Metrics for sqrt times

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze1.0ms (0%)

Memory

3.3MiB live, 3.3MiB 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)

sample606.0ms (17.7%)

Memory

31.9MiB live, 708.5MiB allocated

Samples

395.0ms	8 256×	0	valid
1.0ms	17×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 227.0ms

ival-sqrt: 112.0ms (49.3% of total)

ival-mult: 56.0ms (24.6% of total)

ival-sub: 47.0ms (20.7% of total)

ival-true: 6.0ms (2.6% of total)

exact: 5.0ms (2.2% of total)

ival-assert: 3.0ms (1.3% of total)

Bogosity

explain65.0ms (1.9%)

Memory

21.3MiB live, 103.4MiB 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

28.0ms

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 (50.3% of total)

ival-sub: 3.0ms (21.6% of total)

ival-mult: 3.0ms (21.6% of total)

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

exact: 0.0ms (0% of total)

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

preprocess17.0ms (0.5%)

Memory

-11.2MiB live, 26.5MiB 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 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(*.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: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.2MiB live, 1.2MiB 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

5.1MiB live, 5.1MiB 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 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(*.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)

localize22.0ms (0.6%)

Memory

-5.6MiB live, 31.8MiB 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	0.4609375	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Samples

13.0ms

256×

valid

Compiler

Compiled 38 to 14 computations (63.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-sqrt: 3.0ms (43.8% of total)

ival-mult: 2.0ms (29.2% of total)

ival-sub: 1.0ms (14.6% 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

9.7MiB live, 9.7MiB allocated

Counts

4 → 48

Calls

Call 1

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

Outputs
#s(alt (* (sqrt x) (sqrt -1)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1))) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1))))))) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (* (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))))))))) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt -1) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* 1/2 (/ x (sqrt -1)))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* x (+ (* -1/8 (/ x (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1)))))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1)))))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))) (taylor inf x) (#s(alt (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5))))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 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)))))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (/ 1 x))) (taylor inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (/ 1 x))) (taylor inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (/ 1 x))) (taylor inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -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)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -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)))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -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))))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 x) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 x) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 x) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (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))

simplify169.0ms (4.9%)

Memory

-11.0MiB live, 145.4MiB 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
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(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)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(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)))
(+ (* (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)))))))))
(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 -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (* 1/2 (/ x (sqrt -1))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* x (+ (* -1/8 (/ x (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(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)))
(+ (sqrt -1) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(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)))
-1
#s(literal -1 binary64)
(- x 1)
(-.f64 x #s(literal 1 binary64))
(- x 1)
(-.f64 x #s(literal 1 binary64))
(- x 1)
(-.f64 x #s(literal 1 binary64))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
x
(* x (- 1 (* 1/2 (/ 1 x))))
(-.f64 x #s(literal 1/2 binary64))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 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 x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))))
(*.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)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5)))))))
(*.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)
(* 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))))))))
(*.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
(* x (- 1 (/ 1 x)))
(-.f64 x #s(literal 1 binary64))
(* x (- 1 (/ 1 x)))
(-.f64 x #s(literal 1 binary64))
(* x (- 1 (/ 1 x)))
(-.f64 x #s(literal 1 binary64))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* x (pow (sqrt -1) 2)))
x
(* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))
(-.f64 x #s(literal 1/2 binary64))
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
(* -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))))
(-.f64 x (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal -1/2 binary64)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.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)
(* -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))))))
(*.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)
(* -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)))))))
(*.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
(* -1 (* x (- (/ 1 x) 1)))
(-.f64 x #s(literal 1 binary64))
(* -1 (* x (- (/ 1 x) 1)))
(-.f64 x #s(literal 1 binary64))
(* -1 (* x (- (/ 1 x) 1)))
(-.f64 x #s(literal 1 binary64))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)

rewrite309.0ms (9%)

Memory

9.7MiB live, 162.5MiB 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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eval126.0ms (3.7%)

Memory: -2.8MiB live, 66.9MiB allocated
Compiler: Compiled 8 893 to 1 545 computations (82.6% saved)

prune11.0ms (0.3%)

Memory

-6.5MiB live, 31.7MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	408	5	413
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	409	5	414

Accuracy

100.0%

Counts

414 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	59.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 x #s(literal 1 binary64)) x))))
▶	59.7%	(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
▶	98.9%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
▶	98.4%	#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 60 to 50 computations (16.7% saved)

simplify29.0ms (0.8%)

