Metrics for Rust f64::acosh

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	25%	75%	0%	0%	0%	0
100%	25%	0%	75%	0%	0%	0%	1

Compiler

Compiled 6 to 5 computations (16.7% saved)

sample499.0ms (12.1%)

Memory

42.9MiB live, 943.3MiB allocated

Samples

324.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 179.0ms

ival-acosh: 145.0ms (81% of total)

ival->=: 24.0ms (13.4% of total)

exact: 7.0ms (3.9% of total)

ival-assert: 3.0ms (1.7% of total)

Bogosity

explain106.0ms (2.6%)

Memory

-33.7MiB live, 139.6MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
122	-	-	`(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))`
0	-	-	`(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))`
0	-	-	`(*.f64 x x)`
0	-	-	`(-.f64 (*.f64 x x) #s(literal 1 binary64))`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))`	oflow-rescue	122	0
↳	`(-.f64 (*.f64 x x) #s(literal 1 binary64))`	overflow	122
↳	`(*.f64 x x)`	overflow	122

Confusion

	Predicted +	Predicted -
+	122	0
-	0	134

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	122	0	0
-	0	0	134

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	134
1	122

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

35.0ms

512×

valid

Compiler

Compiled 80 to 25 computations (68.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-log: 6.0ms (31.5% of total)

ival-mult: 4.0ms (21% of total)

ival-sqrt: 4.0ms (21% of total)

ival-sub: 2.0ms (10.5% of total)

ival-add: 2.0ms (10.5% of total)

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

exact: 0.0ms (0% of total)

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

preprocess281.0ms (6.8%)

Memory

5.2MiB live, 318.7MiB allocated

Algorithm

1×	egg-herbie

Rules

29 894×	`lower-fma.f64`
29 894×	`lower-fma.f32`
4 210×	`lower-*.f32`
4 208×	`lower-*.f64`
2 884×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7
1	10	7
2	14	7
3	17	7
4	21	7
5	28	7
6	35	7
0	7	9
0	12	9
1	21	9
2	25	9
3	40	9
4	71	9
5	132	9
6	292	9
7	572	9
8	2045	9
9	3155	9
10	4433	9
11	5106	9
12	5408	9
13	5593	9
14	5695	9
15	6014	9
16	6560	9
17	7671	9
0	8091	8

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 10 to 7 computations (30% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.8%	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))

Compiler

Compiled 10 to 7 computations (30% saved)

simplify267.0ms (6.5%)

Memory

38.1MiB live, 228.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))
cost-diff	0	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))
cost-diff	0	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
cost-diff	128	(-.f64 (*.f64 x x) #s(literal 1 binary64))

Rules

29 894×	`lower-fma.f64`
29 894×	`lower-fma.f32`
4 210×	`lower-*.f32`
4 208×	`lower-*.f64`
2 884×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	33
0	12	33
1	21	33
2	25	33
3	40	33
4	71	33
5	132	33
6	292	33
7	572	33
8	2045	33
9	3155	33
10	4433	33
11	5106	33
12	5408	33
13	5593	33
14	5695	33
15	6014	33
16	6560	33
17	7671	33
0	8091	29

Stop Event

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

Calls

Call 1

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

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

localize92.0ms (2.2%)

Memory

-23.2MiB live, 70.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
accuracy	0.0078125	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))
accuracy	28.388948228275332	(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))

Samples

87.0ms

256×

valid

Compiler

Compiled 35 to 9 computations (74.3% saved)

Precisions

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

ival-sqrt: 7.0ms (49.8% of total)

ival-log: 3.0ms (21.3% of total)

ival-mult: 2.0ms (14.2% of total)

ival-sub: 1.0ms (7.1% of total)

ival-add: 1.0ms (7.1% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.1%)

