Metrics for sqrt times

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze1.0ms (0%)

Memory

2.6MiB live, 2.6MiB 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
0%	0%	50%	0%	0%	50%	0%	2
50%	25%	25%	0%	0%	50%	0%	3
66.7%	25%	12.5%	0%	0%	62.5%	0%	4
80%	25%	6.2%	0%	0%	68.7%	0%	5
88.9%	25%	3.1%	0%	0%	71.8%	0%	6
94.1%	25%	1.6%	0%	0%	73.4%	0%	7
97%	25%	0.8%	0%	0%	74.2%	0%	8
98.5%	25%	0.4%	0%	0%	74.6%	0%	9
99.2%	25%	0.2%	0%	0%	74.8%	0%	10
99.6%	25%	0.1%	0%	0%	74.9%	0%	11
99.8%	25%	0%	0%	0%	74.9%	0%	12

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample637.0ms (18.4%)

Memory

43.6MiB live, 766.2MiB allocated

Samples

429.0ms	8 249×	0	valid
1.0ms	7×	1	valid
1.0ms	12×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 285.0ms

ival-sqrt: 166.0ms (58.2% of total)

ival-mult: 57.0ms (20% of total)

ival-sub: 48.0ms (16.8% of total)

ival-true: 6.0ms (2.1% of total)

exact: 5.0ms (1.8% of total)

ival-assert: 3.0ms (1.1% of total)

adjust: 0.0ms (0% of total)

Bogosity

explain67.0ms (1.9%)

Memory

-10.4MiB live, 73.7MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
-	-	`(sqrt.f64 (-.f64 x #s(literal 1 binary64)))`
-	-	`(sqrt.f64 x)`
-	-	`(-.f64 x #s(literal 1 binary64))`
-	-	`#s(literal 1 binary64)`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

25.0ms

512×

valid

Compiler

Compiled 65 to 28 computations (56.9% saved)

Precisions

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

ival-sqrt: 7.0ms (50.2% of total)

ival-sub: 3.0ms (21.5% of total)

ival-mult: 3.0ms (21.5% of total)

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

exact: 0.0ms (0% of total)

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

preprocess14.0ms (0.4%)

Memory

9.9MiB live, 9.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	22	19
2	38	17
3	59	17
4	77	17
5	97	17
6	116	17
7	131	17
8	132	17
0	6	7
0	10	7
1	16	7
2	17	7
0	17	7

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.3%	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0.1%)

Memory

1.5MiB live, 1.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(-.f64 x #s(literal 1 binary64))
cost-diff	0	(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
cost-diff	0	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	10	18
1	16	18
2	17	18
0	17	18

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize153.0ms (4.4%)

Memory

-17.9MiB live, 20.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(-.f64 x #s(literal 1 binary64))
accuracy	0	(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
accuracy	0	(sqrt.f64 x)
accuracy	0.4765625	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Samples

147.0ms

256×

valid

Compiler

Compiled 38 to 14 computations (63.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 141.0ms

ival-mult: 136.0ms (96.3% of total)

ival-sqrt: 3.0ms (2.1% of total)

ival-sub: 2.0ms (1.4% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.2%)

Memory

8.5MiB live, 8.5MiB allocated

Counts

4 → 48

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	((* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) (sqrt x))
1.0ms	x	@	0	((* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) (sqrt x))
1.0ms	x	@	inf	((* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) (sqrt x))

simplify168.0ms (4.9%)

Memory

-4.0MiB live, 113.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	150	492
1	442	431
2	1561	410
3	4077	392
0	8270	368

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 45

Calls

Call 1

Inputs
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
(sqrt -1)
(+ (sqrt -1) (* 1/2 (/ x (sqrt -1))))
(+ (sqrt -1) (* x (+ (* -1/8 (/ x (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(+ (sqrt -1) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
-1
(- x 1)
(- x 1)
(- x 1)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* -1/16 (sqrt (/ 1 (pow x 7))))))))
x
(* x (- 1 (/ 1 x)))
(* x (- 1 (/ 1 x)))
(* x (- 1 (/ 1 x)))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
x
(* -1 (* x (- (/ 1 x) 1)))
(* -1 (* x (- (/ 1 x) 1)))
(* -1 (* x (- (/ 1 x) 1)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))

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

rewrite228.0ms (6.6%)

