Metrics for Rust f64::acosh

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 6 to 5 computations (16.7% saved)

sample644.0ms (14%)

Memory

43.7MiB live, 867.5MiB allocated

Samples

428.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 166.0ms

ival-acosh: 126.0ms (75.8% of total)

ival->=: 28.0ms (16.8% of total)

exact: 8.0ms (4.8% of total)

ival-assert: 4.0ms (2.4% of total)

Bogosity

explain131.0ms (2.9%)

Memory

-31.6MiB live, 213.1MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
111	-	-	`(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	111	0
↳	`(-.f64 (*.f64 x x) #s(literal 1 binary64))`	overflow	111
↳	`(*.f64 x x)`	overflow	111
`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	111
↳	`(*.f64 x x)`	overflow	111

Confusion

	Predicted +	Predicted -
+	111	0
-	0	145

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	111	0	0
-	0	0	145

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	145
1	110
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

40.0ms

512×

valid

Compiler

Compiled 79 to 25 computations (68.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-sqrt: 7.0ms (29% of total)

ival-log: 6.0ms (24.9% of total)

ival-mult: 4.0ms (16.6% of total)

ival-sub: 3.0ms (12.4% of total)

ival-add: 3.0ms (12.4% of total)

ival-true: 1.0ms (4.1% of total)

exact: 0.0ms (0% of total)

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

preprocess388.0ms (8.4%)

Memory

-9.9MiB live, 360.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	58.0%	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify340.0ms (7.4%)

Memory

21.2MiB live, 299.4MiB 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))

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

localize37.0ms (0.8%)

Memory

3.2MiB live, 42.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(-.f64 (*.f64 x x) #s(literal 1 binary64))
accuracy	0.00390625	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))
accuracy	0.24213560223994607	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
accuracy	25.701679447727663	(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))

Samples

30.0ms

256×

valid

Compiler

Compiled 35 to 9 computations (74.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-sqrt: 16.0ms (67% of total)

ival-log: 3.0ms (12.6% of total)

ival-mult: 2.0ms (8.4% of total)

ival-sub: 1.0ms (4.2% of total)

ival-add: 1.0ms (4.2% of total)

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

exact: 0.0ms (0% of total)

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

series9.0ms (0.2%)

Memory

-26.3MiB live, 11.1MiB 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 (log (sqrt -1)) (taylor 0 x) (#s(alt (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (log (sqrt -1)) (/ x (sqrt -1))) (taylor 0 x) (#s(alt (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1))))) (taylor 0 x) (#s(alt (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1))))) (taylor 0 x) (#s(alt (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (sqrt -1) (taylor 0 x) (#s(alt (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ x (sqrt -1)) (taylor 0 x) (#s(alt (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1)))))) (taylor 0 x) (#s(alt (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1)))))))) (taylor 0 x) (#s(alt (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt -1) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1)))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1)))))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1)))))) (taylor 0 x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (-.f64 (.f64 x x) #s(literal 1 binary64)) (patch (-.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (-.f64 (.f64 x x) #s(literal 1 binary64)) (patch (-.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (-.f64 (.f64 x x) #s(literal 1 binary64)) (patch (-.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (-.f64 (.f64 x x) #s(literal 1 binary64)) (patch (-.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (log 2) (* -1 (log (/ 1 x)))) (taylor inf x) (#s(alt (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2))))) (taylor inf x) (#s(alt (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (- 2 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))) (taylor inf x) (#s(alt (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (-.f64 (.f64 x x) #s(literal 1 binary64)) (patch (-.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (-.f64 (.f64 x x) #s(literal 1 binary64)) (patch (-.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (-.f64 (.f64 x x) #s(literal 1 binary64)) (patch (-.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (-.f64 (.f64 x x) #s(literal 1 binary64)) (patch (-.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (log -1/2) (log (/ -1 x))) (taylor -inf x) (#s(alt (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6))))))) (taylor -inf x) (#s(alt (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 x) (taylor -inf x) (#s(alt (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x) (taylor -inf x) (#s(alt (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x)) (taylor -inf x) (#s(alt (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x)) (taylor -inf x) (#s(alt (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
4.0ms	x	@	inf	((- (* x x) 1) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)))
2.0ms	x	@	0	((- (* x x) 1) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)))
1.0ms	x	@	-inf	((- (* x x) 1) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)))