Memory

8.5MiB live, 8.5MiB allocated

Counts

5 → 60

Calls

Call 1

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

Outputs
#s(alt -1 (taylor 0 x) (#s(alt (-.f64 (.f64 x x) #s(literal 1 binary64)) (patch (-.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt (-.f64 (.f64 x x) #s(literal 1 binary64)) (patch (-.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt (-.f64 (.f64 x x) #s(literal 1 binary64)) (patch (-.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt (-.f64 (.f64 x x) #s(literal 1 binary64)) (patch (-.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (log (sqrt -1)) (taylor 0 x) (#s(alt (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (log (sqrt -1)) (/ x (sqrt -1))) (taylor 0 x) (#s(alt (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1))))) (taylor 0 x) (#s(alt (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1))))) (taylor 0 x) (#s(alt (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (sqrt -1) (taylor 0 x) (#s(alt (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ x (sqrt -1)) (taylor 0 x) (#s(alt (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1)))))) (taylor 0 x) (#s(alt (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1)))))))) (taylor 0 x) (#s(alt (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt -1) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1)))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1)))))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1)))))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (-.f64 (.f64 x x) #s(literal 1 binary64)) (patch (-.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (-.f64 (.f64 x x) #s(literal 1 binary64)) (patch (-.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (-.f64 (.f64 x x) #s(literal 1 binary64)) (patch (-.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (-.f64 (.f64 x x) #s(literal 1 binary64)) (patch (-.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (log 2) (* -1 (log (/ 1 x)))) (taylor inf x) (#s(alt (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2))))) (taylor inf x) (#s(alt (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (- 2 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))) (taylor inf x) (#s(alt (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (-.f64 (.f64 x x) #s(literal 1 binary64)) (patch (-.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (-.f64 (.f64 x x) #s(literal 1 binary64)) (patch (-.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (-.f64 (.f64 x x) #s(literal 1 binary64)) (patch (-.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (-.f64 (.f64 x x) #s(literal 1 binary64)) (patch (-.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (log -1/2) (log (/ -1 x))) (taylor -inf x) (#s(alt (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6))))))) (taylor -inf x) (#s(alt (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 x) (taylor -inf x) (#s(alt (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x) (taylor -inf x) (#s(alt (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x)) (taylor -inf x) (#s(alt (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x)) (taylor -inf x) (#s(alt (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())

Calls

3 calls:

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

Time

Variable

Point

Expression

2.0ms

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

1.0ms

inf

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

1.0ms

-inf

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

simplify203.0ms (4.9%)

Memory

-15.3MiB live, 137.0MiB allocated

Algorithm

1×	egg-herbie

Rules

10 204×	`lower-fma.f64`
10 204×	`lower-fma.f32`
3 650×	`lower-*.f64`
3 650×	`lower-*.f32`
2 854×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	150	595
1	411	569
2	1146	562
3	3331	524
4	7979	524
0	8531	495

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 59

Calls

Call 1

Inputs
-1
(- (pow x 2) 1)
(- (pow x 2) 1)
(- (pow x 2) 1)
(log (sqrt -1))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(sqrt -1)
(+ x (sqrt -1))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(sqrt -1)
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 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))))
(+ (log 2) (* -1 (log (/ 1 x))))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(* 2 x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
x
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 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))))
(+ (log -1/2) (log (/ -1 x)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(* -1 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

Outputs
-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))
(log (sqrt -1))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal 1 binary64)) (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 #s(literal 3/40 binary64) x) (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal 1 binary64)) (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (log.f64 (sqrt.f64 #s(literal -1 binary64)))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ x (sqrt -1))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x #s(literal 1 binary64)) x (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x (sqrt.f64 #s(literal -1 binary64)))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x) x (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x) (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) (.f64 (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) x) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 #s(literal 1/8 binary64) (.f64 x x) #s(literal 1/2 binary64)))) (.f64 x x) (sqrt.f64 #s(literal -1 binary64)))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(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))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64)))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(-.f64 (+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(-.f64 (+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64))) (/.f64 (+.f64 (/.f64 #s(literal 3/32 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (.f64 x x)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(-.f64 (-.f64 (log.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (.f64 x x))) (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 5/96 binary64) (.f64 x x)) #s(literal 3/32 binary64)) (.f64 (.f64 (*.f64 x x) x) x)) (log.f64 x)))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2 binary64) x (/.f64 #s(literal -1/2 binary64) x))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(fma.f64 #s(literal 2 binary64) x (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (-.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (.f64 (.f64 x x) x) x))) x (/.f64 #s(literal -1/2 binary64) x))
x
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(-.f64 x (/.f64 #s(literal 1/2 binary64) x))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(-.f64 x (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x x))) (.f64 (.f64 (.f64 x x) x) x)) x (-.f64 x (/.f64 #s(literal 1/2 binary64) x)))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(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))
(+ (log -1/2) (log (/ -1 x)))
(+.f64 (neg.f64 (log.f64 (neg.f64 x))) (log.f64 #s(literal -1/2 binary64)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+.f64 (+.f64 (log.f64 #s(literal -1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (neg.f64 (log.f64 (neg.f64 x))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+.f64 (+.f64 (/.f64 #s(literal 3/32 binary64) (.f64 (.f64 (.f64 x x) x) x)) (log.f64 #s(literal -1/2 binary64))) (+.f64 (neg.f64 (log.f64 (neg.f64 x))) (/.f64 #s(literal 1/4 binary64) (.f64 x x))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(+.f64 (+.f64 (+.f64 (/.f64 #s(literal 3/32 binary64) (.f64 (.f64 (.f64 x x) x) x)) (log.f64 #s(literal -1/2 binary64))) (/.f64 #s(literal 5/96 binary64) (pow.f64 x #s(literal 6 binary64)))) (+.f64 (neg.f64 (log.f64 (neg.f64 x))) (/.f64 #s(literal 1/4 binary64) (.f64 x x))))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(/.f64 (-.f64 (/.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) (.f64 x x))) (.f64 x x)) #s(literal -1/2 binary64)) x)
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(/.f64 (-.f64 (/.f64 (-.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -5/128 binary64) (.f64 x x))) (.f64 (.f64 (.f64 x x) x) x)) (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))
(-.f64 (/.f64 #s(literal 1/2 binary64) x) x)
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))
(-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) x)
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (.f64 (.f64 x x) x) x)) x (-.f64 (/.f64 #s(literal 1/2 binary64) x) x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

