Metrics for logs (example 3.8)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	23.7%	76.3%	0%	0%	0%	0
100%	23.7%	0%	76.3%	0%	0%	0%	1

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample3.2s (53.7%)

Memory

37.4MiB live, 3 232.3MiB allocated

Samples

2.7s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 2.4s

ival-log: 751.0ms (31.3% of total)

ival-log1p: 732.0ms (30.5% of total)

ival-mult: 341.0ms (14.2% of total)

adjust: 256.0ms (10.7% of total)

ival-sub: 177.0ms (7.4% of total)

ival-add: 104.0ms (4.3% of total)

ival->: 23.0ms (1% of total)

exact: 10.0ms (0.4% of total)

ival-assert: 4.0ms (0.2% of total)

Bogosity

explain352.0ms (5.9%)

Memory

-23.3MiB live, 288.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
256	-	-	`(-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n)))`
0	-	-	`n`
0	-	-	`(*.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64))))`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(+.f64 n #s(literal 1 binary64))`
0	-	-	`(log.f64 n)`
0	-	-	`(-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #s(literal 1 binary64))`
0	-	-	`(*.f64 n (log.f64 n))`
0	-	-	`(log.f64 (+.f64 n #s(literal 1 binary64)))`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n)))`	cancellation	254	0
`-.f64`	`(-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n)))`	nan-rescue	2	0
↳	`(*.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64))))`	overflow	2
↳	`(*.f64 n (log.f64 n))`	overflow	2

Confusion

	Predicted +	Predicted -
+	256	0
-	0	0

Precision

1.0

Recall

1.0

Confusion?

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

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
1	256

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

247.0ms

512×

valid

Compiler

Compiled 122 to 31 computations (74.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 225.0ms

ival-log: 69.0ms (30.7% of total)

ival-log1p: 49.0ms (21.8% of total)

adjust: 46.0ms (20.4% of total)

ival-sub: 41.0ms (18.2% of total)

ival-mult: 13.0ms (5.8% of total)

ival-add: 5.0ms (2.2% of total)

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

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

exact: 0.0ms (0% of total)

preprocess102.0ms (1.7%)

Memory

-34.1MiB live, 91.2MiB allocated

Algorithm

1×	egg-herbie

Rules

1 408×	`lower-fma.f64`
1 408×	`lower-fma.f32`
360×	`lower-+.f32`
360×	`lower--.f32`
358×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	37
1	33	33
2	88	32
3	286	32
4	746	32
5	1388	32
6	1844	32
7	1862	32
0	9	15
0	16	15
1	31	15
2	59	15
3	123	15
4	258	15
5	493	15
6	849	15
7	1201	15
8	1400	15
9	1417	15
0	1417	11

Stop Event

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

Calls

Call 1

Inputs
(-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #s(literal 1 binary64))

Outputs

(-.f64 (-.f64 (*.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (*.f64 n (log.f64 n))) #s(literal 1 binary64))

(-.f64 (*.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) (fma.f64 n (log.f64 n) #s(literal 1 binary64)))

Compiler

Compiled 16 to 9 computations (43.8% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	1.5%	(-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #s(literal 1 binary64))

Compiler

Compiled 16 to 9 computations (43.8% saved)

simplify56.0ms (0.9%)

Memory

26.4MiB live, 26.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64))))
cost-diff	0	(-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n)))
cost-diff	128	(-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #s(literal 1 binary64))
cost-diff	192	(log.f64 (+.f64 n #s(literal 1 binary64)))

Rules

1 408×	`lower-fma.f64`
1 408×	`lower-fma.f32`
360×	`lower-+.f32`
360×	`lower--.f32`
358×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	51
0	16	51
1	31	51
2	59	51
3	123	51
4	258	51
5	493	51
6	849	51
7	1201	51
8	1400	51
9	1417	51
0	1417	39

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

Outputs
(-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #s(literal 1 binary64))
(-.f64 (*.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) (fma.f64 n (log.f64 n) #s(literal 1 binary64)))
(-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n)))
(-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) (.f64 n (log.f64 n)))
(*.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64))))
(*.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n))
(+.f64 n #s(literal 1 binary64))
n
#s(literal 1 binary64)
(log.f64 (+.f64 n #s(literal 1 binary64)))
(log1p.f64 n)
(*.f64 n (log.f64 n))
(log.f64 n)

localize116.0ms (1.9%)

Memory

-0.1MiB live, 38.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #s(literal 1 binary64))
accuracy	0.28125	(*.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64))))
accuracy	0.28125	(*.f64 n (log.f64 n))
accuracy	62.00980376790154	(-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n)))

Samples

103.0ms

256×

valid

Compiler

Compiled 53 to 11 computations (79.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 93.0ms

ival-log: 50.0ms (54% of total)

ival-log1p: 19.0ms (20.5% of total)

ival-mult: 10.0ms (10.8% of total)

adjust: 7.0ms (7.6% of total)

ival-sub: 4.0ms (4.3% of total)

ival-add: 3.0ms (3.2% of total)

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

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

exact: 0.0ms (0% of total)

series73.0ms (1.2%)

Memory

2.5MiB live, 78.4MiB allocated

Counts

5 → 60

Calls

Call 1

Inputs
#s(alt (log.f64 (+.f64 n #s(literal 1 binary64))) (patch (log.f64 (+.f64 n #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #s(literal 1 binary64)) (patch (-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) (patch (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #<representation binary64>) () ())
#s(alt (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (patch (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 n (log.f64 n)) (patch (.f64 n (log.f64 n)) #<representation binary64>) () ())