Time

Variable

Point

Expression

4.0ms

inf

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

2.0ms

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

1.0ms

-inf

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

simplify138.0ms (3%)

Memory

12.0MiB live, 169.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	150	559
1	411	533
2	1146	526
3	3331	488
4	7979	488
0	8531	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)
(log (sqrt -1))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(sqrt -1)
(+ x (sqrt -1))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(sqrt -1)
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(+ (log 2) (* -1 (log (/ 1 x))))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(* 2 x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
x
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(+ (log -1/2) (log (/ -1 x)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(* -1 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))

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

rewrite228.0ms (5%)

Memory

3.2MiB live, 198.4MiB allocated

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
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>

eval96.0ms (2.1%)

Memory: 9.1MiB live, 92.8MiB allocated
Compiler: Compiled 8 015 to 1 572 computations (80.4% saved)

prune17.0ms (0.4%)

Memory

-17.7MiB live, 19.4MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	364	3	367
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	365	3	368

Accuracy

100.0%

Counts

368 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(log.f64 (+.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x)))))
▶	99.1%	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
▶	99.2%	#s(approx (log (+ x (sqrt (- (* x x) 1)))) (+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64))))

Status

Accuracy

Program

▶

99.6%

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

▶

99.1%

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

▶

99.2%

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

Compiler

Compiled 20 to 18 computations (10% saved)

simplify266.0ms (5.8%)

Memory

38.0MiB live, 194.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	107
0	30	107
1	44	107
2	56	107
3	80	107
4	121	107
5	245	107
6	509	107
7	1050	107
8	2643	107
9	4348	107
10	5370	107
11	5813	107
12	5921	107
13	6000	107
14	6076	107
15	6798	107
16	7454	107
17	7886	107
0	8062	101

Stop Event

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

Calls

Call 1

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

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

localize96.0ms (2.1%)

Memory

-19.6MiB live, 140.8MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0	(-.f64 x (/.f64 #s(literal 1/2 binary64) x))
accuracy	0.00390625	(+.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))))
accuracy	0.00390625	#s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x)))
accuracy	0.24213560223994607	(log.f64 (+.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x)))))
accuracy	0	(*.f64 #s(literal 2 binary64) x)
accuracy	0.24213560223994607	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
accuracy	0.40995626039568334	#s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x))
accuracy	0	(log.f64 x)
accuracy	0	(log.f64 #s(literal 2 binary64))
accuracy	0.1875	(+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64)))
accuracy	0.32804600046055943	#s(approx (log (+ x (sqrt (- (* x x) 1)))) (+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64))))

Samples

62.0ms

256×

valid

Compiler

Compiled 77 to 17 computations (77.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 52.0ms

ival-log: 33.0ms (63.9% of total)

ival-mult: 9.0ms (17.4% of total)

ival-div: 2.0ms (3.9% of total)

ival-add: 2.0ms (3.9% of total)

ival-sub: 2.0ms (3.9% of total)

ival-sqrt: 2.0ms (3.9% of total)

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

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

exact: 0.0ms (0% of total)

series124.0ms (2.7%)

Memory

2.2MiB live, 169.2MiB allocated

Counts

11 → 120

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
80.0ms	x	@	0	((log (+ x (sqrt (- (* x x) 1)))) (+ (log x) (log 2)) (log x) (log 2) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (* 2 x) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)) (- x (/ 1/2 x)))
21.0ms	x	@	-inf	((log (+ x (sqrt (- (* x x) 1)))) (+ (log x) (log 2)) (log x) (log 2) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (* 2 x) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)) (- x (/ 1/2 x)))
19.0ms	x	@	inf	((log (+ x (sqrt (- (* x x) 1)))) (+ (log x) (log 2)) (log x) (log 2) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (* 2 x) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)) (- x (/ 1/2 x)))