Memory

-5.3MiB live, 30.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 (-.f64 x #s(literal 1 binary64)) x)
cost-diff	0	(/.f64 #s(literal 1 binary64) (*.f64 (-.f64 x #s(literal 1 binary64)) x))
cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 x #s(literal 1 binary64)) x)))
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 x #s(literal 1 binary64)) x))))
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: 0 (0.0ms)

Iter	Nodes	Cost
0	21	110
0	31	110
1	48	110
2	74	110
3	120	110
4	198	110
5	395	110
6	635	110
7	727	110
8	795	110
9	829	110
10	838	110
11	839	110
0	839	110

Stop Event

1×	iter limit
1×	saturated
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 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 x #s(literal 1 binary64)) x))))
#s(literal 1 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 x #s(literal 1 binary64)) x)))
(/.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
#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 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 x #s(literal 1 binary64)) x))))
#s(literal 1 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 x #s(literal 1 binary64)) x)))
(/.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

localize61.0ms (1.8%)

Memory

-10.1MiB live, 111.1MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 (-.f64 x #s(literal 1 binary64)) x)
accuracy	0.1484375	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 x #s(literal 1 binary64)) x))))
accuracy	0.4591451801911908	(/.f64 #s(literal 1 binary64) (*.f64 (-.f64 x #s(literal 1 binary64)) x))
accuracy	25.288168307152574	(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 x #s(literal 1 binary64)) x)))
accuracy	0	(-.f64 x #s(literal 1 binary64))
accuracy	0	(*.f64 (-.f64 x #s(literal 1 binary64)) x)
accuracy	25.760598166514526	(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
accuracy	0	(-.f64 x #s(literal 1/2 binary64))
accuracy	1.0121379579508836	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
accuracy	1.7360457643523919	#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	0.6925711093301457	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))

Samples

39.0ms

256×

valid

Compiler

Compiled 187 to 36 computations (80.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 28.0ms

ival-sqrt: 13.0ms (46.7% of total)

ival-div: 6.0ms (21.6% of total)

ival-sub: 5.0ms (18% of total)

ival-mult: 3.0ms (10.8% of total)

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

exact: 0.0ms (0% of total)

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

series8.0ms (0.2%)