rewrite234.0ms (5.7%)

Memory

16.1MiB live, 173.5MiB allocated

Rules

4 994×	`lower-fma.f64`
4 994×	`lower-fma.f32`
3 230×	`lower-*.f32`
3 228×	`lower-*.f64`
2 612×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	31
0	12	31
1	49	31
2	322	31
3	3626	31
0	8646	27

Stop Event

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

Counts

5 → 328

Calls

Call 1

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

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

eval56.0ms (1.4%)

Memory: 10.7MiB live, 47.5MiB allocated
Compiler: Compiled 10 847 to 1 555 computations (85.7% saved)

prune98.0ms (2.4%)

Memory

-3.7MiB live, 80.0MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	383	4	387
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	384	4	388

Accuracy

100.0%

Counts

388 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(log.f64 (fma.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x))
▶	53.8%	(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))
▶	99.4%	(log.f64 (+.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x)))))
▶	98.8%	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))

Compiler

Compiled 37 to 24 computations (35.1% saved)

simplify498.0ms (12.1%)

Memory

-3.4MiB live, 163.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 x #s(literal 1 binary64))
cost-diff	0	(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
cost-diff	0	(fma.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x)
cost-diff	0	(log.f64 (fma.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x))
cost-diff	0	(fma.f64 x x #s(literal -1 binary64))
cost-diff	0	(sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))
cost-diff	0	(+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x)
cost-diff	0	(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))
cost-diff	0	(-.f64 x (/.f64 #s(literal 1/2 binary64) x))
cost-diff	0	#s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x)))
cost-diff	0	(+.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))))
cost-diff	0	(log.f64 (+.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x)))))
cost-diff	0	#s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x))
cost-diff	0	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
cost-diff	128	(*.f64 #s(literal 2 binary64) x)

Rules

21 704×	`lower-fma.f32`
21 700×	`lower-fma.f64`
3 580×	`lower-*.f32`
3 578×	`lower-*.f64`
3 136×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	144
0	44	139
1	62	139
2	78	139
3	111	139
4	160	139
5	352	139
6	685	139
7	2133	139
8	3571	139
9	4937	139
10	5559	139
11	5778	139
12	5908	139
13	5955	139
14	6413	139
15	6947	139
16	7170	139
17	7343	139
18	7855	139
0	8035	139

Stop Event

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

Calls

Call 1

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

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

localize100.0ms (2.4%)

Memory

-0.0MiB live, 72.4MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
accuracy	0	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
accuracy	0	(log.f64 (fma.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x))
accuracy	0.09765625	(fma.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x)
accuracy	0	(fma.f64 x x #s(literal -1 binary64))
accuracy	0	(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))
accuracy	0.0078125	(+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x)
accuracy	28.388948228275332	(sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))
accuracy	0	(-.f64 x (/.f64 #s(literal 1/2 binary64) x))
accuracy	0	(log.f64 (+.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x)))))
accuracy	0.0078125	(+.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))))
accuracy	0.4438355132710582	#s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x)))
accuracy	0	(*.f64 #s(literal 2 binary64) x)
accuracy	0	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
accuracy	0.8723006456223057	#s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x))

Samples

85.0ms

256×

valid

Compiler

Compiled 126 to 26 computations (79.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 62.0ms

ival-sub: 34.0ms (55.2% of total)

ival-log: 8.0ms (13% of total)

ival-add: 6.0ms (9.7% of total)

ival-sqrt: 6.0ms (9.7% of total)

ival-mult: 5.0ms (8.1% of total)

ival-div: 2.0ms (3.2% of total)

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

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

exact: 0.0ms (0% of total)

series33.0ms (0.8%)

