Metrics for Hyperbolic arc-cosine

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze116.0ms (1.7%)

Memory

0.7MiB live, 40.2MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample2.6s (39.4%)

Memory

34.9MiB live, 3 034.6MiB allocated

Samples

1.2s	7 293×	1	invalid
667.0ms	8 256×	0	valid
107.0ms	1 106×	0	invalid

Precisions

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

ival-log: 382.0ms (27% of total)

ival-mult: 264.0ms (18.6% of total)

adjust: 233.0ms (16.4% of total)

ival-sqrt: 229.0ms (16.2% of total)

ival-sub: 146.0ms (10.3% of total)

ival-add: 132.0ms (9.3% of total)

ival-true: 13.0ms (0.9% of total)

exact: 12.0ms (0.8% of total)

ival-assert: 7.0ms (0.5% of total)

Bogosity

explain157.0ms (2.4%)

Memory

-18.4MiB live, 141.9MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))`	oflow-rescue	136	0
↳	`(-.f64 (*.f64 x x) #s(literal 1 binary64))`	overflow	136
↳	`(*.f64 x x)`	overflow	136
`log.f64`	`(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))`	oflow-rescue	1	0
↳	`(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))`	overflow	1
↳	`(-.f64 (*.f64 x x) #s(literal 1 binary64))`	overflow	136
↳	`(*.f64 x x)`	overflow	136

Confusion

	Predicted +	Predicted -
+	136	0
-	0	120

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	136	0	0
-	0	0	120

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	120
1	135
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

33.0ms

512×

valid

Compiler

Compiled 79 to 25 computations (68.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-log: 6.0ms (29.6% of total)

ival-mult: 4.0ms (19.7% of total)

ival-sqrt: 4.0ms (19.7% of total)

ival-sub: 3.0ms (14.8% of total)

ival-add: 3.0ms (14.8% of total)

ival-true: 1.0ms (4.9% of total)

exact: 0.0ms (0% of total)

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

preprocess487.0ms (7.3%)

Memory

1.6MiB live, 258.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	27	19
2	59	19
3	130	19
4	295	19
5	579	19
6	1088	19
7	1677	19
8	3021	19
9	4118	19
10	5059	19
11	5487	19
12	5727	19
13	5799	19
14	5883	19
15	6475	19
16	7565	19
17	7621	19
18	7719	19
19	7753	19
20	7769	19
0	7	9
0	12	9
1	21	9
2	25	9
3	40	9
4	71	9
5	132	9
6	292	9
7	572	9
8	2045	9
9	3155	9
10	4433	9
11	5106	9
12	5408	9
13	5593	9
14	5695	9
15	6014	9
16	6560	9
17	7671	9
0	8091	8

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	48.5%	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify375.0ms (5.6%)

Memory

-6.0MiB live, 233.8MiB 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)

localize42.0ms (0.6%)

Memory

-8.1MiB live, 31.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(-.f64 (*.f64 x x) #s(literal 1 binary64))
accuracy	0.01171875	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))
accuracy	0.2421355984240639	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
accuracy	31.59894856529175	(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))

Samples

36.0ms

256×

valid

Compiler

Compiled 35 to 9 computations (74.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 29.0ms

ival-sqrt: 21.0ms (71.2% of total)

ival-log: 3.0ms (10.2% of total)

ival-mult: 2.0ms (6.8% of total)

ival-sub: 1.0ms (3.4% of total)

ival-add: 1.0ms (3.4% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.1%)

Memory

8.5MiB live, 8.5MiB allocated

Counts

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)))

simplify174.0ms (2.6%)

Memory

0.3MiB live, 157.6MiB 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))

rewrite294.0ms (4.4%)

Memory

8.4MiB live, 253.5MiB 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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eval95.0ms (1.4%)

Memory: -2.2MiB live, 73.7MiB allocated
Compiler: Compiled 8 015 to 1 572 computations (80.4% saved)

prune35.0ms (0.5%)

