Metrics for Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze2.0ms (0.1%)

Memory

2.8MiB live, 2.8MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
0%	0%	50%	0%	0%	50%	0%	3
50%	25%	25%	0%	0%	50%	0%	4
75%	37.5%	12.5%	0%	0%	50%	0%	5
87.5%	43.7%	6.2%	0%	0%	50%	0%	6
93.8%	46.9%	3.1%	0%	0%	50%	0%	7
96.9%	48.4%	1.6%	0%	0%	50%	0%	8
98.4%	49.2%	0.8%	0%	0%	50%	0%	9
99.2%	49.6%	0.4%	0%	0%	50%	0%	10
99.6%	49.8%	0.2%	0%	0%	50%	0%	11
99.8%	49.9%	0.1%	0%	0%	50%	0%	12

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample926.0ms (25.6%)

Memory

-119.6MiB live, 754.9MiB allocated

Samples

446.0ms	8 256×	0	valid
0.0ms	7×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 281.0ms

ival-sqrt: 159.0ms (56.6% of total)

ival-mult: 64.0ms (22.8% of total)

ival-sub: 43.0ms (15.3% of total)

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

exact: 5.0ms (1.8% of total)

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

Bogosity

explain63.0ms (1.7%)

Memory

1.8MiB live, 83.9MiB allocated

FPErrors

Click to see full error table

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

23.0ms

512×

valid

Compiler

Compiled 58 to 24 computations (58.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-mult: 4.0ms (37.5% of total)

ival-sqrt: 3.0ms (28.1% of total)

ival-sub: 2.0ms (18.8% of total)

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

exact: 0.0ms (0% of total)

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

preprocess482.0ms (13.3%)

Memory

-8.1MiB live, 317.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	25	13
2	45	13
3	87	13
4	116	13
5	167	13
6	291	13
7	560	13
8	956	13
9	1495	13
10	3861	13
11	5538	13
12	6296	13
13	6594	13
14	6650	13
15	6682	13
16	6950	13
17	7544	13
0	5	6
0	8	6
1	15	6
2	22	6
3	30	6
4	45	6
5	65	6
6	108	6
7	293	6
8	565	6
9	1118	6
10	2024	6
11	3754	6
12	4728	6
13	5061	6
14	5345	6
15	5513	6
16	5590	6
17	5881	6
18	6877	6
0	8007	6

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs x)

Compiler

Compiled 6 to 5 computations (16.7% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify376.0ms (10.4%)

Memory

-24.0MiB live, 254.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	16
0	8	16
1	15	16
2	22	16
3	30	16
4	45	16
5	65	16
6	108	16
7	293	16
8	565	16
9	1118	16
10	2024	16
11	3754	16
12	4728	16
13	5061	16
14	5345	16
15	5513	16
16	5590	16
17	5881	16
18	6877	16
0	8007	16

Stop Event

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

Calls

Call 1

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

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

localize15.0ms (0.4%)

Memory

19.4MiB live, 19.4MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
accuracy	0.0	(-.f64 #s(literal 1 binary64) (*.f64 x x))
accuracy	0.0	(*.f64 x x)
accuracy	0.0	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))

Samples

10.0ms

256×

valid

Compiler

Compiled 34 to 12 computations (64.7% saved)

Precisions

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

ival-mult: 2.0ms (39.7% of total)

ival-sqrt: 2.0ms (39.7% of total)

ival-sub: 1.0ms (19.9% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0.1%)

Memory

2.8MiB live, 2.8MiB allocated

Counts

3 → 16

Calls

Call 1

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

Outputs
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(+ 1 (* -1 (pow x 2)))
(pow x 2)
(* x (sqrt -1))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))

Calls

3 calls:

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

simplify110.0ms (3%)

Memory

-3.9MiB live, 108.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	215
1	149	213
2	432	205
3	1300	191
4	3878	190
5	6400	190
0	8121	179

Stop Event

1×	iter limit
1×	node limit

Counts

16 → 16

Calls

Call 1

Inputs
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(+ 1 (* -1 (pow x 2)))
(pow x 2)
(* x (sqrt -1))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))

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

rewrite187.0ms (5.2%)

Memory

9.2MiB live, 164.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	14
0	8	14
1	32	14
2	187	14
3	1340	14
0	9373	12

