Metrics for Hyperbolic arc-cosine

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze79.0ms (0.7%)

Memory

-23.4MiB live, 93.0MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
0%	0%	100%	0%	0%	0%	0%	3
16.7%	12.5%	62.5%	0%	0%	25%	0%	4
30%	18.7%	43.7%	0%	0%	37.5%	0%	5
38.9%	21.9%	34.4%	0%	0%	43.7%	0%	6
44.1%	23.4%	29.7%	0%	0%	46.9%	0%	7
47%	24.2%	27.3%	0%	0%	48.4%	0%	8
48.5%	24.6%	26.2%	0%	0%	49.2%	0%	9
49.2%	24.8%	25.6%	0%	0%	49.6%	0%	10
49.6%	24.9%	25.3%	0%	0%	49.8%	0%	11
49.8%	24.9%	25.1%	0%	0%	49.9%	0%	12

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample2.5s (22.8%)

Memory

42.4MiB live, 2 492.4MiB allocated

Samples

1.2s	7 146×	1	invalid
587.0ms	8 256×	0	valid
77.0ms	1 141×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 1.4s

ival-sqrt: 398.0ms (29.4% of total)

ival-log: 253.0ms (18.7% of total)

ival-sub: 183.0ms (13.5% of total)

ival-add: 174.0ms (12.9% of total)

ival-mult: 169.0ms (12.5% of total)

adjust: 146.0ms (10.8% of total)

ival-true: 12.0ms (0.9% of total)

exact: 10.0ms (0.7% of total)

ival-assert: 6.0ms (0.4% of total)

Bogosity

explain171.0ms (1.6%)

Memory

5.7MiB live, 127.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
141	-	-	`(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))`
1	-	-	`(log.f64 (+.f64 x (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	-	-	`(*.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	141	0
↳	`(-.f64 (*.f64 x x) #s(literal 1 binary64))`	overflow	141
↳	`(*.f64 x x)`	overflow	141
`log.f64`	`(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))`	oflow-rescue	1	0
↳	`(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))`	overflow	1
↳	`(-.f64 (*.f64 x x) #s(literal 1 binary64))`	overflow	141
↳	`(*.f64 x x)`	overflow	141

Confusion

	Predicted +	Predicted -
+	141	0
-	0	115

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	141	0	0
-	0	0	115

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	115
1	140
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

67.0ms

512×

valid

Compiler

Compiled 80 to 25 computations (68.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 55.0ms

ival-mult: 39.0ms (70.8% of total)

ival-log: 6.0ms (10.9% of total)

ival-sqrt: 4.0ms (7.3% of total)

ival-sub: 3.0ms (5.4% of total)

ival-add: 2.0ms (3.6% of total)

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

exact: 0.0ms (0% of total)

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

preprocess638.0ms (5.9%)

Memory

20.9MiB live, 424.0MiB 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	9	21
1	27	19
2	59	19
3	130	19
4	295	19
5	579	19
6	1088	19
7	1677	19
8	3021	19
9	4118	19
10	5059	19
11	5487	19
12	5727	19
13	5799	19
14	5883	19
15	6475	19
16	7565	19
17	7621	19
18	7719	19
19	7753	19
20	7769	19
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×	node limit

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

Compiler

Compiled 10 to 7 computations (30% saved)

eval19.0ms (0.2%)

Memory: -36.7MiB live, 0.5MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	46.6%	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))

Compiler

Compiled 10 to 7 computations (30% saved)

simplify1.0s (9.6%)

Memory

-334.8MiB live, 561.3MiB 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 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))
(+.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
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)

localize28.0ms (0.3%)

Memory

2.4MiB live, 44.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(-.f64 (*.f64 x x) #s(literal 1 binary64))
accuracy	0.0078125	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))
accuracy	0.2460418533012511	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
accuracy	32.78990350777288	(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))

Samples

16.0ms

256×

valid

Compiler

Compiled 35 to 9 computations (74.3% saved)

Precisions

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

ival-log: 3.0ms (30.9% of total)

ival-mult: 2.0ms (20.6% of total)

ival-sqrt: 2.0ms (20.6% of total)

ival-sub: 1.0ms (10.3% of total)

ival-add: 1.0ms (10.3% 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

13.5MiB live, 13.5MiB allocated

Counts

4 → 48

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>) () ())

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 (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 (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 (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 (+ (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 (+ (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 (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 (* 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 (/ 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 (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 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 (* -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>) () ())) ())

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(log (+ x (sqrt (- (* x x) 1))))
1.0ms	x	@	-inf	(log (+ x (sqrt (- (* x x) 1))))
1.0ms	x	@	inf	(log (+ x (sqrt (- (* x x) 1))))
0.0ms	x	@	inf	(- (* x x) 1)
0.0ms	x	@	-inf	(- (* x x) 1)

simplify266.0ms (2.5%)

Memory

3.4MiB live, 412.3MiB 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	559
1	411	533
2	1143	526
3	3327	488
4	7966	488
0	8526	459

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 47

Calls

Call 1

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

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

rewrite326.0ms (3%)

Memory

-25.6MiB live, 450.1MiB 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	28
0	12	28
1	49	28
2	322	28
3	3626	28
0	8646	24

Stop Event

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

Counts

4 → 320

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)))

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

eval68.0ms (0.6%)

Memory: 32.4MiB live, 69.9MiB allocated
Compiler: Compiled 10 641 to 1 532 computations (85.6% saved)

prune120.0ms (1.1%)

Memory

-2.4MiB live, 85.6MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	362	5	367
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	363	5	368

Accuracy

100.0%

Counts

368 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	24.1%	(+.f64 (log.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))) (.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64))) (-.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))))))) (log.f64 (-.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (*.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))))))
▶	46.6%	(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))
▶	99.0%	(log.f64 (+.f64 x #s(approx (sqrt (- (* x x) 1)) (+.f64 x (/.f64 #s(literal -1/2 binary64) x)))))
▶	98.7%	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 x #s(literal 2 binary64))))
▶	98.7%	#s(approx (log (+ x (sqrt (- (* x x) 1)))) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x)))

Compiler

Compiled 192 to 76 computations (60.4% saved)

simplify568.0ms (5.2%)

Memory

4.1MiB live, 238.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	64	(log.f64 (-.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))))))
cost-diff	128	(+.f64 #s(literal -1 binary64) (*.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))))
cost-diff	192	(fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64)))
cost-diff	704	(-.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))))
cost-diff	0	(log.f64 x)
cost-diff	0	(log.f64 #s(literal 2 binary64))
cost-diff	0	(+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
cost-diff	0	#s(approx (log (+ x (sqrt (- (* x x) 1)))) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 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	#s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 x #s(literal 2 binary64)))
cost-diff	0	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 x #s(literal 2 binary64))))
cost-diff	128	(*.f64 x #s(literal 2 binary64))
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)))))

Rules

16 130×	`lower-fma.f32`
16 124×	`lower-fma.f64`
3 458×	`lower-*.f32`
3 448×	`lower-*.f64`
2 864×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	426
0	66	416
1	101	416
2	171	402
3	494	374
4	2580	374
5	5549	374
0	8166	355

Stop Event

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

Calls

Call 1

Inputs
(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 #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 x #s(literal 2 binary64))
x
#s(literal 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)
#s(approx (log (+ x (sqrt (- (* x x) 1)))) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x)))
(+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(log.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(log.f64 x)
x
(+.f64 (log.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))) (.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64))) (-.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))))))) (log.f64 (-.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (*.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))))))
(log.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))) (.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64))) (-.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (*.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))))))))
(/.f64 (fma.f64 x (.f64 x x) (.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))) (.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64))) (-.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (*.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))))))
(fma.f64 x (.f64 x x) (.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))
x
(*.f64 x x)
(*.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
(fma.f64 x x #s(literal -1 binary64))
#s(literal -1 binary64)
(sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))
(.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64))) (-.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (*.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))))))
(fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64)))
(-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
(-.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))))
(+.f64 #s(literal -1 binary64) (*.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))))
(*.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))
(log.f64 (-.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 x (sqrt.f64 (fma.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)))))
(+.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 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 x #s(literal 2 binary64))))
(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x)))
#s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 x #s(literal 2 binary64)))
#s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x))
(*.f64 x #s(literal 2 binary64))
(+.f64 x x)
x
#s(literal 2 binary64)
(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))
(+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x)
(+.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
(sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))
(fma.f64 x x #s(literal -1 binary64))
x
#s(literal -1 binary64)
#s(approx (log (+ x (sqrt (- (* x x) 1)))) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x)))
(+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(log.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(log.f64 x)
x
(+.f64 (log.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))) (.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64))) (-.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))))))) (log.f64 (-.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (*.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))))))
(+.f64 (log.f64 (/.f64 (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (.f64 x (.f64 x x))) (.f64 (fma.f64 x (-.f64 (+.f64 x x) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) #s(literal -1 binary64)) (fma.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) #s(literal 1 binary64))))) (log1p.f64 (.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))))
(log.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))) (.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64))) (-.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (*.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))))))))
(log.f64 (/.f64 (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (.f64 x (.f64 x x))) (*.f64 (fma.f64 x (-.f64 (+.f64 x x) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) #s(literal -1 binary64)) (fma.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) #s(literal 1 binary64)))))
(/.f64 (fma.f64 x (.f64 x x) (.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))) (.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64))) (-.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (*.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))))))
(/.f64 (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (.f64 x (.f64 x x))) (*.f64 (fma.f64 x (-.f64 (+.f64 x x) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) #s(literal -1 binary64)) (fma.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) #s(literal 1 binary64))))
(fma.f64 x (.f64 x x) (.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))
(fma.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (.f64 x (.f64 x x)))
x
(*.f64 x x)
(*.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
(fma.f64 x x #s(literal -1 binary64))
#s(literal -1 binary64)
(sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))
(.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64))) (-.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (*.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))))))
(*.f64 (fma.f64 x (-.f64 (+.f64 x x) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) #s(literal -1 binary64)) (fma.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) #s(literal 1 binary64)))
(fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64)))
(fma.f64 x (-.f64 (+.f64 x x) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) #s(literal -1 binary64))
(-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
(-.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))))
(fma.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) #s(literal 1 binary64))
(+.f64 #s(literal -1 binary64) (*.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))))
(fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) #s(literal -1 binary64))
(*.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))
(log.f64 (-.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))))))
(log1p.f64 (*.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))

localize293.0ms (2.7%)