Memory

21.2MiB live, 21.2MiB allocated

Counts

13 → 156

Calls

Call 1

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

Outputs
#s(alt (* (sqrt x) (sqrt -1)) (taylor 0 x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) (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 (+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1))) (taylor 0 x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) (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 (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1))))))) (taylor 0 x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) (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 (+ (* (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))))))))) (taylor 0 x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) (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 (/ -1/8 x) (taylor 0 x) (#s(alt (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) (patch (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* -1/2 x) 1/8) x) (taylor 0 x) (#s(alt (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) (patch (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* x (- x 1/2)) 1/8) x) (taylor 0 x) (#s(alt (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) (patch (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* x (- x 1/2)) 1/8) x) (taylor 0 x) (#s(alt (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) (patch (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ 1/8 x) (taylor 0 x) (#s(alt (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1/8 (* 1/2 x)) x) (taylor 0 x) (#s(alt (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1/8 (* 1/2 x)) x) (taylor 0 x) (#s(alt (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1/8 (* 1/2 x)) x) (taylor 0 x) (#s(alt (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (patch (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ -1/8 x) (taylor 0 x) (#s(alt (/.f64 #s(literal -1/8 binary64) x) (patch (/.f64 #s(literal -1/8 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -1/8 x) (taylor 0 x) (#s(alt (/.f64 #s(literal -1/8 binary64) x) (patch (/.f64 #s(literal -1/8 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -1/8 x) (taylor 0 x) (#s(alt (/.f64 #s(literal -1/8 binary64) x) (patch (/.f64 #s(literal -1/8 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -1/8 x) (taylor 0 x) (#s(alt (/.f64 #s(literal -1/8 binary64) x) (patch (/.f64 #s(literal -1/8 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt -1)) (taylor 0 x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) x) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) x) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1))) (taylor 0 x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) x) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) x) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1))))))) (taylor 0 x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) x) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) x) #<representation binary64>) () ())) ())
#s(alt (+ (* (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))))))))) (taylor 0 x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) x) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) x) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt -1)) (taylor 0 x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1))) (taylor 0 x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1))))))) (taylor 0 x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* (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))))))))) (taylor 0 x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) (patch #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt -1/2 (taylor 0 x) (#s(alt (-.f64 x #s(literal 1/2 binary64)) (patch (-.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1/2) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1/2 binary64)) (patch (-.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1/2) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1/2 binary64)) (patch (-.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1/2) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1/2 binary64)) (patch (-.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt -1)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) (patch (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1))) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) (patch (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1))))))) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) (patch (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* (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))))))))) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) (patch (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (.f64 (-.f64 x #s(literal 1 binary64)) x) (patch (.f64 (-.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- x 1)) (taylor 0 x) (#s(alt (.f64 (-.f64 x #s(literal 1 binary64)) x) (patch (.f64 (-.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- x 1)) (taylor 0 x) (#s(alt (.f64 (-.f64 x #s(literal 1 binary64)) x) (patch (.f64 (-.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- x 1)) (taylor 0 x) (#s(alt (.f64 (-.f64 x #s(literal 1 binary64)) x) (patch (.f64 (-.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt -1)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1))))))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (* (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))))))))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 x)) (sqrt -1)) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1))) x) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/2 (* (sqrt x) (/ 1 (sqrt -1)))) (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1))))))) x) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* x (+ (* -1/2 (* (sqrt x) (/ (+ 1 (* 1/4 (/ 1 (* x (pow (sqrt -1) 2))))) (sqrt -1)))) (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1))))))))) x) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x))) #<representation binary64>) () ())) ())
#s(alt (/ -1 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x)) (patch (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (* -1 x) 1) x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x)) (patch (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (* x (- (* -1 x) 1)) 1) x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x)) (patch (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (* x (- (* x (- (* -1 x) 1)) 1)) 1) x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x)) (patch (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) (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 (* x (- 1 (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt #s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))) (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>) () ())) ())
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#s(alt (* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) (patch (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x))))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) (patch (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 (-.f64 x #s(literal 1 binary64)) x) (patch (.f64 (-.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 x))) (taylor -inf x) (#s(alt (.f64 (-.f64 x #s(literal 1 binary64)) x) (patch (.f64 (-.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 x))) (taylor -inf x) (#s(alt (.f64 (-.f64 x #s(literal 1 binary64)) x) (patch (.f64 (-.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 x))) (taylor -inf x) (#s(alt (.f64 (-.f64 x #s(literal 1 binary64)) x) (patch (.f64 (-.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 x) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 x) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 x) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (* 1/2 (/ 1 x))))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x))))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x)))) #<representation binary64>) () ())) ())
#s(alt (/ -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ 1 (* 1/2 (/ 1 x))) x)) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ 1 (+ (/ 3/8 (pow x 2)) (* 1/2 (/ 1 x)))) x)) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (+ 3/8 (* 5/16 (/ 1 x))) x)) 1/2) x))) x)) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x)) (patch (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (/ 1 x)) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x)) (patch (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x)) (patch (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* -1 (/ (- (* -1 (/ (+ 1 (/ 1 x)) x)) 1) x))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x)) (patch (/.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	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) (/ 1 (sqrt (/ 1 (* (- x 1) x)))) (sqrt (/ 1 (* (- x 1) x))) (/ 1 (* (- x 1) x)))
1.0ms	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) (/ 1 (sqrt (/ 1 (* (- x 1) x)))) (sqrt (/ 1 (* (- x 1) x))) (/ 1 (* (- x 1) x)))
1.0ms	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) (/ 1 (sqrt (/ 1 (* (- x 1) x)))) (sqrt (/ 1 (* (- x 1) x))) (/ 1 (* (- x 1) x)))

Time

Variable

Point

Expression

1.0ms

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

1.0ms

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

1.0ms

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

simplify155.0ms (4.5%)

Memory

5.1MiB live, 164.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	203	1522
1	551	1418
2	1749	1319
3	5212	1246
0	8531	1207

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 145

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

rewrite143.0ms (4.2%)

Memory

-4.7MiB live, 188.0MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	92
0	31	85
1	118	84
2	818	84
0	8512	84

Stop Event

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

Counts

13 → 637

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

Outputs
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eval178.0ms (5.2%)

Memory: 6.6MiB live, 170.5MiB allocated
Compiler: Compiled 15 755 to 2 664 computations (83.1% saved)

prune36.0ms (1%)

Memory

-32.3MiB live, 54.0MiB allocated

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	920	1	921
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	921	5	926

Accuracy

100.0%

Counts

926 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	45.5%	(sqrt.f64 (/.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64))))
✓	59.7%	(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
✓	98.9%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
✓	98.4%	#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 31 to 25 computations (19.4% saved)

simplify234.0ms (6.8%)

Memory

23.5MiB live, 215.2MiB 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	(fma.f64 x x #s(literal -1 binary64))
cost-diff	0	(sqrt.f64 (/.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64))))
cost-diff	7040	(/.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64)))

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	7	36
0	13	36
1	22	36
2	45	36
3	104	25
4	250	25
5	1478	25
6	6117	25
0	8205	25