Memory

-4.3MiB live, 243.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	15
1	34	15
2	161	15
3	1388	15
0	8393	15

Stop Event

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

Counts

4 → 368

Calls

Call 1

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

Outputs
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eval51.0ms (1.5%)

Memory: -0.5MiB live, 121.8MiB allocated
Compiler: Compiled 9 072 to 1 550 computations (82.9% saved)

prune29.0ms (0.9%)

Memory

-11.1MiB live, 27.4MiB allocated

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	408	5	413
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	408	6	414

Accuracy

100.0%

Counts

414 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	37.2%	(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
✓	99.3%	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	53.8%	(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
▶	99.3%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
▶	98.9%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
▶	97.3%	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Compiler

Compiled 113 to 88 computations (22.1% saved)

simplify288.0ms (8.3%)

Memory

31.3MiB live, 214.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(sqrt.f64 (-.f64 x #s(literal -1 binary64)))
cost-diff	0	(fma.f64 x x #s(literal -1 binary64))
cost-diff	0	(sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x))
cost-diff	0	(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
cost-diff	0	(-.f64 x #s(literal 1 binary64))
cost-diff	0	(*.f64 (-.f64 x #s(literal 1 binary64)) x)
cost-diff	0	(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
cost-diff	0	(-.f64 x #s(literal 1/2 binary64))
cost-diff	0	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
cost-diff	0	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
cost-diff	0	(/.f64 #s(literal -1/8 binary64) x)
cost-diff	0	(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
cost-diff	0	(-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
cost-diff	0	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	25	113
0	39	113
1	58	113
2	97	113
3	203	110
4	369	110
5	939	110
6	2361	110
7	2962	110
8	3130	110
9	3186	110
10	3206	110
11	3211	110
0	8191	110

Stop Event

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

Calls

Call 1

Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
x
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
#s(literal 1/2 binary64)
(/.f64 #s(literal -1/8 binary64) x)
#s(literal -1/8 binary64)
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
x
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
(-.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(-.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
(sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) x)
(fma.f64 x x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(sqrt.f64 (-.f64 x #s(literal -1 binary64)))
(-.f64 x #s(literal -1 binary64))

Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
x
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
#s(literal 1/2 binary64)
(/.f64 #s(literal -1/8 binary64) x)
#s(literal -1/8 binary64)
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
x
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
(-.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(-.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
(sqrt.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) x))
(-.f64 (pow.f64 x #s(literal 3 binary64)) x)
(fma.f64 x x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(sqrt.f64 (-.f64 x #s(literal -1 binary64)))
(-.f64 x #s(literal -1 binary64))

localize97.0ms (2.8%)

Memory

12.2MiB live, 136.0MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 (-.f64 x #s(literal -1 binary64)))
accuracy	0.078125	(*.f64 (fma.f64 x x #s(literal -1 binary64)) x)
accuracy	18.709570610337828	(sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x))
accuracy	21.189978495975048	(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
accuracy	0	(-.f64 x #s(literal 1 binary64))
accuracy	0	(*.f64 (-.f64 x #s(literal 1 binary64)) x)
accuracy	29.566664404133075	(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
accuracy	0	(-.f64 x #s(literal 1/2 binary64))
accuracy	0.7034145493838815	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
accuracy	1.6983722941129002	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
accuracy	0	(/.f64 #s(literal -1/8 binary64) x)
accuracy	0	(-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
accuracy	0	(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
accuracy	0.46722644600420593	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))

Samples

81.0ms

256×

valid

Compiler

Compiled 218 to 50 computations (77.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 63.0ms

ival-sqrt: 42.0ms (66.5% of total)

ival-mult: 10.0ms (15.8% of total)

ival-sub: 6.0ms (9.5% of total)

ival-div: 3.0ms (4.8% of total)

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

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

exact: 0.0ms (0% of total)

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

series34.0ms (1%)

Memory

-4.5MiB live, 34.3MiB allocated

Counts

15 → 180

Calls

Call 1

Inputs
#s(alt #<batchref> (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 #s(literal -1/8 binary64) x) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) x) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (-.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 (-.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 (-.f64 x #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 (fma.f64 x x #s(literal -1 binary64)) x) #<representation binary64>) () ())