Outputs
#s(alt n (taylor 0 n) (#s(alt (log.f64 (+.f64 n #s(literal 1 binary64))) (patch (log.f64 (+.f64 n #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* n (+ 1 (* -1/2 n))) (taylor 0 n) (#s(alt (log.f64 (+.f64 n #s(literal 1 binary64))) (patch (log.f64 (+.f64 n #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* n (+ 1 (* n (- (* 1/3 n) 1/2)))) (taylor 0 n) (#s(alt (log.f64 (+.f64 n #s(literal 1 binary64))) (patch (log.f64 (+.f64 n #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* n (+ 1 (* n (- (* n (+ 1/3 (* -1/4 n))) 1/2)))) (taylor 0 n) (#s(alt (log.f64 (+.f64 n #s(literal 1 binary64))) (patch (log.f64 (+.f64 n #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (log (/ 1 n))) (taylor inf n) (#s(alt (log.f64 (+.f64 n #s(literal 1 binary64))) (patch (log.f64 (+.f64 n #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (log (/ 1 n))) (/ 1 n)) (taylor inf n) (#s(alt (log.f64 (+.f64 n #s(literal 1 binary64))) (patch (log.f64 (+.f64 n #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (log (/ 1 n))) (/ 1 n)) (/ 1/2 (pow n 2))) (taylor inf n) (#s(alt (log.f64 (+.f64 n #s(literal 1 binary64))) (patch (log.f64 (+.f64 n #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (log (/ 1 n))) (+ (/ 1 n) (* 1/3 (/ 1 (pow n 3))))) (/ 1/2 (pow n 2))) (taylor inf n) (#s(alt (log.f64 (+.f64 n #s(literal 1 binary64))) (patch (log.f64 (+.f64 n #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (* -1 (log (/ -1 n)))) (taylor -inf n) (#s(alt (log.f64 (+.f64 n #s(literal 1 binary64))) (patch (log.f64 (+.f64 n #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (+ (* -1 (log (/ -1 n))) (/ 1 n))) (taylor -inf n) (#s(alt (log.f64 (+.f64 n #s(literal 1 binary64))) (patch (log.f64 (+.f64 n #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* 1/2 (/ 1 n)) 1) n)))) (taylor -inf n) (#s(alt (log.f64 (+.f64 n #s(literal 1 binary64))) (patch (log.f64 (+.f64 n #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* -1 (/ (- (* 1/3 (/ 1 n)) 1/2) n)) 1) n)))) (taylor -inf n) (#s(alt (log.f64 (+.f64 n #s(literal 1 binary64))) (patch (log.f64 (+.f64 n #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 n) (#s(alt (-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #s(literal 1 binary64)) (patch (-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* n (- 1 (log n))) 1) (taylor 0 n) (#s(alt (-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #s(literal 1 binary64)) (patch (-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* n (- (+ 1 (* 1/2 n)) (log n))) 1) (taylor 0 n) (#s(alt (-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #s(literal 1 binary64)) (patch (-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* n (- (+ 1 (* n (+ 1/2 (* -1/6 n)))) (log n))) 1) (taylor 0 n) (#s(alt (-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #s(literal 1 binary64)) (patch (-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (log (/ 1 n))) (taylor inf n) (#s(alt (-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #s(literal 1 binary64)) (patch (-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (log (/ 1 n))) (* 1/2 (/ 1 n))) (taylor inf n) (#s(alt (-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #s(literal 1 binary64)) (patch (-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (log (/ 1 n))) (* 1/2 (/ 1 n))) (/ 1/6 (pow n 2))) (taylor inf n) (#s(alt (-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #s(literal 1 binary64)) (patch (-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (log (/ 1 n))) (+ (* 1/2 (/ 1 n)) (* 1/12 (/ 1 (pow n 3))))) (/ 1/6 (pow n 2))) (taylor inf n) (#s(alt (-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #s(literal 1 binary64)) (patch (-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (* -1 (log (/ -1 n)))) (taylor -inf n) (#s(alt (-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #s(literal 1 binary64)) (patch (-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (+ (* -1 (log (/ -1 n))) (* 1/2 (/ 1 n)))) (taylor -inf n) (#s(alt (-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #s(literal 1 binary64)) (patch (-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* 1/6 (/ 1 n)) 1/2) n)))) (taylor -inf n) (#s(alt (-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #s(literal 1 binary64)) (patch (-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* -1 (/ (- (* 1/12 (/ 1 n)) 1/6) n)) 1/2) n)))) (taylor -inf n) (#s(alt (-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #s(literal 1 binary64)) (patch (-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* n (- 1 (log n))) (taylor 0 n) (#s(alt (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) (patch (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #<representation binary64>) () ())) ())
#s(alt (* n (- (+ 1 (* 1/2 n)) (log n))) (taylor 0 n) (#s(alt (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) (patch (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #<representation binary64>) () ())) ())
#s(alt (* n (- (+ 1 (* n (+ 1/2 (* -1/6 n)))) (log n))) (taylor 0 n) (#s(alt (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) (patch (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #<representation binary64>) () ())) ())
#s(alt (* n (- (+ 1 (* n (+ 1/2 (* n (- (* 1/12 n) 1/6))))) (log n))) (taylor 0 n) (#s(alt (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) (patch (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (log (/ 1 n)))) (taylor inf n) (#s(alt (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) (patch (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (* -1 (log (/ 1 n))) (* 1/2 (/ 1 n)))) (taylor inf n) (#s(alt (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) (patch (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (+ (* -1 (log (/ 1 n))) (* 1/2 (/ 1 n)))) (/ 1/6 (pow n 2))) (taylor inf n) (#s(alt (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) (patch (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (+ (* -1 (log (/ 1 n))) (+ (* 1/2 (/ 1 n)) (* 1/12 (/ 1 (pow n 3)))))) (/ 1/6 (pow n 2))) (taylor inf n) (#s(alt (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) (patch (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (log -1) (* -1 (log (/ -1 n))))) (taylor -inf n) (#s(alt (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) (patch (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (log -1) (+ (* -1 (log (/ -1 n))) (* 1/2 (/ 1 n))))) (taylor -inf n) (#s(alt (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) (patch (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* 1/6 (/ 1 n)) 1/2) n))))) (taylor -inf n) (#s(alt (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) (patch (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* -1 (/ (- (* 1/12 (/ 1 n)) 1/6) n)) 1/2) n))))) (taylor -inf n) (#s(alt (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) (patch (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #<representation binary64>) () ())) ())
#s(alt n (taylor 0 n) (#s(alt (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (patch (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* n (+ 1 (* 1/2 n))) (taylor 0 n) (#s(alt (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (patch (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* n (+ 1 (* n (+ 1/2 (* -1/6 n))))) (taylor 0 n) (#s(alt (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (patch (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* n (+ 1 (* n (+ 1/2 (* n (- (* 1/12 n) 1/6)))))) (taylor 0 n) (#s(alt (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (patch (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* n (log (/ 1 n)))) (taylor inf n) (#s(alt (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (patch (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* n (+ (* -1 (log (/ 1 n))) (+ (* -1 (/ (log (/ 1 n)) n)) (/ 1 n)))) (taylor inf n) (#s(alt (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (patch (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* n (+ (* -1 (log (/ 1 n))) (+ (* -1 (/ (log (/ 1 n)) n)) (+ (/ 1/2 (pow n 2)) (/ 1 n))))) (taylor inf n) (#s(alt (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (patch (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* n (- (+ (* -1 (log (/ 1 n))) (+ (* -1 (/ (log (/ 1 n)) n)) (+ (/ 1/2 (pow n 2)) (/ 1 n)))) (* 1/6 (/ 1 (pow n 3))))) (taylor inf n) (#s(alt (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (patch (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* n (+ (log -1) (* -1 (log (/ -1 n))))) (taylor -inf n) (#s(alt (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (patch (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* n (+ (* -1 (+ (log -1) (* -1 (log (/ -1 n))))) (* -1 (/ (+ 1 (+ (log -1) (* -1 (log (/ -1 n))))) n))))) (taylor -inf n) (#s(alt (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (patch (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* n (+ (* -1 (+ (log -1) (* -1 (log (/ -1 n))))) (* -1 (/ (+ 1 (+ (log -1) (+ (* -1 (log (/ -1 n))) (* 1/2 (/ 1 n))))) n))))) (taylor -inf n) (#s(alt (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (patch (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* n (+ (* -1 (+ (log -1) (* -1 (log (/ -1 n))))) (* -1 (/ (+ 1 (+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* 1/6 (/ 1 n)) 1/2) n))))) n))))) (taylor -inf n) (#s(alt (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (patch (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* n (log n)) (taylor 0 n) (#s(alt (.f64 n (log.f64 n)) (patch (.f64 n (log.f64 n)) #<representation binary64>) () ())) ())
#s(alt (* n (log n)) (taylor 0 n) (#s(alt (.f64 n (log.f64 n)) (patch (.f64 n (log.f64 n)) #<representation binary64>) () ())) ())
#s(alt (* n (log n)) (taylor 0 n) (#s(alt (.f64 n (log.f64 n)) (patch (.f64 n (log.f64 n)) #<representation binary64>) () ())) ())
#s(alt (* n (log n)) (taylor 0 n) (#s(alt (.f64 n (log.f64 n)) (patch (.f64 n (log.f64 n)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* n (log (/ 1 n)))) (taylor inf n) (#s(alt (.f64 n (log.f64 n)) (patch (.f64 n (log.f64 n)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* n (log (/ 1 n)))) (taylor inf n) (#s(alt (.f64 n (log.f64 n)) (patch (.f64 n (log.f64 n)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* n (log (/ 1 n)))) (taylor inf n) (#s(alt (.f64 n (log.f64 n)) (patch (.f64 n (log.f64 n)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* n (log (/ 1 n)))) (taylor inf n) (#s(alt (.f64 n (log.f64 n)) (patch (.f64 n (log.f64 n)) #<representation binary64>) () ())) ())
#s(alt (* n (+ (log -1) (* -1 (log (/ -1 n))))) (taylor -inf n) (#s(alt (.f64 n (log.f64 n)) (patch (.f64 n (log.f64 n)) #<representation binary64>) () ())) ())
#s(alt (* n (+ (log -1) (* -1 (log (/ -1 n))))) (taylor -inf n) (#s(alt (.f64 n (log.f64 n)) (patch (.f64 n (log.f64 n)) #<representation binary64>) () ())) ())
#s(alt (* n (+ (log -1) (* -1 (log (/ -1 n))))) (taylor -inf n) (#s(alt (.f64 n (log.f64 n)) (patch (.f64 n (log.f64 n)) #<representation binary64>) () ())) ())
#s(alt (* n (+ (log -1) (* -1 (log (/ -1 n))))) (taylor -inf n) (#s(alt (.f64 n (log.f64 n)) (patch (.f64 n (log.f64 n)) #<representation binary64>) () ())) ())

Calls

15 calls:

Time	Variable		Point	Expression
48.0ms	n	@	0	(* n (log n))
13.0ms	n	@	-inf	(* n (log n))
7.0ms	n	@	inf	(* n (log n))
1.0ms	n	@	-inf	(- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1)
0.0ms	n	@	inf	(- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1)

simplify330.0ms (5.5%)

Memory

-19.8MiB live, 456.0MiB allocated

Algorithm

1×	egg-herbie

Rules

12 704×	`lower-fma.f64`
12 704×	`lower-fma.f32`
3 310×	`lower-+.f64`
3 310×	`lower-+.f32`
2 942×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	154	748
1	486	661
2	1401	636
3	4863	620
0	8506	591

