (/ 1 x))))
(* x (+ 3/2 (* 2 (/ 1 x))))
(/ -1/2 (sqrt 1/2))
(- (* -1 (* x (sqrt 1/2))) (* 1/2 (/ 1 (sqrt 1/2))))
(- (* -1 (* x (sqrt 1/2))) (* 1/2 (/ 1 (sqrt 1/2))))
(- (* -1 (* x (sqrt 1/2))) (* 1/2 (/ 1 (sqrt 1/2))))
(* -1 (* x (sqrt 1/2)))
(* x (- (* -1 (sqrt 1/2)) (* 1/2 (/ 1 (* x (sqrt 1/2))))))
(* x (- (* -1 (sqrt 1/2)) (* 1/2 (/ 1 (* x (sqrt 1/2))))))
(* x (- (* -1 (sqrt 1/2)) (* 1/2 (/ 1 (* 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) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))
(* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))

Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 3/4 (/ x (sqrt 2))))
(fma.f64 #s(literal 3/4 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* -9/32 (/ x (pow (sqrt 2) 3))) (* 3/4 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal -9/64 binary64) #s(literal 3/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (- (* 27/128 (/ x (pow (sqrt 2) 5))) (* 9/32 (/ 1 (pow (sqrt 2) 3))))) (* 3/4 (/ 1 (sqrt 2))))))
(fma.f64 x (/.f64 (.f64 x (.f64 x #s(literal 27/128 binary64))) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal -9/64 binary64) #s(literal 3/4 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(* (sqrt x) (sqrt 3/2))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 3/2 binary64)))
(* x (+ (* (sqrt (/ 1 x)) (sqrt 3/2)) (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 3/2)))))
(.f64 x (fma.f64 (sqrt.f64 #s(literal 3/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 #s(literal 3/2 binary64)))))
(* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 3/2) 3)))) (+ (* (sqrt (/ 1 x)) (sqrt 3/2)) (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 3/2))))))
(.f64 x (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3/2 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 (sqrt.f64 #s(literal 3/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 3/2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 3/2) 5)))) (+ (* (sqrt (/ 1 x)) (sqrt 3/2)) (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 3/2)))))))
(.f64 x (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3/2 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sqrt.f64 #s(literal 3/2 binary64)) #s(literal 5 binary64))) (.f64 (sqrt.f64 #s(literal 3/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* (sqrt x) (* (sqrt -3/2) (sqrt -1))))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 #s(literal -3/2 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* x (+ (* (sqrt (/ 1 x)) (* (sqrt -3/2) (sqrt -1))) (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -3/2))))))
(.f64 x (.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -3/2 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal -3/2 binary64))))))
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -3/2) 3)))) (+ (* (sqrt (/ 1 x)) (* (sqrt -3/2) (sqrt -1))) (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -3/2)))))))
(.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -3/2 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -3/2 binary64)) (sqrt.f64 #s(literal -1 binary64))))) (neg.f64 x))
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -3/2) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -3/2) 5)))) (+ (* (sqrt (/ 1 x)) (* (sqrt -3/2) (sqrt -1))) (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -3/2))))))))
(.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -3/2 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 #s(literal -3/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (sqrt.f64 #s(literal -3/2 binary64)) #s(literal 5 binary64)))))) (neg.f64 x))
2
#s(literal 2 binary64)
(+ 2 (* 3/2 x))
(fma.f64 x #s(literal 3/2 binary64) #s(literal 2 binary64))
(+ 2 (* 3/2 x))
(fma.f64 x #s(literal 3/2 binary64) #s(literal 2 binary64))
(+ 2 (* 3/2 x))
(fma.f64 x #s(literal 3/2 binary64) #s(literal 2 binary64))
(* 3/2 x)
(*.f64 x #s(literal 3/2 binary64))
(* x (+ 3/2 (* 2 (/ 1 x))))
(fma.f64 x #s(literal 3/2 binary64) #s(literal 2 binary64))
(* x (+ 3/2 (* 2 (/ 1 x))))
(fma.f64 x #s(literal 3/2 binary64) #s(literal 2 binary64))
(* x (+ 3/2 (* 2 (/ 1 x))))
(fma.f64 x #s(literal 3/2 binary64) #s(literal 2 binary64))
(* 3/2 x)
(*.f64 x #s(literal 3/2 binary64))
(* x (+ 3/2 (* 2 (/ 1 x))))
(fma.f64 x #s(literal 3/2 binary64) #s(literal 2 binary64))
(* x (+ 3/2 (* 2 (/ 1 x))))
(fma.f64 x #s(literal 3/2 binary64) #s(literal 2 binary64))
(* x (+ 3/2 (* 2 (/ 1 x))))
(fma.f64 x #s(literal 3/2 binary64) #s(literal 2 binary64))
(/ -1/2 (sqrt 1/2))
(/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(- (* -1 (* x (sqrt 1/2))) (* 1/2 (/ 1 (sqrt 1/2))))
(-.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(- (* -1 (* x (sqrt 1/2))) (* 1/2 (/ 1 (sqrt 1/2))))
(-.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(- (* -1 (* x (sqrt 1/2))) (* 1/2 (/ 1 (sqrt 1/2))))
(-.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* x (sqrt 1/2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(* x (- (* -1 (sqrt 1/2)) (* 1/2 (/ 1 (* x (sqrt 1/2))))))
(-.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(* x (- (* -1 (sqrt 1/2)) (* 1/2 (/ 1 (* x (sqrt 1/2))))))
(-.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(* x (- (* -1 (sqrt 1/2)) (* 1/2 (/ 1 (* x (sqrt 1/2))))))
(-.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* x (sqrt 1/2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))
(-.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))
(-.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))
(-.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))