Memory

-30.2MiB live, 170.9MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	32.78990350777286	(sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))
accuracy	34.14066231884289	(log.f64 (-.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))))))
accuracy	47.529212169496645	(/.f64 (fma.f64 x (.f64 x x) (.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))) (.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64))) (-.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (*.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))))))
accuracy	59.38229263217467	(-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
accuracy	0	(log.f64 x)
accuracy	0	(log.f64 #s(literal 2 binary64))
accuracy	0.21484375	(+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
accuracy	0.5988465209460974	#s(approx (log (+ x (sqrt (- (* x x) 1)))) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x)))
accuracy	0	(fma.f64 x x #s(literal -1 binary64))
accuracy	0.0078125	(+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x)
accuracy	0.2460418533012511	(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))
accuracy	32.78990350777286	(sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))
accuracy	0	(*.f64 x #s(literal 2 binary64))
accuracy	0.2460418533012511	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 x #s(literal 2 binary64))))
accuracy	0.6671186042790875	#s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 x #s(literal 2 binary64)))
accuracy	0	(+.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	0.2460418533012511	(log.f64 (+.f64 x #s(approx (sqrt (- (* x x) 1)) (+.f64 x (/.f64 #s(literal -1/2 binary64) x)))))
accuracy	0.4208919529851219	#s(approx (sqrt (- (* x x) 1)) (+.f64 x (/.f64 #s(literal -1/2 binary64) x)))

Samples

162.0ms	248×	1	valid
2.0ms	8×	0	valid

Compiler

Compiled 441 to 35 computations (92.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 137.0ms

ival-log: 48.0ms (35.2% of total)

ival-add: 26.0ms (19% of total)

ival-sqrt: 20.0ms (14.7% of total)

adjust: 19.0ms (13.9% of total)

ival-mult: 12.0ms (8.8% of total)

ival-sub: 6.0ms (4.4% of total)

ival-div: 5.0ms (3.7% of total)

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

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

exact: 0.0ms (0% of total)

series144.0ms (1.3%)

Memory

18.3MiB live, 90.4MiB allocated

Counts

21 → 240

Calls

Call 1

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

Outputs
#s(alt (log (sqrt -1)) (taylor 0 x) (#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 (+ (log (sqrt -1)) (/ x (sqrt -1))) (taylor 0 x) (#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 (+ (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 #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 (+ (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 #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 (+ (log 2) (* -1 (log (/ 1 x)))) (taylor inf x) (#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 (- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2)))) (taylor inf x) (#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 (+ (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 #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 (- (+ (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 #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 (+ (log -1/2) (log (/ -1 x))) (taylor -inf x) (#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 (+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2))))) (taylor -inf x) (#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 (+ (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 #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 (+ (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 #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 (sqrt -1) (taylor 0 x) (#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 (+ x (sqrt -1)) (taylor 0 x) (#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 (+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1)))))) (taylor 0 x) (#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 (+ (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 #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 (* 2 x) (taylor inf x) (#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 (* x (- 2 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#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 (* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))) (taylor inf x) (#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 (* 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 #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 (/ 1/2 x) (taylor -inf x) (#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 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x) (taylor -inf x) (#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 (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x)) (taylor -inf x) (#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 (* -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 #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 (sqrt -1) (taylor 0 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 (+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1)))) (taylor 0 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 (+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1)))))) (taylor 0 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 (+ (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 #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 #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 (- 1 (* 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 (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (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 (- (+ 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 (* -1 x) (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 (* -1 (* x (- 1 (* 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 (* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (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 (* -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 (/ -1/2 x) (taylor 0 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 (/ (- (pow x 2) 1/2) x) (taylor 0 x) (#s(alt (+.f64 x (/.f64 #s(literal -1/2 binary64) x)) (patch (+.f64 x (/.f64 #s(literal -1/2 binary64) x)) #<representation binary64>) () ())) ())
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#s(alt (/ (- 2 (* 3/2 (/ 1 (pow x 2)))) x) (taylor inf x) (#s(alt (/.f64 (fma.f64 x (.f64 x x) (.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))) (.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64))) (-.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))))))) (patch (/.f64 (fma.f64 x (.f64 x x) (.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))) (.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64))) (-.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))))))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 2 (/ 7/8 (pow x 4))) (* 3/2 (/ 1 (pow x 2)))) x) (taylor inf x) (#s(alt (/.f64 (fma.f64 x (.f64 x x) (.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))) (.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64))) (-.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))))))) (patch (/.f64 (fma.f64 x (.f64 x x) (.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))) (.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64))) (-.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))))))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 2 (/ 7/8 (pow x 4))) (+ (* 3/2 (/ 1 (pow x 2))) (* 9/16 (/ 1 (pow x 6))))) x) (taylor inf x) (#s(alt (/.f64 (fma.f64 x (.f64 x x) (.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))) (.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64))) (-.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))))))) (patch (/.f64 (fma.f64 x (.f64 x x) (.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))) (.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64))) (-.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))))))) #<representation binary64>) () ())) ())
#s(alt (/ -1/2 (pow x 3)) (taylor -inf x) (#s(alt (/.f64 (fma.f64 x (.f64 x x) (.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))) (.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64))) (-.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))))))) (patch (/.f64 (fma.f64 x (.f64 x x) (.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))) (.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64))) (-.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ 1/2 (* 7/8 (/ 1 (pow x 2)))) (pow x 3))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 x (.f64 x x) (.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))) (.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64))) (-.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))))))) (patch (/.f64 (fma.f64 x (.f64 x x) (.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))) (.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64))) (-.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ 1/2 (+ (* 7/8 (/ 1 (pow x 2))) (/ 23/16 (pow x 4)))) (pow x 3))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 x (.f64 x x) (.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))) (.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64))) (-.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))))))) (patch (/.f64 (fma.f64 x (.f64 x x) (.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))) (.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64))) (-.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ 1/2 (+ (* 7/8 (/ 1 (pow x 2))) (+ (* 299/128 (/ 1 (pow x 6))) (/ 23/16 (pow x 4))))) (pow x 3))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 x (.f64 x x) (.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))) (.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64))) (-.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))))))) (patch (/.f64 (fma.f64 x (.f64 x x) (.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))) (.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64))) (-.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))))))) #<representation binary64>) () ())) ())

Calls

60 calls:

Time	Variable		Point	Expression
79.0ms	x	@	0	(+ (log 2) (log x))
30.0ms	x	@	0	(log (- (* x x) (+ -1 (* x (- x (sqrt (+ (* x x) -1)))))))
12.0ms	x	@	-inf	(+ (log 2) (log x))
6.0ms	x	@	inf	(+ (log 2) (log x))
1.0ms	x	@	0	(/ (+ (* x (* x x)) (* (+ (* x x) -1) (sqrt (+ (* x x) -1)))) (* (+ (* x (- x (sqrt (+ (* x x) -1)))) (+ (* x x) -1)) (- (* x x) (+ -1 (* x (- x (sqrt (+ (* x x) -1))))))))

simplify481.0ms (4.4%)

Memory

11.4MiB live, 321.9MiB allocated

Algorithm

1×	egg-herbie

Rules

11 740×	`lower-fma.f64`
11 740×	`lower-fma.f32`
5 914×	`lower-+.f64`
5 914×	`lower-+.f32`
3 870×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	390	2921
1	1137	2708
2	3508	2603
0	8538	2494