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 58

Calls

Call 1

Inputs
n
(* n (+ 1 (* -1/2 n)))
(* n (+ 1 (* n (- (* 1/3 n) 1/2))))
(* n (+ 1 (* n (- (* n (+ 1/3 (* -1/4 n))) 1/2))))
(* -1 (log (/ 1 n)))
(+ (* -1 (log (/ 1 n))) (/ 1 n))
(- (+ (* -1 (log (/ 1 n))) (/ 1 n)) (/ 1/2 (pow n 2)))
(- (+ (* -1 (log (/ 1 n))) (+ (/ 1 n) (* 1/3 (/ 1 (pow n 3))))) (/ 1/2 (pow n 2)))
(+ (log -1) (* -1 (log (/ -1 n))))
(+ (log -1) (+ (* -1 (log (/ -1 n))) (/ 1 n)))
(+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* 1/2 (/ 1 n)) 1) n))))
(+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* -1 (/ (- (* 1/3 (/ 1 n)) 1/2) n)) 1) n))))
-1
(- (* n (- 1 (log n))) 1)
(- (* n (- (+ 1 (* 1/2 n)) (log n))) 1)
(- (* n (- (+ 1 (* n (+ 1/2 (* -1/6 n)))) (log n))) 1)
(* -1 (log (/ 1 n)))
(+ (* -1 (log (/ 1 n))) (* 1/2 (/ 1 n)))
(- (+ (* -1 (log (/ 1 n))) (* 1/2 (/ 1 n))) (/ 1/6 (pow n 2)))
(- (+ (* -1 (log (/ 1 n))) (+ (* 1/2 (/ 1 n)) (* 1/12 (/ 1 (pow n 3))))) (/ 1/6 (pow n 2)))
(+ (log -1) (* -1 (log (/ -1 n))))
(+ (log -1) (+ (* -1 (log (/ -1 n))) (* 1/2 (/ 1 n))))
(+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* 1/6 (/ 1 n)) 1/2) n))))
(+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* -1 (/ (- (* 1/12 (/ 1 n)) 1/6) n)) 1/2) n))))
(* n (- 1 (log n)))
(* n (- (+ 1 (* 1/2 n)) (log n)))
(* n (- (+ 1 (* n (+ 1/2 (* -1/6 n)))) (log n)))
(* n (- (+ 1 (* n (+ 1/2 (* n (- (* 1/12 n) 1/6))))) (log n)))
(+ 1 (* -1 (log (/ 1 n))))
(+ 1 (+ (* -1 (log (/ 1 n))) (* 1/2 (/ 1 n))))
(- (+ 1 (+ (* -1 (log (/ 1 n))) (* 1/2 (/ 1 n)))) (/ 1/6 (pow n 2)))
(- (+ 1 (+ (* -1 (log (/ 1 n))) (+ (* 1/2 (/ 1 n)) (* 1/12 (/ 1 (pow n 3)))))) (/ 1/6 (pow n 2)))
(+ 1 (+ (log -1) (* -1 (log (/ -1 n)))))
(+ 1 (+ (log -1) (+ (* -1 (log (/ -1 n))) (* 1/2 (/ 1 n)))))
(+ 1 (+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* 1/6 (/ 1 n)) 1/2) n)))))
(+ 1 (+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* -1 (/ (- (* 1/12 (/ 1 n)) 1/6) n)) 1/2) n)))))
n
(* n (+ 1 (* 1/2 n)))
(* n (+ 1 (* n (+ 1/2 (* -1/6 n)))))
(* n (+ 1 (* n (+ 1/2 (* n (- (* 1/12 n) 1/6))))))
(* -1 (* n (log (/ 1 n))))
(* n (+ (* -1 (log (/ 1 n))) (+ (* -1 (/ (log (/ 1 n)) n)) (/ 1 n))))
(* n (+ (* -1 (log (/ 1 n))) (+ (* -1 (/ (log (/ 1 n)) n)) (+ (/ 1/2 (pow n 2)) (/ 1 n)))))
(* n (- (+ (* -1 (log (/ 1 n))) (+ (* -1 (/ (log (/ 1 n)) n)) (+ (/ 1/2 (pow n 2)) (/ 1 n)))) (* 1/6 (/ 1 (pow n 3)))))
(* n (+ (log -1) (* -1 (log (/ -1 n)))))
(* -1 (* n (+ (* -1 (+ (log -1) (* -1 (log (/ -1 n))))) (* -1 (/ (+ 1 (+ (log -1) (* -1 (log (/ -1 n))))) n)))))
(* -1 (* n (+ (* -1 (+ (log -1) (* -1 (log (/ -1 n))))) (* -1 (/ (+ 1 (+ (log -1) (+ (* -1 (log (/ -1 n))) (* 1/2 (/ 1 n))))) n)))))
(* -1 (* n (+ (* -1 (+ (log -1) (* -1 (log (/ -1 n))))) (* -1 (/ (+ 1 (+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* 1/6 (/ 1 n)) 1/2) n))))) n)))))
(* n (log n))
(* n (log n))
(* n (log n))
(* n (log n))
(* -1 (* n (log (/ 1 n))))
(* -1 (* n (log (/ 1 n))))
(* -1 (* n (log (/ 1 n))))
(* -1 (* n (log (/ 1 n))))
(* n (+ (log -1) (* -1 (log (/ -1 n)))))
(* n (+ (log -1) (* -1 (log (/ -1 n)))))
(* n (+ (log -1) (* -1 (log (/ -1 n)))))
(* n (+ (log -1) (* -1 (log (/ -1 n)))))