Memory

-15.1MiB live, 24.5MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

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

Accuracy

100.0%

Counts

368 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	48.5%	(log.f64 (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))
▶	48.5%	(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))
▶	98.9%	(log.f64 (+.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x)))))
▶	98.6%	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
▶	98.6%	#s(approx (log (+ x (sqrt (- (* x x) 1)))) (+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64))))

Compiler

Compiled 78 to 62 computations (20.5% saved)

simplify174.0ms (2.6%)

Memory

5.9MiB live, 241.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(log.f64 #s(literal 2 binary64))
cost-diff	0	(log.f64 x)
cost-diff	0	(+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64)))
cost-diff	0	#s(approx (log (+ x (sqrt (- (* x x) 1)))) (+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64))))
cost-diff	0	(sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(log.f64 (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))
cost-diff	1472	(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (sqrt.f64 (fma.f64 x x #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 #s(literal 2 binary64) x)
cost-diff	0	#s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x))
cost-diff	0	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
cost-diff	0	(-.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)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	167
0	46	155
1	62	155
2	87	155
3	133	155
4	242	155
5	721	155
6	2314	155
7	5873	155
8	7882	155
0	8002	155

Stop Event

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

Calls

Call 1

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

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

localize98.0ms (1.5%)

Memory

-6.0MiB live, 157.5MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	(log.f64 x)
accuracy	0	(log.f64 #s(literal 2 binary64))
accuracy	0.24609375	(+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64)))
accuracy	0.6497871153757037	#s(approx (log (+ x (sqrt (- (* x x) 1)))) (+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64))))
accuracy	0	(sqrt.f64 x)
accuracy	0.07421875	(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
accuracy	0.2421355984240639	(log.f64 (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))
accuracy	31.59894856529175	(sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))
accuracy	0	(fma.f64 x x #s(literal -1 binary64))
accuracy	0.01171875	(+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x)
accuracy	0.2421355984240639	(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))
accuracy	31.59894856529175	(sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))
accuracy	0	(*.f64 #s(literal 2 binary64) x)
accuracy	0.2421355984240639	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
accuracy	0.7032586947651761	#s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x))
accuracy	0	(-.f64 x (/.f64 #s(literal 1/2 binary64) x))
accuracy	0.01171875	(+.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))))
accuracy	0.2421355984240639	(log.f64 (+.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x)))))
accuracy	0.4573919727385882	#s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x)))

Samples

49.0ms

256×

valid

Compiler

Compiled 147 to 26 computations (82.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-log: 13.0ms (36.3% of total)

ival-add: 6.0ms (16.7% of total)

ival-mult: 5.0ms (13.9% of total)

ival-sqrt: 5.0ms (13.9% of total)

ival-sub: 3.0ms (8.4% of total)

ival-div: 2.0ms (5.6% of total)

exact: 1.0ms (2.8% of total)

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

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

series93.0ms (1.4%)

Memory

26.4MiB live, 182.0MiB allocated

Counts

18 → 204

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
46.0ms	x	@	0	((log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)) (- x (/ 1/2 x)) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (* 2 x) (log (+ (sqrt (+ (* x x) -1)) x)) (+ (sqrt (+ (* x x) -1)) x) (sqrt (+ (* x x) -1)) (+ (* x x) -1) (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) (log (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1)))) (sqrt x) (log (+ x (sqrt (- (* x x) 1)))) (+ (log x) (log 2)) (log x) (log 2))
23.0ms	x	@	-inf	((log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)) (- x (/ 1/2 x)) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (* 2 x) (log (+ (sqrt (+ (* x x) -1)) x)) (+ (sqrt (+ (* x x) -1)) x) (sqrt (+ (* x x) -1)) (+ (* x x) -1) (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) (log (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1)))) (sqrt x) (log (+ x (sqrt (- (* x x) 1)))) (+ (log x) (log 2)) (log x) (log 2))
18.0ms	x	@	inf	((log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)) (- x (/ 1/2 x)) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (* 2 x) (log (+ (sqrt (+ (* x x) -1)) x)) (+ (sqrt (+ (* x x) -1)) x) (sqrt (+ (* x x) -1)) (+ (* x x) -1) (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) (log (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1)))) (sqrt x) (log (+ x (sqrt (- (* x x) 1)))) (+ (log x) (log 2)) (log x) (log 2))

