Metrics for Hyperbolic arc-(co)secant

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze3.0ms (0.1%)

Memory

4.4MiB live, 4.4MiB 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%	50%	0%	0%	50%	0%	3
33.3%	12.5%	25%	0%	0%	62.5%	0%	4
60%	18.7%	12.5%	0%	0%	68.7%	0%	5
77.8%	21.9%	6.2%	0%	0%	71.8%	0%	6
88.2%	23.4%	3.1%	0%	0%	73.4%	0%	7
93.9%	24.2%	1.6%	0%	0%	74.2%	0%	8
96.9%	24.6%	0.8%	0%	0%	74.6%	0%	9
98.4%	24.8%	0.4%	0%	0%	74.8%	0%	10
99.2%	24.9%	0.2%	0%	0%	74.9%	0%	11
99.6%	24.9%	0.1%	0%	0%	74.9%	0%	12

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.0s (17.6%)

Memory

31.5MiB live, 1 253.2MiB allocated

Samples

762.0ms	8 256×	0	valid
1.0ms	19×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 512.0ms

ival-log: 145.0ms (28.3% of total)

ival-div: 128.0ms (25% of total)

ival-sqrt: 73.0ms (14.3% of total)

ival-mult: 55.0ms (10.7% of total)

ival-sub: 55.0ms (10.7% of total)

ival-add: 43.0ms (8.4% of total)

ival-true: 6.0ms (1.2% of total)

exact: 5.0ms (1% of total)

ival-assert: 3.0ms (0.6% of total)

Bogosity

explain193.0ms (3.2%)

Memory

-38.6MiB live, 115.7MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))`
-	-	`#s(literal 1 binary64)`
-	-	`(/.f64 #s(literal 1 binary64) x)`
-	-	`(*.f64 x x)`
-	-	`(-.f64 #s(literal 1 binary64) (*.f64 x x))`
-	-	`(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))`
-	-	`(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)`
-	-	`x`
-	-	`(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

61.0ms

512×

valid

Compiler

Compiled 173 to 40 computations (76.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 46.0ms

ival-add: 22.0ms (47.4% of total)

ival-div: 7.0ms (15.1% of total)

ival-log: 6.0ms (12.9% of total)

ival-sqrt: 4.0ms (8.6% of total)

ival-mult: 3.0ms (6.5% of total)

ival-sub: 3.0ms (6.5% of total)

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

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

exact: 0.0ms (0% of total)

preprocess402.0ms (6.8%)

Memory

-10.8MiB live, 145.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 14 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	34	27
2	71	27
3	153	27
4	261	27
5	409	27
6	633	23
7	1008	23
8	1424	23
9	1995	23
10	4391	23
11	5872	23
12	6901	23
13	7311	23
14	7679	23
15	7835	23
0	9	13
0	16	13
1	24	13
2	31	13
3	39	13
4	54	13
5	74	13
6	117	13
7	315	13
8	597	13
9	1167	13
10	2099	13
11	3834	13
12	4826	13
13	5183	13
14	5518	11
15	5777	11
16	5858	11
17	6069	11
18	6989	11
0	8045	11

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 13 to 9 computations (30.8% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))

Compiler

Compiled 13 to 9 computations (30.8% saved)

simplify343.0ms (5.8%)

Memory

7.3MiB live, 163.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)
cost-diff	0	(/.f64 #s(literal 1 binary64) x)
cost-diff	0	(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
cost-diff	704	(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))

Iterations

Useful iterations: 14 (0.0ms)

Iter	Nodes	Cost
0	9	52
0	16	52
1	24	52
2	31	52
3	39	52
4	54	52
5	74	52
6	117	52
7	315	52
8	597	52
9	1167	52
10	2099	52
11	3834	52
12	4826	52
13	5183	52
14	5518	48
15	5777	48
16	5858	48
17	6069	48
18	6989	48
0	8045	48

Stop Event

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

Calls

Call 1

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

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

localize36.0ms (0.6%)

Memory

2.9MiB live, 41.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))
accuracy	0.00390625	(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
accuracy	0.015625	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))

Samples

29.0ms

256×

valid

Compiler

Compiled 106 to 20 computations (81.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-sqrt: 11.0ms (49.9% of total)

ival-div: 4.0ms (18.1% of total)

ival-log: 3.0ms (13.6% of total)

ival-mult: 2.0ms (9.1% of total)

ival-add: 1.0ms (4.5% of total)

ival-sub: 1.0ms (4.5% of total)

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

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

exact: 0.0ms (0% of total)

series9.0ms (0.1%)