Memory

-4.7MiB live, 29.9MiB allocated

Counts

16 → 192

Calls

Call 1

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

Outputs
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (log (sqrt -1)) (taylor 0 x) (#s(alt (log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (.f64 #s(literal 2 binary64) x))) (patch (log.f64 #s(approx (+ x (sqrt (- ( x x) 1))) (*.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (log (sqrt -1)) (/ x (sqrt -1))) (taylor 0 x) (#s(alt (log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (.f64 #s(literal 2 binary64) x))) (patch (log.f64 #s(approx (+ x (sqrt (- ( x x) 1))) (*.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1))))) (taylor 0 x) (#s(alt (log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (.f64 #s(literal 2 binary64) x))) (patch (log.f64 #s(approx (+ x (sqrt (- ( x x) 1))) (*.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1))))) (taylor 0 x) (#s(alt (log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (.f64 #s(literal 2 binary64) x))) (patch (log.f64 #s(approx (+ x (sqrt (- ( x x) 1))) (*.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (sqrt -1) (taylor 0 x) (#s(alt #s(approx (+ x (sqrt (- (* x x) 1))) (.f64 #s(literal 2 binary64) x)) (patch #s(approx (+ x (sqrt (- ( x x) 1))) (*.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) (patch #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1/2 binary64) x)) (patch (-.f64 x (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1/2 binary64) x)) (patch (-.f64 x (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1/2 binary64) x)) (patch (-.f64 x (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 #s(literal 1/2 binary64) x)) (patch (-.f64 x (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (log -1/2) (log (/ -1 x))) (taylor -inf x) (#s(alt (log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x)) (patch (log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x)) (patch (log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x)) (patch (log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6))))))) (taylor -inf x) (#s(alt (log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x)) (patch (log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 x) (taylor -inf x) (#s(alt (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x) (patch (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x) (taylor -inf x) (#s(alt (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x) (patch (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x)) (taylor -inf x) (#s(alt (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x) (patch (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x)) (taylor -inf x) (#s(alt (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x) (patch (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (patch (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (patch (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (patch (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (patch (sqrt.f64 (fma.f64 x 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 (+ (log (- (pow (sqrt -1) 2) 1)) (* -1 (log (/ -1 x)))) (taylor -inf x) (#s(alt (log.f64 (fma.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x)) (patch (log.f64 (fma.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x)) #<representation binary64>) () ())) ())
#s(alt (+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (* 1/2 (/ 1 (* (pow x 2) (- (pow (sqrt -1) 2) 1)))))) (taylor -inf x) (#s(alt (log.f64 (fma.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x)) (patch (log.f64 (fma.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x)) #<representation binary64>) () ())) ())
#s(alt (+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1)))))) (taylor -inf x) (#s(alt (log.f64 (fma.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x)) (patch (log.f64 (fma.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x)) #<representation binary64>) () ())) ())
#s(alt (+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (+ (* 1/720 (/ (+ (* 45 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (+ (* 45 (/ 1 (* (pow (sqrt -1) 4) (- (pow (sqrt -1) 2) 1)))) (* 30 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3))))) (pow x 6))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))) (taylor -inf x) (#s(alt (log.f64 (fma.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x)) (patch (log.f64 (fma.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (pow (sqrt -1) 2) 1))) (taylor -inf x) (#s(alt (fma.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x) (patch (fma.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) 1))) (taylor -inf x) (#s(alt (fma.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x) (patch (fma.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) (+ 1 (/ 1/8 (* (pow x 4) (pow (sqrt -1) 2))))))) (taylor -inf x) (#s(alt (fma.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x) (patch (fma.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 4)))) (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2))) (+ 1 (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 2)))))))) (taylor -inf x) (#s(alt (fma.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x) (patch (fma.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) 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 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

5.0ms

-inf

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

2.0ms

inf

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

1.0ms

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

simplify211.0ms (5.1%)

Memory

-5.1MiB live, 275.3MiB allocated

Algorithm

1×	egg-herbie

Rules

17 302×	`lower-fma.f64`
17 302×	`lower-fma.f32`
5 086×	`lower-*.f64`
5 086×	`lower-*.f32`
3 476×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	325	2485
1	910	2226
2	2918	2180
0	8287	2074