Outputs
n
(* n (+ 1 (* -1/2 n)))
(fma.f64 n (*.f64 n #s(literal -1/2 binary64)) n)
(* n (+ 1 (* n (- (* 1/3 n) 1/2))))
(fma.f64 n (*.f64 n (fma.f64 n #s(literal 1/3 binary64) #s(literal -1/2 binary64))) n)
(* n (+ 1 (* n (- (* n (+ 1/3 (* -1/4 n))) 1/2))))
(fma.f64 (fma.f64 n (fma.f64 n #s(literal -1/4 binary64) #s(literal 1/3 binary64)) #s(literal -1/2 binary64)) (*.f64 n n) n)
(* -1 (log (/ 1 n)))
(log.f64 n)
(+ (* -1 (log (/ 1 n))) (/ 1 n))
(+.f64 (/.f64 #s(literal 1 binary64) n) (log.f64 n))
(- (+ (* -1 (log (/ 1 n))) (/ 1 n)) (/ 1/2 (pow n 2)))
(+.f64 (log.f64 n) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) n)) n))
(- (+ (* -1 (log (/ 1 n))) (+ (/ 1 n) (* 1/3 (/ 1 (pow n 3))))) (/ 1/2 (pow n 2)))
(+.f64 (log.f64 n) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/3 binary64) n)) n)) n))
(+ (log -1) (* -1 (log (/ -1 n))))
(-.f64 (log.f64 #s(literal -1 binary64)) (neg.f64 (log.f64 (neg.f64 n))))
(+ (log -1) (+ (* -1 (log (/ -1 n))) (/ 1 n)))
(+.f64 (/.f64 #s(literal 1 binary64) n) (-.f64 (log.f64 #s(literal -1 binary64)) (neg.f64 (log.f64 (neg.f64 n)))))
(+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* 1/2 (/ 1 n)) 1) n))))
(+.f64 (log.f64 #s(literal -1 binary64)) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) n)) n) (neg.f64 (log.f64 (neg.f64 n)))))
(+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* -1 (/ (- (* 1/3 (/ 1 n)) 1/2) n)) 1) n))))
(+.f64 (log.f64 #s(literal -1 binary64)) (-.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/3 binary64) n)) n)) n) (neg.f64 (log.f64 (neg.f64 n)))))
-1
#s(literal -1 binary64)
(- (* n (- 1 (log n))) 1)
(fma.f64 n (-.f64 #s(literal 1 binary64) (log.f64 n)) #s(literal -1 binary64))
(- (* n (- (+ 1 (* 1/2 n)) (log n))) 1)
(fma.f64 n (fma.f64 n #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (log.f64 n))) #s(literal -1 binary64))
(- (* n (- (+ 1 (* n (+ 1/2 (* -1/6 n)))) (log n))) 1)
(fma.f64 n (fma.f64 n (fma.f64 n #s(literal -1/6 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (log.f64 n))) #s(literal -1 binary64))
(* -1 (log (/ 1 n)))
(log.f64 n)
(+ (* -1 (log (/ 1 n))) (* 1/2 (/ 1 n)))
(+.f64 (log.f64 n) (/.f64 #s(literal 1/2 binary64) n))
(- (+ (* -1 (log (/ 1 n))) (* 1/2 (/ 1 n))) (/ 1/6 (pow n 2)))
(+.f64 (log.f64 n) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/6 binary64) n)) n))
(- (+ (* -1 (log (/ 1 n))) (+ (* 1/2 (/ 1 n)) (* 1/12 (/ 1 (pow n 3))))) (/ 1/6 (pow n 2)))
(+.f64 (log.f64 n) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1/12 binary64) n)) n)) n))
(+ (log -1) (* -1 (log (/ -1 n))))
(-.f64 (log.f64 #s(literal -1 binary64)) (neg.f64 (log.f64 (neg.f64 n))))
(+ (log -1) (+ (* -1 (log (/ -1 n))) (* 1/2 (/ 1 n))))
(+.f64 (log.f64 #s(literal -1 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) n) (neg.f64 (log.f64 (neg.f64 n)))))
(+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* 1/6 (/ 1 n)) 1/2) n))))
(+.f64 (log.f64 #s(literal -1 binary64)) (-.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/6 binary64) n)) n) (neg.f64 (log.f64 (neg.f64 n)))))
(+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* -1 (/ (- (* 1/12 (/ 1 n)) 1/6) n)) 1/2) n))))
(+.f64 (log.f64 #s(literal -1 binary64)) (-.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1/12 binary64) n)) n)) n) (neg.f64 (log.f64 (neg.f64 n)))))
(* n (- 1 (log n)))
(fma.f64 (log.f64 n) (neg.f64 n) n)
(* n (- (+ 1 (* 1/2 n)) (log n)))
(*.f64 n (fma.f64 n #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (log.f64 n))))
(* n (- (+ 1 (* n (+ 1/2 (* -1/6 n)))) (log n)))
(*.f64 n (fma.f64 n (fma.f64 n #s(literal -1/6 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (log.f64 n))))
(* n (- (+ 1 (* n (+ 1/2 (* n (- (* 1/12 n) 1/6))))) (log n)))
(fma.f64 n (fma.f64 n (fma.f64 n (fma.f64 n #s(literal 1/12 binary64) #s(literal -1/6 binary64)) #s(literal 1/2 binary64)) (neg.f64 (log.f64 n))) n)
(+ 1 (* -1 (log (/ 1 n))))
(+.f64 #s(literal 1 binary64) (log.f64 n))
(+ 1 (+ (* -1 (log (/ 1 n))) (* 1/2 (/ 1 n))))
(+.f64 #s(literal 1 binary64) (+.f64 (log.f64 n) (/.f64 #s(literal 1/2 binary64) n)))
(- (+ 1 (+ (* -1 (log (/ 1 n))) (* 1/2 (/ 1 n)))) (/ 1/6 (pow n 2)))
(+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/6 binary64) n)) n) (+.f64 #s(literal 1 binary64) (log.f64 n)))
(- (+ 1 (+ (* -1 (log (/ 1 n))) (+ (* 1/2 (/ 1 n)) (* 1/12 (/ 1 (pow n 3)))))) (/ 1/6 (pow n 2)))
(+.f64 #s(literal 1 binary64) (+.f64 (log.f64 n) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1/12 binary64) n)) n)) n)))
(+ 1 (+ (log -1) (* -1 (log (/ -1 n)))))
(-.f64 (+.f64 #s(literal 1 binary64) (log.f64 #s(literal -1 binary64))) (neg.f64 (log.f64 (neg.f64 n))))
(+ 1 (+ (log -1) (+ (* -1 (log (/ -1 n))) (* 1/2 (/ 1 n)))))
(+.f64 (log.f64 #s(literal -1 binary64)) (-.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) n)) (neg.f64 (log.f64 (neg.f64 n)))))
(+ 1 (+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* 1/6 (/ 1 n)) 1/2) n)))))
(+.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (neg.f64 (log.f64 (neg.f64 n)))) (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/6 binary64) n)) n)))
(+ 1 (+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* -1 (/ (- (* 1/12 (/ 1 n)) 1/6) n)) 1/2) n)))))
(+.f64 (-.f64 (log.f64 #s(literal -1 binary64)) (neg.f64 (log.f64 (neg.f64 n)))) (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1/12 binary64) n)) n)) n)))
n
(* n (+ 1 (* 1/2 n)))
(fma.f64 n (*.f64 n #s(literal 1/2 binary64)) n)
(* n (+ 1 (* n (+ 1/2 (* -1/6 n)))))
(fma.f64 (*.f64 n n) (fma.f64 n #s(literal -1/6 binary64) #s(literal 1/2 binary64)) n)
(* n (+ 1 (* n (+ 1/2 (* n (- (* 1/12 n) 1/6))))))
(fma.f64 (*.f64 n n) (fma.f64 n (fma.f64 n #s(literal 1/12 binary64) #s(literal -1/6 binary64)) #s(literal 1/2 binary64)) n)
(* -1 (* n (log (/ 1 n))))
(*.f64 n (log.f64 n))
(* n (+ (* -1 (log (/ 1 n))) (+ (* -1 (/ (log (/ 1 n)) n)) (/ 1 n))))
(fma.f64 (neg.f64 (log.f64 n)) (+.f64 (neg.f64 n) #s(literal -1 binary64)) #s(literal 1 binary64))
(* n (+ (* -1 (log (/ 1 n))) (+ (* -1 (/ (log (/ 1 n)) n)) (+ (/ 1/2 (pow n 2)) (/ 1 n)))))
(fma.f64 (neg.f64 (log.f64 n)) (+.f64 (neg.f64 n) #s(literal -1 binary64)) (fma.f64 n (/.f64 #s(literal 1/2 binary64) (*.f64 n n)) #s(literal 1 binary64)))
(* n (- (+ (* -1 (log (/ 1 n))) (+ (* -1 (/ (log (/ 1 n)) n)) (+ (/ 1/2 (pow n 2)) (/ 1 n)))) (* 1/6 (/ 1 (pow n 3)))))
(fma.f64 n (/.f64 #s(literal -1/6 binary64) (.f64 n (.f64 n n))) (fma.f64 (neg.f64 (log.f64 n)) (+.f64 (neg.f64 n) #s(literal -1 binary64)) (fma.f64 n (/.f64 #s(literal 1/2 binary64) (*.f64 n n)) #s(literal 1 binary64))))
(* n (+ (log -1) (* -1 (log (/ -1 n)))))
(*.f64 n (-.f64 (log.f64 #s(literal -1 binary64)) (neg.f64 (log.f64 (neg.f64 n)))))
(* -1 (* n (+ (* -1 (+ (log -1) (* -1 (log (/ -1 n))))) (* -1 (/ (+ 1 (+ (log -1) (* -1 (log (/ -1 n))))) n)))))
(fma.f64 n (-.f64 (log.f64 #s(literal -1 binary64)) (neg.f64 (log.f64 (neg.f64 n)))) (-.f64 (+.f64 #s(literal 1 binary64) (log.f64 #s(literal -1 binary64))) (neg.f64 (log.f64 (neg.f64 n)))))
(* -1 (* n (+ (* -1 (+ (log -1) (* -1 (log (/ -1 n))))) (* -1 (/ (+ 1 (+ (log -1) (+ (* -1 (log (/ -1 n))) (* 1/2 (/ 1 n))))) n)))))
(-.f64 (*.f64 n (-.f64 (log.f64 #s(literal -1 binary64)) (neg.f64 (log.f64 (neg.f64 n))))) (+.f64 (neg.f64 (log.f64 (neg.f64 n))) (+.f64 (/.f64 #s(literal -1/2 binary64) n) (-.f64 #s(literal -1 binary64) (log.f64 #s(literal -1 binary64))))))
(* -1 (* n (+ (* -1 (+ (log -1) (* -1 (log (/ -1 n))))) (* -1 (/ (+ 1 (+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* 1/6 (/ 1 n)) 1/2) n))))) n)))))
(-.f64 (*.f64 n (-.f64 (log.f64 #s(literal -1 binary64)) (neg.f64 (log.f64 (neg.f64 n))))) (+.f64 (neg.f64 (log.f64 (neg.f64 n))) (+.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/6 binary64) n)) n) (-.f64 #s(literal -1 binary64) (log.f64 #s(literal -1 binary64))))))
(* n (log n))
(*.f64 n (log.f64 n))
(* n (log n))
(*.f64 n (log.f64 n))
(* n (log n))
(*.f64 n (log.f64 n))
(* n (log n))
(*.f64 n (log.f64 n))
(* -1 (* n (log (/ 1 n))))
(*.f64 n (log.f64 n))
(* -1 (* n (log (/ 1 n))))
(*.f64 n (log.f64 n))
(* -1 (* n (log (/ 1 n))))
(*.f64 n (log.f64 n))
(* -1 (* n (log (/ 1 n))))
(*.f64 n (log.f64 n))
(* n (+ (log -1) (* -1 (log (/ -1 n)))))
(*.f64 n (-.f64 (log.f64 #s(literal -1 binary64)) (neg.f64 (log.f64 (neg.f64 n)))))
(* n (+ (log -1) (* -1 (log (/ -1 n)))))
(*.f64 n (-.f64 (log.f64 #s(literal -1 binary64)) (neg.f64 (log.f64 (neg.f64 n)))))
(* n (+ (log -1) (* -1 (log (/ -1 n)))))
(*.f64 n (-.f64 (log.f64 #s(literal -1 binary64)) (neg.f64 (log.f64 (neg.f64 n)))))
(* n (+ (log -1) (* -1 (log (/ -1 n)))))
(*.f64 n (-.f64 (log.f64 #s(literal -1 binary64)) (neg.f64 (log.f64 (neg.f64 n)))))

rewrite380.0ms (6.4%)

Memory

21.9MiB live, 538.5MiB allocated

Rules

8 652×	`lower-fma.f64`
8 652×	`lower-fma.f32`
5 492×	`lower-*.f32`
5 488×	`lower-*.f64`
3 876×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	44
0	16	44
1	66	44
2	516	44
0	8397	35