Memory

12.7MiB live, 12.7MiB allocated

Counts

6 → 72

Calls

Call 1

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

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

Calls

3 calls:

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

Time

Variable

Point

Expression

2.0ms

inf

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

2.0ms

-inf

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

2.0ms

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

simplify237.0ms (4%)

Memory

-7.0MiB live, 150.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	155	803
1	409	778
2	1098	758
3	3208	745
4	7995	745
0	8477	716

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

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

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

rewrite227.0ms (3.8%)

Memory

-14.3MiB live, 223.5MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	45
0	16	45
1	69	45
2	624	41
3	7596	41
0	8354	41

Stop Event

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

Counts

6 → 334

Calls

Call 1

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

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
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#<batchref>
#<batchref>
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#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
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#<batchref>
#<batchref>
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#<batchref>
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#<batchref>
#<batchref>
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#<batchref>
#<batchref>
#<batchref>
#<batchref>
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#<batchref>
#<batchref>
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#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
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#<batchref>
#<batchref>
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#<batchref>
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#<batchref>
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eval62.0ms (1%)

Memory: 24.3MiB live, 104.9MiB allocated
Compiler: Compiled 10 106 to 1 419 computations (86% saved)

prune8.0ms (0.1%)

Memory

-9.7MiB live, 28.2MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	402	4	406
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	403	4	407

Accuracy

100.0%

Counts

407 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(log.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x))
▶	99.4%	(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)))
▶	98.8%	(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x)))
▶	0.0%	(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64))))

Compiler

Compiled 66 to 47 computations (28.8% saved)

simplify173.0ms (2.9%)

Memory

13.8MiB live, 135.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))
cost-diff	0	(+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64))
cost-diff	0	(/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x)
cost-diff	0	(log.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x))
cost-diff	0	(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64))
cost-diff	0	#s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x))
cost-diff	0	(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)))
cost-diff	320	(/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)
cost-diff	0	(/.f64 #s(literal 2 binary64) x)
cost-diff	0	#s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x))
cost-diff	0	(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x)))
cost-diff	0	(sqrt.f64 #s(literal -1 binary64))
cost-diff	0	#s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64)))
cost-diff	0	(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	179
0	44	179
1	59	179
2	67	179
3	78	179
4	91	179
5	111	179
6	171	179
7	376	179
8	652	179
9	1256	179
10	2343	179
11	3474	179
12	4592	164
13	6135	164
0	8197	161

Stop Event

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

Calls

Call 1

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

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

localize147.0ms (2.5%)

Memory

-28.4MiB live, 130.2MiB allocated

Localize:

Found 14 expressions of interest:

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

Samples

97.0ms

256×

invalid

Compiler

Compiled 335 to 55 computations (83.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 84.0ms

ival-neg: 24.0ms (28.4% of total)

ival-log: 22.0ms (26% of total)

ival-sqrt: 18.0ms (21.3% of total)

ival-div: 8.0ms (9.5% of total)

ival-add: 5.0ms (5.9% of total)

ival-mult: 5.0ms (5.9% of total)

ival-sub: 1.0ms (1.2% of total)

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

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

exact: 0.0ms (0% of total)

series13.0ms (0.2%)

Memory

17.0MiB live, 17.0MiB allocated

Counts

16 → 180

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	((log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt -1) (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/ 2 x) (/ (+ (* (* x x) -1/2) 2) x) (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (+ (* (* x x) -1/2) 2) (log (/ (+ (sqrt (+ (* (neg x) x) 1)) 1) x)) (/ (+ (sqrt (+ (* (neg x) x) 1)) 1) x) (+ (sqrt (+ (* (neg x) x) 1)) 1) (sqrt (+ (* (neg x) x) 1)) (* x x) (neg x))
2.0ms	x	@	inf	((log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt -1) (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/ 2 x) (/ (+ (* (* x x) -1/2) 2) x) (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (+ (* (* x x) -1/2) 2) (log (/ (+ (sqrt (+ (* (neg x) x) 1)) 1) x)) (/ (+ (sqrt (+ (* (neg x) x) 1)) 1) x) (+ (sqrt (+ (* (neg x) x) 1)) 1) (sqrt (+ (* (neg x) x) 1)) (* x x) (neg x))
1.0ms	x	@	0	((log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt -1) (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/ 2 x) (/ (+ (* (* x x) -1/2) 2) x) (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (+ (* (* x x) -1/2) 2) (log (/ (+ (sqrt (+ (* (neg x) x) 1)) 1) x)) (/ (+ (sqrt (+ (* (neg x) x) 1)) 1) x) (+ (sqrt (+ (* (neg x) x) 1)) 1) (sqrt (+ (* (neg x) x) 1)) (* x x) (neg x))