Time

Variable

Point

Expression

80.0ms

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

21.0ms

-inf

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

19.0ms

inf

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

simplify134.0ms (2.9%)

Memory

21.0MiB live, 170.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	160	1268
1	432	1208
2	1180	1168
3	3425	1121
0	8329	1087

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 117

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

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

rewrite191.0ms (4.2%)

Memory

-16.2MiB live, 227.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	98
0	30	96
1	112	96
2	784	96
0	8443	90

Stop Event

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

Counts

11 → 186

Calls

Call 1

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

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>

eval38.0ms (0.8%)

Memory: -0.4MiB live, 72.9MiB allocated
Compiler: Compiled 6 209 to 969 computations (84.4% saved)

prune9.0ms (0.2%)

Memory

-14.6MiB live, 22.8MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	302	1	303
Fresh	0	0	0
Picked	1	2	3
Done	0	0	0
Total	303	3	306

Accuracy

100.0%

Counts

306 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

✓

99.6%

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

✓

99.1%

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

▶

99.5%

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

Compiler

Compiled 20 to 18 computations (10% saved)

simplify345.0ms (7.5%)

Memory

-2.8MiB live, 246.9MiB 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	(log.f64 (/.f64 #s(literal 1/2 binary64) x))
cost-diff	0	(neg.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x)))
cost-diff	0	#s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	29
0	15	29
1	26	29
2	32	29
3	49	29
4	82	29
5	147	29
6	314	29
7	593	29
8	2124	29
9	3252	29
10	4538	29
11	5242	29
12	5555	29
13	5746	29
14	5848	29
15	6167	29
16	6713	29
17	7824	29
0	8060	28

Stop Event

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

Calls

Call 1

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

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

localize48.0ms (1%)

Memory

6.2MiB live, 43.7MiB 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 (/.f64 #s(literal 1/2 binary64) x)))
accuracy	0.00390625	(log.f64 (/.f64 #s(literal 1/2 binary64) x))
accuracy	0.32804600046055943	#s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x))))

Samples

41.0ms

256×

valid

Compiler

Compiled 25 to 13 computations (48% saved)

Precisions

Click to see histograms. Total time spent on operations: 34.0ms

ival-log: 25.0ms (72.9% of total)

ival-div: 2.0ms (5.8% of total)

ival-mult: 2.0ms (5.8% of total)

ival-sqrt: 2.0ms (5.8% of total)

ival-add: 1.0ms (2.9% of total)

ival-sub: 1.0ms (2.9% of total)

ival-neg: 1.0ms (2.9% of total)

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

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

exact: 0.0ms (0% of total)

series71.0ms (1.6%)

