Metrics for Rust f64::acosh

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB 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)

sample855.0ms (17.4%)

Memory

-14.9MiB live, 976.9MiB allocated

Samples

661.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 310.0ms

ival-acosh: 270.0ms (87% of total)

ival->=: 28.0ms (9% of total)

exact: 8.0ms (2.6% of total)

ival-assert: 4.0ms (1.3% of total)

Bogosity

explain175.0ms (3.6%)

Memory

15.3MiB live, 293.7MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))`	oflow-rescue	128	0
↳	`(-.f64 (*.f64 x x) #s(literal 1 binary64))`	overflow	128
↳	`(*.f64 x x)`	overflow	128

Confusion

	Predicted +	Predicted -
+	128	0
-	0	128

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	128	0	0
-	0	0	128

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	128
1	128

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

39.0ms

512×

valid

Compiler

Compiled 178 to 66 computations (62.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-log: 7.0ms (28.1% of total)

ival-sqrt: 7.0ms (28.1% of total)

ival-mult: 4.0ms (16.1% of total)

ival-sub: 3.0ms (12% of total)

ival-add: 3.0ms (12% of total)

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

exact: 0.0ms (0% of total)

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

preprocess294.0ms (6%)

Memory

-29.1MiB live, 311.5MiB 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: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	51.6%	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify264.0ms (5.4%)

Memory

32.8MiB live, 261.5MiB 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)

localize27.0ms (0.6%)

Memory

-33.1MiB live, 49.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(-.f64 (*.f64 x x) #s(literal 1 binary64))
accuracy	0.00390625	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
accuracy	0.0078125	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))
accuracy	29.8490463837099	(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))

Samples

17.0ms

256×

valid

Compiler

Compiled 68 to 16 computations (76.5% saved)

Precisions

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

ival-log: 3.0ms (29.5% of total)

ival-mult: 2.0ms (19.7% of total)

ival-sqrt: 2.0ms (19.7% of total)

ival-sub: 1.0ms (9.8% of total)

ival-add: 1.0ms (9.8% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.1%)

Memory

12.3MiB live, 12.3MiB 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
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)))
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

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)))

1.0ms

-inf

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

simplify212.0ms (4.3%)

Memory

-9.2MiB live, 272.8MiB 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))

rewrite151.0ms (3.1%)

Memory

1.4MiB live, 239.2MiB 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
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eval48.0ms (1%)

Memory: 24.4MiB live, 100.3MiB allocated
Compiler: Compiled 8 015 to 1 572 computations (80.4% saved)

prune8.0ms (0.2%)

Memory

-19.4MiB live, 24.9MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	363	4	367
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	364	4	368

Accuracy

100.0%

Counts

368 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	51.6%	(neg.f64 (log.f64 (/.f64 (pow.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x) #s(literal -1 binary64)) #s(literal 1 binary64))))
▶	51.6%	(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))
▶	99.6%	(log.f64 (+.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x)))))
▶	98.8%	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))

Compiler

Compiled 35 to 28 computations (20% saved)

simplify412.0ms (8.4%)

Memory

20.1MiB live, 252.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score
cost-diff	0	(pow.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x) #s(literal -1 binary64))
cost-diff	256	(neg.f64 (log.f64 (/.f64 (pow.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x) #s(literal -1 binary64)) #s(literal 1 binary64))))
cost-diff	704	(/.f64 (pow.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x) #s(literal -1 binary64)) #s(literal 1 binary64))
cost-diff	6336	(log.f64 (/.f64 (pow.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x) #s(literal -1 binary64)) #s(literal 1 binary64)))
cost-diff	0	(fma.f64 x x #s(literal -1 binary64))
cost-diff	0	(sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))
cost-diff	0	(+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x)
cost-diff	0	(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))
cost-diff	0	(-.f64 x (/.f64 #s(literal 1/2 binary64) x))
cost-diff	0	#s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x)))
cost-diff	0	(+.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))))
cost-diff	0	(log.f64 (+.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x)))))
cost-diff	0	(*.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)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	171
0	39	157
1	59	156
2	76	156
3	120	156
4	168	156
5	308	156
6	554	156
7	1101	156
8	2796	156
9	4541	156
10	5594	156
11	6043	156
12	6146	156
13	6219	156
14	6293	156
15	7175	156
16	7671	156
0	8003	156

Stop Event

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

Calls

Call 1

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

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

localize71.0ms (1.4%)