Outputs
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) #<representation binary64>) () ())) ())
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#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (-.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (-.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (-.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (-.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sqrt.f64 (-.f64 x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sqrt.f64 (-.f64 x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sqrt.f64 (-.f64 x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sqrt.f64 (-.f64 x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (fma.f64 x x #s(literal -1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (fma.f64 x x #s(literal -1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (fma.f64 x x #s(literal -1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (fma.f64 x x #s(literal -1 binary64)) x) #<representation binary64>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
4.0ms	x	@	-inf	((* (sqrt (- x 1)) (sqrt x)) (- x (- 1/2 (/ -1/8 x))) (- 1/2 (/ -1/8 x)) (/ -1/8 x) (* (sqrt (- x 1)) (sqrt x)) (* (sqrt (- x 1)) (sqrt x)) (- x 1/2) (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1) (/ (sqrt (* (+ (* x x) -1) x)) (sqrt (- x -1))) (sqrt (* (+ (* x x) -1) x)) (+ (* x x) -1) (sqrt (- x -1)) (* (+ (* x x) -1) x))
2.0ms	x	@	0	((* (sqrt (- x 1)) (sqrt x)) (- x (- 1/2 (/ -1/8 x))) (- 1/2 (/ -1/8 x)) (/ -1/8 x) (* (sqrt (- x 1)) (sqrt x)) (* (sqrt (- x 1)) (sqrt x)) (- x 1/2) (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1) (/ (sqrt (* (+ (* x x) -1) x)) (sqrt (- x -1))) (sqrt (* (+ (* x x) -1) x)) (+ (* x x) -1) (sqrt (- x -1)) (* (+ (* x x) -1) x))
2.0ms	x	@	inf	((* (sqrt (- x 1)) (sqrt x)) (- x (- 1/2 (/ -1/8 x))) (- 1/2 (/ -1/8 x)) (/ -1/8 x) (* (sqrt (- x 1)) (sqrt x)) (* (sqrt (- x 1)) (sqrt x)) (- x 1/2) (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1) (/ (sqrt (* (+ (* x x) -1) x)) (sqrt (- x -1))) (sqrt (* (+ (* x x) -1) x)) (+ (* x x) -1) (sqrt (- x -1)) (* (+ (* x x) -1) x))

Time

Variable

Point

Expression

4.0ms

-inf

((* (sqrt (- x 1)) (sqrt x)) (- x (- 1/2 (/ -1/8 x))) (- 1/2 (/ -1/8 x)) (/ -1/8 x) (* (sqrt (- x 1)) (sqrt x)) (* (sqrt (- x 1)) (sqrt x)) (- x 1/2) (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1) (/ (sqrt (* (+ (* x x) -1) x)) (sqrt (- x -1))) (sqrt (* (+ (* x x) -1) x)) (+ (* x x) -1) (sqrt (- x -1)) (* (+ (* x x) -1) x))

2.0ms

((* (sqrt (- x 1)) (sqrt x)) (- x (- 1/2 (/ -1/8 x))) (- 1/2 (/ -1/8 x)) (/ -1/8 x) (* (sqrt (- x 1)) (sqrt x)) (* (sqrt (- x 1)) (sqrt x)) (- x 1/2) (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1) (/ (sqrt (* (+ (* x x) -1) x)) (sqrt (- x -1))) (sqrt (* (+ (* x x) -1) x)) (+ (* x x) -1) (sqrt (- x -1)) (* (+ (* x x) -1) x))

2.0ms

inf

((* (sqrt (- x 1)) (sqrt x)) (- x (- 1/2 (/ -1/8 x))) (- 1/2 (/ -1/8 x)) (/ -1/8 x) (* (sqrt (- x 1)) (sqrt x)) (* (sqrt (- x 1)) (sqrt x)) (- x 1/2) (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1) (/ (sqrt (* (+ (* x x) -1) x)) (sqrt (- x -1))) (sqrt (* (+ (* x x) -1) x)) (+ (* x x) -1) (sqrt (- x -1)) (* (+ (* x x) -1) x))

simplify201.0ms (5.8%)

Memory

-23.6MiB live, 232.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	271	1979
1	797	1744
2	2813	1619
3	7596	1617
0	8047	1535