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 186

Calls

Call 1

Inputs
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(log (sqrt -1))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(sqrt -1)
(+ x (sqrt -1))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(log (sqrt -1))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(sqrt -1)
(+ x (sqrt -1))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(sqrt -1)
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(/ -1/2 x)
(/ (- (pow x 2) 1/2) x)
(/ (- (pow x 2) 1/2) x)
(/ (- (pow x 2) 1/2) x)
(log (sqrt -1))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(sqrt -1)
(+ x (sqrt -1))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(sqrt -1)
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
-1
(- (pow x 2) 1)
(- (pow x 2) 1)
(- (pow x 2) 1)
(log (sqrt -1))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(sqrt -1)
(+ x (sqrt -1))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(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)
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(+ (log 2) (* -1 (log (/ 1 x))))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(* 2 x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(+ (log 2) (* -1 (log (/ 1 x))))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(* 2 x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
x
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
x
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(+ (log 2) (* -1 (log (/ 1 x))))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(* 2 x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
x
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 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))))
(+ (log 2) (* -1 (log (/ 1 x))))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(* 2 x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(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)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(+ (log -1/2) (log (/ -1 x)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(+ (log -1/2) (log (/ -1 x)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(* -1 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))
x
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 1)))
(+ (log -1/2) (log (/ -1 x)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(* -1 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 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))))
(+ (log (- (pow (sqrt -1) 2) 1)) (* -1 (log (/ -1 x))))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (* 1/2 (/ 1 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (+ (* 1/720 (/ (+ (* 45 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (+ (* 45 (/ 1 (* (pow (sqrt -1) 4) (- (pow (sqrt -1) 2) 1)))) (* 30 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3))))) (pow x 6))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1)))))))
(* -1 (* x (- (pow (sqrt -1) 2) 1)))
(* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) 1)))
(* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) (+ 1 (/ 1/8 (* (pow x 4) (pow (sqrt -1) 2)))))))
(* -1 (* x (- (+ (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 4)))) (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2))) (+ 1 (* 1/8 (/ 1 (* (pow x 4) (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 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))

Outputs
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(log (sqrt -1))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) x (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 3/40 binary64) x) (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal 1/6 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 x x) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) x (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ x (sqrt -1))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x #s(literal 1 binary64)) x (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) x) (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) x #s(literal 1 binary64)) x (sqrt.f64 #s(literal -1 binary64)))
(log (sqrt -1))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) x (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 3/40 binary64) x) (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal 1/6 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 x x) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) x (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ x (sqrt -1))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x #s(literal 1 binary64)) x (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) x) (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) x #s(literal 1 binary64)) x (sqrt.f64 #s(literal -1 binary64)))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x) x (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) x) (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 x x) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) x) (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 x x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 x x) (sqrt.f64 #s(literal -1 binary64)))
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ (- (pow x 2) 1/2) x)
(-.f64 x (/.f64 #s(literal 1/2 binary64) x))
(/ (- (pow x 2) 1/2) x)
(-.f64 x (/.f64 #s(literal 1/2 binary64) x))
(/ (- (pow x 2) 1/2) x)
(-.f64 x (/.f64 #s(literal 1/2 binary64) x))
(log (sqrt -1))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) x (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 3/40 binary64) x) (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal 1/6 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 x x) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) x (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ x (sqrt -1))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x #s(literal 1 binary64)) x (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) x) (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) x #s(literal 1 binary64)) x (sqrt.f64 #s(literal -1 binary64)))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x) x (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) x) (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 x x) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) x) (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 x x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 x x) (sqrt.f64 #s(literal -1 binary64)))
-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))
(log (sqrt -1))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) x (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 3/40 binary64) x) (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal 1/6 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 x x) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) x (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ x (sqrt -1))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x #s(literal 1 binary64)) x (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) x) (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) x #s(literal 1 binary64)) x (sqrt.f64 #s(literal -1 binary64)))
(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 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) x (/.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))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64)))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
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(.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) x x) x)
(+ (log (- (pow (sqrt -1) 2) 1)) (* -1 (log (/ -1 x))))
(-.f64 (log.f64 #s(literal -2 binary64)) (neg.f64 (log.f64 (neg.f64 x))))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (* 1/2 (/ 1 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))
(-.f64 (-.f64 (log.f64 #s(literal -2 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (neg.f64 (log.f64 (neg.f64 x))))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))
(-.f64 (+.f64 (-.f64 (/.f64 #s(literal -3/32 binary64) (.f64 (.f64 (.f64 x x) x) x)) (/.f64 #s(literal 1/4 binary64) (.f64 x x))) (log.f64 #s(literal -2 binary64))) (neg.f64 (log.f64 (neg.f64 x))))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (+ (* 1/720 (/ (+ (* 45 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (+ (* 45 (/ 1 (* (pow (sqrt -1) 4) (- (pow (sqrt -1) 2) 1)))) (* 30 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3))))) (pow x 6))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1)))))))
(fma.f64 (/.f64 (+.f64 #s(literal -15 binary64) (/.f64 #s(literal -45/2 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/720 binary64) (-.f64 (+.f64 (-.f64 (/.f64 #s(literal -3/32 binary64) (.f64 (.f64 (.f64 x x) x) x)) (/.f64 #s(literal 1/4 binary64) (.f64 x x))) (log.f64 #s(literal -2 binary64))) (neg.f64 (log.f64 (neg.f64 x)))))
(* -1 (* x (- (pow (sqrt -1) 2) 1)))
(+.f64 x x)
(* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) 1)))
(.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) x)
(* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) (+ 1 (/ 1/8 (* (pow x 4) (pow (sqrt -1) 2)))))))
(.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 (*.f64 x x) x) x))) (neg.f64 x))
(* -1 (* x (- (+ (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 4)))) (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2))) (+ 1 (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 2))))))))
(.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) (pow.f64 x #s(literal 6 binary64)))) (-.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 2 binary64)) (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 (.f64 x x) x) x)))) (neg.f64 x))
(* -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) (.f64 (*.f64 x x) x))) #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) (.f64 (*.f64 x x) x))) #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 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) x))) #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 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) x))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.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) (.f64 (*.f64 x x) x))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) x))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (neg.f64 x))

