Metrics for logs (example 3.8)

analyze0.0ms (0%)

Memory

0.6MiB live, 0.6MiB 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)

sample2.8s (60.1%)

Memory

82.8MiB live, 3 912.4MiB allocated

Samples

2.4s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 2.1s

ival-log1p: 706.0ms (33.1% of total)

ival-log: 596.0ms (27.9% of total)

ival-mult: 249.0ms (11.7% of total)

adjust: 242.0ms (11.3% of total)

ival-sub: 174.0ms (8.1% of total)

ival-add: 130.0ms (6.1% of total)

ival->: 24.0ms (1.1% of total)

exact: 10.0ms (0.5% of total)

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

Bogosity

preprocess133.0ms (2.9%)

Memory

-29.9MiB live, 52.2MiB 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)))

explain254.0ms (5.5%)

Memory

-26.7MiB live, 408.7MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
256	-	256	(5.0912519553709154e+72)	`(*.f64 n (log.f64 n))`
256	-	256	(5.0912519553709154e+72)	`(+.f64 n #s(literal 1 binary64))`
256	-	256	(5.0912519553709154e+72)	`(log.f64 n)`
256	-	0	-	`(-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n)))`
256	-	256	(5.0912519553709154e+72)	`(log.f64 (+.f64 n #s(literal 1 binary64)))`
256	-	256	(5.0912519553709154e+72)	`(*.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64))))`
0	-	0	-	`n`
0	-	0	-	`#s(literal 1 binary64)`
0	-	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))`

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	253	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	3	0
↳	`(*.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64))))`	overflow	3
↳	`(*.f64 n (log.f64 n))`	overflow	3

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

156.0ms

512×

valid

Compiler

Compiled 190 to 49 computations (74.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 134.0ms

ival-log1p: 53.0ms (39.6% of total)

ival-log: 37.0ms (27.7% of total)

adjust: 16.0ms (12% of total)

ival-mult: 13.0ms (9.7% of total)

ival-sub: 9.0ms (6.7% of total)

ival-add: 5.0ms (3.7% of total)

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

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

exact: 0.0ms (0% of total)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	1.6%	(-.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)

simplify63.0ms (1.4%)

Memory

6.4MiB live, 47.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	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)

localize88.0ms (1.9%)

Memory

7.8MiB live, 83.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	14.0%	(*.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64))))
✓	accuracy	5.1%	(log.f64 (+.f64 n #s(literal 1 binary64)))
✓	accuracy	5.0%	(*.f64 n (log.f64 n))
✓	accuracy	2.4%	(-.f64 (.f64 (+.f64 n #s(literal 1 binary64)) (log.f64 (+.f64 n #s(literal 1 binary64)))) (.f64 n (log.f64 n)))

Samples

75.0ms

256×

valid

Compiler

Compiled 105 to 20 computations (81% saved)

Precisions

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

ival-log1p: 24.0ms (37.4% of total)

ival-log: 19.0ms (29.6% of total)

adjust: 7.0ms (10.9% of total)

ival-mult: 6.0ms (9.3% of total)

ival-sub: 4.0ms (6.2% of total)

ival-add: 3.0ms (4.7% of total)

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

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

exact: 0.0ms (0% of total)

series61.0ms (1.3%)