Memory

-16.0MiB live, 107.2MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0	(neg.f64 (log.f64 (/.f64 (pow.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x) #s(literal -1 binary64)) #s(literal 1 binary64))))
accuracy	0	(log.f64 (/.f64 (pow.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x) #s(literal -1 binary64)) #s(literal 1 binary64)))
accuracy	0.0078125	(+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x)
accuracy	29.8490463837099	(sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))
accuracy	0	(fma.f64 x x #s(literal -1 binary64))
accuracy	0.00390625	(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))
accuracy	0.0078125	(+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x)
accuracy	29.8490463837099	(sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))
accuracy	0	(-.f64 x (/.f64 #s(literal 1/2 binary64) x))
accuracy	0.00390625	(log.f64 (+.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x)))))
accuracy	0.0078125	(+.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))))
accuracy	0.31679762499980807	#s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x)))
accuracy	0	(*.f64 #s(literal 2 binary64) x)
accuracy	0.00390625	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
accuracy	0.9062005938815855	#s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x))

Samples

48.0ms

256×

valid

Compiler

Compiled 295 to 44 computations (85.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 35.0ms

ival-log: 12.0ms (34.4% of total)

ival-add: 4.0ms (11.5% of total)

ival-mult: 4.0ms (11.5% of total)

ival-sub: 4.0ms (11.5% of total)

ival-sqrt: 4.0ms (11.5% of total)

ival-div: 3.0ms (8.6% of total)

ival-pow: 3.0ms (8.6% of total)

exact: 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)

series13.0ms (0.3%)

Memory

22.4MiB live, 22.4MiB allocated

Counts

15 → 180

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	x	@	0	((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)) (log (+ (sqrt (+ (* x x) -1)) x)) (+ (sqrt (+ (* x x) -1)) x) (sqrt (+ (* x x) -1)) (+ (* x x) -1) (log (/ (pow (+ (sqrt (+ (* x x) -1)) x) -1) 1)) (/ (pow (+ (sqrt (+ (* x x) -1)) x) -1) 1) (neg (log (/ (pow (+ (sqrt (+ (* x x) -1)) x) -1) 1))) (pow (+ (sqrt (+ (* x x) -1)) x) -1))
2.0ms	x	@	inf	((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)) (log (+ (sqrt (+ (* x x) -1)) x)) (+ (sqrt (+ (* x x) -1)) x) (sqrt (+ (* x x) -1)) (+ (* x x) -1) (log (/ (pow (+ (sqrt (+ (* x x) -1)) x) -1) 1)) (/ (pow (+ (sqrt (+ (* x x) -1)) x) -1) 1) (neg (log (/ (pow (+ (sqrt (+ (* x x) -1)) x) -1) 1))) (pow (+ (sqrt (+ (* x x) -1)) x) -1))
2.0ms	x	@	-inf	((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)) (log (+ (sqrt (+ (* x x) -1)) x)) (+ (sqrt (+ (* x x) -1)) x) (sqrt (+ (* x x) -1)) (+ (* x x) -1) (log (/ (pow (+ (sqrt (+ (* x x) -1)) x) -1) 1)) (/ (pow (+ (sqrt (+ (* x x) -1)) x) -1) 1) (neg (log (/ (pow (+ (sqrt (+ (* x x) -1)) x) -1) 1))) (pow (+ (sqrt (+ (* x x) -1)) x) -1))

Time

Variable

Point

Expression

3.0ms

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

2.0ms

inf

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

2.0ms

-inf

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

simplify247.0ms (5%)

Memory

10.6MiB live, 197.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	240	2291
1	674	2151
2	1977	2087
0	8473	2013

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 176

Calls

Call 1

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

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

rewrite199.0ms (4%)

Memory

7.3MiB live, 195.4MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	143
0	39	129
1	155	128
2	969	128
0	8721	128

Stop Event

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

Counts

15 → 726

Calls

Call 1

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

Outputs
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eval266.0ms (5.4%)

Memory: -1.8MiB live, 366.2MiB allocated
Compiler: Compiled 26 427 to 3 840 computations (85.5% saved)

prune23.0ms (0.5%)

Memory

1.7MiB live, 78.1MiB allocated

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	1 164	2	1 166
Fresh	0	0	0
Picked	1	3	4
Done	0	0	0
Total	1 165	5	1 170