eval15.0ms (0.3%)

Memory: -18.6MiB live, 23.8MiB allocated
Compiler: Compiled 1 595 to 268 computations (83.2% saved)

prune13.0ms (0.2%)

Memory

-15.9MiB live, 22.9MiB allocated

Pruning

8 alts after pruning (1 fresh and 7 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	0	0	0
Picked	0	2	2
Done	0	5	5
Total	106	8	114

Accuracy

100.0%

Counts

114 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	2.8%	(fma.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
✓	2.8%	(fma.f64 x (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
✓	70.4%	(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓	71.8%	(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓	69.5%	(sqrt.f64 (fma.f64 x #s(literal 3/2 binary64) #s(literal 2 binary64)))
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓	70.2%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓	75.6%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 70 to 51 computations (27.1% saved)

simplify68.0ms (1.3%)

Memory

4.8MiB live, 43.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	192	(+.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
✓	cost-diff	192	(-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
✓	cost-diff	1344	(fma.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
✓	cost-diff	1600	(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))

Rules

544×	`lower-fma.f32`
542×	`lower-fma.f64`
460×	`associate-r`
364×	`times-frac`
352×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	56
0	19	28
1	39	26
2	70	26
3	119	26
4	208	26
5	458	26
6	1020	26
7	2076	26
8	2526	26
9	2538	26
10	2578	26
11	2594	26
0	2594	25

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(fma.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
x
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(literal 0 binary64)
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(+.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
#s(literal -1/2 binary64)

Outputs
(fma.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
x
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(literal -1/2 binary64)
#s(literal 0 binary64)
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
#s(literal 1/2 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(+.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 1/2 binary64))
(/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
#s(literal -1/2 binary64)

localize32.0ms (0.6%)

Memory

22.1MiB live, 22.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	3.1%	(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
✓	accuracy	1.6%	(-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
✓	accuracy	1.6%	(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
✓	accuracy	1.6%	(sqrt.f64 #s(literal 1/2 binary64))

Samples

19.0ms

256×

valid

Compiler

Compiled 116 to 25 computations (78.4% saved)

Precisions

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

ival-div: 3.0ms (25.7% of total)

ival-mult: 3.0ms (25.7% of total)

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

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

ival-sub: 1.0ms (8.6% 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

1.0MiB live, 1.0MiB allocated

Counts

6 → 12

Calls

Call 1

Inputs
#<alt (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))>
#<alt (fma.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))>
#<alt (-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))>
#<alt (+.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))>
#<alt (sqrt.f64 #s(literal 1/2 binary64))>
#<alt (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))>