Memory

15.8MiB live, 98.2MiB allocated

Counts

4 → 48

Calls

Call 1

Inputs
#s(alt #s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x)))) (patch #s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x)))) #<representation binary64>) () ())
#s(alt (neg.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x))) (patch (neg.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())
#s(alt (log.f64 (/.f64 #s(literal 1/2 binary64) x)) (patch (log.f64 (/.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 (log (sqrt -1)) (taylor 0 x) (#s(alt #s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x)))) (patch #s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (log (sqrt -1)) (/ x (sqrt -1))) (taylor 0 x) (#s(alt #s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x)))) (patch #s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f64 (log.f64 (/.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 #s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x)))) (patch #s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f64 (log.f64 (/.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 #s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x)))) (patch #s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ (log 1/2) (* -1 (log x)))) (taylor 0 x) (#s(alt (neg.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x))) (patch (neg.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ (log 1/2) (* -1 (log x)))) (taylor 0 x) (#s(alt (neg.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x))) (patch (neg.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ (log 1/2) (* -1 (log x)))) (taylor 0 x) (#s(alt (neg.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x))) (patch (neg.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ (log 1/2) (* -1 (log x)))) (taylor 0 x) (#s(alt (neg.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x))) (patch (neg.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (log 1/2) (* -1 (log x))) (taylor 0 x) (#s(alt (log.f64 (/.f64 #s(literal 1/2 binary64) x)) (patch (log.f64 (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (log 1/2) (* -1 (log x))) (taylor 0 x) (#s(alt (log.f64 (/.f64 #s(literal 1/2 binary64) x)) (patch (log.f64 (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (log 1/2) (* -1 (log x))) (taylor 0 x) (#s(alt (log.f64 (/.f64 #s(literal 1/2 binary64) x)) (patch (log.f64 (/.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (log 1/2) (* -1 (log x))) (taylor 0 x) (#s(alt (log.f64 (/.f64 #s(literal 1/2 binary64) x)) (patch (log.f64 (/.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 (+ (log 2) (* -1 (log (/ 1 x)))) (taylor inf x) (#s(alt #s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x)))) (patch #s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f64 (log.f64 (/.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 #s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x)))) (patch #s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f64 (log.f64 (/.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 #s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x)))) (patch #s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f64 (log.f64 (/.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 #s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x)))) (patch #s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f64 (log.f64 (/.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 (/.f64 #s(literal 1/2 binary64) x))) (patch (neg.f64 (log.f64 (/.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 (/.f64 #s(literal 1/2 binary64) x))) (patch (neg.f64 (log.f64 (/.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 (/.f64 #s(literal 1/2 binary64) x))) (patch (neg.f64 (log.f64 (/.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 (/.f64 #s(literal 1/2 binary64) x))) (patch (neg.f64 (log.f64 (/.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 #s(literal 1/2 binary64) x)) (patch (log.f64 (/.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 #s(literal 1/2 binary64) x)) (patch (log.f64 (/.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 #s(literal 1/2 binary64) x)) (patch (log.f64 (/.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 #s(literal 1/2 binary64) x)) (patch (log.f64 (/.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 (+ (log -1/2) (log (/ -1 x))) (taylor -inf x) (#s(alt #s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x)))) (patch #s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f64 (log.f64 (/.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 #s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x)))) (patch #s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f64 (log.f64 (/.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 #s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x)))) (patch #s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f64 (log.f64 (/.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 #s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x)))) (patch #s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f64 (log.f64 (/.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 (/.f64 #s(literal 1/2 binary64) x))) (patch (neg.f64 (log.f64 (/.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 (/.f64 #s(literal 1/2 binary64) x))) (patch (neg.f64 (log.f64 (/.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 (/.f64 #s(literal 1/2 binary64) x))) (patch (neg.f64 (log.f64 (/.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 (/.f64 #s(literal 1/2 binary64) x))) (patch (neg.f64 (log.f64 (/.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 #s(literal 1/2 binary64) x)) (patch (log.f64 (/.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 #s(literal 1/2 binary64) x)) (patch (log.f64 (/.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 #s(literal 1/2 binary64) x)) (patch (log.f64 (/.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 #s(literal 1/2 binary64) x)) (patch (log.f64 (/.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

3 calls:

Time

Variable

Point

Expression

44.0ms

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

19.0ms

-inf

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

7.0ms

inf

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

simplify124.0ms (2.7%)

Memory

7.2MiB live, 45.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	86	394
1	207	364
2	509	353
3	1209	351
4	2910	351
5	4922	330
6	6910	330
0	8080	327