Stop Event

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

Calls

Call 1

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

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

localize25.0ms (0.7%)

Memory

23.7MiB live, 60.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(-.f64 x #s(literal -1 binary64))
accuracy	0.125	(*.f64 (fma.f64 x x #s(literal -1 binary64)) x)
accuracy	8.891385466419507	(/.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64)))
accuracy	25.760598166514526	(sqrt.f64 (/.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64))))

Samples

16.0ms

256×

valid

Compiler

Compiled 78 to 17 computations (78.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-mult: 3.0ms (31.5% of total)

ival-div: 2.0ms (21% of total)

ival-sqrt: 2.0ms (21% of total)

ival-sub: 1.0ms (10.5% of total)

ival-add: 1.0ms (10.5% of total)

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

exact: 0.0ms (0% of total)

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

series8.0ms (0.2%)

Memory

-18.5MiB live, 18.6MiB allocated

Counts

5 → 60

Calls

Call 1

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

Outputs
#s(alt (* -1 x) (taylor 0 x) (#s(alt (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64))) (patch (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- x 1)) (taylor 0 x) (#s(alt (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64))) (patch (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- x 1)) (taylor 0 x) (#s(alt (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64))) (patch (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- x 1)) (taylor 0 x) (#s(alt (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64))) (patch (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt -1)) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64)))) (patch (sqrt.f64 (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1))) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64)))) (patch (sqrt.f64 (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1))))))) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64)))) (patch (sqrt.f64 (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* (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))))))))) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64)))) (patch (sqrt.f64 (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (-.f64 x #s(literal -1 binary64)) (patch (-.f64 x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (-.f64 x #s(literal -1 binary64)) (patch (-.f64 x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (-.f64 x #s(literal -1 binary64)) (patch (-.f64 x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (-.f64 x #s(literal -1 binary64)) (patch (-.f64 x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (patch (.f64 (fma.f64 x x #s(literal -1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (pow x 2) 1)) (taylor 0 x) (#s(alt (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (patch (.f64 (fma.f64 x x #s(literal -1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (pow x 2) 1)) (taylor 0 x) (#s(alt (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (patch (.f64 (fma.f64 x x #s(literal -1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (pow x 2) 1)) (taylor 0 x) (#s(alt (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (patch (.f64 (fma.f64 x x #s(literal -1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64))) (patch (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 x))) (taylor inf x) (#s(alt (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64))) (patch (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 x))) (taylor inf x) (#s(alt (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64))) (patch (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 x))) (taylor inf x) (#s(alt (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64))) (patch (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (sqrt.f64 (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64)))) (patch (sqrt.f64 (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64)))) (patch (sqrt.f64 (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64)))) (patch (sqrt.f64 (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64)))) (patch (sqrt.f64 (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (-.f64 x #s(literal -1 binary64)) (patch (-.f64 x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (-.f64 x #s(literal -1 binary64)) (patch (-.f64 x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (-.f64 x #s(literal -1 binary64)) (patch (-.f64 x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (-.f64 x #s(literal -1 binary64)) (patch (-.f64 x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (patch (.f64 (fma.f64 x x #s(literal -1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (patch (.f64 (fma.f64 x x #s(literal -1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (patch (.f64 (fma.f64 x x #s(literal -1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (patch (.f64 (fma.f64 x x #s(literal -1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64))) (patch (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 x))) (taylor -inf x) (#s(alt (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64))) (patch (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 x))) (taylor -inf x) (#s(alt (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64))) (patch (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 x))) (taylor -inf x) (#s(alt (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64))) (patch (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64)))) (patch (sqrt.f64 (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (/ 1 x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64)))) (patch (sqrt.f64 (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ (- (* 1/8 (/ 1 (* x (pow (sqrt -1) 2)))) 1/2) x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64)))) (patch (sqrt.f64 (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -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)))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64)))) (patch (sqrt.f64 (/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x #s(literal -1 binary64)) (patch (-.f64 x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (-.f64 x #s(literal -1 binary64)) (patch (-.f64 x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (-.f64 x #s(literal -1 binary64)) (patch (-.f64 x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (-.f64 x #s(literal -1 binary64)) (patch (-.f64 x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (patch (.f64 (fma.f64 x x #s(literal -1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1))) (taylor -inf x) (#s(alt (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (patch (.f64 (fma.f64 x x #s(literal -1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1))) (taylor -inf x) (#s(alt (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (patch (.f64 (fma.f64 x x #s(literal -1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1))) (taylor -inf x) (#s(alt (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (patch (.f64 (fma.f64 x x #s(literal -1 binary64)) x) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