rewrite184.0ms (4.5%)

Memory

40.9MiB live, 229.9MiB allocated

Rules

8 138×	`lower-fma.f32`
8 134×	`lower-fma.f64`
4 154×	`lower-/.f32`
4 152×	`lower-/.f64`
3 582×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	130
0	44	119
1	170	119
2	1212	119
0	8433	119

Stop Event

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

Counts

16 → 764

Calls

Call 1

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

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

eval218.0ms (5.3%)

Memory: -39.8MiB live, 332.0MiB allocated
Compiler: Compiled 24 143 to 3 260 computations (86.5% saved)

prune179.0ms (4.3%)

Memory

14.2MiB live, 341.9MiB allocated

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	949	1	950
Fresh	0	0	0
Picked	1	3	4
Done	0	0	0
Total	950	4	954

Accuracy

100.0%

Counts

954 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(log.f64 (fma.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x))
✓	53.8%	(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))
✓	99.4%	(log.f64 (+.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x)))))
▶	98.8%	(log.f64 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x)))

Compiler

Compiled 37 to 23 computations (37.8% saved)

simplify6.0ms (0.1%)

Memory

-27.1MiB live, 10.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(+.f64 x x)
cost-diff	0	#s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x))
cost-diff	0	(log.f64 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x)))

Rules

14×	`lower-+.f32`
12×	`lower-+.f64`
8×	`lower-*.f64`
8×	`lower-*.f32`
6×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	35
0	13	35
1	23	35
2	25	35
0	25	33

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(log.f64 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x)))
#s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x))
(+.f64 x x)
x

Outputs
(log.f64 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x)))
#s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x))
(+.f64 x x)
x

localize25.0ms (0.6%)

Memory

15.1MiB live, 53.8MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x x)
accuracy	0	(log.f64 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x)))
accuracy	0.8723006456223057	#s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x))

Samples

19.0ms

256×

valid

Compiler

Compiled 29 to 12 computations (58.6% saved)

Precisions

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

ival-log: 4.0ms (28.6% of total)

ival-add: 4.0ms (28.6% of total)

ival-sqrt: 3.0ms (21.4% of total)

ival-sub: 1.0ms (7.1% of total)

ival-mult: 1.0ms (7.1% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

5.5MiB live, 5.5MiB allocated

Counts

3 → 36

Calls

Call 1

Inputs

#s(alt (log.f64 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x))) (patch (log.f64 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x))) #<representation binary64>) () ())

#s(alt #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x)) (patch #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x)) #<representation binary64>) () ())

#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())

Outputs
#s(alt (log (sqrt -1)) (taylor 0 x) (#s(alt (log.f64 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x))) (patch (log.f64 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ (log (sqrt -1)) (/ x (sqrt -1))) (taylor 0 x) (#s(alt (log.f64 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x))) (patch (log.f64 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1))))) (taylor 0 x) (#s(alt (log.f64 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x))) (patch (log.f64 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1))))) (taylor 0 x) (#s(alt (log.f64 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x))) (patch (log.f64 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (sqrt -1) (taylor 0 x) (#s(alt #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x)) (patch #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ x (sqrt -1)) (taylor 0 x) (#s(alt #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x)) (patch #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1)))))) (taylor 0 x) (#s(alt #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x)) (patch #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1)))))))) (taylor 0 x) (#s(alt #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x)) (patch #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (+ (log 2) (* -1 (log (/ 1 x)))) (taylor inf x) (#s(alt (log.f64 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x))) (patch (log.f64 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (log.f64 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x))) (patch (log.f64 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2))))) (taylor inf x) (#s(alt (log.f64 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x))) (patch (log.f64 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (log.f64 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x))) (patch (log.f64 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x)) (patch #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* x (- 2 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x)) (patch #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))) (taylor inf x) (#s(alt #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x)) (patch #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x)) (patch #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (+ (log (- (pow (sqrt -1) 2) 1)) (* -1 (log (/ -1 x)))) (taylor -inf x) (#s(alt (log.f64 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x))) (patch (log.f64 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (* 1/2 (/ 1 (* (pow x 2) (- (pow (sqrt -1) 2) 1)))))) (taylor -inf x) (#s(alt (log.f64 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x))) (patch (log.f64 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1)))))) (taylor -inf x) (#s(alt (log.f64 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x))) (patch (log.f64 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (+ (* 1/720 (/ (+ (* 45 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (+ (* 45 (/ 1 (* (pow (sqrt -1) 4) (- (pow (sqrt -1) 2) 1)))) (* 30 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3))))) (pow x 6))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))) (taylor -inf x) (#s(alt (log.f64 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x))) (patch (log.f64 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (pow (sqrt -1) 2) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x)) (patch #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) 1))) (taylor -inf x) (#s(alt #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x)) (patch #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) (+ 1 (/ 1/8 (* (pow x 4) (pow (sqrt -1) 2))))))) (taylor -inf x) (#s(alt #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x)) (patch #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 4)))) (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2))) (+ 1 (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 2)))))))) (taylor -inf x) (#s(alt #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x)) (patch #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