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 169

Calls

Call 1

Inputs
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
(/ -1/8 x)
(/ (- (* -1/2 x) 1/8) x)
(/ (- (* x (- x 1/2)) 1/8) x)
(/ (- (* x (- x 1/2)) 1/8) x)
(/ 1/8 x)
(/ (+ 1/8 (* 1/2 x)) x)
(/ (+ 1/8 (* 1/2 x)) x)
(/ (+ 1/8 (* 1/2 x)) x)
(/ -1/8 x)
(/ -1/8 x)
(/ -1/8 x)
(/ -1/8 x)
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
-1/2
(- x 1/2)
(- x 1/2)
(- x 1/2)
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
(* -1 x)
(* x (- x 1))
(* x (- x 1))
(* x (- x 1))
-1
(- x 1)
(- x 1)
(- x 1)
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 5)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 3) (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 3) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 3) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt x) (/ 1 (pow (sqrt -1) 5)))))))))
-1
(- (pow x 2) 1)
(- (pow x 2) 1)
(- (pow x 2) 1)
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(* -1 x)
(* x (- (pow x 2) 1))
(* x (- (pow x 2) 1))
(* x (- (pow x 2) 1))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
1/2
(+ 1/2 (* 1/8 (/ 1 x)))
(+ 1/2 (* 1/8 (/ 1 x)))
(+ 1/2 (* 1/8 (/ 1 x)))
(/ -1/8 x)
(/ -1/8 x)
(/ -1/8 x)
(/ -1/8 x)
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (- 1 (* 1/2 (/ 1 x))))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (- 1 (/ 1 x)))
x
(* x (- 1 (/ 1 x)))
(* x (- 1 (/ 1 x)))
(* x (- 1 (/ 1 x)))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(sqrt (pow x 3))
(* (pow x 2) (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))))
(* (pow x 2) (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* -1/8 (sqrt (/ 1 (pow x 9)))))))
(* (pow x 2) (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (sqrt (/ 1 (pow x 9)))) (* -1/16 (sqrt (/ 1 (pow x 13))))))))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(pow x 3)
(* (pow x 3) (- 1 (/ 1 (pow x 2))))
(* (pow x 3) (- 1 (/ 1 (pow x 2))))
(* (pow x 3) (- 1 (/ 1 (pow x 2))))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
x
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
1/2
(+ 1/2 (* 1/8 (/ 1 x)))
(+ 1/2 (* 1/8 (/ 1 x)))
(+ 1/2 (* 1/8 (/ 1 x)))
(/ -1/8 x)
(/ -1/8 x)
(/ -1/8 x)
(/ -1/8 x)
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
x
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x)))))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (- 1 (/ 1 x)))
x
(* -1 (* x (- (/ 1 x) 1)))
(* -1 (* x (- (/ 1 x) 1)))
(* -1 (* x (- (/ 1 x) 1)))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (/ 1 x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (- (* 1/8 (/ 1 (* x (pow (sqrt -1) 2)))) 1/2) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 (* x (pow (sqrt -1) 4)))) (* 1/8 (/ 1 (pow (sqrt -1) 2)))) x)) 1/2) x)) (pow (sqrt -1) 2))))
(* (sqrt (pow x 3)) (pow (sqrt -1) 2))
(* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (pow (sqrt -1) 2))) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (pow x 3))) (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))) (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(pow x 3)
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1)))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1)))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1)))