Accuracy

100.0%

Counts

1 170 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(neg.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) x))))
▶	98.8%	(neg.f64 (log.f64 #s(approx (/ (pow (+ (sqrt (+ (* x x) -1)) x) -1) 1) (/.f64 #s(literal 1/2 binary64) x))))
✓	51.6%	(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))
✓	99.6%	(log.f64 (+.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x)))))
✓	98.8%	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))

Compiler

Compiled 40 to 34 computations (15% saved)

simplify354.0ms (7.2%)

Memory

9.0MiB live, 169.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) x)
cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) x))
cost-diff	256	(neg.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) x))))
cost-diff	576	(log.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) x)))
cost-diff	0	(/.f64 #s(literal 1/2 binary64) x)
cost-diff	0	#s(approx (/ (pow (+ (sqrt (+ (* x x) -1)) x) -1) 1) (/.f64 #s(literal 1/2 binary64) x))
cost-diff	0	(log.f64 #s(approx (/ (pow (+ (sqrt (+ (* x x) -1)) x) -1) 1) (/.f64 #s(literal 1/2 binary64) x)))
cost-diff	0	(neg.f64 (log.f64 #s(approx (/ (pow (+ (sqrt (+ (* x x) -1)) x) -1) 1) (/.f64 #s(literal 1/2 binary64) x))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	144
0	30	136
1	50	134
2	71	134
3	122	134
4	161	134
5	294	134
6	542	134
7	1061	134
8	2662	134
9	4461	134
10	5472	134
11	5936	134
12	6047	134
13	6121	134
14	6195	134
15	7077	134
16	7573	134
0	8009	126

Stop Event

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

Calls

Call 1

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

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

localize334.0ms (6.8%)

Memory

-56.8MiB live, 96.8MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(neg.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) x))))
accuracy	0	(log.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) x)))
accuracy	0.0078125	(+.f64 #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) x)
accuracy	0.31679762499980807	#s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x)))
accuracy	0	(/.f64 #s(literal 1/2 binary64) x)
accuracy	0	(neg.f64 (log.f64 #s(approx (/ (pow (+ (sqrt (+ (* x x) -1)) x) -1) 1) (/.f64 #s(literal 1/2 binary64) x))))
accuracy	0	(log.f64 #s(approx (/ (pow (+ (sqrt (+ (* x x) -1)) x) -1) 1) (/.f64 #s(literal 1/2 binary64) x)))
accuracy	0.902565842509187	#s(approx (/ (pow (+ (sqrt (+ (* x x) -1)) x) -1) 1) (/.f64 #s(literal 1/2 binary64) x))

Samples

322.0ms

256×

valid

Compiler

Compiled 182 to 35 computations (80.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 312.0ms

ival-log: 140.0ms (44.9% of total)

ival-pow: 119.0ms (38.1% of total)

ival-add: 36.0ms (11.5% of total)

ival-div: 5.0ms (1.6% of total)

ival-sqrt: 4.0ms (1.3% of total)

ival-sub: 3.0ms (1% of total)

ival-mult: 2.0ms (0.6% of total)

ival-neg: 2.0ms (0.6% of total)

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

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

exact: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory

8.0MiB live, 8.0MiB allocated

Counts

9 → 108

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

inf

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

1.0ms

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

1.0ms

-inf

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

simplify166.0ms (3.4%)

Memory

-1.4MiB live, 152.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	209	1489
1	596	1369
2	1748	1339
0	8266	1306