Time

Variable

Point

Expression

46.0ms

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

23.0ms

-inf

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

18.0ms

inf

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

simplify121.0ms (1.8%)

Memory

-2.5MiB live, 153.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	217	2374
1	601	2169
2	1824	2096
0	5316	2018

Stop Event

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

Counts

204 → 200

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

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)))
(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)))
(* 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
#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))
(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)))
(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 x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(log (sqrt -1))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f64 (/.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)))))
(+ (log 2) (log x))
(+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64)))
(+ (log 2) (log x))
(+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64)))
(+ (log 2) (log x))
(+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64)))
(+ (log 2) (log x))
(+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64)))
(log x)
(log.f64 x)
(log x)
(log.f64 x)
(log x)
(log.f64 x)
(log x)
(log.f64 x)
(+ (log 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 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) x) #s(literal 1 binary64) (.f64 #s(literal 2 binary64) 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)
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(- (+ (log (+ 1 (pow (sqrt -1) 2))) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (* 3 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2)))) (pow x 4))) (* -1/720 (/ (+ (* 45 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (+ (* 45 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2))) (* 30 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 3))))) (pow x 6)))))) (/ 1/2 (* (pow x 2) (+ 1 (pow (sqrt -1) 2)))))
(fma.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)) #s(literal 90 binary64) (/.f64 #s(literal 30 binary64) #s(literal 0 binary64))) (pow.f64 x #s(literal 6 binary64))) #s(literal -1/720 binary64) (-.f64 (-.f64 (+.f64 (/.f64 (*.f64 (/.f64 #s(literal 3 binary64) #s(literal 0 binary64)) #s(literal -1/12 binary64)) (pow.f64 x #s(literal 4 binary64))) (log.f64 #s(literal 0 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) x))) (/.f64 #s(literal -1/2 binary64) #s(literal 0 binary64))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(+ (log -1/2) (log (/ -1 x)))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal -1/2 binary64)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (log.f64 #s(literal -1/2 binary64)))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+.f64 (+.f64 (+.f64 (/.f64 #s(literal 3/32 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (log.f64 (/.f64 #s(literal -1 binary64) x))) (log.f64 #s(literal -1/2 binary64)))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(+.f64 (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 5/96 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 #s(literal 3/32 binary64) (pow.f64 x #s(literal 4 binary64)))) (log.f64 (/.f64 #s(literal -1 binary64) x))) (log.f64 #s(literal -1/2 binary64)))
(+ (log -1) (+ (log 2) (* -1 (log (/ -1 x)))))
(+.f64 (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x))) (log.f64 #s(literal -1 binary64)))
(+ (log -1) (+ (log 2) (* -1 (log (/ -1 x)))))
(+.f64 (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x))) (log.f64 #s(literal -1 binary64)))
(+ (log -1) (+ (log 2) (* -1 (log (/ -1 x)))))
(+.f64 (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x))) (log.f64 #s(literal -1 binary64)))
(+ (log -1) (+ (log 2) (* -1 (log (/ -1 x)))))
(+.f64 (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x))) (log.f64 #s(literal -1 binary64)))
(+ (log -1) (* -1 (log (/ -1 x))))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))
(+ (log -1) (* -1 (log (/ -1 x))))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))
(+ (log -1) (* -1 (log (/ -1 x))))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))
(+ (log -1) (* -1 (log (/ -1 x))))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))

rewrite168.0ms (2.5%)

Memory

-0.7MiB live, 228.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	145
0	46	131
1	164	131
2	1039	131
0	8709	131