Outputs
#<alt (/ -1/2 (sqrt 1/2))>
#<alt (- (* -1 (* x (sqrt 1/2))) (* 1/2 (/ 1 (sqrt 1/2))))>
#<alt (- (* -1 (* x (sqrt 1/2))) (* 1/2 (/ 1 (sqrt 1/2))))>
#<alt (- (* -1 (* x (sqrt 1/2))) (* 1/2 (/ 1 (sqrt 1/2))))>
#<alt (* -1 (* x (sqrt 1/2)))>
#<alt (* x (- (* -1 (sqrt 1/2)) (* 1/2 (/ 1 (* x (sqrt 1/2))))))>
#<alt (* x (- (* -1 (sqrt 1/2)) (* 1/2 (/ 1 (* x (sqrt 1/2))))))>
#<alt (* x (- (* -1 (sqrt 1/2)) (* 1/2 (/ 1 (* 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) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))>

Calls

3 calls:

Time

Variable

Point

Expression

0.0ms

(+ (* x (/ (- 0 (* (sqrt 1/2) (sqrt 1/2))) (+ 0 (sqrt 1/2)))) (/ -1/2 (sqrt 1/2)))

0.0ms

inf

(+ (* x (/ (- 0 (* (sqrt 1/2) (sqrt 1/2))) (+ 0 (sqrt 1/2)))) (/ -1/2 (sqrt 1/2)))

0.0ms

-inf

(+ (* x (/ (- 0 (* (sqrt 1/2) (sqrt 1/2))) (+ 0 (sqrt 1/2)))) (/ -1/2 (sqrt 1/2)))

Compiler

Compiled 40 to 28 computations (30% saved)

rewrite69.0ms (1.3%)

Memory

-18.7MiB live, 19.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

216×	`lower-*.f64`
216×	`lower-*.f32`
204×	`lower-fma.f32`
202×	`lower-fma.f64`
198×	`lower-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	48
0	19	20
1	102	16
0	626	16

Stop Event

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

Counts

6 → 115

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(fma.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))
(+.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 1/2 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))

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

simplify283.0ms (5.3%)

Memory

14.7MiB live, 176.9MiB allocated

Algorithm

1×	egg-herbie

Rules

2 948×	`div-sub`
2 212×	`lower-fma.f64`
2 212×	`lower-fma.f32`
1 860×	`lower-*.f64`
1 860×	`lower-*.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	104
1	56	104
2	141	95
3	365	95
4	796	95
5	1823	95
6	3300	95
7	3987	95
8	4363	95
9	4486	95
10	4512	95
11	4528	95
12	5000	95
13	5249	95
14	5378	95
15	5490	95
16	5508	95
17	5520	95
18	5646	95
19	6024	95
20	6024	95
21	6024	95
22	6311	95
23	7037	95
24	7777	95
0	8007	95

Stop Event

1×	iter limit
1×	node limit

Counts

12 → 12

Calls

Call 1

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

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

eval36.0ms (0.7%)

Memory: -10.7MiB live, 72.3MiB allocated
Compiler: Compiled 3 782 to 569 computations (85% saved)

prune28.0ms (0.5%)

Memory

-11.6MiB live, 65.1MiB allocated

Pruning

9 alts after pruning (3 fresh and 6 done)

	Pruned	Kept	Total
New	202	3	205
Fresh	0	0	0
Picked	1	0	1
Done	1	6	7
Total	204	9	213

Accuracy

100.0%

Counts

213 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	2.8%	(fma.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
	2.8%	(fma.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
	2.8%	(*.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))
✓	70.4%	(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓	71.8%	(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓	69.5%	(sqrt.f64 (fma.f64 x #s(literal 3/2 binary64) #s(literal 2 binary64)))
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓	70.2%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓	75.6%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 209 to 112 computations (46.4% saved)

regimes12.0ms (0.2%)

Memory

22.0MiB live, 22.0MiB allocated

Counts

13 → 1

Calls

Call 1

Inputs
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
(sqrt.f64 (fma.f64 x #s(literal 3/2 binary64) #s(literal 2 binary64)))
(*.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
(fma.f64 x (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(fma.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(fma.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(fma.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.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
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))