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 236

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)))))
(+ (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))))
(+ (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)))))))
(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)
(* 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)))))
(/ 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))
(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))))))
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)))))
(* -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))))))
(/ -1/2 x)
(/ (- (pow x 2) 1/2) x)
(/ (- (pow x 2) 1/2) x)
(/ (- (pow x 2) 1/2) x)
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)))))
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)))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 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)))))
(+ (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))))
(+ (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)))))))
(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)
(* 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)))))
(/ 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 (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)))))
(+ (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))))
(+ (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)))))))
(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)
(* 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)))))
(/ 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))
(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))))))
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)))))
(* -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))))))
-1
(- (pow x 2) 1)
(- (pow x 2) 1)
(- (pow x 2) 1)
(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))))
(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 (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)))))
(+ (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))))
(+ (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)))))))
(+ (log 2) (log x))
(+ (log 2) (log x))
(+ (log 2) (log x))
(+ (log 2) (log x))
(+ (log 2) (* -1 (log (/ 1 x))))
(+ (log 2) (* -1 (log (/ 1 x))))
(+ (log 2) (* -1 (log (/ 1 x))))
(+ (log 2) (* -1 (log (/ 1 x))))
(+ (log -1) (+ (log 2) (* -1 (log (/ -1 x)))))
(+ (log -1) (+ (log 2) (* -1 (log (/ -1 x)))))
(+ (log -1) (+ (log 2) (* -1 (log (/ -1 x)))))
(+ (log -1) (+ (log 2) (* -1 (log (/ -1 x)))))
(log x)
(log x)
(log x)
(log x)
(* -1 (log (/ 1 x)))
(* -1 (log (/ 1 x)))
(* -1 (log (/ 1 x)))
(* -1 (log (/ 1 x)))
(+ (log -1) (* -1 (log (/ -1 x))))
(+ (log -1) (* -1 (log (/ -1 x))))
(+ (log -1) (* -1 (log (/ -1 x))))
(+ (log -1) (* -1 (log (/ -1 x))))
1
(+ 1 (* x (sqrt -1)))
(+ 1 (* x (- (* 1/2 (/ (pow x 2) (sqrt -1))) (* -1 (sqrt -1)))))
(+ 1 (* x (- (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))) (* -1 (sqrt -1)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(* (pow x 2) (+ 1 (+ (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(* -1 (pow x 2))
(* (pow x 2) (- (* 3/2 (/ 1 (pow x 2))) 1))
(* (pow x 2) (- (+ (/ 1/8 (pow x 4)) (* 3/2 (/ 1 (pow x 2)))) 1))
(* (pow x 2) (- (+ (/ 1/8 (pow x 4)) (+ (* 3/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) 1))
-1
(- (* -1 (* x (sqrt -1))) 1)
(- (* x (+ (* -1 (sqrt -1)) (* 2 x))) 1)
(- (* x (+ (* -1 (sqrt -1)) (* x (+ 2 (* -1/2 (/ x (sqrt -1))))))) 1)
(pow x 2)
(* (pow x 2) (- 1 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- (+ 1 (/ 1/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- (+ 1 (+ (/ 1/8 (pow x 4)) (* 1/16 (/ 1 (pow x 6))))) (* 1/2 (/ 1 (pow x 2)))))
(* 3 (pow x 2))
(* (pow x 2) (- 3 (* 3/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 3 (* -1 (/ (+ 3/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* (pow x 2) (- (+ 3 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 3/2 (/ 1 (pow x 2)))))
-1
(- (* -1 (* x (sqrt -1))) 1)
(- (* x (+ x (* -1 (sqrt -1)))) 1)
(- (* x (+ (* -1 (sqrt -1)) (* x (+ 1 (* -1/2 (/ x (sqrt -1))))))) 1)
-1/2
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(- (+ (/ 1/16 (pow x 4)) (* 1/8 (/ 1 (pow x 2)))) 1/2)
(- (+ (/ 1/16 (pow x 4)) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) 1/2)
(* 2 (pow x 2))
(* (pow x 2) (- 2 (* 3/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 2 (* -1 (/ (+ 3/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* (pow x 2) (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 3/2 (/ 1 (pow x 2)))))
(* x (sqrt -1))
(* x (+ (sqrt -1) (* -1/2 (* x (pow (sqrt -1) 2)))))
(* x (+ (sqrt -1) (* x (+ (* -1/2 (pow (sqrt -1) 2)) (* 1/6 (* x (+ (* 2 (pow (sqrt -1) 3)) (* 3 (/ 1 (sqrt -1))))))))))
(* x (+ (sqrt -1) (* x (+ (* -1/2 (pow (sqrt -1) 2)) (* x (+ (* 1/24 (* x (- (* -6 (pow (sqrt -1) 4)) 12))) (* 1/6 (+ (* 2 (pow (sqrt -1) 3)) (* 3 (/ 1 (sqrt -1)))))))))))
(* -2 (log (/ 1 x)))
(+ (* -2 (log (/ 1 x))) (* 1/2 (/ 1 (pow x 2))))
(- (+ (* -2 (log (/ 1 x))) (* 1/2 (/ 1 (pow x 2)))) (/ 1/4 (pow x 4)))
(- (+ (* -2 (log (/ 1 x))) (+ (* 1/2 (/ 1 (pow x 2))) (* 1/24 (/ 1 (pow x 6))))) (/ 1/4 (pow x 4)))
(+ (log -1) (* -2 (log (/ -1 x))))
(- (+ (log -1) (* -2 (log (/ -1 x)))) (* 3/2 (/ 1 (pow x 2))))
(+ (log -1) (+ (* -2 (log (/ -1 x))) (* -1 (/ (+ 3/2 (* 5/4 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log -1) (+ (* -2 (log (/ -1 x))) (* -1 (/ (+ 5/4 (* 11/8 (/ 1 (pow x 2)))) (pow x 4))))) (* 3/2 (/ 1 (pow x 2))))
(* -1 (sqrt -1))
(- x (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))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(/ (+ 1/2 (+ (/ 1/16 (pow x 4)) (* 1/8 (/ 1 (pow x 2))))) x)
(/ (+ 1/2 (+ (/ 1/16 (pow x 4)) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6)))))) x)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 2)))
(* -1 (* x (- (+ (/ 1/8 (pow x 4)) (* 1/2 (/ 1 (pow x 2)))) 2)))
(* -1 (* x (- (+ (/ 1/8 (pow x 4)) (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) 2)))
(* -1 (sqrt -1))
(+ (* -1 (sqrt -1)) (* 2 (* x (pow (sqrt -1) 2))))
(+ (* -1 (sqrt -1)) (* x (- (* -1 (* x (+ (* 3/2 (/ 1 (sqrt -1))) (+ (* 4 (pow (sqrt -1) 3)) (* (sqrt -1) (+ 2 (* -1 (pow (sqrt -1) 2)))))))) (* -2 (pow (sqrt -1) 2)))))
(+ (* -1 (sqrt -1)) (* x (- (* x (- (* -1 (* x (+ 1 (+ (* -2 (* (sqrt -1) (+ (* 3/2 (/ 1 (sqrt -1))) (+ (* 4 (pow (sqrt -1) 3)) (* (sqrt -1) (+ 2 (* -1 (pow (sqrt -1) 2)))))))) (+ (* -2 (* (pow (sqrt -1) 2) (+ 2 (* -1 (pow (sqrt -1) 2))))) (* (sqrt -1) (- (* 2 (sqrt -1)) (/ 1 (sqrt -1))))))))) (+ (* 3/2 (/ 1 (sqrt -1))) (+ (* 4 (pow (sqrt -1) 3)) (* (sqrt -1) (+ 2 (* -1 (pow (sqrt -1) 2)))))))) (* -2 (pow (sqrt -1) 2)))))
(/ 2 x)
(/ (- 2 (* 3/2 (/ 1 (pow x 2)))) x)
(/ (- (+ 2 (/ 7/8 (pow x 4))) (* 3/2 (/ 1 (pow x 2)))) x)
(/ (- (+ 2 (/ 7/8 (pow x 4))) (+ (* 3/2 (/ 1 (pow x 2))) (* 9/16 (/ 1 (pow x 6))))) x)
(/ -1/2 (pow x 3))
(* -1 (/ (+ 1/2 (* 7/8 (/ 1 (pow x 2)))) (pow x 3)))
(* -1 (/ (+ 1/2 (+ (* 7/8 (/ 1 (pow x 2))) (/ 23/16 (pow x 4)))) (pow x 3)))
(* -1 (/ (+ 1/2 (+ (* 7/8 (/ 1 (pow x 2))) (+ (* 299/128 (/ 1 (pow x 6))) (/ 23/16 (pow x 4))))) (pow x 3)))