Stop Event

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

Counts

5 → 431

Calls

Call 1

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

Outputs
(log.f64 (+.f64 n #s(literal 1 binary64)))
(+.f64 (log1p.f64 (.f64 n (.f64 n n))) (log.f64 (/.f64 #s(literal 1 binary64) (fma.f64 n n (-.f64 #s(literal 1 binary64) n)))))
(+.f64 (log1p.f64 (.f64 n (.f64 n n))) (neg.f64 (log.f64 (fma.f64 n n (-.f64 #s(literal 1 binary64) n)))))
(+.f64 (log.f64 (fma.f64 n n #s(literal -1 binary64))) (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 n #s(literal -1 binary64)))))
(+.f64 (log.f64 (fma.f64 n n #s(literal -1 binary64))) (neg.f64 (log.f64 (+.f64 n #s(literal -1 binary64)))))
(-.f64 #s(literal 0 binary64) (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 n #s(literal 1 binary64)))))
(-.f64 (log1p.f64 (.f64 n (.f64 n n))) (log.f64 (fma.f64 n n (-.f64 #s(literal 1 binary64) n))))
(-.f64 (log1p.f64 (.f64 n (.f64 n n))) (log1p.f64 (-.f64 (*.f64 n n) n)))
(-.f64 (log.f64 (fma.f64 n n #s(literal -1 binary64))) (log.f64 (+.f64 n #s(literal -1 binary64))))
(-.f64 (log.f64 (neg.f64 (fma.f64 n (*.f64 n n) #s(literal 1 binary64)))) (log.f64 (neg.f64 (fma.f64 n n (-.f64 #s(literal 1 binary64) n)))))
(-.f64 (log.f64 (neg.f64 (fma.f64 n n #s(literal -1 binary64)))) (log.f64 (+.f64 (neg.f64 n) #s(literal 1 binary64))))
(-.f64 (log1p.f64 (*.f64 (neg.f64 n) n)) (log1p.f64 (neg.f64 n)))
(neg.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 n #s(literal 1 binary64)))))
(/.f64 (-.f64 (pow.f64 (log1p.f64 (.f64 n (.f64 n n))) #s(literal 3 binary64)) (pow.f64 (log.f64 (fma.f64 n n (-.f64 #s(literal 1 binary64) n))) #s(literal 3 binary64))) (fma.f64 (log1p.f64 (.f64 n (.f64 n n))) (log1p.f64 (.f64 n (.f64 n n))) (fma.f64 (log.f64 (fma.f64 n n (-.f64 #s(literal 1 binary64) n))) (log.f64 (fma.f64 n n (-.f64 #s(literal 1 binary64) n))) (.f64 (log1p.f64 (.f64 n (*.f64 n n))) (log.f64 (fma.f64 n n (-.f64 #s(literal 1 binary64) n)))))))
(/.f64 (-.f64 (pow.f64 (log.f64 (fma.f64 n n #s(literal -1 binary64))) #s(literal 3 binary64)) (pow.f64 (log.f64 (+.f64 n #s(literal -1 binary64))) #s(literal 3 binary64))) (fma.f64 (log.f64 (fma.f64 n n #s(literal -1 binary64))) (log.f64 (fma.f64 n n #s(literal -1 binary64))) (fma.f64 (log.f64 (+.f64 n #s(literal -1 binary64))) (log.f64 (+.f64 n #s(literal -1 binary64))) (*.f64 (log.f64 (fma.f64 n n #s(literal -1 binary64))) (log.f64 (+.f64 n #s(literal -1 binary64)))))))
(/.f64 (-.f64 (.f64 (log1p.f64 (.f64 n (.f64 n n))) (log1p.f64 (.f64 n (.f64 n n)))) (.f64 (log.f64 (fma.f64 n n (-.f64 #s(literal 1 binary64) n))) (log.f64 (fma.f64 n n (-.f64 #s(literal 1 binary64) n))))) (+.f64 (log1p.f64 (.f64 n (.f64 n n))) (log.f64 (fma.f64 n n (-.f64 #s(literal 1 binary64) n)))))
(/.f64 (-.f64 (.f64 (log.f64 (fma.f64 n n #s(literal -1 binary64))) (log.f64 (fma.f64 n n #s(literal -1 binary64)))) (.f64 (log.f64 (+.f64 n #s(literal -1 binary64))) (log.f64 (+.f64 n #s(literal -1 binary64))))) (+.f64 (log.f64 (fma.f64 n n #s(literal -1 binary64))) (log.f64 (+.f64 n #s(literal -1 binary64)))))
(log1p.f64 n)
(*.f64 #s(literal 1 binary64) (log1p.f64 n))
(*.f64 (log1p.f64 n) #s(literal 1 binary64))
(+.f64 (log1p.f64 n) (fma.f64 (log1p.f64 n) n (fma.f64 (log.f64 n) (neg.f64 n) #s(literal -1 binary64))))
(+.f64 (log1p.f64 n) (fma.f64 n (log1p.f64 n) (fma.f64 (log.f64 n) (neg.f64 n) #s(literal -1 binary64))))
(+.f64 (log1p.f64 n) (-.f64 (*.f64 (log1p.f64 n) n) (fma.f64 n (log.f64 n) #s(literal 1 binary64))))
(+.f64 (log1p.f64 n) (-.f64 (*.f64 n (log1p.f64 n)) (fma.f64 n (log.f64 n) #s(literal 1 binary64))))
(+.f64 (*.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) (fma.f64 (log.f64 n) (neg.f64 n) #s(literal -1 binary64)))
(+.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) (.f64 n (log.f64 n))) #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) (.f64 n (log.f64 n))))
(+.f64 (*.f64 (log.f64 n) (neg.f64 n)) (fma.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n) #s(literal -1 binary64)))
(+.f64 (.f64 (log.f64 n) (neg.f64 n)) (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) #s(literal 1 binary64)))
(+.f64 (/.f64 (pow.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) (.f64 n (log.f64 n))) #s(literal 3 binary64)) (+.f64 (pow.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) (.f64 n (log.f64 n))) #s(literal 2 binary64)) (fma.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n) (fma.f64 (log.f64 n) (neg.f64 n) #s(literal 1 binary64))))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) (.f64 n (log.f64 n))) #s(literal 2 binary64)) (fma.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n) (fma.f64 (log.f64 n) (neg.f64 n) #s(literal 1 binary64)))))))
(+.f64 (/.f64 (pow.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) (.f64 n (log.f64 n))) #s(literal 2 binary64)) (fma.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n) (fma.f64 (log.f64 n) (neg.f64 n) #s(literal 1 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n) (fma.f64 (log.f64 n) (neg.f64 n) #s(literal 1 binary64))))))
(+.f64 (*.f64 (log1p.f64 n) n) (+.f64 (log1p.f64 n) (fma.f64 (log.f64 n) (neg.f64 n) #s(literal -1 binary64))))
(+.f64 (*.f64 (log1p.f64 n) n) (-.f64 (log1p.f64 n) (fma.f64 n (log.f64 n) #s(literal 1 binary64))))
(+.f64 (*.f64 n (log1p.f64 n)) (+.f64 (log1p.f64 n) (fma.f64 (log.f64 n) (neg.f64 n) #s(literal -1 binary64))))
(+.f64 (*.f64 n (log1p.f64 n)) (-.f64 (log1p.f64 n) (fma.f64 n (log.f64 n) #s(literal 1 binary64))))
(+.f64 (fma.f64 (log.f64 n) (neg.f64 n) #s(literal -1 binary64)) (*.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)))
(+.f64 (+.f64 #s(literal -1 binary64) (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n))) (.f64 (log.f64 n) (neg.f64 n)))
(-.f64 (*.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) (fma.f64 n (log.f64 n) #s(literal 1 binary64)))
(-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) (.f64 n (log.f64 n))) #s(literal 1 binary64))
(-.f64 (/.f64 (pow.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) (.f64 n (log.f64 n))) #s(literal 3 binary64)) (+.f64 (pow.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) (.f64 n (log.f64 n))) #s(literal 2 binary64)) (fma.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n) (fma.f64 (log.f64 n) (neg.f64 n) #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) (.f64 n (log.f64 n))) #s(literal 2 binary64)) (fma.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n) (fma.f64 (log.f64 n) (neg.f64 n) #s(literal 1 binary64))))))
(-.f64 (/.f64 (pow.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) (.f64 n (log.f64 n))) #s(literal 2 binary64)) (fma.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n) (fma.f64 (log.f64 n) (neg.f64 n) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n) (fma.f64 (log.f64 n) (neg.f64 n) #s(literal 1 binary64)))))
(-.f64 (/.f64 (pow.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) #s(literal 3 binary64)) (fma.f64 n (.f64 (log.f64 n) (fma.f64 n (log.f64 n) (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)))) (pow.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) #s(literal 2 binary64)))) (-.f64 (/.f64 (pow.f64 (.f64 n (log.f64 n)) #s(literal 3 binary64)) (fma.f64 n (.f64 (log.f64 n) (fma.f64 n (log.f64 n) (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)))) (pow.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) #s(literal 2 binary64)))) #s(literal -1 binary64)))
(-.f64 (/.f64 (pow.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) #s(literal 3 binary64)) (fma.f64 n (.f64 (log.f64 n) (fma.f64 n (log.f64 n) (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)))) (pow.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) #s(literal 2 binary64)))) (+.f64 (/.f64 (pow.f64 (.f64 n (log.f64 n)) #s(literal 3 binary64)) (fma.f64 n (.f64 (log.f64 n) (fma.f64 n (log.f64 n) (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)))) (pow.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) #s(literal 2 binary64)))) #s(literal 1 binary64)))
(-.f64 (/.f64 (pow.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) #s(literal 2 binary64)) (fma.f64 n (log.f64 n) (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)))) (-.f64 (/.f64 (pow.f64 (.f64 n (log.f64 n)) #s(literal 2 binary64)) (fma.f64 n (log.f64 n) (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)))) #s(literal -1 binary64)))
(-.f64 (/.f64 (pow.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) #s(literal 2 binary64)) (fma.f64 n (log.f64 n) (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)))) (+.f64 (/.f64 (pow.f64 (.f64 n (log.f64 n)) #s(literal 2 binary64)) (fma.f64 n (log.f64 n) (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)))) #s(literal 1 binary64)))
(-.f64 (/.f64 (pow.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) (.f64 n (log.f64 n))) #s(literal 3 binary64)) (+.f64 (pow.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) (.f64 n (log.f64 n))) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) (.f64 n (log.f64 n))) #s(literal -1 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) (.f64 n (log.f64 n))) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) (.f64 n (log.f64 n))) #s(literal -1 binary64))))))
(-.f64 (/.f64 (pow.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) #s(literal 3 binary64)) (+.f64 (pow.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) #s(literal 2 binary64)) (.f64 (fma.f64 n (log.f64 n) #s(literal 1 binary64)) (+.f64 (fma.f64 n (log.f64 n) #s(literal 1 binary64)) (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)))))) (/.f64 (pow.f64 (fma.f64 n (log.f64 n) #s(literal 1 binary64)) #s(literal 3 binary64)) (+.f64 (pow.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) #s(literal 2 binary64)) (.f64 (fma.f64 n (log.f64 n) #s(literal 1 binary64)) (+.f64 (fma.f64 n (log.f64 n) #s(literal 1 binary64)) (*.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)))))))
(-.f64 (/.f64 (pow.f64 (*.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) #s(literal 2 binary64)) (fma.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n) (fma.f64 n (log.f64 n) #s(literal 1 binary64)))) (/.f64 (pow.f64 (fma.f64 n (log.f64 n) #s(literal 1 binary64)) #s(literal 2 binary64)) (fma.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n) (fma.f64 n (log.f64 n) #s(literal 1 binary64)))))
(-.f64 (+.f64 #s(literal -1 binary64) (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n))) (.f64 n (log.f64 n)))
(-.f64 (+.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) #s(literal 3 binary64)) (fma.f64 n (.f64 (log.f64 n) (fma.f64 n (log.f64 n) (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)))) (pow.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) #s(literal 2 binary64))))) (/.f64 (pow.f64 (.f64 n (log.f64 n)) #s(literal 3 binary64)) (fma.f64 n (.f64 (log.f64 n) (fma.f64 n (log.f64 n) (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)))) (pow.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) #s(literal 2 binary64)))))
(-.f64 (+.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) #s(literal 2 binary64)) (fma.f64 n (log.f64 n) (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n))))) (/.f64 (pow.f64 (.f64 n (log.f64 n)) #s(literal 2 binary64)) (fma.f64 n (log.f64 n) (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)))))
(-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n)) #s(literal 1 binary64)) (.f64 n (log.f64 n)))
(fma.f64 n (log1p.f64 n) (+.f64 (log1p.f64 n) (fma.f64 (log.f64 n) (neg.f64 n) #s(literal -1 binary64))))
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(fma.f64 n (neg.f64 (log.f64 n)) (fma.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n) #s(literal -1 binary64)))
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(/.f64 (.f64 (log1p.f64 n) (-.f64 #s(literal 1 binary64) (.f64 n n))) (-.f64 #s(literal 1 binary64) n))
(/.f64 (.f64 (neg.f64 (fma.f64 n (.f64 n n) #s(literal 1 binary64))) (log1p.f64 n)) (neg.f64 (fma.f64 n n (-.f64 #s(literal 1 binary64) n))))
(/.f64 (*.f64 (neg.f64 (fma.f64 n n #s(literal -1 binary64))) (log1p.f64 n)) (+.f64 (neg.f64 n) #s(literal 1 binary64)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 n n)) (log1p.f64 n)) (-.f64 #s(literal 1 binary64) n))
(*.f64 (+.f64 n #s(literal 1 binary64)) (log1p.f64 n))
(*.f64 (log1p.f64 n) (+.f64 n #s(literal 1 binary64)))
(.f64 (fma.f64 n (.f64 n n) #s(literal 1 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 n n (-.f64 #s(literal 1 binary64) n))) (log1p.f64 n)))
(.f64 (fma.f64 n n #s(literal -1 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 n #s(literal -1 binary64))) (log1p.f64 n)))
(.f64 (.f64 (log1p.f64 n) (fma.f64 n (*.f64 n n) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 n n (-.f64 #s(literal 1 binary64) n))))
(.f64 (.f64 (log1p.f64 n) (fma.f64 n n #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 n #s(literal -1 binary64))))
(.f64 (.f64 (fma.f64 n (*.f64 n n) #s(literal 1 binary64)) (log1p.f64 n)) (/.f64 #s(literal 1 binary64) (fma.f64 n n (-.f64 #s(literal 1 binary64) n))))
(.f64 (.f64 (fma.f64 n n #s(literal -1 binary64)) (log1p.f64 n)) (/.f64 #s(literal 1 binary64) (+.f64 n #s(literal -1 binary64))))
(.f64 (/.f64 (.f64 (log1p.f64 n) (fma.f64 n (.f64 n n) #s(literal 1 binary64))) (fma.f64 n (.f64 (.f64 n n) (.f64 n (.f64 n n))) (.f64 (-.f64 #s(literal 1 binary64) n) (.f64 (-.f64 #s(literal 1 binary64) n) (-.f64 #s(literal 1 binary64) n))))) (fma.f64 n (.f64 n (.f64 n n)) (.f64 (-.f64 #s(literal 1 binary64) n) (-.f64 (-.f64 #s(literal 1 binary64) n) (*.f64 n n)))))
(.f64 (/.f64 (.f64 (log1p.f64 n) (fma.f64 n (.f64 n n) #s(literal 1 binary64))) (.f64 (fma.f64 n n (-.f64 #s(literal 1 binary64) n)) (+.f64 (fma.f64 n n #s(literal -1 binary64)) n))) (+.f64 (fma.f64 n n #s(literal -1 binary64)) n))
(.f64 (/.f64 (.f64 (log1p.f64 n) (fma.f64 n n #s(literal -1 binary64))) (fma.f64 n n #s(literal -1 binary64))) (+.f64 n #s(literal 1 binary64)))
(.f64 (/.f64 (.f64 (log1p.f64 n) (fma.f64 n n #s(literal -1 binary64))) (fma.f64 n (*.f64 n n) #s(literal -1 binary64))) (+.f64 (fma.f64 n n n) #s(literal 1 binary64)))
(.f64 (/.f64 (.f64 (fma.f64 n (.f64 n n) #s(literal 1 binary64)) (log1p.f64 n)) (fma.f64 n (.f64 (.f64 n n) (.f64 n (.f64 n n))) (.f64 (-.f64 #s(literal 1 binary64) n) (.f64 (-.f64 #s(literal 1 binary64) n) (-.f64 #s(literal 1 binary64) n))))) (fma.f64 n (.f64 n (.f64 n n)) (.f64 (-.f64 #s(literal 1 binary64) n) (-.f64 (-.f64 #s(literal 1 binary64) n) (*.f64 n n)))))
(.f64 (/.f64 (.f64 (fma.f64 n (.f64 n n) #s(literal 1 binary64)) (log1p.f64 n)) (.f64 (fma.f64 n n (-.f64 #s(literal 1 binary64) n)) (+.f64 (fma.f64 n n #s(literal -1 binary64)) n))) (+.f64 (fma.f64 n n #s(literal -1 binary64)) n))
(.f64 (/.f64 (.f64 (fma.f64 n n #s(literal -1 binary64)) (log1p.f64 n)) (fma.f64 n n #s(literal -1 binary64))) (+.f64 n #s(literal 1 binary64)))
(.f64 (/.f64 (.f64 (fma.f64 n n #s(literal -1 binary64)) (log1p.f64 n)) (fma.f64 n (*.f64 n n) #s(literal -1 binary64))) (+.f64 (fma.f64 n n n) #s(literal 1 binary64)))
(*.f64 n (log.f64 n))
(.f64 n (.f64 (log.f64 n) #s(literal 1 binary64)))
(.f64 n (.f64 #s(literal 1 binary64) (log.f64 n)))
(.f64 #s(literal 1 binary64) (.f64 n (log.f64 n)))
(*.f64 (log.f64 n) n)
(.f64 (.f64 n (log.f64 n)) #s(literal 1 binary64))
(.f64 (.f64 (log.f64 n) #s(literal 1 binary64)) n)