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 107

Calls

Call 1

Inputs
(* -1 (log (/ 1 (sqrt -1))))
(- (/ x (sqrt -1)) (log (/ 1 (sqrt -1))))
(- (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))) (log (/ 1 (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 (/ 1 (sqrt -1))))
(log (/ 1 (sqrt -1)))
(+ (log (/ 1 (sqrt -1))) (* -1 (/ x (sqrt -1))))
(+ (log (/ 1 (sqrt -1))) (* x (- (* 1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(+ (log (/ 1 (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 (sqrt -1))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (/ 1 (sqrt -1)))
(+ (* x (- (* 1/2 (/ x (pow (sqrt -1) 3))) (/ 1 (pow (sqrt -1) 2)))) (/ 1 (sqrt -1)))
(+ (* x (- (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/2 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (pow (sqrt -1) 2)))) (/ 1 (sqrt -1)))
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(log (/ 1 (sqrt -1)))
(+ (log (/ 1 (sqrt -1))) (* -1 (/ x (sqrt -1))))
(+ (log (/ 1 (sqrt -1))) (* x (- (* 1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(+ (log (/ 1 (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 (sqrt -1))))
(- (/ x (sqrt -1)) (log (/ 1 (sqrt -1))))
(- (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))) (log (/ 1 (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 (/ 1 (sqrt -1))))
(/ 1 (sqrt -1))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (/ 1 (sqrt -1)))
(+ (* x (- (* 1/2 (/ x (pow (sqrt -1) 3))) (/ 1 (pow (sqrt -1) 2)))) (/ 1 (sqrt -1)))
(+ (* x (- (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/2 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (pow (sqrt -1) 2)))) (/ 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 (+ (log 1/2) (log (/ 1 x))))
(* -1 (+ (log 1/2) (+ (log (/ 1 x)) (* 1/4 (/ 1 (pow x 2))))))
(- (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2))) (+ (log 1/2) (log (/ 1 x))))
(- (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))) (+ (log 1/2) (+ (log (/ 1 x)) (* 1/4 (/ 1 (pow x 2))))))
(+ (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)
(/ (+ 1/2 (+ (/ 1/16 (pow x 4)) (* 1/8 (/ 1 (pow x 2))))) x)
(/ (+ 1/2 (+ (/ 1/16 (pow x 4)) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6)))))) x)
(/ 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)) (* 1/4 (/ 1 (pow x 2))))))
(- (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2))) (+ (log 1/2) (log (/ 1 x))))
(- (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))) (+ (log 1/2) (+ (log (/ 1 x)) (* 1/4 (/ 1 (pow x 2))))))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(/ (+ 1/2 (+ (/ 1/16 (pow x 4)) (* 1/8 (/ 1 (pow x 2))))) x)
(/ (+ 1/2 (+ (/ 1/16 (pow x 4)) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6)))))) x)
(* 2 x)
(* 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)))))
(* -1 (+ (log -2) (* -1 (log (/ -1 x)))))
(- (* 1/4 (/ 1 (pow x 2))) (+ (log -2) (* -1 (log (/ -1 x)))))
(- (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2)))) (+ (log -2) (* -1 (log (/ -1 x)))))
(- (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6))))) (+ (log -2) (* -1 (log (/ -1 x)))))
(+ (log -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)
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 2)))
(* -1 (* x (- (+ (/ 1/8 (pow x 4)) (* 1/2 (/ 1 (pow x 2)))) 2)))
(* -1 (* x (- (+ (/ 1/8 (pow x 4)) (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) 2)))
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(+ (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 -2) (* -1 (log (/ -1 x)))))
(- (* 1/4 (/ 1 (pow x 2))) (+ (log -2) (* -1 (log (/ -1 x)))))
(- (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2)))) (+ (log -2) (* -1 (log (/ -1 x)))))
(- (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6))))) (+ (log -2) (* -1 (log (/ -1 x)))))
(* 2 x)
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 2)))
(* -1 (* x (- (+ (/ 1/8 (pow x 4)) (* 1/2 (/ 1 (pow x 2)))) 2)))
(* -1 (* x (- (+ (/ 1/8 (pow x 4)) (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) 2)))
(/ 1/2 x)
(/ (+ 1/2 (* 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 (log (/ 1 (sqrt -1))))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(- (/ x (sqrt -1)) (log (/ 1 (sqrt -1))))
(+.f64 (log.f64 (sqrt.f64 #s(literal -1 binary64))) (/.f64 x (sqrt.f64 #s(literal -1 binary64))))
(- (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))) (log (/ 1 (sqrt -1))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/6 binary64) (+.f64 (log.f64 (sqrt.f64 #s(literal -1 binary64))) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(- (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))) (log (/ 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 (log.f64 (sqrt.f64 #s(literal -1 binary64))) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(log (/ 1 (sqrt -1)))
(neg.f64 (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (log (/ 1 (sqrt -1))) (* -1 (/ x (sqrt -1))))
(neg.f64 (+.f64 (log.f64 (sqrt.f64 #s(literal -1 binary64))) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(+ (log (/ 1 (sqrt -1))) (* x (- (* 1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 #s(literal -1/6 binary64) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (+.f64 (log.f64 (sqrt.f64 #s(literal -1 binary64))) (/.f64 x (sqrt.f64 #s(literal -1 binary64))))))
(+ (log (/ 1 (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)))) (neg.f64 (+.f64 (log.f64 (sqrt.f64 #s(literal -1 binary64))) (/.f64 x (sqrt.f64 #s(literal -1 binary64))))))
(/ 1 (sqrt -1))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (/ 1 (sqrt -1)))
(+.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(+ (* x (- (* 1/2 (/ x (pow (sqrt -1) 3))) (/ 1 (pow (sqrt -1) 2)))) (/ 1 (sqrt -1)))
(fma.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) x (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(+ (* x (- (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/2 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (pow (sqrt -1) 2)))) (/ 1 (sqrt -1)))
(fma.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) #s(literal -1/8 binary64) (fma.f64 #s(literal -1/2 binary64) (/.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64))) x (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(log (/ 1 (sqrt -1)))
(neg.f64 (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (log (/ 1 (sqrt -1))) (* -1 (/ x (sqrt -1))))
(neg.f64 (+.f64 (log.f64 (sqrt.f64 #s(literal -1 binary64))) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(+ (log (/ 1 (sqrt -1))) (* x (- (* 1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 #s(literal -1/6 binary64) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (+.f64 (log.f64 (sqrt.f64 #s(literal -1 binary64))) (/.f64 x (sqrt.f64 #s(literal -1 binary64))))))
(+ (log (/ 1 (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)))) (neg.f64 (+.f64 (log.f64 (sqrt.f64 #s(literal -1 binary64))) (/.f64 x (sqrt.f64 #s(literal -1 binary64))))))
(* -1 (log (/ 1 (sqrt -1))))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
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rewrite161.0ms (3.3%)