Outputs
(log (sqrt -1))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f64 (log.f64 (sqrt.f64 #s(literal -1 binary64))) (/.f64 x (sqrt.f64 #s(literal -1 binary64))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f64 x (fma.f64 #s(literal 1/6 binary64) (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (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 x (fma.f64 x (.f64 x (fma.f64 #s(literal 3/40 binary64) (/.f64 (.f64 x 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 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+.f64 (log.f64 x) (+.f64 (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 #s(literal 2 binary64)) (log.f64 x)) (/.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 3/32 binary64) (.f64 x x))) (.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)) (log.f64 x)) (-.f64 (/.f64 (+.f64 #s(literal 3/32 binary64) (/.f64 #s(literal 5/96 binary64) (.f64 x x))) (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))))
(+ (log -1/2) (log (/ -1 x)))
(+.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (+.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (+.f64 (log.f64 #s(literal -1/2 binary64)) (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 3/32 binary64) (.f64 (.f64 x x) (.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 #s(literal 1/4 binary64) (.f64 x x)) (+.f64 (+.f64 (/.f64 #s(literal 3/32 binary64) (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal 5/96 binary64) (pow.f64 x #s(literal 6 binary64)))) (+.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))))
(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 x (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) (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 x (fma.f64 x (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(fma.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) x) (.f64 x #s(literal 2 binary64)))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (-.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x x))) (.f64 (.f64 x x) (.f64 x x)))))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x x))) (.f64 x x))) (neg.f64 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 x x) (.f64 x x))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))) x)
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(fma.f64 x (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (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 x x) (fma.f64 #s(literal 1/8 binary64) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 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 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1 binary64)))
x
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 x (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) x)
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(fma.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x) x)
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 x (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x x))) (neg.f64 (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))
(neg.f64 (fma.f64 x (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) x))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))
(neg.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x) x))
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))
(neg.f64 (fma.f64 x (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x x))) (neg.f64 (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x))
(/ -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))
x
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 x (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) x)
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 x (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) x)
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 x (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) x)
x
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 1)))
(fma.f64 x (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) x)
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 1)))
(fma.f64 x (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) x)
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 1)))
(fma.f64 x (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) x)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(log (sqrt -1))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f64 (log.f64 (sqrt.f64 #s(literal -1 binary64))) (/.f64 x (sqrt.f64 #s(literal -1 binary64))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f64 x (fma.f64 #s(literal 1/6 binary64) (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (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 x (fma.f64 x (.f64 x (fma.f64 #s(literal 3/40 binary64) (/.f64 (.f64 x 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 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+.f64 (log.f64 x) (+.f64 (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 #s(literal 2 binary64)) (log.f64 x)) (/.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 3/32 binary64) (.f64 x x))) (.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)) (log.f64 x)) (-.f64 (/.f64 (+.f64 #s(literal 3/32 binary64) (/.f64 #s(literal 5/96 binary64) (.f64 x x))) (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))))
(+ (log -1/2) (log (/ -1 x)))
(+.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (+.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (+.f64 (log.f64 #s(literal -1/2 binary64)) (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 3/32 binary64) (.f64 (.f64 x x) (.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 #s(literal 1/4 binary64) (.f64 x x)) (+.f64 (+.f64 (/.f64 #s(literal 3/32 binary64) (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal 5/96 binary64) (pow.f64 x #s(literal 6 binary64)))) (+.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))))
(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 x (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) (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 x (fma.f64 x (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(fma.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) x) (.f64 x #s(literal 2 binary64)))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (-.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x x))) (.f64 (.f64 x x) (.f64 x x)))))
(/ 1/2 x)
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(fma.f64 x (.f64 x #s(literal 3 binary64)) (.f64 x (/.f64 (+.f64 #s(literal -3/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x x))) x)))
(* (pow x 2) (- (+ 3 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 3/2 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (-.f64 #s(literal 3 binary64) (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x x))) (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal -3/2 binary64) (*.f64 x x))))))
-1
#s(literal -1 binary64)
(- (* -1 (* x (sqrt -1))) 1)
(-.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))
(- (* x (+ x (* -1 (sqrt -1)))) 1)
(fma.f64 x (-.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal -1 binary64))
(- (* x (+ (* -1 (sqrt -1)) (* x (+ 1 (* -1/2 (/ x (sqrt -1))))))) 1)
(fma.f64 x (-.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (*.f64 x #s(literal -1/2 binary64)) x) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1 binary64))
-1/2
#s(literal -1/2 binary64)
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(- (+ (/ 1/16 (pow x 4)) (* 1/8 (/ 1 (pow x 2)))) 1/2)
(+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) (/.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (.f64 x x))))
(- (+ (/ 1/16 (pow x 4)) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) 1/2)
(+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x)))))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* (pow x 2) (- 2 (* 3/2 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -3/2 binary64) (*.f64 x x))))
(* (pow x 2) (+ 2 (* -1 (/ (+ 3/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(fma.f64 x (.f64 x #s(literal 2 binary64)) (.f64 x (/.f64 (+.f64 #s(literal -3/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x x))) x)))
(* (pow x 2) (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 3/2 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 2 binary64) (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x x))) (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal -3/2 binary64) (*.f64 x x)))))
(* x (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(* x (+ (sqrt -1) (* -1/2 (* x (pow (sqrt -1) 2)))))
(*.f64 x (fma.f64 x #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* x (+ (sqrt -1) (* x (+ (* -1/2 (pow (sqrt -1) 2)) (* 1/6 (* x (+ (* 2 (pow (sqrt -1) 3)) (* 3 (/ 1 (sqrt -1))))))))))
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/3 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(* x (+ (sqrt -1) (* x (+ (* -1/2 (pow (sqrt -1) 2)) (* x (+ (* 1/24 (* x (- (* -6 (pow (sqrt -1) 4)) 12))) (* 1/6 (+ (* 2 (pow (sqrt -1) 3)) (* 3 (/ 1 (sqrt -1)))))))))))
(.f64 x (fma.f64 x (fma.f64 x (fma.f64 (fma.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) #s(literal -6 binary64) #s(literal -12 binary64)) (.f64 x #s(literal 1/24 binary64)) (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/3 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(* -2 (log (/ 1 x)))
(*.f64 #s(literal 2 binary64) (log.f64 x))
(+ (* -2 (log (/ 1 x))) (* 1/2 (/ 1 (pow x 2))))
(fma.f64 #s(literal 2 binary64) (log.f64 x) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(- (+ (* -2 (log (/ 1 x))) (* 1/2 (/ 1 (pow x 2)))) (/ 1/4 (pow x 4)))
(+.f64 (fma.f64 #s(literal 2 binary64) (log.f64 x) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (/.f64 #s(literal -1/4 binary64) (.f64 (.f64 x x) (.f64 x x))))
(- (+ (* -2 (log (/ 1 x))) (+ (* 1/2 (/ 1 (pow x 2))) (* 1/24 (/ 1 (pow x 6))))) (/ 1/4 (pow x 4)))
(+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (fma.f64 #s(literal 2 binary64) (log.f64 x) (+.f64 (/.f64 #s(literal 1/24 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1/4 binary64) (.f64 (.f64 x x) (.f64 x x))))))
(+ (log -1) (* -2 (log (/ -1 x))))
(fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) #s(literal -2 binary64) (log.f64 #s(literal -1 binary64)))
(- (+ (log -1) (* -2 (log (/ -1 x)))) (* 3/2 (/ 1 (pow x 2))))
(+.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) #s(literal -2 binary64) (log.f64 #s(literal -1 binary64))) (/.f64 #s(literal -3/2 binary64) (*.f64 x x)))
(+ (log -1) (+ (* -2 (log (/ -1 x))) (* -1 (/ (+ 3/2 (* 5/4 (/ 1 (pow x 2)))) (pow x 2)))))
(-.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) #s(literal -2 binary64) (log.f64 #s(literal -1 binary64))) (/.f64 (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 5/4 binary64) (.f64 x x))) (.f64 x x)))
(- (+ (log -1) (+ (* -2 (log (/ -1 x))) (* -1 (/ (+ 5/4 (* 11/8 (/ 1 (pow x 2)))) (pow x 4))))) (* 3/2 (/ 1 (pow x 2))))
(+.f64 (-.f64 (fma.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) #s(literal -2 binary64) (log.f64 #s(literal -1 binary64))) (/.f64 (+.f64 #s(literal 5/4 binary64) (/.f64 #s(literal 11/8 binary64) (.f64 x x))) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal -3/2 binary64) (*.f64 x x)))
(* -1 (sqrt -1))
(neg.f64 (sqrt.f64 #s(literal -1 binary64)))
(- x (sqrt -1))
(-.f64 x (sqrt.f64 #s(literal -1 binary64)))
(- (* x (+ 1 (* -1/2 (/ x (sqrt -1))))) (sqrt -1))
(-.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (*.f64 x #s(literal -1/2 binary64)) x) (sqrt.f64 #s(literal -1 binary64)))
(- (* x (+ 1 (* x (- (* 1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))) (sqrt -1))
(fma.f64 (.f64 x x) (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (-.f64 x (sqrt.f64 #s(literal -1 binary64))))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)
(/ (+ 1/2 (+ (/ 1/16 (pow x 4)) (* 1/8 (/ 1 (pow x 2))))) x)
(/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) (/.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (.f64 x x)))) x)
(/ (+ 1/2 (+ (/ 1/16 (pow x 4)) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6)))))) x)
(/.f64 (+.f64 (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) (/.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (.f64 x x))))) x)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 2)))
(.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
(* -1 (* x (- (+ (/ 1/8 (pow x 4)) (* 1/2 (/ 1 (pow x 2)))) 2)))
(.f64 x (+.f64 (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))
(* -1 (* x (- (+ (/ 1/8 (pow x 4)) (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) 2)))
(.f64 (neg.f64 x) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (*.f64 x x))) #s(literal -2 binary64)))))
(* -1 (sqrt -1))
(neg.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (sqrt -1)) (* 2 (* x (pow (sqrt -1) 2))))
(-.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (sqrt -1)) (* x (- (* -1 (* x (+ (* 3/2 (/ 1 (sqrt -1))) (+ (* 4 (pow (sqrt -1) 3)) (* (sqrt -1) (+ 2 (* -1 (pow (sqrt -1) 2)))))))) (* -2 (pow (sqrt -1) 2)))))
(fma.f64 x (fma.f64 x (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal -3/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -2 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (* -1 (sqrt -1)) (* x (- (* x (- (* -1 (* x (+ 1 (+ (* -2 (* (sqrt -1) (+ (* 3/2 (/ 1 (sqrt -1))) (+ (* 4 (pow (sqrt -1) 3)) (* (sqrt -1) (+ 2 (* -1 (pow (sqrt -1) 2)))))))) (+ (* -2 (* (pow (sqrt -1) 2) (+ 2 (* -1 (pow (sqrt -1) 2))))) (* (sqrt -1) (- (* 2 (sqrt -1)) (/ 1 (sqrt -1))))))))) (+ (* 3/2 (/ 1 (sqrt -1))) (+ (* 4 (pow (sqrt -1) 3)) (* (sqrt -1) (+ 2 (* -1 (pow (sqrt -1) 2)))))))) (* -2 (pow (sqrt -1) 2)))))
(fma.f64 x (fma.f64 x (+.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal -3/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x)) #s(literal -2 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (- 2 (* 3/2 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -3/2 binary64) (*.f64 x x))) x)
(/ (- (+ 2 (/ 7/8 (pow x 4))) (* 3/2 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 #s(literal 7/8 binary64) (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal -3/2 binary64) (.f64 x x)))) x)
(/ (- (+ 2 (/ 7/8 (pow x 4))) (+ (* 3/2 (/ 1 (pow x 2))) (* 9/16 (/ 1 (pow x 6))))) x)
(/.f64 (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 7/8 binary64) (.f64 (.f64 x x) (.f64 x x)))) (+.f64 (/.f64 #s(literal -3/2 binary64) (.f64 x x)) (/.f64 #s(literal -9/16 binary64) (pow.f64 x #s(literal 6 binary64))))) x)
(/ -1/2 (pow x 3))
(/.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x x)))
(* -1 (/ (+ 1/2 (* 7/8 (/ 1 (pow x 2)))) (pow x 3)))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 7/8 binary64) (.f64 x x))) (.f64 x (*.f64 x (neg.f64 x))))
(* -1 (/ (+ 1/2 (+ (* 7/8 (/ 1 (pow x 2))) (/ 23/16 (pow x 4)))) (pow x 3)))
(/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 7/8 binary64) (.f64 x x)) (/.f64 #s(literal 23/16 binary64) (.f64 (.f64 x x) (.f64 x x))))) (.f64 x (.f64 x (neg.f64 x))))
(* -1 (/ (+ 1/2 (+ (* 7/8 (/ 1 (pow x 2))) (+ (* 299/128 (/ 1 (pow x 6))) (/ 23/16 (pow x 4))))) (pow x 3)))
(/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 7/8 binary64) (.f64 x x)) (+.f64 (/.f64 #s(literal 23/16 binary64) (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal 299/128 binary64) (pow.f64 x #s(literal 6 binary64)))))) (.f64 x (.f64 x (neg.f64 x))))