Stop Event

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

Counts

3 → 355

Calls

Call 1

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

Outputs
(*.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 #s(literal 1 binary64) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 x #s(literal 4 binary64)))))) (sqrt.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64))))
(*.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 3 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) (-.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) #s(literal 1 binary64))))
(*.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64))))) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)))))
(*.f64 (sqrt.f64 (/.f64 (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64))))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (sqrt.f64 (/.f64 (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64))))
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal -1 binary64))))
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (neg.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)))))
(*.f64 (pow.f64 (/.f64 (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64))))
(*.f64 (pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 #s(literal 1 binary64) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 x #s(literal 4 binary64))))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64))))
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 3 binary64)) #s(literal 1 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) (-.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) #s(literal 1 binary64))))
(*.f64 (pow.f64 (/.f64 (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64)))))
(*.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (pow.f64 (neg.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64))) #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 (pow.f64 (neg.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))))
(*.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1/2 binary64)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log1p.f64 (*.f64 x x)))
(pow.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
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(-.f64 (/.f64 #s(literal 0 binary64) (fma.f64 (neg.f64 x) x #s(literal -1 binary64))) (fma.f64 (neg.f64 x) x #s(literal -1 binary64)))
(-.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal -1 binary64)) (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64))) (/.f64 (/.f64 (pow.f64 x #s(literal 12 binary64)) (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64))))
(-.f64 (/.f64 (pow.f64 (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 12 binary64))) (pow.f64 x #s(literal 6 binary64))) #s(literal -1 binary64)) (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64))) (/.f64 (/.f64 (pow.f64 x #s(literal 18 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 12 binary64))) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64))))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))))) (/.f64 (pow.f64 x #s(literal 8 binary64)) (.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 8 binary64))) (pow.f64 x #s(literal 4 binary64))))) (/.f64 (pow.f64 x #s(literal 12 binary64)) (.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 8 binary64))) (pow.f64 x #s(literal 4 binary64))))))
(-.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (/.f64 (/.f64 (pow.f64 x #s(literal 8 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 x x #s(literal 1 binary64))))
(-.f64 (/.f64 (pow.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 8 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (/.f64 (/.f64 (pow.f64 x #s(literal 12 binary64)) (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 8 binary64))) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 x x #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)))) (fma.f64 (neg.f64 x) x #s(literal -1 binary64)))
(-.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64)))
(-.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))))
(-.f64 (pow.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64))))
(-.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (neg.f64 x) x) #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) x))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(exp.f64 (.f64 (neg.f64 (log1p.f64 (.f64 x x))) #s(literal -1 binary64)))
(exp.f64 (log1p.f64 (*.f64 x x)))
(+.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64)))))
(+.f64 (pow.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)))))
(+.f64 (*.f64 (neg.f64 x) x) #s(literal 1 binary64))
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (neg.f64 x)) x))
(+.f64 #s(literal 1 binary64) (neg.f64 (*.f64 (neg.f64 x) x)))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) x))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 (neg.f64 x) (neg.f64 x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
(.f64 #s(literal 1 binary64) (.f64 x x))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval114.0ms (3.2%)

Memory: -9.4MiB live, 114.3MiB allocated
Compiler: Compiled 9 582 to 1 267 computations (86.8% saved)

prune4.0ms (0.1%)

Memory

18.0MiB live, 18.0MiB allocated

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	368	2	370
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	369	2	371

Accuracy

100.0%

Counts

371 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
▶	99.5%	#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

Compiler

Compiled 21 to 17 computations (19% saved)

simplify382.0ms (10.6%)

Memory

10.0MiB live, 277.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	34
0	13	34
1	24	34
2	34	34
3	42	34
4	57	34
5	77	34
6	120	34
7	314	34
8	613	34
9	1201	34
10	2251	34
11	3262	34
12	4104	34
13	4416	34
14	4720	34
15	4876	34
16	4953	34
17	5186	34
18	5965	34
19	6186	34
20	7867	34
0	8117	34

Stop Event

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

Calls

Call 1

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

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

localize23.0ms (0.6%)

Memory

10.9MiB live, 48.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
accuracy	0.0	(*.f64 x x)
accuracy	0.0	#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
accuracy	0.28882061239423845	#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

Samples

17.0ms

256×

valid

Compiler

Compiled 62 to 21 computations (66.1% saved)

Precisions

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

ival-mult: 3.0ms (37.9% of total)

ival-sqrt: 2.0ms (25.3% of total)

ival-sub: 1.0ms (12.6% of total)

ival-add: 1.0ms (12.6% 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

-31.3MiB live, 5.8MiB allocated

Counts

4 → 15

Calls

Call 1

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

Outputs
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(pow x 2)
(* x (sqrt -1))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))

Calls

3 calls:

Time	Variable		Point	Expression
4.0ms	x	@	0	((sqrt (- 1 (* x x))) (sqrt (- 1 (* x x))) (+ (* (* x x) -1/2) 1) (* x x))
1.0ms	x	@	inf	((sqrt (- 1 (* x x))) (sqrt (- 1 (* x x))) (+ (* (* x x) -1/2) 1) (* x x))
1.0ms	x	@	-inf	((sqrt (- 1 (* x x))) (sqrt (- 1 (* x x))) (+ (* (* x x) -1/2) 1) (* x x))

Time

Variable

Point

Expression

4.0ms

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

1.0ms

inf

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

1.0ms

-inf

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

simplify148.0ms (4.1%)

Memory

5.1MiB live, 130.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	211
1	144	211
2	417	203
3	1274	189
4	3865	188
5	6441	188
0	8092	176