-inf

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

1.0ms

inf

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

0.0ms

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

simplify182.0ms (4.4%)

Memory

-12.8MiB live, 264.1MiB allocated

Algorithm

1×	egg-herbie

Rules

16 976×	`lower-fma.f64`
16 976×	`lower-fma.f32`
4 112×	`lower-+.f64`
4 112×	`lower-+.f32`
3 628×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	161	534
1	433	369
2	1327	366
3	3624	357
0	8431	342

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

Calls

Call 1

Inputs
(log (sqrt -1))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(sqrt -1)
(+ x (sqrt -1))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(+ (log 2) (* -1 (log (/ 1 x))))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(* 2 x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(+ (log (- (pow (sqrt -1) 2) 1)) (* -1 (log (/ -1 x))))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (* 1/2 (/ 1 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (+ (* 1/720 (/ (+ (* 45 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (+ (* 45 (/ 1 (* (pow (sqrt -1) 4) (- (pow (sqrt -1) 2) 1)))) (* 30 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3))))) (pow x 6))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1)))))))
(* -1 (* x (- (pow (sqrt -1) 2) 1)))
(* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) 1)))
(* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) (+ 1 (/ 1/8 (* (pow x 4) (pow (sqrt -1) 2)))))))
(* -1 (* x (- (+ (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 4)))) (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2))) (+ 1 (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 2))))))))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)

Outputs
(log (sqrt -1))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal 1 binary64)) (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(fma.f64 (.f64 (.f64 #s(literal 3/40 binary64) (.f64 x x)) (.f64 (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) x)) x (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal 1 binary64)) (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (log.f64 (sqrt.f64 #s(literal -1 binary64)))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ x (sqrt -1))
(+.f64 x (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x #s(literal 1 binary64)) x (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x (sqrt.f64 #s(literal -1 binary64)))
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64)))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(-.f64 (+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(-.f64 (+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64))) (/.f64 (+.f64 (/.f64 #s(literal 3/32 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (.f64 x x)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(-.f64 (-.f64 (log.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (.f64 x x))) (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 5/96 binary64) (.f64 x x)) #s(literal 3/32 binary64)) (pow.f64 x #s(literal 4 binary64))) (log.f64 x)))
(* 2 x)
(+.f64 x x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64) (+.f64 x x))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(fma.f64 #s(literal 2 binary64) x (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (-.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 4 binary64)))) x (.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)))
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(+ (log (- (pow (sqrt -1) 2) 1)) (* -1 (log (/ -1 x))))
(-.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (* 1/2 (/ 1 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))
(-.f64 (-.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))
(+.f64 (-.f64 (-.f64 (/.f64 #s(literal -3/32 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (log.f64 (/.f64 #s(literal -1 binary64) x))) (log.f64 #s(literal -2 binary64)))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (+ (* 1/720 (/ (+ (* 45 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (+ (* 45 (/ 1 (* (pow (sqrt -1) 4) (- (pow (sqrt -1) 2) 1)))) (* 30 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3))))) (pow x 6))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1)))))))
(fma.f64 (+.f64 #s(literal -15 binary64) (/.f64 #s(literal -45/2 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (/.f64 #s(literal 1/720 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 (-.f64 (-.f64 (/.f64 #s(literal -3/32 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (log.f64 (/.f64 #s(literal -1 binary64) x))) (log.f64 #s(literal -2 binary64))))
(* -1 (* x (- (pow (sqrt -1) 2) 1)))
(+.f64 x x)
(* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) 1)))
(fma.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64) (+.f64 x x))
(* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) (+ 1 (/ 1/8 (* (pow x 4) (pow (sqrt -1) 2)))))))
(fma.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64)))) x))
(* -1 (* x (- (+ (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 4)))) (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2))) (+ 1 (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 2))))))))
(.f64 (-.f64 (-.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (/.f64 #s(literal 1/16 binary64) (*.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))) x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)

rewrite33.0ms (0.8%)