rewrite471.0ms (4.3%)

Memory

4.3MiB live, 412.2MiB allocated

Rules

5 064×	`lower-/.f32`
5 060×	`lower-/.f64`
3 718×	`lower-*.f32`
3 708×	`lower-*.f64`
3 468×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	229
0	62	220
1	243	199
2	1985	199
0	8218	194

Stop Event

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

Counts

21 → 804

Calls

Call 1

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

eval347.0ms (3.2%)

Memory: 31.9MiB live, 596.3MiB allocated
Compiler: Compiled 149 793 to 8 981 computations (94% saved)

prune335.0ms (3.1%)

Memory

-10.0MiB live, 512.0MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	2 041	2	2 043
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	2 042	6	2 048

Accuracy

100.0%

Counts

2 048 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	32.0%	(neg.f64 (log.f64 (/.f64 (fma.f64 x (+.f64 (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) x) #s(literal -1 binary64)) (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (.f64 x (.f64 x x))))))
✓	46.6%	(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))
✓	99.0%	(log.f64 (+.f64 x #s(approx (sqrt (- (* x x) 1)) (+.f64 x (/.f64 #s(literal -1/2 binary64) x)))))
▶	31.4%	(log.f64 (+.f64 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f64 #s(literal -1/2 binary64) x)))))
✓	98.7%	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 x #s(literal 2 binary64))))
✓	98.7%	#s(approx (log (+ x (sqrt (- (* x x) 1)))) (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x)))

Compiler

Compiled 72 to 39 computations (45.8% saved)

simplify187.0ms (1.7%)

Memory

11.9MiB live, 249.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Rules

11 446×	`lower-fma.f32`
11 440×	`lower-fma.f64`
2 406×	`lower--.f32`
2 404×	`lower--.f64`
2 258×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	216
0	41	203
1	69	203
2	108	203
3	217	203
4	568	203
5	1548	203
6	4544	203
0	8239	203

Stop Event

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

Calls

Call 1

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

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

localize137.0ms (1.3%)

Memory

17.6MiB live, 204.8MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.06640625	(.f64 x (.f64 x x))
accuracy	32.78990350777288	(sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))
accuracy	42.80117668893845	(/.f64 (fma.f64 x (+.f64 (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) x) #s(literal -1 binary64)) (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (.f64 x (.f64 x x))))
accuracy	59.38229263217467	(-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
accuracy	0.0078125	(+.f64 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f64 #s(literal -1/2 binary64) x))))
accuracy	0.2460418533012511	(log.f64 (+.f64 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f64 #s(literal -1/2 binary64) x)))))
accuracy	0.4208919529851219	#s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f64 #s(literal -1/2 binary64) x)))
accuracy	62.99781557904869	#s(approx (+ x (/ -1/2 x)) (/.f64 #s(literal -1/2 binary64) x))

Samples

61.0ms	127×	2	valid
48.0ms	122×	1	valid
1.0ms	7×	0	valid

Compiler

Compiled 208 to 25 computations (88% saved)

Precisions

Click to see histograms. Total time spent on operations: 88.0ms

ival-add: 20.0ms (22.8% of total)

adjust: 18.0ms (20.6% of total)

ival-log: 13.0ms (14.8% of total)

ival-div: 12.0ms (13.7% of total)

ival-mult: 10.0ms (11.4% of total)

ival-sqrt: 7.0ms (8% of total)

ival-sub: 4.0ms (4.6% of total)

ival-neg: 2.0ms (2.3% of total)

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

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

exact: 0.0ms (0% of total)

series16.0ms (0.1%)

Memory

-27.0MiB live, 18.1MiB allocated

Counts

11 → 132

Calls

Call 1

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

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

Calls

33 calls:

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

simplify204.0ms (1.9%)

Memory

31.0MiB live, 297.3MiB allocated

Algorithm

1×	egg-herbie

Rules

8 234×	`lower-fma.f64`
8 234×	`lower-fma.f32`
4 834×	`lower-+.f64`
4 834×	`lower-+.f32`
3 746×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	303	1757
1	915	1638
2	2842	1528
0	8516	1468

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 128

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)))))
(+ (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))))
(+ (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)))))))
(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)
(* 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)))))
(/ 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))
(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))))))
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)))))
(* -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))))))
(/ -1/2 x)
(/ (- (pow x 2) 1/2) x)
(/ (- (pow x 2) 1/2) x)
(/ (- (pow x 2) 1/2) x)
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)))))
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)))
(* -1 (log (/ -1 (sqrt -1))))
(- (* -1 (* x (sqrt -1))) (log (/ -1 (sqrt -1))))
(- (* x (- (* -1/2 (* x (+ (* -2 (* (sqrt -1) (+ (* 2 (/ 1 (sqrt -1))) (* 3/2 (/ 1 (pow (sqrt -1) 3)))))) (* -1 (pow (sqrt -1) 2))))) (sqrt -1))) (log (/ -1 (sqrt -1))))
(- (* x (- (* x (- (* -1/6 (* x (- (+ (* 2 (pow (sqrt -1) 3)) (* 6 (* (pow (sqrt -1) 2) (+ (* 2 (/ 1 (sqrt -1))) (* 3/2 (/ 1 (pow (sqrt -1) 3))))))) (* 12 (/ 1 (sqrt -1)))))) (* 1/2 (+ (* -2 (* (sqrt -1) (+ (* 2 (/ 1 (sqrt -1))) (* 3/2 (/ 1 (pow (sqrt -1) 3)))))) (* -1 (pow (sqrt -1) 2)))))) (sqrt -1))) (log (/ -1 (sqrt -1))))
(* -1 (+ (log 1/2) (log (/ 1 x))))
(* -1 (+ (log 1/2) (+ (log (/ 1 x)) (* 1/4 (/ 1 (pow x 2))))))
(- (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2))) (+ (log 1/2) (log (/ 1 x))))
(- (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))) (+ (log 1/2) (+ (log (/ 1 x)) (* 1/4 (/ 1 (pow x 2))))))
(* -1 (+ (log -2) (* -1 (log (/ -1 x)))))
(- (* 1/4 (/ 1 (pow x 2))) (+ (log -2) (* -1 (log (/ -1 x)))))
(- (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2)))) (+ (log -2) (* -1 (log (/ -1 x)))))
(- (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6))))) (+ (log -2) (* -1 (log (/ -1 x)))))
(log (/ -1 (sqrt -1)))
(+ (log (/ -1 (sqrt -1))) (* x (sqrt -1)))
(+ (log (/ -1 (sqrt -1))) (* x (+ (sqrt -1) (* 1/2 (* x (+ (* -2 (* (sqrt -1) (+ (* 2 (/ 1 (sqrt -1))) (* 3/2 (/ 1 (pow (sqrt -1) 3)))))) (* -1 (pow (sqrt -1) 2))))))))
(+ (log (/ -1 (sqrt -1))) (* x (+ (sqrt -1) (* x (+ (* 1/6 (* x (- (+ (* 2 (pow (sqrt -1) 3)) (* 6 (* (pow (sqrt -1) 2) (+ (* 2 (/ 1 (sqrt -1))) (* 3/2 (/ 1 (pow (sqrt -1) 3))))))) (* 12 (/ 1 (sqrt -1)))))) (* 1/2 (+ (* -2 (* (sqrt -1) (+ (* 2 (/ 1 (sqrt -1))) (* 3/2 (/ 1 (pow (sqrt -1) 3)))))) (* -1 (pow (sqrt -1) 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)))))))
(+ (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))))
(/ -1 (sqrt -1))
(- (* -1 x) (/ 1 (sqrt -1)))
(- (* x (- (* x (+ (* 2 (/ 1 (sqrt -1))) (* 3/2 (/ 1 (pow (sqrt -1) 3))))) 1)) (/ 1 (sqrt -1)))
(- (* x (- (* x (+ (* 3/2 (/ 1 (pow (sqrt -1) 3))) (+ (* 2 (/ 1 (sqrt -1))) (* 2 (/ x (pow (sqrt -1) 2)))))) 1)) (/ 1 (sqrt -1)))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(/ (+ 1/2 (+ (/ 1/16 (pow x 4)) (* 1/8 (/ 1 (pow x 2))))) x)
(/ (+ 1/2 (+ (/ 1/16 (pow x 4)) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6)))))) x)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 2)))
(* -1 (* x (- (+ (/ 1/8 (pow x 4)) (* 1/2 (/ 1 (pow x 2)))) 2)))
(* -1 (* x (- (+ (/ 1/8 (pow x 4)) (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) 2)))
-1
(- (* -1 (* x (sqrt -1))) 1)
(- (* x (+ (* -1 (sqrt -1)) (* 2 x))) 1)
(- (* x (+ (* -1 (sqrt -1)) (* x (+ 2 (* -1/2 (/ x (sqrt -1))))))) 1)
(pow x 2)
(* (pow x 2) (- 1 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- (+ 1 (/ 1/8 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- (+ 1 (+ (/ 1/8 (pow x 4)) (* 1/16 (/ 1 (pow x 6))))) (* 1/2 (/ 1 (pow x 2)))))
(* 3 (pow x 2))
(* (pow x 2) (- 3 (* 3/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 3 (* -1 (/ (+ 3/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* (pow x 2) (- (+ 3 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 3/2 (/ 1 (pow x 2)))))
(* -1 (sqrt -1))
(- x (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))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(/ (+ 1/2 (+ (/ 1/16 (pow x 4)) (* 1/8 (/ 1 (pow x 2))))) x)
(/ (+ 1/2 (+ (/ 1/16 (pow x 4)) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6)))))) x)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 2)))
(* -1 (* x (- (+ (/ 1/8 (pow x 4)) (* 1/2 (/ 1 (pow x 2)))) 2)))
(* -1 (* x (- (+ (/ 1/8 (pow x 4)) (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) 2)))
(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))))))
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)))))
(* -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 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)