Time

Variable

Point

Expression

3.0ms

-inf

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

2.0ms

inf

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

1.0ms

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

simplify203.0ms (3.4%)

Memory

-12.4MiB live, 268.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	178	2001
1	493	1924
2	1355	1865
3	3978	1857
0	8160	1765

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

Calls

Call 1

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

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

rewrite171.0ms (2.9%)

Memory

15.3MiB live, 278.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	166
0	44	166
1	161	154
2	1215	154
0	8665	143

Stop Event

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

Counts

16 → 504

Calls

Call 1

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

Outputs
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eval440.0ms (7.4%)

Memory: 17.3MiB live, 138.8MiB allocated
Compiler: Compiled 16 316 to 2 249 computations (86.2% saved)

prune19.0ms (0.3%)

Memory

3.4MiB live, 39.2MiB allocated

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	683	1	684
Fresh	0	0	0
Picked	1	3	4
Done	0	0	0
Total	684	4	688

Accuracy

100.0%

Counts

688 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(log.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x))
✓	99.4%	(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 2 binary64)) x)))
✓	98.8%	(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x)))
▶	0.0%	(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))))

Compiler

Compiled 77 to 53 computations (31.2% saved)

simplify178.0ms (3%)

Memory

-29.8MiB live, 140.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	71
0	19	71
1	32	71
2	40	71
3	48	71
4	63	71
5	83	71
6	126	71
7	331	71
8	617	71
9	1233	71
10	2290	71
11	3370	71
12	4467	65
13	6031	65
0	8114	62

Stop Event

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

Calls

Call 1

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

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

localize71.0ms (1.2%)

Memory

-1.3MiB live, 44.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 #s(literal -1/2 binary64) x)
accuracy	0.00390625	(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))))
accuracy	0.43233018253998057	#s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x)))
accuracy	62.99851158579934	#s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))

Samples

26.0ms

256×

valid

Compiler

Compiled 112 to 35 computations (68.8% saved)

Precisions

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

ival-div: 5.0ms (26.5% of total)

ival-mult: 5.0ms (26.5% of total)

ival-log: 3.0ms (15.9% of total)

ival-add: 2.0ms (10.6% of total)

ival-sqrt: 2.0ms (10.6% of total)

ival-sub: 1.0ms (5.3% of total)

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

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

exact: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory

5.2MiB live, 5.2MiB allocated

Counts

4 → 48

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

simplify121.0ms (2%)

Memory

16.5MiB live, 89.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	132	473
1	333	458
2	857	450
3	2374	449
4	5928	437
0	8102	416

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

rewrite150.0ms (2.5%)

Memory

10.7MiB live, 129.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	69
0	19	69
1	95	69
2	826	65
0	8755	62

Stop Event

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

Counts

4 → 11

Calls

Call 1

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

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

eval19.0ms (0.3%)

Memory: -25.3MiB live, 10.9MiB allocated
Compiler: Compiled 1 687 to 192 computations (88.6% saved)

prune5.0ms (0.1%)

Memory

13.2MiB live, 13.2MiB allocated

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	0	0	0
Picked	0	1	1
Done	1	2	3
Total	59	4	63

Accuracy

100.0%

Counts

63 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(log.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x))
✓	98.8%	(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x)))
▶	99.4%	(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))))
✓	0.0%	(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))))

Compiler

Compiled 85 to 58 computations (31.8% saved)

simplify147.0ms (2.5%)

Memory

8.2MiB live, 132.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 12 (0.0ms)

Iter	Nodes	Cost
0	18	87
0	22	87
1	36	87
2	44	87
3	52	87
4	67	87
5	87	87
6	130	87
7	336	87
8	624	87
9	1249	87
10	2321	87
11	3417	87
12	4508	78
13	6053	78
0	8127	78

Stop Event

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

Calls

Call 1

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

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

localize41.0ms (0.7%)

Memory

-13.8MiB live, 63.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	#s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))
accuracy	0.00390625	(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))))
accuracy	0.0078125	(fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))
accuracy	0.43233018253998057	#s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x))))

Samples

30.0ms

256×

valid

Compiler

Compiled 136 to 39 computations (71.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 23.0ms

ival-div: 7.0ms (30.5% of total)

ival-mult: 5.0ms (21.8% of total)

ival-log: 4.0ms (17.4% of total)

ival-add: 3.0ms (13.1% of total)

ival-sqrt: 2.0ms (8.7% of total)

ival-sub: 1.0ms (4.4% of total)