Outputs
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x) (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x))) (.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(/.f64 #s(literal -1/8 binary64) x)
(-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))
(-.f64 (-.f64 x #s(literal 1/2 binary64)) (/.f64 #s(literal 1/8 binary64) x))
(-.f64 (-.f64 x #s(literal 1/2 binary64)) (/.f64 #s(literal 1/8 binary64) x))
(/.f64 #s(literal 1/8 binary64) x)
(/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/8 binary64)) x)
(/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/8 binary64)) x)
(/.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/8 binary64)) x)
(/.f64 #s(literal -1/8 binary64) x)
(/.f64 #s(literal -1/8 binary64) x)
(/.f64 #s(literal -1/8 binary64) x)
(/.f64 #s(literal -1/8 binary64) x)
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x) (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x))) (.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x) (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x))) (.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
#s(literal -1/2 binary64)
(-.f64 x #s(literal 1/2 binary64))
(-.f64 x #s(literal 1/2 binary64))
(-.f64 x #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x) (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x))) (.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(neg.f64 x)
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
#s(literal -1 binary64)
(-.f64 x #s(literal 1 binary64))
(-.f64 x #s(literal 1 binary64))
(-.f64 x #s(literal 1 binary64))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x) (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x))) (.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (pow.f64 x #s(literal 5 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (pow.f64 x #s(literal 3 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (sqrt.f64 x))) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 x #s(literal 3 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
#s(literal -1 binary64)
(fma.f64 x x #s(literal -1 binary64))
(fma.f64 x x #s(literal -1 binary64))
(fma.f64 x x #s(literal -1 binary64))
#s(literal 1 binary64)
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(neg.f64 x)
(-.f64 (pow.f64 x #s(literal 3 binary64)) x)
(-.f64 (pow.f64 x #s(literal 3 binary64)) x)
(-.f64 (pow.f64 x #s(literal 3 binary64)) x)
x
(-.f64 x #s(literal 1/2 binary64))
(-.f64 x (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))
(fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) x)) x #s(literal -1/2 binary64))
x
(-.f64 x #s(literal 1/2 binary64))
(-.f64 x (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))
(-.f64 x (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))
#s(literal 1/2 binary64)
(-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))
(-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))
(-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))
(/.f64 #s(literal -1/8 binary64) x)
(/.f64 #s(literal -1/8 binary64) x)
(/.f64 #s(literal -1/8 binary64) x)
(/.f64 #s(literal -1/8 binary64) x)
x
(-.f64 x #s(literal 1/2 binary64))
(-.f64 x (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))
(fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) x)) x #s(literal -1/2 binary64))
x
(-.f64 x #s(literal 1/2 binary64))
(-.f64 x (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))
(fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) x)) x #s(literal -1/2 binary64))
x
(-.f64 x #s(literal 1/2 binary64))
(-.f64 x #s(literal 1/2 binary64))
(-.f64 x #s(literal 1/2 binary64))
x
(-.f64 x #s(literal 1/2 binary64))
(-.f64 x (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))
(fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) x)) x #s(literal -1/2 binary64))
(*.f64 x x)
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
x
(-.f64 x #s(literal 1 binary64))
(-.f64 x #s(literal 1 binary64))
(-.f64 x #s(literal 1 binary64))
x
(-.f64 x #s(literal 1/2 binary64))
(-.f64 x (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))
(fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) x)) x #s(literal -1/2 binary64))
(sqrt.f64 (pow.f64 x #s(literal 3 binary64)))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 x x))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 9 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 13 binary64)))) #s(literal -1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 9 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (.f64 x x))
(*.f64 x x)
(*.f64 x (fma.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) x x))
(*.f64 x (fma.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) x x))
(*.f64 x (fma.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) x x))
(sqrt.f64 x)
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x)
(pow.f64 x #s(literal 3 binary64))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) x)) (pow.f64 x #s(literal 3 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) x)) (pow.f64 x #s(literal 3 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) x)) (pow.f64 x #s(literal 3 binary64)))
x
(-.f64 x #s(literal 1/2 binary64))
(-.f64 x (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))
(-.f64 x (*.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
x
(-.f64 x #s(literal 1/2 binary64))
(-.f64 x (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))
(-.f64 x (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))
#s(literal 1/2 binary64)
(-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))
(-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))
(-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))
(/.f64 #s(literal -1/8 binary64) x)
(/.f64 #s(literal -1/8 binary64) x)
(/.f64 #s(literal -1/8 binary64) x)
(/.f64 #s(literal -1/8 binary64) x)
x
(-.f64 x #s(literal 1/2 binary64))
(-.f64 x (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))
(-.f64 x (*.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
x
(-.f64 x #s(literal 1/2 binary64))
(-.f64 x (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))
(-.f64 x (*.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
x
(-.f64 x #s(literal 1/2 binary64))
(-.f64 x #s(literal 1/2 binary64))
(-.f64 x #s(literal 1/2 binary64))
(neg.f64 x)
(-.f64 #s(literal 1/2 binary64) x)
(-.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) x)
(neg.f64 (fma.f64 (fma.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) x) x) #s(literal 1/2 binary64)) #s(literal -1 binary64) (/.f64 #s(literal -1/8 binary64) x)) #s(literal 1 binary64) x))
(*.f64 x x)
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
x
(-.f64 x #s(literal 1 binary64))
(-.f64 x #s(literal 1 binary64))
(-.f64 x #s(literal 1 binary64))
x
(-.f64 x #s(literal 1/2 binary64))
(-.f64 x (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))
(-.f64 x (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) x)) #s(literal -1/8 binary64)) x) #s(literal -1/2 binary64)))
(neg.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))))
(.f64 (.f64 (neg.f64 x) x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(.f64 (.f64 (neg.f64 x) x) (+.f64 (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 x) (/.f64 (fma.f64 #s(literal -1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/8 binary64) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))))) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 x #s(literal 3 binary64)))) (*.f64 x x))
(*.f64 x x)
(*.f64 x (fma.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) x x))
(*.f64 x (fma.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) x x))
(*.f64 x (fma.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) x x))
(sqrt.f64 x)
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 x))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 x))
(*.f64 (fma.f64 (/.f64 #s(literal 1/16 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 7 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x))
(pow.f64 x #s(literal 3 binary64))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) x)) (pow.f64 x #s(literal 3 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) x)) (pow.f64 x #s(literal 3 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) x)) (pow.f64 x #s(literal 3 binary64)))