Stop Event

1×	iter limit
1×	node limit

Counts

15 → 15

Calls

Call 1

Inputs
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(pow x 2)
(* x (sqrt -1))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))

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

rewrite192.0ms (5.3%)

Memory

13.0MiB live, 174.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	30
0	13	30
1	51	30
2	330	30
3	2676	30
0	8793	28

Stop Event

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

Counts

4 → 132

Calls

Call 1

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

Outputs
#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))
#s(approx (sqrt (- 1 (* x x))) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64)) (fma.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 8 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64)) (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 12 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 8 binary64)) (fma.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64))) (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 12 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64))) (fma.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 18 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 12 binary64)) (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64))))) (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)))
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(/.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (fma.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) #s(literal -1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(neg.f64 (/.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64))))
(neg.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)) (fma.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))))
(neg.f64 (/.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
(neg.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))))
(fma.f64 (exp.f64 (log.f64 #s(literal -1/2 binary64))) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (exp.f64 (log.f64 (*.f64 #s(literal -1/2 binary64) x))) x #s(literal 1 binary64))
(fma.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) x #s(literal 1 binary64))
(fma.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64))) (fma.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64))) (neg.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))))
(fma.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) (neg.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))))
(fma.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/2 binary64)) (/.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64))) (neg.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))))
(fma.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64))) (neg.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))))
(fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (/.f64 (.f64 x x) (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64))) (neg.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))))
(fma.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64))) (neg.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64))) (neg.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))))
(fma.f64 (.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64)) (neg.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64))) (neg.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64))) (neg.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (*.f64 x x) (exp.f64 (log.f64 #s(literal -1/2 binary64))) #s(literal 1 binary64))
(fma.f64 (.f64 x x) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64))) (neg.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(fma.f64 x (exp.f64 (log.f64 (*.f64 #s(literal -1/2 binary64) x))) #s(literal 1 binary64))
(fma.f64 x (pow.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 x (/.f64 (.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal -1/2 binary64)) (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64))) (neg.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))))
(fma.f64 x (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))
(-.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
(-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64)))) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64)))) (neg.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(*.f64 (neg.f64 x) (neg.f64 x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
(.f64 #s(literal 1 binary64) (.f64 x x))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval24.0ms (0.7%)

Memory: -2.8MiB live, 35.2MiB allocated
Compiler: Compiled 4 021 to 547 computations (86.4% saved)

prune3.0ms (0.1%)

Memory

9.6MiB live, 9.6MiB allocated

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	146	2	148

Accuracy

100.0%

Counts

148 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
✓	99.5%	#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

Compiler

Compiled 48 to 30 computations (37.5% saved)

regimes73.0ms (2%)

Memory

-24.6MiB live, 24.6MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

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

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

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

Calls

4 calls:

69.0ms	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
2.0ms	x
1.0ms	(*.f64 x x)
1.0ms	(-.f64 #s(literal 1 binary64) (*.f64 x x))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))`
100.0%	1	`(-.f64 #s(literal 1 binary64) (*.f64 x x))`
100.0%	1	`(*.f64 x x)`

Compiler

Compiled 15 to 12 computations (20% saved)

regimes4.0ms (0.1%)

Memory

9.6MiB live, 9.6MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	1	`(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))`
99.5%	1	`(-.f64 #s(literal 1 binary64) (*.f64 x x))`
99.5%	1	`(*.f64 x x)`

Compiler

Compiled 15 to 12 computations (20% saved)

simplify144.0ms (4%)

Memory

1.5MiB live, 75.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	17	21
2	24	21
3	33	21
4	54	21
5	78	21
6	191	21
7	1121	21
8	2857	21
9	5563	21

Stop Event

1×	node limit

Calls

Call 1

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

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

soundness315.0ms (8.7%)

Memory

-24.8MiB live, 141.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	215
1	149	213
2	432	205
3	1300	191
4	3878	190
5	6400	190
0	8121	179

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 28 to 18 computations (35.7% saved)

preprocess16.0ms (0.5%)

Memory: 28.5MiB live, 28.5MiB allocated
Remove: (abs x)
Compiler: Compiled 80 to 52 computations (35% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze2.0ms (0.1%)

sample926.0ms (25.6%)

explain63.0ms (1.7%)

preprocess482.0ms (13.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify376.0ms (10.4%)

localize15.0ms (0.4%)

series2.0ms (0.1%)

simplify110.0ms (3%)

rewrite187.0ms (5.2%)

eval114.0ms (3.2%)

prune4.0ms (0.1%)

simplify382.0ms (10.6%)

localize23.0ms (0.6%)

series6.0ms (0.2%)

simplify148.0ms (4.1%)

rewrite192.0ms (5.3%)

eval24.0ms (0.7%)

prune3.0ms (0.1%)

regimes73.0ms (2%)

regimes4.0ms (0.1%)

simplify144.0ms (4%)

soundness315.0ms (8.7%)

preprocess16.0ms (0.5%)

end0.0ms (0%)

Profiling