Stop Event

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

Counts

18 → 531

Calls

Call 1

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

Outputs
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eval158.0ms (2.4%)

Memory: 22.3MiB live, 302.0MiB allocated
Compiler: Compiled 17 709 to 2 411 computations (86.4% saved)

prune24.0ms (0.4%)

Memory

-22.7MiB live, 66.1MiB allocated

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	906	3	909
Fresh	0	0	0
Picked	2	3	5
Done	0	0	0
Total	908	6	914

Accuracy

100.0%

Counts

914 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	48.5%	(neg.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))))
✓	48.5%	(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))
✓	98.9%	(log.f64 (+.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x)))))
▶	0.6%	(log.f64 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary64)))
✓	98.6%	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
▶	99.0%	#s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x))))

Compiler

Compiled 42 to 37 computations (11.9% saved)

simplify133.0ms (2%)

Memory

29.3MiB live, 187.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	106
0	37	95
1	53	93
2	73	93
3	115	93
4	216	93
5	603	93
6	1927	93
7	5290	93
0	8701	93

Stop Event

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

Calls

Call 1

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

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

localize83.0ms (1.2%)

Memory

-51.5MiB live, 170.7MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x)
accuracy	0.017910009768442016	(log.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x)))
accuracy	0.19979285510091666	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))
accuracy	31.59894856529175	(sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))
accuracy	0.2421355984240639	(log.f64 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary64)))
accuracy	62.55855820189363	#s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary64))
accuracy	0	(/.f64 #s(literal 1/2 binary64) x)
accuracy	0	(neg.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x)))
accuracy	0.0078125	(log.f64 (/.f64 #s(literal 1/2 binary64) x))
accuracy	0.6497871153757037	#s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x))))

Samples

56.0ms

256×

valid

Compiler

Compiled 106 to 25 computations (76.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-log: 11.0ms (30.8% of total)

ival-sqrt: 6.0ms (16.8% of total)

ival-add: 5.0ms (14% of total)

ival-mult: 5.0ms (14% of total)

ival-div: 4.0ms (11.2% of total)

ival-neg: 3.0ms (8.4% of total)

ival-sub: 1.0ms (2.8% of total)

exact: 1.0ms (2.8% of total)

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

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

series58.0ms (0.9%)

Memory

29.0MiB live, 65.7MiB allocated

Counts

11 → 132

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

32.0ms

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

13.0ms

-inf

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

7.0ms

inf

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

simplify129.0ms (1.9%)

Memory

-13.3MiB live, 137.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	286	1749
1	819	1534
2	2532	1473
0	8176	1434