Memory

8.2MiB live, 86.1MiB allocated

Counts

5 → 60

Calls

Call 1

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

Outputs
#<alt n>
#<alt (* n (+ 1 (* -1/2 n)))>
#<alt (* n (+ 1 (* n (- (* 1/3 n) 1/2))))>
#<alt (* n (+ 1 (* n (- (* n (+ 1/3 (* -1/4 n))) 1/2))))>
#<alt (* -1 (log (/ 1 n)))>
#<alt (+ (* -1 (log (/ 1 n))) (/ 1 n))>
#<alt (- (+ (* -1 (log (/ 1 n))) (/ 1 n)) (/ 1/2 (pow n 2)))>
#<alt (- (+ (* -1 (log (/ 1 n))) (+ (/ 1 n) (* 1/3 (/ 1 (pow n 3))))) (/ 1/2 (pow n 2)))>
#<alt (+ (log -1) (* -1 (log (/ -1 n))))>
#<alt (+ (log -1) (+ (* -1 (log (/ -1 n))) (/ 1 n)))>
#<alt (+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* 1/2 (/ 1 n)) 1) n))))>
#<alt (+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* -1 (/ (- (* 1/3 (/ 1 n)) 1/2) n)) 1) n))))>
#<alt -1>
#<alt (- (* n (- 1 (log n))) 1)>
#<alt (- (* n (- (+ 1 (* 1/2 n)) (log n))) 1)>
#<alt (- (* n (- (+ 1 (* n (+ 1/2 (* -1/6 n)))) (log n))) 1)>
#<alt (* -1 (log (/ 1 n)))>
#<alt (+ (* -1 (log (/ 1 n))) (* 1/2 (/ 1 n)))>
#<alt (- (+ (* -1 (log (/ 1 n))) (* 1/2 (/ 1 n))) (/ 1/6 (pow n 2)))>
#<alt (- (+ (* -1 (log (/ 1 n))) (+ (* 1/2 (/ 1 n)) (* 1/12 (/ 1 (pow n 3))))) (/ 1/6 (pow n 2)))>
#<alt (+ (log -1) (* -1 (log (/ -1 n))))>
#<alt (+ (log -1) (+ (* -1 (log (/ -1 n))) (* 1/2 (/ 1 n))))>
#<alt (+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* 1/6 (/ 1 n)) 1/2) n))))>
#<alt (+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* -1 (/ (- (* 1/12 (/ 1 n)) 1/6) n)) 1/2) n))))>
#<alt (* n (- 1 (log n)))>
#<alt (* n (- (+ 1 (* 1/2 n)) (log n)))>
#<alt (* n (- (+ 1 (* n (+ 1/2 (* -1/6 n)))) (log n)))>
#<alt (* n (- (+ 1 (* n (+ 1/2 (* n (- (* 1/12 n) 1/6))))) (log n)))>
#<alt (+ 1 (* -1 (log (/ 1 n))))>
#<alt (+ 1 (+ (* -1 (log (/ 1 n))) (* 1/2 (/ 1 n))))>
#<alt (- (+ 1 (+ (* -1 (log (/ 1 n))) (* 1/2 (/ 1 n)))) (/ 1/6 (pow n 2)))>
#<alt (- (+ 1 (+ (* -1 (log (/ 1 n))) (+ (* 1/2 (/ 1 n)) (* 1/12 (/ 1 (pow n 3)))))) (/ 1/6 (pow n 2)))>
#<alt (+ 1 (+ (log -1) (* -1 (log (/ -1 n)))))>
#<alt (+ 1 (+ (log -1) (+ (* -1 (log (/ -1 n))) (* 1/2 (/ 1 n)))))>
#<alt (+ 1 (+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* 1/6 (/ 1 n)) 1/2) n)))))>
#<alt (+ 1 (+ (log -1) (+ (* -1 (log (/ -1 n))) (* -1 (/ (- (* -1 (/ (- (* 1/12 (/ 1 n)) 1/6) n)) 1/2) n)))))>
#<alt n>
#<alt (* n (+ 1 (* 1/2 n)))>
#<alt (* n (+ 1 (* n (+ 1/2 (* -1/6 n)))))>
#<alt (* n (+ 1 (* n (+ 1/2 (* n (- (* 1/12 n) 1/6))))))>
#<alt (* -1 (* n (log (/ 1 n))))>
#<alt (* n (+ (* -1 (log (/ 1 n))) (+ (* -1 (/ (log (/ 1 n)) n)) (/ 1 n))))>
#<alt (* n (+ (* -1 (log (/ 1 n))) (+ (* -1 (/ (log (/ 1 n)) n)) (+ (/ 1/2 (pow n 2)) (/ 1 n)))))>
#<alt (* n (- (+ (* -1 (log (/ 1 n))) (+ (* -1 (/ (log (/ 1 n)) n)) (+ (/ 1/2 (pow n 2)) (/ 1 n)))) (* 1/6 (/ 1 (pow n 3)))))>
#<alt (* n (+ (log -1) (* -1 (log (/ -1 n)))))>
#<alt (* -1 (* n (+ (* -1 (+ (log -1) (* -1 (log (/ -1 n))))) (* -1 (/ (+ 1 (+ (log -1) (* -1 (log (/ -1 n))))) n)))))>
#<alt (* -1 (* n (+ (* -1 (+ (log -1) (* -1 (log (/ -1 n))))) (* -1 (/ (+ 1 (+ (log -1) (+ (* -1 (log (/ -1 n))) (* 1/2 (/ 1 n))))) n)))))>
#<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)))))>
#<alt (* n (log n))>
#<alt (* n (log n))>
#<alt (* n (log n))>
#<alt (* n (log n))>
#<alt (* -1 (* n (log (/ 1 n))))>
#<alt (* -1 (* n (log (/ 1 n))))>
#<alt (* -1 (* n (log (/ 1 n))))>
#<alt (* -1 (* n (log (/ 1 n))))>
#<alt (* -1 (* n (log (/ -1 n))))>
#<alt (* -1 (* n (log (/ -1 n))))>
#<alt (* -1 (* n (log (/ -1 n))))>
#<alt (* -1 (* n (log (/ -1 n))))>