Memory

24.1MiB live, 62.4MiB allocated

Rules

228×	`lower-fma.f64`
228×	`lower-fma.f32`
194×	`lower-*.f64`
194×	`lower-*.f32`
188×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	34
0	13	32
1	65	28
0	489	26

Stop Event

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

Counts

3 → 15

Calls

Call 1

Inputs
(log.f64 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x)))
#s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x))
(+.f64 x x)

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

eval7.0ms (0.2%)

Memory: -20.5MiB live, 17.7MiB allocated
Compiler: Compiled 554 to 138 computations (75.1% saved)

prune7.0ms (0.2%)

Memory

22.6MiB live, 22.6MiB allocated

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	51	0	51
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	51	4	55

Accuracy

100.0%

Counts

55 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(log.f64 (fma.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x))
✓	53.8%	(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))
✓	99.4%	(log.f64 (+.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x)))))
✓	98.8%	(log.f64 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x)))

Compiler

Compiled 85 to 51 computations (40% saved)

regimes12.0ms (0.3%)

Memory

-18.8MiB live, 26.7MiB allocated

Counts

6 → 1

Calls

Call 1

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

Outputs
(log.f64 (fma.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x))

Calls

3 calls:

6.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
2.0ms	x
2.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))

Results

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

Compiler

Compiled 21 to 14 computations (33.3% saved)

regimes7.0ms (0.2%)

Memory

21.2MiB live, 21.2MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.4%	1	`x`
99.4%	1	`(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))`
99.4%	1	`(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))`

Compiler

Compiled 21 to 14 computations (33.3% saved)

regimes6.0ms (0.1%)

Memory

-22.9MiB live, 15.7MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

2 → 1

Calls

Call 1

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

Outputs
(log.f64 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x)))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.8%	1	`x`
98.8%	1	`(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))`
98.8%	1	`(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))`

Compiler

Compiled 21 to 14 computations (33.3% saved)

simplify7.0ms (0.2%)

Memory

21.2MiB live, 21.3MiB allocated

Algorithm

1×	egg-herbie

Rules

18×	`+-commutative_binary64`
18×	`neg-mul-1_binary64`
16×	`unsub-neg_binary64`
14×	`*-commutative_binary64`
12×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	42
1	35	42
2	46	42
3	57	42
4	73	42
5	96	42
6	99	42

Stop Event

1×

saturated

Calls

Call 1

Inputs

(log.f64 (fma.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x))

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

(log.f64 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f64 x x)))

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

soundness465.0ms (11.3%)

Memory

7.0MiB live, 363.9MiB allocated

Rules

17 302×	`lower-fma.f64`
17 302×	`lower-fma.f32`
10 204×	`lower-fma.f64`
10 204×	`lower-fma.f32`
5 086×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	150	595
1	411	569
2	1146	562
3	3331	524
4	7979	524
0	8531	495
0	325	2485
1	910	2226
2	2918	2180
0	8287	2074
0	7	31
0	12	31
1	49	31
2	322	31
3	3626	31
0	8646	27

Stop Event

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

Compiler

Compiled 74 to 45 computations (39.2% saved)

preprocess85.0ms (2.1%)

Memory: -16.4MiB live, 100.6MiB allocated
Compiler: Compiled 98 to 62 computations (36.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample499.0ms (12.1%)

explain106.0ms (2.6%)

preprocess281.0ms (6.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify267.0ms (6.5%)

localize92.0ms (2.2%)

series6.0ms (0.1%)

simplify203.0ms (4.9%)

rewrite234.0ms (5.7%)

eval56.0ms (1.4%)

prune98.0ms (2.4%)

simplify498.0ms (12.1%)

localize100.0ms (2.4%)

series33.0ms (0.8%)

simplify211.0ms (5.1%)

rewrite184.0ms (4.5%)

eval218.0ms (5.3%)

prune179.0ms (4.3%)

simplify6.0ms (0.1%)

localize25.0ms (0.6%)

series3.0ms (0.1%)

simplify182.0ms (4.4%)

rewrite33.0ms (0.8%)

eval7.0ms (0.2%)

prune7.0ms (0.2%)

regimes12.0ms (0.3%)

regimes7.0ms (0.2%)

regimes6.0ms (0.1%)

simplify7.0ms (0.2%)

soundness465.0ms (11.3%)

preprocess85.0ms (2.1%)

end0.0ms (0%)

Profiling