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

rewrite373.0ms (3.4%)

Memory

-8.8MiB live, 364.4MiB allocated

Rules

5 848×	`lower-fma.f32`
5 842×	`lower-fma.f64`
4 478×	`lower-/.f32`
4 474×	`lower-/.f64`
3 736×	`lower-*.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	178
0	41	167
1	175	157
2	1401	157
0	8177	157

Stop Event

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

Counts

11 → 340

Calls

Call 1

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

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

eval150.0ms (1.4%)

Memory: 5.5MiB live, 115.4MiB allocated
Compiler: Compiled 24 758 to 2 382 computations (90.4% saved)

prune235.0ms (2.2%)

Memory

-18.9MiB live, 104.0MiB allocated

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	513	1	514
Fresh	0	0	0
Picked	1	1	2
Done	1	3	4
Total	515	5	520

Accuracy

100.0%

Counts

520 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	32.0%	(neg.f64 (log.f64 (/.f64 (fma.f64 x (+.f64 (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) x) #s(literal -1 binary64)) (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (.f64 x (.f64 x x))))))
▶	99.1%	(neg.f64 (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x))))
✓	46.6%	(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))
✓	99.0%	(log.f64 (+.f64 x #s(approx (sqrt (- (* x x) 1)) (+.f64 x (/.f64 #s(literal -1/2 binary64) x)))))
✓	98.7%	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 x #s(literal 2 binary64))))

Compiler

Compiled 63 to 34 computations (46% saved)

simplify238.0ms (2.2%)

Memory

20.1MiB live, 186.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

12 992×	`lower-fma.f64`
12 992×	`lower-fma.f32`
2 490×	`lower--.f64`
2 490×	`lower--.f32`
2 120×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	119
0	21	113
1	45	113
2	86	113
3	194	113
4	509	113
5	1427	113
6	4274	113
7	7967	113
0	8127	98

Stop Event

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

Calls

Call 1

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

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

localize101.0ms (0.9%)

Memory

-26.5MiB live, 59.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 #s(literal 1/2 binary64) x)
accuracy	0	(neg.f64 (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x))))
accuracy	0.00390625	(log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)))
accuracy	0.6639436971732589	#s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x))

Samples

89.0ms

256×

valid

Compiler

Compiled 109 to 19 computations (82.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 83.0ms

ival-neg: 41.0ms (49.6% of total)

ival-sub: 23.0ms (27.8% of total)

ival-mult: 6.0ms (7.3% of total)

ival-add: 4.0ms (4.8% of total)

ival-div: 3.0ms (3.6% of total)

ival-log: 3.0ms (3.6% of total)

ival-sqrt: 2.0ms (2.4% of total)

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

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

exact: 0.0ms (0% of total)

series3.0ms (0%)

Memory

4.0MiB live, 4.0MiB allocated

Counts

4 → 48

Calls

Call 1

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

Outputs
#s(alt (* -1 (log (/ -1 (sqrt -1)))) (taylor 0 x) (#s(alt (neg.f64 (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)))) (patch (neg.f64 (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (* x (sqrt -1))) (log (/ -1 (sqrt -1)))) (taylor 0 x) (#s(alt (neg.f64 (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)))) (patch (neg.f64 (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (- (* x (- (* -1/2 (* x (+ (* -2 (* (sqrt -1) (+ (* 2 (/ 1 (sqrt -1))) (* 3/2 (/ 1 (pow (sqrt -1) 3)))))) (* -1 (pow (sqrt -1) 2))))) (sqrt -1))) (log (/ -1 (sqrt -1)))) (taylor 0 x) (#s(alt (neg.f64 (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)))) (patch (neg.f64 (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (- (* x (- (* x (- (* -1/6 (* x (- (+ (* 2 (pow (sqrt -1) 3)) (* 6 (* (pow (sqrt -1) 2) (+ (* 2 (/ 1 (sqrt -1))) (* 3/2 (/ 1 (pow (sqrt -1) 3))))))) (* 12 (/ 1 (sqrt -1)))))) (* 1/2 (+ (* -2 (* (sqrt -1) (+ (* 2 (/ 1 (sqrt -1))) (* 3/2 (/ 1 (pow (sqrt -1) 3)))))) (* -1 (pow (sqrt -1) 2)))))) (sqrt -1))) (log (/ -1 (sqrt -1)))) (taylor 0 x) (#s(alt (neg.f64 (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)))) (patch (neg.f64 (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ (log 1/2) (log (/ 1 x)))) (taylor inf x) (#s(alt (neg.f64 (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)))) (patch (neg.f64 (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ (log 1/2) (+ (log (/ 1 x)) (* 1/4 (/ 1 (pow x 2)))))) (taylor inf x) (#s(alt (neg.f64 (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)))) (patch (neg.f64 (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2))) (+ (log 1/2) (log (/ 1 x)))) (taylor inf x) (#s(alt (neg.f64 (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)))) (patch (neg.f64 (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))) (+ (log 1/2) (+ (log (/ 1 x)) (* 1/4 (/ 1 (pow x 2)))))) (taylor inf x) (#s(alt (neg.f64 (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)))) (patch (neg.f64 (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ (log -2) (* -1 (log (/ -1 x))))) (taylor -inf x) (#s(alt (neg.f64 (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)))) (patch (neg.f64 (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/4 (/ 1 (pow x 2))) (+ (log -2) (* -1 (log (/ -1 x))))) (taylor -inf x) (#s(alt (neg.f64 (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)))) (patch (neg.f64 (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (- (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2)))) (+ (log -2) (* -1 (log (/ -1 x))))) (taylor -inf x) (#s(alt (neg.f64 (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)))) (patch (neg.f64 (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (- (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6))))) (+ (log -2) (* -1 (log (/ -1 x))))) (taylor -inf x) (#s(alt (neg.f64 (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)))) (patch (neg.f64 (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (log (/ -1 (sqrt -1))) (taylor 0 x) (#s(alt (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x))) (patch (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (log (/ -1 (sqrt -1))) (* x (sqrt -1))) (taylor 0 x) (#s(alt (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x))) (patch (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (log (/ -1 (sqrt -1))) (* x (+ (sqrt -1) (* 1/2 (* x (+ (* -2 (* (sqrt -1) (+ (* 2 (/ 1 (sqrt -1))) (* 3/2 (/ 1 (pow (sqrt -1) 3)))))) (* -1 (pow (sqrt -1) 2)))))))) (taylor 0 x) (#s(alt (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x))) (patch (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (log (/ -1 (sqrt -1))) (* x (+ (sqrt -1) (* x (+ (* 1/6 (* x (- (+ (* 2 (pow (sqrt -1) 3)) (* 6 (* (pow (sqrt -1) 2) (+ (* 2 (/ 1 (sqrt -1))) (* 3/2 (/ 1 (pow (sqrt -1) 3))))))) (* 12 (/ 1 (sqrt -1)))))) (* 1/2 (+ (* -2 (* (sqrt -1) (+ (* 2 (/ 1 (sqrt -1))) (* 3/2 (/ 1 (pow (sqrt -1) 3)))))) (* -1 (pow (sqrt -1) 2))))))))) (taylor 0 x) (#s(alt (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x))) (patch (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x 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 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x))) (patch (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 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 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x))) (patch (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 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 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x))) (patch (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 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 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x))) (patch (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (log -2) (* -1 (log (/ -1 x)))) (taylor -inf x) (#s(alt (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x))) (patch (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) 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 (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x))) (patch (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) 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 (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x))) (patch (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) 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 (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x))) (patch (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ -1 (sqrt -1)) (taylor 0 x) (#s(alt #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 x) (/ 1 (sqrt -1))) (taylor 0 x) (#s(alt #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (- (* x (- (* x (+ (* 2 (/ 1 (sqrt -1))) (* 3/2 (/ 1 (pow (sqrt -1) 3))))) 1)) (/ 1 (sqrt -1))) (taylor 0 x) (#s(alt #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (- (* x (- (* x (+ (* 3/2 (/ 1 (pow (sqrt -1) 3))) (+ (* 2 (/ 1 (sqrt -1))) (* 2 (/ x (pow (sqrt -1) 2)))))) 1)) (/ 1 (sqrt -1))) (taylor 0 x) (#s(alt #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 x) (taylor inf x) (#s(alt #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x) (taylor inf x) (#s(alt #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1/2 (+ (/ 1/16 (pow x 4)) (* 1/8 (/ 1 (pow x 2))))) x) (taylor inf x) (#s(alt #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1/2 (+ (/ 1/16 (pow x 4)) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6)))))) x) (taylor inf x) (#s(alt #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 2))) (taylor -inf x) (#s(alt #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (/ 1/8 (pow x 4)) (* 1/2 (/ 1 (pow x 2)))) 2))) (taylor -inf x) (#s(alt #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (/ 1/8 (pow x 4)) (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) 2))) (taylor -inf x) (#s(alt #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1/2 binary64) x) (patch (/.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1/2 binary64) x) (patch (/.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1/2 binary64) x) (patch (/.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1/2 binary64) x) (patch (/.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 x) (taylor inf x) (#s(alt (/.f64 #s(literal 1/2 binary64) x) (patch (/.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 x) (taylor inf x) (#s(alt (/.f64 #s(literal 1/2 binary64) x) (patch (/.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 x) (taylor inf x) (#s(alt (/.f64 #s(literal 1/2 binary64) x) (patch (/.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 x) (taylor inf x) (#s(alt (/.f64 #s(literal 1/2 binary64) x) (patch (/.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/2 binary64) x) (patch (/.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/2 binary64) x) (patch (/.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/2 binary64) x) (patch (/.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 x) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/2 binary64) x) (patch (/.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())