eval64.0ms (1.1%)

Memory: 19.6MiB live, 133.5MiB allocated
Compiler: Compiled 15 910 to 1 442 computations (90.9% saved)

prune66.0ms (1.1%)

Memory

-31.8MiB live, 127.1MiB allocated

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	487	2	489
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	488	2	490

Accuracy

100.0%

Counts

490 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	#s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n))
▶	1.6%	#s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64))

Compiler

Compiled 7 to 4 computations (42.9% saved)

simplify64.0ms (1.1%)

Memory

34.9MiB live, 74.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

1 408×	`lower-fma.f64`
1 408×	`lower-fma.f32`
360×	`lower-+.f64`
360×	`lower--.f64`
360×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	39
0	14	39
1	28	39
2	56	39
3	123	39
4	257	39
5	494	39
6	849	39
7	1198	39
8	1394	39
9	1411	39
0	1411	31

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64))
#s(literal -1 binary64)
#s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n))
(log.f64 n)
n

Outputs
#s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64))
#s(literal -1 binary64)
#s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n))
(log.f64 n)
n

localize83.0ms (1.4%)

Memory

-28.1MiB live, 102.1MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(log.f64 n)
accuracy	0	#s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n))
accuracy	63.004298765689335	#s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64))

Samples

73.0ms

256×

valid

Compiler

Compiled 36 to 12 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 64.0ms

ival-log1p: 20.0ms (31.5% of total)

ival-log: 18.0ms (28.3% of total)

ival-add: 7.0ms (11% of total)

adjust: 7.0ms (11% of total)

ival-mult: 7.0ms (11% of total)

ival-sub: 4.0ms (6.3% of total)