rewrite174.0ms (5%)

Memory

3.3MiB live, 191.9MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	25	100
0	39	91
1	144	91
2	1015	89
0	8648	89

Stop Event

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

Counts

15 → 759

Calls

Call 1

Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
(/.f64 #s(literal -1/8 binary64) x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
(-.f64 x #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(-.f64 x #s(literal 1 binary64))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))
(sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x))
(fma.f64 x x #s(literal -1 binary64))
(sqrt.f64 (-.f64 x #s(literal -1 binary64)))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) x)

Outputs
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eval187.0ms (5.4%)

Memory: -6.1MiB live, 305.6MiB allocated
Compiler: Compiled 21 279 to 2 972 computations (86% saved)

prune23.0ms (0.7%)

Memory

16.0MiB live, 100.6MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	927	1	928
Fresh	0	0	0
Picked	1	4	5
Done	0	1	1
Total	928	6	934

Accuracy

100.0%

Counts

934 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.3%	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	53.7%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 x #s(literal 1 binary64)) x))))
✓	53.8%	(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
✓	99.3%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
✓	98.9%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
✓	97.3%	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Compiler

Compiled 58 to 46 computations (20.7% saved)

simplify33.0ms (1%)

Memory

-4.2MiB live, 35.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 x #s(literal 1 binary64))
cost-diff	0	(*.f64 (-.f64 x #s(literal 1 binary64)) x)
cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 x #s(literal 1 binary64)) x))))
cost-diff	1792	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 x #s(literal 1 binary64)) x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	36
0	12	28
1	25	28
2	42	28
3	72	28
4	89	28
5	107	28
6	149	28
7	200	28
8	321	28
9	472	28
10	661	28
11	712	28
12	729	28
13	732	28
14	733	28
0	733	28

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize44.0ms (1.3%)

Memory

13.2MiB live, 52.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 (-.f64 x #s(literal 1 binary64)) x)
accuracy	0.15625	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 x #s(literal 1 binary64)) x)))
accuracy	0.8397116448092165	(/.f64 #s(literal 1 binary64) (*.f64 (-.f64 x #s(literal 1 binary64)) x))
accuracy	29.566664404133075	(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 x #s(literal 1 binary64)) x))))

Samples

38.0ms

256×

valid

Compiler

Compiled 74 to 16 computations (78.4% saved)

Precisions

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

ival-div: 25.0ms (80.9% of total)

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

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

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

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

5.9MiB live, 5.9MiB allocated

Counts

5 → 60

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

0.0ms

inf

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

0.0ms

-inf

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

0.0ms

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

simplify243.0ms (7%)

Memory

8.9MiB live, 161.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	105	459
1	277	443
2	835	417
3	2524	403
4	7035	385
0	8556	378