Calls

12 calls:

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

simplify268.0ms (2.5%)

Memory

7.5MiB live, 120.4MiB allocated

Algorithm

1×	egg-herbie

Rules

11 178×	`lower-fma.f64`
11 178×	`lower-fma.f32`
3 554×	`lower-*.f64`
3 554×	`lower-*.f32`
2 548×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	159	659
1	462	598
2	1479	548
3	5486	531
0	8194	518

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

Inputs
(* -1 (log (/ -1 (sqrt -1))))
(- (* -1 (* x (sqrt -1))) (log (/ -1 (sqrt -1))))
(- (* x (- (* -1/2 (* x (+ (* -2 (* (sqrt -1) (+ (* 2 (/ 1 (sqrt -1))) (* 3/2 (/ 1 (pow (sqrt -1) 3)))))) (* -1 (pow (sqrt -1) 2))))) (sqrt -1))) (log (/ -1 (sqrt -1))))
(- (* x (- (* x (- (* -1/6 (* x (- (+ (* 2 (pow (sqrt -1) 3)) (* 6 (* (pow (sqrt -1) 2) (+ (* 2 (/ 1 (sqrt -1))) (* 3/2 (/ 1 (pow (sqrt -1) 3))))))) (* 12 (/ 1 (sqrt -1)))))) (* 1/2 (+ (* -2 (* (sqrt -1) (+ (* 2 (/ 1 (sqrt -1))) (* 3/2 (/ 1 (pow (sqrt -1) 3)))))) (* -1 (pow (sqrt -1) 2)))))) (sqrt -1))) (log (/ -1 (sqrt -1))))
(* -1 (+ (log 1/2) (log (/ 1 x))))
(* -1 (+ (log 1/2) (+ (log (/ 1 x)) (* 1/4 (/ 1 (pow x 2))))))
(- (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2))) (+ (log 1/2) (log (/ 1 x))))
(- (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))) (+ (log 1/2) (+ (log (/ 1 x)) (* 1/4 (/ 1 (pow x 2))))))
(* -1 (+ (log -2) (* -1 (log (/ -1 x)))))
(- (* 1/4 (/ 1 (pow x 2))) (+ (log -2) (* -1 (log (/ -1 x)))))
(- (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2)))) (+ (log -2) (* -1 (log (/ -1 x)))))
(- (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6))))) (+ (log -2) (* -1 (log (/ -1 x)))))
(log (/ -1 (sqrt -1)))
(+ (log (/ -1 (sqrt -1))) (* x (sqrt -1)))
(+ (log (/ -1 (sqrt -1))) (* x (+ (sqrt -1) (* 1/2 (* x (+ (* -2 (* (sqrt -1) (+ (* 2 (/ 1 (sqrt -1))) (* 3/2 (/ 1 (pow (sqrt -1) 3)))))) (* -1 (pow (sqrt -1) 2))))))))
(+ (log (/ -1 (sqrt -1))) (* x (+ (sqrt -1) (* x (+ (* 1/6 (* x (- (+ (* 2 (pow (sqrt -1) 3)) (* 6 (* (pow (sqrt -1) 2) (+ (* 2 (/ 1 (sqrt -1))) (* 3/2 (/ 1 (pow (sqrt -1) 3))))))) (* 12 (/ 1 (sqrt -1)))))) (* 1/2 (+ (* -2 (* (sqrt -1) (+ (* 2 (/ 1 (sqrt -1))) (* 3/2 (/ 1 (pow (sqrt -1) 3)))))) (* -1 (pow (sqrt -1) 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)))))))
(+ (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))))
(/ -1 (sqrt -1))
(- (* -1 x) (/ 1 (sqrt -1)))
(- (* x (- (* x (+ (* 2 (/ 1 (sqrt -1))) (* 3/2 (/ 1 (pow (sqrt -1) 3))))) 1)) (/ 1 (sqrt -1)))
(- (* x (- (* x (+ (* 3/2 (/ 1 (pow (sqrt -1) 3))) (+ (* 2 (/ 1 (sqrt -1))) (* 2 (/ x (pow (sqrt -1) 2)))))) 1)) (/ 1 (sqrt -1)))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(/ (+ 1/2 (+ (/ 1/16 (pow x 4)) (* 1/8 (/ 1 (pow x 2))))) x)
(/ (+ 1/2 (+ (/ 1/16 (pow x 4)) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6)))))) x)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 2)))
(* -1 (* x (- (+ (/ 1/8 (pow x 4)) (* 1/2 (/ 1 (pow x 2)))) 2)))
(* -1 (* x (- (+ (/ 1/8 (pow x 4)) (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) 2)))
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)