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

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

exact: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory

6.6MiB live, 6.6MiB allocated

Counts

4 → 48

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

-inf

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

1.0ms

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

1.0ms

inf

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

simplify185.0ms (3.1%)

Memory

-5.7MiB live, 76.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	132	527
1	333	512
2	857	504
3	2363	503
4	5915	479
0	8079	449

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

rewrite166.0ms (2.8%)

Memory

13.1MiB live, 88.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	81
0	22	81
1	117	81
2	1033	77
0	8781	74

Stop Event

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

Counts

4 → 52

Calls

Call 1

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

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

eval94.0ms (1.6%)

Memory: -11.2MiB live, 31.6MiB allocated
Compiler: Compiled 3 746 to 439 computations (88.3% saved)

prune5.0ms (0.1%)

Memory

10.9MiB live, 10.9MiB allocated

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	100	4	104

Accuracy

100.0%

Counts

104 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(log.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) #s(literal 1 binary64)) x))
✓	98.8%	(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x)))
✓	99.4%	(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (fma.f64 #s(literal -1/2 binary64) x (/.f64 #s(literal 2 binary64) x)))))
✓	0.0%	(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) #s(approx (/ (+ (* (* x x) -1/2) 2) x) (*.f64 #s(literal -1/2 binary64) x))))

Compiler

Compiled 221 to 106 computations (52% saved)

regimes34.0ms (0.6%)

Memory

-24.9MiB live, 12.2MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

3 calls:

27.0ms

3.0ms

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

3.0ms

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

Results

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

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes8.0ms (0.1%)

Memory

10.0MiB live, 10.0MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

3 calls:

3.0ms

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

2.0ms

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

2.0ms

Results

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

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes6.0ms (0.1%)

Memory

9.1MiB live, 9.1MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

3 calls:

2.0ms

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

2.0ms

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

2.0ms

Results

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

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes5.0ms (0.1%)

Memory

7.5MiB live, 7.5MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

2 → 1

Calls

Call 1

Inputs

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

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

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

Calls

3 calls:

2.0ms

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

2.0ms

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

1.0ms

Results

Accuracy	Segments	Branch
0.0%	1	`x`
0.0%	1	`(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))`
0.0%	1	`(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))`

Compiler

Compiled 26 to 18 computations (30.8% saved)

simplify44.0ms (0.7%)

Memory

-7.7MiB live, 31.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	85
1	38	85
2	40	85
3	41	85

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness844.0ms (14.2%)

Memory

20.2MiB live, 370.2MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	132	473
1	333	458
2	857	450
3	2374	449
4	5928	437
0	8102	416
0	9	45
0	16	45
1	69	45
2	624	41
3	7596	41
0	8354	41
0	155	803
1	409	778
2	1098	758
3	3208	745
4	7995	745
0	8477	716
0	178	2001
1	493	1924
2	1355	1865
3	3978	1857
0	8160	1765

Stop Event

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

Compiler

Compiled 142 to 72 computations (49.3% saved)

preprocess88.0ms (1.5%)

Memory: -14.9MiB live, 109.7MiB allocated
Compiler: Compiled 196 to 84 computations (57.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze3.0ms (0.1%)

sample1.0s (17.6%)

explain193.0ms (3.2%)

preprocess402.0ms (6.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify343.0ms (5.8%)

localize36.0ms (0.6%)

series9.0ms (0.1%)

simplify237.0ms (4%)

rewrite227.0ms (3.8%)

eval62.0ms (1%)

prune8.0ms (0.1%)

simplify173.0ms (2.9%)

localize147.0ms (2.5%)

series13.0ms (0.2%)

simplify203.0ms (3.4%)

rewrite171.0ms (2.9%)

eval440.0ms (7.4%)

prune19.0ms (0.3%)

simplify178.0ms (3%)

localize71.0ms (1.2%)

series5.0ms (0.1%)

simplify121.0ms (2%)

rewrite150.0ms (2.5%)

eval19.0ms (0.3%)

prune5.0ms (0.1%)

simplify147.0ms (2.5%)

localize41.0ms (0.7%)

series5.0ms (0.1%)

simplify185.0ms (3.1%)

rewrite166.0ms (2.8%)

eval94.0ms (1.6%)

prune5.0ms (0.1%)

regimes34.0ms (0.6%)

regimes8.0ms (0.1%)

regimes6.0ms (0.1%)

regimes5.0ms (0.1%)

simplify44.0ms (0.7%)

soundness844.0ms (14.2%)

preprocess88.0ms (1.5%)

end0.0ms (0%)

Profiling