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

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

exact: 0.0ms (0% of total)

series1.0ms (0%)

Memory

2.4MiB live, 2.4MiB allocated

Counts

3 → 36

Calls

Call 1

Inputs

#s(alt #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64)) (patch #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64)) #<representation binary64>) () ())

#s(alt #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n)) (patch #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n)) #<representation binary64>) () ())

#s(alt (log.f64 n) (patch (log.f64 n) #<representation binary64>) () ())

Outputs
#s(alt -1 (taylor 0 n) (#s(alt #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64)) (patch #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* n (- 1 (log n))) 1) (taylor 0 n) (#s(alt #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64)) (patch #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* n (- (+ 1 (* 1/2 n)) (log n))) 1) (taylor 0 n) (#s(alt #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64)) (patch #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* n (- (+ 1 (* n (+ 1/2 (* -1/6 n)))) (log n))) 1) (taylor 0 n) (#s(alt #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64)) (patch #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (log (/ 1 n))) (taylor inf n) (#s(alt #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64)) (patch #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (log (/ 1 n))) (* 1/2 (/ 1 n))) (taylor inf n) (#s(alt #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64)) (patch #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (log (/ 1 n))) (* 1/2 (/ 1 n))) (/ 1/6 (pow n 2))) (taylor inf n) (#s(alt #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64)) (patch #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (log (/ 1 n))) (+ (* 1/2 (/ 1 n)) (* 1/12 (/ 1 (pow n 3))))) (/ 1/6 (pow n 2))) (taylor inf n) (#s(alt #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64)) (patch #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (* -1 (log (/ -1 n)))) (taylor -inf n) (#s(alt #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64)) (patch #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (+ (* -1 (log (/ -1 n))) (* 1/2 (/ 1 n)))) (taylor -inf n) (#s(alt #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64)) (patch #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* 1/6 (/ 1 n)) 1/2) n)))) (taylor -inf n) (#s(alt #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64)) (patch #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* -1 (/ (- (* 1/12 (/ 1 n)) 1/6) n)) 1/2) n)))) (taylor -inf n) (#s(alt #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64)) (patch #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 n) (#s(alt #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n)) (patch #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n)) #<representation binary64>) () ())) ())
#s(alt (- (* n (- 1 (log n))) 1) (taylor 0 n) (#s(alt #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n)) (patch #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n)) #<representation binary64>) () ())) ())
#s(alt (- (* n (- (+ 1 (* 1/2 n)) (log n))) 1) (taylor 0 n) (#s(alt #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n)) (patch #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n)) #<representation binary64>) () ())) ())
#s(alt (- (* n (- (+ 1 (* n (+ 1/2 (* -1/6 n)))) (log n))) 1) (taylor 0 n) (#s(alt #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n)) (patch #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n)) #<representation binary64>) () ())) ())
#s(alt (* -1 (log (/ 1 n))) (taylor inf n) (#s(alt #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n)) (patch #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (log (/ 1 n))) (* 1/2 (/ 1 n))) (taylor inf n) (#s(alt #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n)) (patch #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n)) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (log (/ 1 n))) (* 1/2 (/ 1 n))) (/ 1/6 (pow n 2))) (taylor inf n) (#s(alt #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n)) (patch #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n)) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (log (/ 1 n))) (+ (* 1/2 (/ 1 n)) (* 1/12 (/ 1 (pow n 3))))) (/ 1/6 (pow n 2))) (taylor inf n) (#s(alt #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n)) (patch #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n)) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (* -1 (log (/ -1 n)))) (taylor -inf n) (#s(alt #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n)) (patch #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n)) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (+ (* -1 (log (/ -1 n))) (* 1/2 (/ 1 n)))) (taylor -inf n) (#s(alt #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n)) (patch #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n)) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* 1/6 (/ 1 n)) 1/2) n)))) (taylor -inf n) (#s(alt #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n)) (patch #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n)) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* -1 (/ (- (* 1/12 (/ 1 n)) 1/6) n)) 1/2) n)))) (taylor -inf n) (#s(alt #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n)) (patch #s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n)) #<representation binary64>) () ())) ())
#s(alt (log n) (taylor 0 n) (#s(alt (log.f64 n) (patch (log.f64 n) #<representation binary64>) () ())) ())
#s(alt (log n) (taylor 0 n) (#s(alt (log.f64 n) (patch (log.f64 n) #<representation binary64>) () ())) ())
#s(alt (log n) (taylor 0 n) (#s(alt (log.f64 n) (patch (log.f64 n) #<representation binary64>) () ())) ())
#s(alt (log n) (taylor 0 n) (#s(alt (log.f64 n) (patch (log.f64 n) #<representation binary64>) () ())) ())
#s(alt (* -1 (log (/ 1 n))) (taylor inf n) (#s(alt (log.f64 n) (patch (log.f64 n) #<representation binary64>) () ())) ())
#s(alt (* -1 (log (/ 1 n))) (taylor inf n) (#s(alt (log.f64 n) (patch (log.f64 n) #<representation binary64>) () ())) ())
#s(alt (* -1 (log (/ 1 n))) (taylor inf n) (#s(alt (log.f64 n) (patch (log.f64 n) #<representation binary64>) () ())) ())
#s(alt (* -1 (log (/ 1 n))) (taylor inf n) (#s(alt (log.f64 n) (patch (log.f64 n) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (* -1 (log (/ -1 n)))) (taylor -inf n) (#s(alt (log.f64 n) (patch (log.f64 n) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (* -1 (log (/ -1 n)))) (taylor -inf n) (#s(alt (log.f64 n) (patch (log.f64 n) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (* -1 (log (/ -1 n)))) (taylor -inf n) (#s(alt (log.f64 n) (patch (log.f64 n) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (* -1 (log (/ -1 n)))) (taylor -inf n) (#s(alt (log.f64 n) (patch (log.f64 n) #<representation binary64>) () ())) ())

Calls

9 calls:

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

simplify380.0ms (6.4%)

Memory

2.0MiB live, 462.7MiB allocated

Algorithm

1×	egg-herbie

Rules

13 742×	`lower-fma.f64`
13 742×	`lower-fma.f32`
2 484×	`lower-+.f64`
2 484×	`lower-+.f32`
2 332×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	348
1	159	300
2	382	290
3	957	286
4	2620	274
5	4930	274
6	6112	274
7	7139	274
8	7558	274
9	7776	274
10	7916	274
11	7916	274
0	8031	262

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

Calls

Call 1

Inputs
-1
(- (* n (- 1 (log n))) 1)
(- (* n (- (+ 1 (* 1/2 n)) (log n))) 1)
(- (* n (- (+ 1 (* n (+ 1/2 (* -1/6 n)))) (log n))) 1)
(* -1 (log (/ 1 n)))
(+ (* -1 (log (/ 1 n))) (* 1/2 (/ 1 n)))
(- (+ (* -1 (log (/ 1 n))) (* 1/2 (/ 1 n))) (/ 1/6 (pow n 2)))
(- (+ (* -1 (log (/ 1 n))) (+ (* 1/2 (/ 1 n)) (* 1/12 (/ 1 (pow n 3))))) (/ 1/6 (pow n 2)))
(+ (log -1) (* -1 (log (/ -1 n))))
(+ (log -1) (+ (* -1 (log (/ -1 n))) (* 1/2 (/ 1 n))))
(+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* 1/6 (/ 1 n)) 1/2) n))))
(+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* -1 (/ (- (* 1/12 (/ 1 n)) 1/6) n)) 1/2) n))))
-1
(- (* n (- 1 (log n))) 1)
(- (* n (- (+ 1 (* 1/2 n)) (log n))) 1)
(- (* n (- (+ 1 (* n (+ 1/2 (* -1/6 n)))) (log n))) 1)
(* -1 (log (/ 1 n)))
(+ (* -1 (log (/ 1 n))) (* 1/2 (/ 1 n)))
(- (+ (* -1 (log (/ 1 n))) (* 1/2 (/ 1 n))) (/ 1/6 (pow n 2)))
(- (+ (* -1 (log (/ 1 n))) (+ (* 1/2 (/ 1 n)) (* 1/12 (/ 1 (pow n 3))))) (/ 1/6 (pow n 2)))
(+ (log -1) (* -1 (log (/ -1 n))))
(+ (log -1) (+ (* -1 (log (/ -1 n))) (* 1/2 (/ 1 n))))
(+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* 1/6 (/ 1 n)) 1/2) n))))
(+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* -1 (/ (- (* 1/12 (/ 1 n)) 1/6) n)) 1/2) n))))
(log n)
(log n)
(log n)
(log n)
(* -1 (log (/ 1 n)))
(* -1 (log (/ 1 n)))
(* -1 (log (/ 1 n)))
(* -1 (log (/ 1 n)))
(+ (log -1) (* -1 (log (/ -1 n))))
(+ (log -1) (* -1 (log (/ -1 n))))
(+ (log -1) (* -1 (log (/ -1 n))))
(+ (log -1) (* -1 (log (/ -1 n))))