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 131

Calls

Call 1

Inputs
(log (sqrt -1))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(* -1 (+ (log 1/2) (* -1 (log x))))
(* -1 (+ (log 1/2) (* -1 (log x))))
(* -1 (+ (log 1/2) (* -1 (log x))))
(* -1 (+ (log 1/2) (* -1 (log x))))
(+ (log 1/2) (* -1 (log x)))
(+ (log 1/2) (* -1 (log x)))
(+ (log 1/2) (* -1 (log x)))
(+ (log 1/2) (* -1 (log x)))
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(log (sqrt -1))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(sqrt -1)
(+ x (sqrt -1))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(log (/ 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))))))
(+ (log 2) (* -1 (log (/ 1 x))))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(* -1 (+ (log 1/2) (log (/ 1 x))))
(* -1 (+ (log 1/2) (log (/ 1 x))))
(* -1 (+ (log 1/2) (log (/ 1 x))))
(* -1 (+ (log 1/2) (log (/ 1 x))))
(+ (log 1/2) (log (/ 1 x)))
(+ (log 1/2) (log (/ 1 x)))
(+ (log 1/2) (log (/ 1 x)))
(+ (log 1/2) (log (/ 1 x)))
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(+ (log 2) (* -1 (log (/ 1 x))))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(* 2 x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(+ (log 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)))))
(+ (log -1/2) (log (/ -1 x)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(* -1 (+ (log -1/2) (log (/ -1 x))))
(* -1 (+ (log -1/2) (log (/ -1 x))))
(* -1 (+ (log -1/2) (log (/ -1 x))))
(* -1 (+ (log -1/2) (log (/ -1 x))))
(+ (log -1/2) (log (/ -1 x)))
(+ (log -1/2) (log (/ -1 x)))
(+ (log -1/2) (log (/ -1 x)))
(+ (log -1/2) (log (/ -1 x)))
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(+ (log (+ 1 (pow (sqrt -1) 2))) (* -1 (log (/ -1 x))))
(- (+ (log (+ 1 (pow (sqrt -1) 2))) (* -1 (log (/ -1 x)))) (* 1/2 (/ 1 (* (pow x 2) (+ 1 (pow (sqrt -1) 2))))))
(- (+ (log (+ 1 (pow (sqrt -1) 2))) (+ (* -1 (log (/ -1 x))) (* -1/24 (/ (+ (* 3 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (* 3 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2)))) (pow x 4))))) (/ 1/2 (* (pow x 2) (+ 1 (pow (sqrt -1) 2)))))
(- (+ (log (+ 1 (pow (sqrt -1) 2))) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (* 3 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2)))) (pow x 4))) (* -1/720 (/ (+ (* 45 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (+ (* 45 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2))) (* 30 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 3))))) (pow x 6)))))) (/ 1/2 (* (pow x 2) (+ 1 (pow (sqrt -1) 2)))))
(* -1 (* x (+ 1 (pow (sqrt -1) 2))))
(* -1 (* x (- (+ 1 (pow (sqrt -1) 2)) (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) (pow (sqrt -1) 2)))))
(* -1 (* x (- (+ 1 (+ (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4))) (pow (sqrt -1) 2))) (* 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))))
(* -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
(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)))))
(* -1 (+ (log 1/2) (* -1 (log x))))
(-.f64 (log.f64 x) (log.f64 #s(literal 1/2 binary64)))
(* -1 (+ (log 1/2) (* -1 (log x))))
(-.f64 (log.f64 x) (log.f64 #s(literal 1/2 binary64)))
(* -1 (+ (log 1/2) (* -1 (log x))))
(-.f64 (log.f64 x) (log.f64 #s(literal 1/2 binary64)))
(* -1 (+ (log 1/2) (* -1 (log x))))
(-.f64 (log.f64 x) (log.f64 #s(literal 1/2 binary64)))
(+ (log 1/2) (* -1 (log x)))
(-.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 x))
(+ (log 1/2) (* -1 (log x)))
(-.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 x))
(+ (log 1/2) (* -1 (log x)))
(-.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 x))
(+ (log 1/2) (* -1 (log x)))
(-.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 x))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(log (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) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) x #s(literal 1 binary64)) x (sqrt.f64 #s(literal -1 binary64)))
(log (/ 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))))
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(- (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2)))) (+ (log -2) (* -1 (log (/ -1 x)))))
(-.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 (/.f64 #s(literal 1/2 binary64) x) x)) x)
(* -1 (* x (- (+ (/ 1/8 (pow x 4)) (* 1/2 (/ 1 (pow x 2)))) 2)))
(*.f64 (neg.f64 x) (-.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) #s(literal 2 binary64)))
(* -1 (* x (- (+ (/ 1/8 (pow x 4)) (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) 2)))
(*.f64 (neg.f64 x) (-.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64)))) #s(literal 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 (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) x))
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 5/128 binary64) (.f64 x x)) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 4 binary64))) (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64))) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) x) x (neg.f64 x))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))
(fma.f64 (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) x) x (neg.f64 x))
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))
(neg.f64 (fma.f64 (-.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (*.f64 x x)) #s(literal -1/8 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) x x))

rewrite159.0ms (2.4%)