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 57

Calls

Call 1

Inputs
(* -1 x)
(* x (- x 1))
(* x (- x 1))
(* x (- x 1))
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
(* -1 x)
(* x (- x 1))
(* x (- x 1))
(* x (- x 1))
-1
(- x 1)
(- x 1)
(- x 1)
(/ -1 x)
(/ (- (* -1 x) 1) x)
(/ (- (* x (- (* -1 x) 1)) 1) x)
(/ (- (* x (- (* x (- (* -1 x) 1)) 1)) 1) x)
(pow x 2)
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (- 1 (/ 1 x)))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (- 1 (/ 1 x)))
x
(* x (- 1 (/ 1 x)))
(* x (- 1 (/ 1 x)))
(* x (- 1 (/ 1 x)))
(/ 1 (pow x 2))
(/ (+ 1 (/ 1 x)) (pow x 2))
(/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) (pow x 2))
(/ (+ 1 (+ (/ 1 x) (+ (/ 1 (pow x 2)) (/ 1 (pow x 3))))) (pow x 2))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (- 1 (/ 1 x)))
(* -1 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x)))))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (- 1 (/ 1 x)))
x
(* -1 (* x (- (/ 1 x) 1)))
(* -1 (* x (- (/ 1 x) 1)))
(* -1 (* x (- (/ 1 x) 1)))
(/ 1 (pow x 2))
(/ (+ 1 (/ 1 x)) (pow x 2))
(/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) (pow x 2))
(/ (+ 1 (* -1 (/ (- (* -1 (/ (+ 1 (/ 1 x)) x)) 1) x))) (pow x 2))

Outputs
(neg.f64 x)
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(fma.f64 (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (.f64 (sqrt.f64 x) #s(literal 1/8 binary64)))) x) x (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (.f64 x x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) (.f64 x x))) (.f64 x x) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(neg.f64 x)
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
#s(literal -1 binary64)
(-.f64 x #s(literal 1 binary64))
(-.f64 x #s(literal 1 binary64))
(-.f64 x #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) x)
(/.f64 (-.f64 #s(literal -1 binary64) x) x)
(-.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) x) #s(literal 1 binary64))
(/.f64 (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)) x)
(*.f64 x x)
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
x
(-.f64 x #s(literal 1/2 binary64))
(-.f64 x (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))
(-.f64 x (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x) #s(literal -1/2 binary64)))
(*.f64 x x)
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
x
(-.f64 x #s(literal 1 binary64))
(-.f64 x #s(literal 1 binary64))
(-.f64 x #s(literal 1 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) x) x)
(neg.f64 (/.f64 (-.f64 #s(literal -1 binary64) x) (pow.f64 x #s(literal 3 binary64))))
(/.f64 (/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x) #s(literal -1 binary64)) x) x)
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x)) x)) x) x)
(*.f64 x x)
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(neg.f64 x)
(-.f64 #s(literal 1/2 binary64) x)
(-.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) x)
(-.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x) #s(literal -1/2 binary64)) x)
(*.f64 x x)
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
x
(-.f64 x #s(literal 1 binary64))
(-.f64 x #s(literal 1 binary64))
(-.f64 x #s(literal 1 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) x) x)
(neg.f64 (/.f64 (-.f64 #s(literal -1 binary64) x) (pow.f64 x #s(literal 3 binary64))))
(/.f64 (/.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x) #s(literal -1 binary64)) x) x)
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) x)) x)) x) x)

rewrite99.0ms (2.9%)

Memory

-0.2MiB live, 119.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	34
0	12	26
1	55	26
2	293	26
0	2346	26

Stop Event

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

Counts

5 → 418

Calls

Call 1

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

Outputs
#<batchref>
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eval120.0ms (3.5%)

Memory: -30.3MiB live, 146.1MiB allocated
Compiler: Compiled 8 030 to 1 666 computations (79.3% saved)

prune17.0ms (0.5%)

Memory

1.6MiB live, 39.0MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	475	0	475
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	475	6	481

Accuracy

100.0%

Counts

481 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.3%	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	53.7%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 x #s(literal 1 binary64)) x))))
✓	53.8%	(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
✓	99.3%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
✓	98.9%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
✓	97.3%	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Compiler

Compiled 128 to 78 computations (39.1% saved)

regimes14.0ms (0.4%)

Memory

-18.6MiB live, 18.4MiB allocated

Counts

7 → 1

Calls

Call 1

Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 x #s(literal 1 binary64)) x))))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal -1 binary64))))

Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))

Calls

2 calls:

6.0ms	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
5.0ms	x

Results

Accuracy	Segments	Branch
99.3%	1	`x`
99.3%	1	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes7.0ms (0.2%)

Memory

12.8MiB live, 12.8MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

2 calls:

3.0ms	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
3.0ms	x

Results

Accuracy	Segments	Branch
98.9%	1	`x`
98.9%	1	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes5.0ms (0.2%)

Memory

13.0MiB live, 13.0MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Calls

2 calls:

3.0ms	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
2.0ms	x

Results

Accuracy	Segments	Branch
97.3%	1	`x`
97.3%	1	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify69.0ms (2%)

Memory

-33.5MiB live, 55.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	35
1	24	35
2	40	35
3	62	35
4	92	35
5	126	35
6	163	35
7	235	35
8	337	35
9	357	35
10	359	35

Stop Event

1×

saturated

Calls

Call 1

Inputs

#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))

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

#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Outputs

#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))

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

#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

soundness361.0ms (10.4%)

Memory

8.0MiB live, 201.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	150	492
1	442	431
2	1561	410
3	4077	392
0	8270	368

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 36 to 17 computations (52.8% saved)

preprocess77.0ms (2.2%)

Memory: 11.9MiB live, 49.7MiB allocated
Compiler: Compiled 84 to 42 computations (50% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	8	19
1	22	19
2	38	17
3	59	17
4	77	17
5	97	17
6	116	17
7	131	17
8	132	17
0	6	7
0	10	7
1	16	7
2	17	7
0	17	7

Iter	Nodes	Cost
0	7	36
0	12	28
1	25	28
2	42	28
3	72	28
4	89	28
5	107	28
6	149	28
7	200	28
8	321	28
9	472	28
10	661	28
11	712	28
12	729	28
13	732	28
14	733	28
0	733	28

Iter	Nodes	Cost
0	15	35
1	24	35
2	40	35
3	62	35
4	92	35
5	126	35
6	163	35
7	235	35
8	337	35
9	357	35
10	359	35

Iter	Nodes	Cost
0	8	19
1	22	19
2	38	17
3	59	17
4	77	17
5	97	17
6	116	17
7	131	17
8	132	17
0	6	7
0	10	7
1	16	7
2	17	7
0	17	7

Iter	Nodes	Cost
0	7	36
0	12	28
1	25	28
2	42	28
3	72	28
4	89	28
5	107	28
6	149	28
7	200	28
8	321	28
9	472	28
10	661	28
11	712	28
12	729	28
13	732	28
14	733	28
0	733	28

Iter	Nodes	Cost
0	15	35
1	24	35
2	40	35
3	62	35
4	92	35
5	126	35
6	163	35
7	235	35
8	337	35
9	357	35
10	359	35

start0.0ms (0%)

analyze1.0ms (0%)

sample637.0ms (18.4%)

explain67.0ms (1.9%)

preprocess14.0ms (0.4%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize153.0ms (4.4%)

series6.0ms (0.2%)

simplify168.0ms (4.9%)

rewrite228.0ms (6.6%)

eval51.0ms (1.5%)

prune29.0ms (0.9%)

simplify288.0ms (8.3%)

localize97.0ms (2.8%)

series34.0ms (1%)

simplify201.0ms (5.8%)

rewrite174.0ms (5%)

eval187.0ms (5.4%)

prune23.0ms (0.7%)

simplify33.0ms (1%)

localize44.0ms (1.3%)

series3.0ms (0.1%)

simplify243.0ms (7%)

rewrite99.0ms (2.9%)

eval120.0ms (3.5%)

prune17.0ms (0.5%)

regimes14.0ms (0.4%)

regimes7.0ms (0.2%)

regimes5.0ms (0.2%)

simplify69.0ms (2%)

soundness361.0ms (10.4%)

preprocess77.0ms (2.2%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	19
1	22	19
2	38	17
3	59	17
4	77	17
5	97	17
6	116	17
7	131	17
8	132	17
0	6	7
0	10	7
1	16	7
2	17	7
0	17	7

Iter	Nodes	Cost
0	7	36
0	12	28
1	25	28
2	42	28
3	72	28
4	89	28
5	107	28
6	149	28
7	200	28
8	321	28
9	472	28
10	661	28
11	712	28
12	729	28
13	732	28
14	733	28
0	733	28

Iter	Nodes	Cost
0	15	35
1	24	35
2	40	35
3	62	35
4	92	35
5	126	35
6	163	35
7	235	35
8	337	35
9	357	35
10	359	35