Calls

3 calls:

4.0ms

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

3.0ms

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

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)

regimes12.0ms (0.2%)

Memory

-22.0MiB live, 21.3MiB allocated

Accuracy

Total -47.7b remaining (-305.7%)

Threshold costs -47.7b (-305.7%)

Counts

10 → 1

Calls

Call 1

Inputs
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
(sqrt.f64 (fma.f64 x #s(literal 3/2 binary64) #s(literal 2 binary64)))
(*.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
(fma.f64 x (neg.f64 (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(fma.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(fma.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) (+.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(fma.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))

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

Calls

3 calls:

5.0ms

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

3.0ms

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

Results

Accuracy	Segments	Branch
75.6%	1	`x`
75.6%	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))))`
75.6%	1	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`

Compiler

Compiled 27 to 20 computations (25.9% saved)

simplify5.0ms (0.1%)

Memory

11.8MiB live, 11.8MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness310.0ms (5.8%)

Memory

1.2MiB live, 221.7MiB allocated

Rules

12 518×	`lower-fma.f64`
12 518×	`lower-fma.f32`
5 402×	`lower-fma.f64`
5 402×	`lower-fma.f32`
4 492×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	26
0	15	26
1	56	19
2	378	19
3	4533	19
0	8161	15
0	51	330
1	158	330
2	339	330
3	763	330
4	1221	290
5	1557	274
6	2048	274
7	3388	274
8	6635	274
0	8418	220

Stop Event

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

Compiler

Compiled 17 to 15 computations (11.8% saved)

preprocess22.0ms (0.4%)

Memory: 17.5MiB live, 52.9MiB allocated
Compiler: Compiled 42 to 34 computations (19% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	11	33
0	19	33
1	29	33
2	41	33
3	57	33
4	69	33
5	95	33
6	146	33
7	190	33
8	263	33
9	275	33
10	292	33
11	324	33
12	334	33
13	347	33
14	361	33
15	369	33
16	378	33
17	382	33
0	382	33

Iter	Nodes	Cost
0	11	33
0	19	33
1	29	33
2	41	33
3	57	33
4	69	33
5	95	33
6	146	33
7	190	33
8	263	33
9	275	33
10	292	33
11	324	33
12	334	33
13	347	33
14	361	33
15	369	33
16	378	33
17	382	33
0	382	33

analyze2.0ms (0%)

sample916.0ms (17.3%)

preprocess395.0ms (7.4%)

explain195.0ms (3.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify415.0ms (7.8%)

localize32.0ms (0.6%)

series8.0ms (0.1%)

rewrite363.0ms (6.8%)

simplify398.0ms (7.5%)

eval147.0ms (2.8%)

prune87.0ms (1.6%)

simplify16.0ms (0.3%)

localize73.0ms (1.4%)

series15.0ms (0.3%)

rewrite328.0ms (6.2%)

simplify324.0ms (6.1%)

eval78.0ms (1.5%)

prune61.0ms (1.1%)

simplify23.0ms (0.4%)

localize34.0ms (0.6%)

series4.0ms (0.1%)

rewrite55.0ms (1%)

simplify432.0ms (8.1%)

eval15.0ms (0.3%)

prune13.0ms (0.2%)

simplify68.0ms (1.3%)

localize32.0ms (0.6%)

series2.0ms (0%)

rewrite69.0ms (1.3%)

simplify283.0ms (5.3%)

eval36.0ms (0.7%)

prune28.0ms (0.5%)

regimes12.0ms (0.2%)

regimes12.0ms (0.2%)

simplify5.0ms (0.1%)

soundness310.0ms (5.8%)

preprocess22.0ms (0.4%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	11	33
0	19	33
1	29	33
2	41	33
3	57	33
4	69	33
5	95	33
6	146	33
7	190	33
8	263	33
9	275	33
10	292	33
11	324	33
12	334	33
13	347	33
14	361	33
15	369	33
16	378	33
17	382	33
0	382	33