Memory

8.9MiB live, 168.1MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	96
0	37	85
1	137	81
2	773	81
0	8637	81

Stop Event

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

Counts

11 → 606

Calls

Call 1

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

Outputs
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eval115.0ms (1.7%)

Memory: -0.8MiB live, 153.7MiB allocated
Compiler: Compiled 15 673 to 2 902 computations (81.5% saved)

prune21.0ms (0.3%)

Memory

1.7MiB live, 40.7MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	737	0	737
Fresh	0	0	0
Picked	0	3	3
Done	0	3	3
Total	737	6	743

Accuracy

100.0%

Counts

743 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	48.5%	(neg.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))))
✓	48.5%	(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))
✓	98.9%	(log.f64 (+.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x)))))
✓	0.6%	(log.f64 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary64)))
✓	98.6%	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
✓	99.0%	#s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) x))))

Compiler

Compiled 110 to 75 computations (31.8% saved)

regimes10.0ms (0.2%)

Memory

18.5MiB live, 18.5MiB allocated

Counts

9 → 1

Calls

Call 1

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

Outputs
#s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f64 (log.f64 (/.f64 #s(literal 1/2 binary64) 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
99.0%	1	`x`
99.0%	1	`(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))`
99.0%	1	`(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))`

Compiler

Compiled 18 to 14 computations (22.2% saved)

regimes10.0ms (0.2%)

Memory

-40.8MiB live, 9.2MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

3 calls:

7.0ms	x
2.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
2.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))

Results

Accuracy	Segments	Branch
98.6%	1	`x`
98.6%	1	`(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))`
98.6%	1	`(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))`

Compiler

Compiled 18 to 14 computations (22.2% saved)

regimes4.0ms (0.1%)

Memory

8.3MiB live, 8.3MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
0.6%	1	`x`
0.6%	1	`(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))`
0.6%	1	`(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))`

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify24.0ms (0.4%)

Memory

13.7MiB live, 51.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	43
1	30	43
2	32	43
3	33	43

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

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

(log.f64 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary64)))

Outputs

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

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

(log.f64 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary64)))

soundness631.0ms (9.5%)

Memory

14.7MiB live, 361.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	145
0	46	131
1	164	131
2	1039	131
0	8709	131
0	217	2374
1	601	2169
2	1824	2096
0	5316	2018
0	7	28
0	12	28
1	49	28
2	322	28
3	3626	28
0	8646	24
0	150	559
1	411	533
2	1146	526
3	3331	488
4	7979	488
0	8531	459

Stop Event

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

Compiler

Compiled 63 to 46 computations (27% saved)

preprocess43.0ms (0.6%)

Memory: 18.2MiB live, 55.6MiB allocated
Compiler: Compiled 46 to 40 computations (13% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze116.0ms (1.7%)

sample2.6s (39.4%)

explain157.0ms (2.4%)

preprocess487.0ms (7.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify375.0ms (5.6%)

localize42.0ms (0.6%)

series6.0ms (0.1%)

simplify174.0ms (2.6%)

rewrite294.0ms (4.4%)

eval95.0ms (1.4%)

prune35.0ms (0.5%)

simplify174.0ms (2.6%)

localize98.0ms (1.5%)

series93.0ms (1.4%)

simplify121.0ms (1.8%)

rewrite168.0ms (2.5%)

eval158.0ms (2.4%)

prune24.0ms (0.4%)

simplify133.0ms (2%)

localize83.0ms (1.2%)

series58.0ms (0.9%)

simplify129.0ms (1.9%)

rewrite159.0ms (2.4%)

eval115.0ms (1.7%)

prune21.0ms (0.3%)

regimes10.0ms (0.2%)

regimes10.0ms (0.2%)

regimes4.0ms (0.1%)

simplify24.0ms (0.4%)

soundness631.0ms (9.5%)

preprocess43.0ms (0.6%)

end0.0ms (0%)

Profiling