Calls

15 calls:

Time	Variable		Point	Expression
43.0ms	n	@	0	(* n (log n))
7.0ms	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)
1.0ms	n	@	inf	(- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1)

Compiler

Compiled 193 to 106 computations (45.1% saved)

rewrite367.0ms (8%)

Memory

11.7MiB live, 586.5MiB allocated

Algorithm

1×	batch-egg-rewrite

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

simplify384.0ms (8.3%)

Memory

15.8MiB live, 659.5MiB allocated

Algorithm

1×	egg-herbie

Rules

12 720×	`lower-fma.f64`
12 720×	`lower-fma.f32`
3 314×	`lower-+.f64`
3 314×	`lower-+.f32`
2 942×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	156	736
1	492	653
2	1403	628
3	4873	612
0	8501	583

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

eval62.0ms (1.3%)

Memory: 8.6MiB live, 160.4MiB allocated
Compiler: Compiled 15 844 to 1 450 computations (90.8% saved)

prune92.0ms (2%)

Memory

-16.9MiB live, 153.5MiB 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%	(log.f64 n)
▶	1.6%	#s(literal -1 binary64)

Compiler

Compiled 5 to 4 computations (20% saved)

simplify4.0ms (0.1%)

Memory

8.0MiB live, 8.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(log.f64 n)

Rules

2×	`lift-log.f64`
2×	`lower-log.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
0	4	4
0	4	4

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize20.0ms (0.4%)

Memory

-16.9MiB live, 24.0MiB allocated

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	accuracy	5.1%	(log.f64 n)

Samples

15.0ms

256×

valid

Compiler

Compiled 11 to 8 computations (27.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-log: 11.0ms (98.8% of total)

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

exact: 0.0ms (0% of total)

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

series26.0ms (0.6%)

Memory

-8.8MiB live, 61.8MiB allocated

Counts

1 → 12

Calls

Call 1

Inputs
#<alt (log.f64 n)>

Outputs
#<alt (log n)>
#<alt (log n)>
#<alt (log n)>
#<alt (log n)>
#<alt (* -1 (log (/ 1 n)))>
#<alt (* -1 (log (/ 1 n)))>
#<alt (* -1 (log (/ 1 n)))>
#<alt (* -1 (log (/ 1 n)))>
#<alt (* -1 (log (/ -1 n)))>
#<alt (* -1 (log (/ -1 n)))>
#<alt (* -1 (log (/ -1 n)))>
#<alt (* -1 (log (/ -1 n)))>