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

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)))))
(* -1 (+ (log 1/2) (* -1 (log x))))
(* -1 (+ (log 1/2) (* -1 (log x))))
(* -1 (+ (log 1/2) (* -1 (log x))))
(* -1 (+ (log 1/2) (* -1 (log x))))
(+ (log 1/2) (* -1 (log x)))
(+ (log 1/2) (* -1 (log x)))
(+ (log 1/2) (* -1 (log x)))
(+ (log 1/2) (* -1 (log x)))
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(+ (log 2) (* -1 (log (/ 1 x))))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(* -1 (+ (log 1/2) (log (/ 1 x))))
(* -1 (+ (log 1/2) (log (/ 1 x))))
(* -1 (+ (log 1/2) (log (/ 1 x))))
(* -1 (+ (log 1/2) (log (/ 1 x))))
(+ (log 1/2) (log (/ 1 x)))
(+ (log 1/2) (log (/ 1 x)))
(+ (log 1/2) (log (/ 1 x)))
(+ (log 1/2) (log (/ 1 x)))
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(+ (log -1/2) (log (/ -1 x)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(* -1 (+ (log -1/2) (log (/ -1 x))))
(* -1 (+ (log -1/2) (log (/ -1 x))))
(* -1 (+ (log -1/2) (log (/ -1 x))))
(* -1 (+ (log -1/2) (log (/ -1 x))))
(+ (log -1/2) (log (/ -1 x)))
(+ (log -1/2) (log (/ -1 x)))
(+ (log -1/2) (log (/ -1 x)))
(+ (log -1/2) (log (/ -1 x)))
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)

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

rewrite206.0ms (4.5%)

Memory

-16.4MiB live, 138.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	27
0	15	27
1	66	25
2	415	25
3	4249	25
0	8118	24

Stop Event

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

Counts

4 → 153

Calls

Call 1

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

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>

eval38.0ms (0.8%)

Memory: -8.9MiB live, 28.7MiB allocated
Compiler: Compiled 2 335 to 637 computations (72.7% saved)

prune4.0ms (0.1%)

Memory

10.5MiB live, 10.5MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	201	3	204

Accuracy

100.0%

Counts

204 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

✓

99.6%

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

✓

99.1%

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

✓

99.5%

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

Compiler

Compiled 55 to 42 computations (23.6% saved)

regimes7.0ms (0.2%)

Memory

8.0MiB live, 8.0MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))`
99.6%	1	`(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))`

Compiler

Compiled 18 to 14 computations (22.2% saved)

regimes5.0ms (0.1%)

Memory

10.8MiB live, 10.8MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 18 to 14 computations (22.2% saved)

regimes4.0ms (0.1%)

Memory

6.4MiB live, 6.4MiB 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 #s(literal 2 binary64) x)))

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

Calls

3 calls:

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))))
1.0ms	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 18 to 14 computations (22.2% saved)

simplify118.0ms (2.6%)

Memory

-43.3MiB live, 51.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	43
1	30	43
2	39	43
3	46	43
4	51	43
5	53	43

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

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

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

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

soundness539.0ms (11.7%)

Memory

21.3MiB live, 252.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	98
0	30	96
1	112	96
2	784	96
0	8443	90
0	150	559
1	411	533
2	1146	526
3	3331	488
4	7979	488
0	8531	459

Stop Event

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

Compiler

Compiled 35 to 30 computations (14.3% saved)

preprocess197.0ms (4.3%)

Memory: -8.2MiB live, 73.3MiB allocated
Compiler: Compiled 82 to 60 computations (26.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample644.0ms (14%)

explain131.0ms (2.9%)

preprocess388.0ms (8.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify340.0ms (7.4%)

localize37.0ms (0.8%)

series9.0ms (0.2%)

simplify138.0ms (3%)

rewrite228.0ms (5%)

eval96.0ms (2.1%)

prune17.0ms (0.4%)

simplify266.0ms (5.8%)

localize96.0ms (2.1%)

series124.0ms (2.7%)

simplify134.0ms (2.9%)

rewrite191.0ms (4.2%)

eval38.0ms (0.8%)

prune9.0ms (0.2%)

simplify345.0ms (7.5%)

localize48.0ms (1%)

series71.0ms (1.6%)

simplify124.0ms (2.7%)

rewrite206.0ms (4.5%)

eval38.0ms (0.8%)

prune4.0ms (0.1%)

regimes7.0ms (0.2%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

simplify118.0ms (2.6%)

soundness539.0ms (11.7%)

preprocess197.0ms (4.3%)

end0.0ms (0%)

Profiling