Memory

2.4MiB live, 156.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	131
0	30	123
1	139	121
2	916	121
0	8475	113

Stop Event

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

Counts

9 → 293

Calls

Call 1

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

Outputs
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eval86.0ms (1.7%)

Memory: 15.5MiB live, 87.5MiB allocated
Compiler: Compiled 9 355 to 1 623 computations (82.7% saved)

prune12.0ms (0.3%)

Memory

-19.3MiB live, 27.2MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	430	0	430
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	430	5	435

Accuracy

100.0%

Counts

435 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(neg.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) x))))
✓	98.8%	(neg.f64 (log.f64 #s(approx (/ (pow (+ (sqrt (+ (* x x) -1)) x) -1) 1) (/.f64 #s(literal 1/2 binary64) x))))
✓	51.6%	(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))
✓	99.6%	(log.f64 (+.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x)))))
✓	98.8%	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))

Compiler

Compiled 102 to 67 computations (34.3% saved)

regimes9.0ms (0.2%)

Memory

18.7MiB live, 18.7MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

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)

regimes7.0ms (0.1%)

Memory

15.6MiB live, 15.6MiB allocated

Counts

5 → 1

Calls

Call 1

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

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	x
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)))))

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)

regimes8.0ms (0.2%)

Memory

-22.1MiB live, 13.4MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

3 calls:

4.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))
2.0ms	x
1.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))

Results

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

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify27.0ms (0.6%)

Memory

-6.9MiB live, 67.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

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

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

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

soundness390.0ms (7.9%)

Memory

14.4MiB live, 302.4MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	150	559
1	411	533
2	1146	526
3	3331	488
4	7979	488
0	8531	459
0	25	143
0	39	129
1	155	128
2	969	128
0	8721	128

Stop Event

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

Compiler

Compiled 39 to 28 computations (28.2% saved)

preprocess84.0ms (1.7%)

Memory: -23.0MiB live, 100.2MiB allocated
Compiler: Compiled 94 to 62 computations (34% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample855.0ms (17.4%)

explain175.0ms (3.6%)

preprocess294.0ms (6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify264.0ms (5.4%)

localize27.0ms (0.6%)

series6.0ms (0.1%)

simplify212.0ms (4.3%)

rewrite151.0ms (3.1%)

eval48.0ms (1%)

prune8.0ms (0.2%)

simplify412.0ms (8.4%)

localize71.0ms (1.4%)

series13.0ms (0.3%)

simplify247.0ms (5%)

rewrite199.0ms (4%)

eval266.0ms (5.4%)

prune23.0ms (0.5%)

simplify354.0ms (7.2%)

localize334.0ms (6.8%)

series6.0ms (0.1%)

simplify166.0ms (3.4%)

rewrite161.0ms (3.3%)

eval86.0ms (1.7%)

prune12.0ms (0.3%)

regimes9.0ms (0.2%)

regimes7.0ms (0.1%)

regimes8.0ms (0.2%)

simplify27.0ms (0.6%)

soundness390.0ms (7.9%)

preprocess84.0ms (1.7%)

end0.0ms (0%)

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