Calls

3 calls:

Time	Variable		Point	Expression
11.0ms	n	@	inf	(log n)
8.0ms	n	@	-inf	(log n)
6.0ms	n	@	0	(log n)

Compiler

Compiled 13 to 10 computations (23.1% saved)

rewrite8.0ms (0.2%)

Memory

18.0MiB live, 18.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

2×	`lift-log.f64`
2×	`lower-log.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2	2
0	3	2
0	3	2

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Counts

1 → 1

Calls

Call 1

Inputs
(log.f64 n)

Outputs
(log.f64 n)

simplify5.0ms (0.1%)

Memory

12.2MiB live, 12.2MiB allocated

Algorithm

1×	egg-herbie

Rules

20×	`lower-*.f64`
20×	`lower-fma.f64`
20×	`lower-fma.f32`
20×	`lower-*.f32`
16×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	36
1	17	36
2	23	36
3	37	36
4	50	36
5	56	36
6	59	36
7	61	36
0	61	36

Stop Event

1×	iter limit
1×	saturated

Counts

12 → 12

Calls

Call 1

Inputs
(log n)
(log n)
(log n)
(log n)
(* -1 (log (/ 1 n)))
(* -1 (log (/ 1 n)))
(* -1 (log (/ 1 n)))
(* -1 (log (/ 1 n)))
(* -1 (log (/ -1 n)))
(* -1 (log (/ -1 n)))
(* -1 (log (/ -1 n)))
(* -1 (log (/ -1 n)))

Outputs
(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)
(* -1 (log (/ -1 n)))
(neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)))
(* -1 (log (/ -1 n)))
(neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)))
(* -1 (log (/ -1 n)))
(neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)))
(* -1 (log (/ -1 n)))
(neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) n)))

eval1.0ms (0%)

Memory: 3.2MiB live, 3.2MiB allocated
Compiler: Compiled 39 to 6 computations (84.6% saved)

prune2.0ms (0%)

Memory

4.7MiB live, 4.7MiB allocated

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	13	0	13
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	13	2	15

Accuracy

100.0%

Counts

15 → 2

Alt Table

Click to see full alt table

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

Compiler

Compiled 24 to 14 computations (41.7% saved)

regimes7.0ms (0.2%)

Memory

-23.7MiB live, 15.3MiB allocated

Counts

3 → 1

Calls

Call 1

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

Calls

3 calls:

3.0ms

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

2.0ms

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

10.3MiB live, 10.3MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal -1 binary64)

Outputs
#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)

simplify10.0ms (0.2%)

Memory

-25.1MiB live, 19.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness193.0ms (4.2%)

Memory

5.5MiB live, 164.8MiB allocated

Rules

12 720×	`lower-fma.f64`
12 720×	`lower-fma.f32`
3 314×	`lower-+.f64`
3 314×	`lower-+.f32`
2 942×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	156	736
1	492	653
2	1403	628
3	4873	612
0	8501	583

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 9 to 7 computations (22.2% saved)

preprocess59.0ms (1.3%)

Memory: 4.3MiB live, 81.4MiB allocated
Compiler: Compiled 90 to 58 computations (35.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

sample2.8s (60.1%)

preprocess133.0ms (2.9%)

explain254.0ms (5.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify63.0ms (1.4%)

localize88.0ms (1.9%)

series61.0ms (1.3%)

rewrite367.0ms (8%)

simplify384.0ms (8.3%)

eval62.0ms (1.3%)

prune92.0ms (2%)

simplify4.0ms (0.1%)

localize20.0ms (0.4%)

series26.0ms (0.6%)

rewrite8.0ms (0.2%)

simplify5.0ms (0.1%)

eval1.0ms (0%)

prune2.0ms (0%)

regimes7.0ms (0.2%)

regimes4.0ms (0.1%)

simplify10.0ms (0.2%)

soundness193.0ms (4.2%)

preprocess59.0ms (1.3%)

end0.0ms (0%)

Profiling