Outputs
-1
#s(literal -1 binary64)
(- (* n (- 1 (log n))) 1)
(-.f64 n (fma.f64 n (log.f64 n) #s(literal 1 binary64)))
(- (* n (- (+ 1 (* 1/2 n)) (log n))) 1)
(fma.f64 n (fma.f64 n #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (log.f64 n))) #s(literal -1 binary64))
(- (* n (- (+ 1 (* n (+ 1/2 (* -1/6 n)))) (log n))) 1)
(fma.f64 n (fma.f64 n (fma.f64 n #s(literal -1/6 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (log.f64 n))) #s(literal -1 binary64))
(* -1 (log (/ 1 n)))
(log.f64 n)
(+ (* -1 (log (/ 1 n))) (* 1/2 (/ 1 n)))
(+.f64 (log.f64 n) (/.f64 #s(literal 1/2 binary64) n))
(- (+ (* -1 (log (/ 1 n))) (* 1/2 (/ 1 n))) (/ 1/6 (pow n 2)))
(-.f64 (log.f64 n) (/.f64 (+.f64 (/.f64 #s(literal 1/6 binary64) n) #s(literal -1/2 binary64)) n))
(- (+ (* -1 (log (/ 1 n))) (+ (* 1/2 (/ 1 n)) (* 1/12 (/ 1 (pow n 3))))) (/ 1/6 (pow n 2)))
(+.f64 (log.f64 n) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1/12 binary64) n)) n)) n))
(+ (log -1) (* -1 (log (/ -1 n))))
(+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (neg.f64 n)))
(+ (log -1) (+ (* -1 (log (/ -1 n))) (* 1/2 (/ 1 n))))
(+.f64 (log.f64 (neg.f64 n)) (+.f64 (/.f64 #s(literal 1/2 binary64) n) (log.f64 #s(literal -1 binary64))))
(+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* 1/6 (/ 1 n)) 1/2) n))))
(+.f64 (log.f64 (neg.f64 n)) (-.f64 (log.f64 #s(literal -1 binary64)) (/.f64 (+.f64 (/.f64 #s(literal 1/6 binary64) n) #s(literal -1/2 binary64)) n)))
(+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* -1 (/ (- (* 1/12 (/ 1 n)) 1/6) n)) 1/2) n))))
(+.f64 (log.f64 (neg.f64 n)) (+.f64 (log.f64 #s(literal -1 binary64)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1/12 binary64) n)) n)) n)))
-1
#s(literal -1 binary64)
(- (* n (- 1 (log n))) 1)
(-.f64 n (fma.f64 n (log.f64 n) #s(literal 1 binary64)))
(- (* n (- (+ 1 (* 1/2 n)) (log n))) 1)
(fma.f64 n (fma.f64 n #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (log.f64 n))) #s(literal -1 binary64))
(- (* n (- (+ 1 (* n (+ 1/2 (* -1/6 n)))) (log n))) 1)
(fma.f64 n (fma.f64 n (fma.f64 n #s(literal -1/6 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (log.f64 n))) #s(literal -1 binary64))
(* -1 (log (/ 1 n)))
(log.f64 n)
(+ (* -1 (log (/ 1 n))) (* 1/2 (/ 1 n)))
(+.f64 (log.f64 n) (/.f64 #s(literal 1/2 binary64) n))
(- (+ (* -1 (log (/ 1 n))) (* 1/2 (/ 1 n))) (/ 1/6 (pow n 2)))
(-.f64 (log.f64 n) (/.f64 (+.f64 (/.f64 #s(literal 1/6 binary64) n) #s(literal -1/2 binary64)) n))
(- (+ (* -1 (log (/ 1 n))) (+ (* 1/2 (/ 1 n)) (* 1/12 (/ 1 (pow n 3))))) (/ 1/6 (pow n 2)))
(+.f64 (log.f64 n) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1/12 binary64) n)) n)) n))
(+ (log -1) (* -1 (log (/ -1 n))))
(+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (neg.f64 n)))
(+ (log -1) (+ (* -1 (log (/ -1 n))) (* 1/2 (/ 1 n))))
(+.f64 (log.f64 (neg.f64 n)) (+.f64 (/.f64 #s(literal 1/2 binary64) n) (log.f64 #s(literal -1 binary64))))
(+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* 1/6 (/ 1 n)) 1/2) n))))
(+.f64 (log.f64 (neg.f64 n)) (-.f64 (log.f64 #s(literal -1 binary64)) (/.f64 (+.f64 (/.f64 #s(literal 1/6 binary64) n) #s(literal -1/2 binary64)) n)))
(+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* -1 (/ (- (* 1/12 (/ 1 n)) 1/6) n)) 1/2) n))))
(+.f64 (log.f64 (neg.f64 n)) (+.f64 (log.f64 #s(literal -1 binary64)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1/12 binary64) n)) n)) n)))
(log n)
(log.f64 n)
(log n)
(log.f64 n)
(log n)
(log.f64 n)
(log n)
(log.f64 n)
(* -1 (log (/ 1 n)))
(log.f64 n)
(* -1 (log (/ 1 n)))
(log.f64 n)
(* -1 (log (/ 1 n)))
(log.f64 n)
(* -1 (log (/ 1 n)))
(log.f64 n)
(+ (log -1) (* -1 (log (/ -1 n))))
(+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (neg.f64 n)))
(+ (log -1) (* -1 (log (/ -1 n))))
(+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (neg.f64 n)))
(+ (log -1) (* -1 (log (/ -1 n))))
(+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (neg.f64 n)))
(+ (log -1) (* -1 (log (/ -1 n))))
(+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (neg.f64 n)))

rewrite425.0ms (7.1%)

Memory

20.0MiB live, 429.0MiB allocated

Rules

8 652×	`lower-fma.f64`
8 652×	`lower-fma.f32`
5 492×	`lower-*.f64`
5 492×	`lower-*.f32`
3 876×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	37
0	14	37
1	63	37
2	513	37
0	8392	31

Stop Event

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

Counts

3 → 5

Calls

Call 1

Inputs
#s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64))
#s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n))
(log.f64 n)

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

eval3.0ms (0.1%)

Memory: 7.1MiB live, 7.1MiB allocated
Compiler: Compiled 329 to 42 computations (87.2% saved)

prune4.0ms (0.1%)

Memory

-31.9MiB live, 7.3MiB allocated

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	41	0	41
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	41	2	43

Accuracy

100.0%

Counts

43 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	#s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n))
✓	1.6%	#s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64))

Compiler

Compiled 28 to 14 computations (50% saved)

regimes5.0ms (0.1%)

Memory

10.3MiB live, 10.3MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

#s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64))

#s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n))

(-.f64 (-.f64 (*.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (*.f64 n (log.f64 n))) #s(literal 1 binary64))

Outputs
#s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n))

Calls

3 calls:

2.0ms

1.0ms

(-.f64 (*.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (*.f64 n (log.f64 n)))

1.0ms

(-.f64 (-.f64 (*.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (*.f64 n (log.f64 n))) #s(literal 1 binary64))

Results

Accuracy	Segments	Branch
100.0%	1	`n`
100.0%	1	`(-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #s(literal 1 binary64))`
100.0%	1	`(-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n)))`

Compiler

Compiled 32 to 18 computations (43.8% saved)

regimes4.0ms (0.1%)

Memory

7.8MiB live, 7.8MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64))

Outputs
#s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64))

Calls

3 calls:

1.0ms

(-.f64 (-.f64 (*.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (*.f64 n (log.f64 n))) #s(literal 1 binary64))

1.0ms

(-.f64 (*.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (*.f64 n (log.f64 n)))

Results

Accuracy	Segments	Branch
1.6%	1	`n`
1.6%	1	`(-.f64 (-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n))) #s(literal 1 binary64))`
1.6%	1	`(-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n)))`

Compiler

Compiled 32 to 18 computations (43.8% saved)

simplify5.0ms (0.1%)

Memory

10.4MiB live, 10.4MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	35
1	16	35

Stop Event

1×

saturated

Calls

Call 1

Inputs
#s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n))
#s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64))

Outputs
#s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) (log.f64 n))
#s(approx (- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1) #s(literal -1 binary64))

soundness180.0ms (3%)

Memory

-35.2MiB live, 86.4MiB allocated

Rules

12 704×	`lower-fma.f64`
12 704×	`lower-fma.f32`
3 310×	`lower-+.f64`
3 310×	`lower-+.f32`
2 942×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	154	748
1	486	661
2	1401	636
3	4863	620
0	8506	591

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 11 to 7 computations (36.4% saved)

preprocess67.0ms (1.1%)

Memory: 14.0MiB live, 52.5MiB allocated
Compiler: Compiled 94 to 58 computations (38.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample3.2s (53.7%)

explain352.0ms (5.9%)

preprocess102.0ms (1.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify56.0ms (0.9%)

localize116.0ms (1.9%)

series73.0ms (1.2%)

simplify330.0ms (5.5%)

rewrite380.0ms (6.4%)

eval64.0ms (1.1%)

prune66.0ms (1.1%)

simplify64.0ms (1.1%)

localize83.0ms (1.4%)

series1.0ms (0%)

simplify380.0ms (6.4%)

rewrite425.0ms (7.1%)

eval3.0ms (0.1%)

prune4.0ms (0.1%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

simplify5.0ms (0.1%)

soundness180.0ms (3%)

preprocess67.0ms (1.1%)

end0.0ms (0%)

Profiling