Outputs
(* -1 (log (/ -1 (sqrt -1))))
(log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(- (* -1 (* x (sqrt -1))) (log (/ -1 (sqrt -1))))
(fma.f64 x (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(- (* x (- (* -1/2 (* x (+ (* -2 (* (sqrt -1) (+ (* 2 (/ 1 (sqrt -1))) (* 3/2 (/ 1 (pow (sqrt -1) 3)))))) (* -1 (pow (sqrt -1) 2))))) (sqrt -1))) (log (/ -1 (sqrt -1))))
(fma.f64 x (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(- (* x (- (* x (- (* -1/6 (* x (- (+ (* 2 (pow (sqrt -1) 3)) (* 6 (* (pow (sqrt -1) 2) (+ (* 2 (/ 1 (sqrt -1))) (* 3/2 (/ 1 (pow (sqrt -1) 3))))))) (* 12 (/ 1 (sqrt -1)))))) (* 1/2 (+ (* -2 (* (sqrt -1) (+ (* 2 (/ 1 (sqrt -1))) (* 3/2 (/ 1 (pow (sqrt -1) 3)))))) (* -1 (pow (sqrt -1) 2)))))) (sqrt -1))) (log (/ -1 (sqrt -1))))
(fma.f64 x (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x (fma.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -2 binary64) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 12 binary64))))))) (sqrt.f64 #s(literal -1 binary64))) (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (+ (log 1/2) (log (/ 1 x))))
(-.f64 (log.f64 x) (log.f64 #s(literal 1/2 binary64)))
(* -1 (+ (log 1/2) (+ (log (/ 1 x)) (* 1/4 (/ 1 (pow x 2))))))
(+.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) (-.f64 (log.f64 x) (log.f64 #s(literal 1/2 binary64))))
(- (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2))) (+ (log 1/2) (log (/ 1 x))))
(+.f64 (/.f64 (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal -3/32 binary64) (.f64 x x))) (.f64 x x)) (-.f64 (log.f64 x) (log.f64 #s(literal 1/2 binary64))))
(- (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))) (+ (log 1/2) (+ (log (/ 1 x)) (* 1/4 (/ 1 (pow x 2))))))
(+.f64 (/.f64 (+.f64 #s(literal -3/32 binary64) (/.f64 #s(literal -5/96 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64))) (+.f64 (/.f64 #s(literal -1/4 binary64) (.f64 x x)) (-.f64 (log.f64 x) (log.f64 #s(literal 1/2 binary64)))))
(* -1 (+ (log -2) (* -1 (log (/ -1 x)))))
(-.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal -2 binary64)))
(- (* 1/4 (/ 1 (pow x 2))) (+ (log -2) (* -1 (log (/ -1 x)))))
(+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (-.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal -2 binary64))))
(- (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2)))) (+ (log -2) (* -1 (log (/ -1 x)))))
(+.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (-.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal -2 binary64)))) (/.f64 #s(literal 3/32 binary64) (pow.f64 x #s(literal 4 binary64))))
(- (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6))))) (+ (log -2) (* -1 (log (/ -1 x)))))
(+.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (-.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal -2 binary64)))) (+.f64 (/.f64 #s(literal 3/32 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 5/96 binary64) (pow.f64 x #s(literal 6 binary64)))))
(log (/ -1 (sqrt -1)))
(neg.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(+ (log (/ -1 (sqrt -1))) (* x (sqrt -1)))
(-.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(+ (log (/ -1 (sqrt -1))) (* x (+ (sqrt -1) (* 1/2 (* x (+ (* -2 (* (sqrt -1) (+ (* 2 (/ 1 (sqrt -1))) (* 3/2 (/ 1 (pow (sqrt -1) 3)))))) (* -1 (pow (sqrt -1) 2))))))))
(-.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(+ (log (/ -1 (sqrt -1))) (* x (+ (sqrt -1) (* x (+ (* 1/6 (* x (- (+ (* 2 (pow (sqrt -1) 3)) (* 6 (* (pow (sqrt -1) 2) (+ (* 2 (/ 1 (sqrt -1))) (* 3/2 (/ 1 (pow (sqrt -1) 3))))))) (* 12 (/ 1 (sqrt -1)))))) (* 1/2 (+ (* -2 (* (sqrt -1) (+ (* 2 (/ 1 (sqrt -1))) (* 3/2 (/ 1 (pow (sqrt -1) 3)))))) (* -1 (pow (sqrt -1) 2)))))))))
(-.f64 (.f64 x (fma.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -2 binary64) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 12 binary64)))) (.f64 x (.f64 x #s(literal 1/6 binary64))) (sqrt.f64 #s(literal -1 binary64)))) (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(+ (log 1/2) (log (/ 1 x)))
(-.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 x))
(+ (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))) (log.f64 x))
(+ (log 1/2) (+ (log (/ 1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+.f64 (log.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (-.f64 (/.f64 #s(literal 3/32 binary64) (pow.f64 x #s(literal 4 binary64))) (log.f64 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 (log.f64 #s(literal 1/2 binary64)) (log.f64 x)) (+.f64 (/.f64 #s(literal 3/32 binary64) (pow.f64 x #s(literal 4 binary64))) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal 5/96 binary64) (pow.f64 x #s(literal 6 binary64))))))
(+ (log -2) (* -1 (log (/ -1 x))))
(-.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))
(- (+ (log -2) (* -1 (log (/ -1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+.f64 (log.f64 #s(literal -2 binary64)) (-.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) (log.f64 (/.f64 #s(literal -1 binary64) x))))
(+ (log -2) (+ (* -1 (log (/ -1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(+.f64 (/.f64 (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal -3/32 binary64) (.f64 x x))) (.f64 x x)) (-.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) 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 (+.f64 #s(literal -3/32 binary64) (/.f64 #s(literal -5/96 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64))) (+.f64 (log.f64 #s(literal -2 binary64)) (-.f64 (/.f64 #s(literal -1/4 binary64) (.f64 x x)) (log.f64 (/.f64 #s(literal -1 binary64) x)))))
(/ -1 (sqrt -1))
(/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))
(- (* -1 x) (/ 1 (sqrt -1)))
(-.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) x)
(- (* x (- (* x (+ (* 2 (/ 1 (sqrt -1))) (* 3/2 (/ 1 (pow (sqrt -1) 3))))) 1)) (/ 1 (sqrt -1)))
(fma.f64 x (fma.f64 x (fma.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3/2 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(- (* x (- (* x (+ (* 3/2 (/ 1 (pow (sqrt -1) 3))) (+ (* 2 (/ 1 (sqrt -1))) (* 2 (/ x (pow (sqrt -1) 2)))))) 1)) (/ 1 (sqrt -1)))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -2 binary64) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3/2 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)
(/ (+ 1/2 (+ (/ 1/16 (pow x 4)) (* 1/8 (/ 1 (pow x 2))))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64))))) x)
(/ (+ 1/2 (+ (/ 1/16 (pow x 4)) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6)))))) x)
(/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) (+.f64 (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64)))))) x)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 2)))
(.f64 x (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))))
(* -1 (* x (- (+ (/ 1/8 (pow x 4)) (* 1/2 (/ 1 (pow x 2)))) 2)))
(.f64 x (-.f64 #s(literal 2 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64))))))
(* -1 (* x (- (+ (/ 1/8 (pow x 4)) (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) 2)))
(.f64 x (-.f64 #s(literal 2 binary64) (+.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64)))))))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)

rewrite374.0ms (3.4%)

Memory

-20.8MiB live, 478.5MiB allocated

Rules

10 706×	`lower-fma.f64`
10 706×	`lower-fma.f32`
4 652×	`lower-*.f64`
4 652×	`lower-*.f32`
3 556×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	117
0	21	111
1	118	96
2	980	48
0	8815	45

Stop Event

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

Counts

4 → 44

Calls

Call 1

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

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

eval14.0ms (0.1%)

Memory: -24.6MiB live, 27.0MiB allocated
Compiler: Compiled 1 166 to 275 computations (76.4% saved)

prune13.0ms (0.1%)

Memory

34.4MiB live, 34.4MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	92	5	97

Accuracy

100.0%

Counts

97 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	32.0%	(neg.f64 (log.f64 (/.f64 (fma.f64 x (+.f64 (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) x) #s(literal -1 binary64)) (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (.f64 x (.f64 x x))))))
✓	99.1%	(neg.f64 (log.f64 #s(approx (/ (+ (* x (+ (- x (sqrt (+ (* x x) -1))) x)) -1) (+ (* (+ (* x x) -1) (sqrt (+ (* x x) -1))) (* x (* x x)))) (/.f64 #s(literal 1/2 binary64) x))))
✓	46.6%	(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))
✓	99.0%	(log.f64 (+.f64 x #s(approx (sqrt (- (* x x) 1)) (+.f64 x (/.f64 #s(literal -1/2 binary64) x)))))
✓	98.7%	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 x #s(literal 2 binary64))))

Compiler

Compiled 208 to 81 computations (61.1% saved)

regimes42.0ms (0.4%)

Memory

-16.9MiB live, 20.9MiB allocated

Counts

9 → 1

Calls

Call 1

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

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

Calls

3 calls:

35.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))
3.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
3.0ms	x

Results

Accuracy	Segments	Branch
99.1%	1	`x`
99.1%	1	`(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))`
99.1%	1	`(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))`

Compiler

Compiled 21 to 14 computations (33.3% saved)

regimes4.0ms (0%)

Memory

9.7MiB live, 9.7MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.7%	1	`x`
98.7%	1	`(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))`
98.7%	1	`(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))`

Compiler

Compiled 21 to 14 computations (33.3% saved)

simplify6.0ms (0.1%)

Memory

11.6MiB live, 11.6MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
2×	`1-exp_binary64`
2×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	52
1	32	52
2	34	52
3	35	52

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

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

Outputs

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

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

soundness544.0ms (5%)

Memory

-33.4MiB live, 528.5MiB allocated

Rules

10 204×	`lower-fma.f64`
10 204×	`lower-fma.f32`
8 234×	`lower-fma.f64`
8 234×	`lower-fma.f32`
5 064×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	150	559
1	411	533
2	1143	526
3	3327	488
4	7966	488
0	8526	459
0	303	1757
1	915	1638
2	2842	1528
0	8516	1468
0	37	229
0	62	220
1	243	199
2	1985	199
0	8218	194
0	7	28
0	12	28
1	49	28
2	322	28
3	3626	28
0	8646	24

Stop Event

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

Compiler

Compiled 59 to 37 computations (37.3% saved)

preprocess49.0ms (0.5%)

Memory: 11.7MiB live, 87.3MiB allocated
Compiler: Compiled 44 to 30 computations (31.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze79.0ms (0.7%)

sample2.5s (22.8%)

explain171.0ms (1.6%)

preprocess638.0ms (5.9%)

eval19.0ms (0.2%)

prune1.0ms (0%)

simplify1.0s (9.6%)

localize28.0ms (0.3%)

series6.0ms (0.1%)

simplify266.0ms (2.5%)

rewrite326.0ms (3%)

eval68.0ms (0.6%)

prune120.0ms (1.1%)

simplify568.0ms (5.2%)

localize293.0ms (2.7%)

series144.0ms (1.3%)

simplify481.0ms (4.4%)

rewrite471.0ms (4.3%)

eval347.0ms (3.2%)

prune335.0ms (3.1%)

simplify187.0ms (1.7%)

localize137.0ms (1.3%)

series16.0ms (0.1%)

simplify204.0ms (1.9%)

rewrite373.0ms (3.4%)

eval150.0ms (1.4%)

prune235.0ms (2.2%)

simplify238.0ms (2.2%)

localize101.0ms (0.9%)

series3.0ms (0%)

simplify268.0ms (2.5%)

rewrite374.0ms (3.4%)

eval14.0ms (0.1%)

prune13.0ms (0.1%)

regimes42.0ms (0.4%)

regimes4.0ms (0%)

simplify6.0ms (0.1%)

soundness544.0ms (5%)

preprocess49.0ms (0.5%)

end0.0ms (0%)

Profiling