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

2.0ms

inf

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

1.0ms

-inf

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

simplify188.0ms (5.5%)

Memory

-12.5MiB live, 237.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	107	405
1	308	372
2	982	337
3	3964	334
0	8061	318

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

rewrite179.0ms (5.2%)

Memory

23.8MiB live, 209.5MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	34
0	13	34
1	58	24
2	397	24
3	5374	24
0	8196	24

Stop Event

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

Counts

5 → 780

Calls

Call 1

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

Outputs
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eval149.0ms (4.4%)

Memory: 24.5MiB live, 252.1MiB allocated
Compiler: Compiled 17 148 to 2 994 computations (82.5% saved)

prune19.0ms (0.6%)

Memory

-14.9MiB live, 57.7MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	837	0	837
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	837	5	842

Accuracy

100.0%

Counts

842 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	45.5%	(sqrt.f64 (/.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64))))
✓	59.7%	(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
✓	98.9%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
✓	98.4%	#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 79 to 51 computations (35.4% saved)

regimes6.0ms (0.2%)

Memory

13.8MiB live, 13.8MiB 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 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 x #s(literal 1 binary64)) x))))

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

Calls

2 calls:

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

-17.4MiB live, 19.1MiB allocated

Counts

4 → 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))

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:

4.0ms	x
2.0ms	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 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)

regimes3.0ms (0.1%)

Memory

16.4MiB live, 16.4MiB 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:

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

Results

Accuracy	Segments	Branch
98.4%	1	`x`
98.4%	1	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes3.0ms (0.1%)

Memory

12.5MiB live, 12.5MiB 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:

1.0ms	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
1.0ms	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)

simplify56.0ms (1.6%)

Memory

-11.6MiB live, 85.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	42
1	31	42
2	50	42
3	77	42
4	120	42
5	175	42
6	207	42
7	242	42
8	291	42
9	312	42
10	315	42

Stop Event

1×

saturated

Calls

Call 1

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

soundness381.0ms (11.1%)

Memory

-30.2MiB live, 203.5MiB 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 22 to 17 computations (22.7% saved)

preprocess225.0ms (6.6%)

Memory: 23.6MiB live, 66.4MiB allocated
Compiler: Compiled 56 to 42 computations (25% 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	21	110
0	31	110
1	48	110
2	74	110
3	120	110
4	198	110
5	395	110
6	635	110
7	727	110
8	795	110
9	829	110
10	838	110
11	839	110
0	839	110

Iter	Nodes	Cost
0	19	42
1	31	42
2	50	42
3	77	42
4	120	42
5	175	42
6	207	42
7	242	42
8	291	42
9	312	42
10	315	42

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	21	110
0	31	110
1	48	110
2	74	110
3	120	110
4	198	110
5	395	110
6	635	110
7	727	110
8	795	110
9	829	110
10	838	110
11	839	110
0	839	110

Iter	Nodes	Cost
0	19	42
1	31	42
2	50	42
3	77	42
4	120	42
5	175	42
6	207	42
7	242	42
8	291	42
9	312	42
10	315	42

start0.0ms (0%)

analyze1.0ms (0%)

sample606.0ms (17.7%)

explain65.0ms (1.9%)

preprocess17.0ms (0.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize22.0ms (0.6%)

series6.0ms (0.2%)

simplify169.0ms (4.9%)

rewrite309.0ms (9%)

eval126.0ms (3.7%)

prune11.0ms (0.3%)

simplify29.0ms (0.8%)

localize61.0ms (1.8%)

series8.0ms (0.2%)

simplify155.0ms (4.5%)

rewrite143.0ms (4.2%)

eval178.0ms (5.2%)

prune36.0ms (1%)

simplify234.0ms (6.8%)

localize25.0ms (0.7%)

series8.0ms (0.2%)

simplify188.0ms (5.5%)

rewrite179.0ms (5.2%)

eval149.0ms (4.4%)

prune19.0ms (0.6%)

regimes6.0ms (0.2%)

regimes7.0ms (0.2%)

regimes3.0ms (0.1%)

regimes3.0ms (0.1%)

simplify56.0ms (1.6%)

soundness381.0ms (11.1%)

preprocess225.0ms (6.6%)

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	21	110
0	31	110
1	48	110
2	74	110
3	120	110
4	198	110
5	395	110
6	635	110
7	727	110
8	795	110
9	829	110
10	838	110
11	839	110
0	839	110

Iter	Nodes	Cost
0	19	42
1	31	42
2	50	42
3	77	42
4	120	42
5	175	42
6	207	42
7	242	42
8	291	42
9	312	42
10	315	42